Daily Papers

Accurate modeling is crucial in many engineering and scientific applications, yet obtaining a reliable process model for complex systems is often challenging. To address this challenge, we propose a novel framework, reservoir computing with unscented Kalman filtering (RCUKF), which integrates data-driven modeling via reservoir computing (RC) with Bayesian estimation through the unscented Kalman filter (UKF). The RC component learns the nonlinear system dynamics directly from data, serving as a surrogate process model in the UKF prediction step to generate state estimates in high-dimensional or chaotic regimes where nominal mathematical models may fail. Meanwhile, the UKF measurement update integrates real-time sensor data to correct potential drift in the data-driven model. We demonstrate RCUKF effectiveness on well-known benchmark problems and a real-time vehicle trajectory estimation task in a high-fidelity simulation environment.

Bayesian optimization (BO) has established itself as a leading strategy for efficiently optimizing expensive-to-evaluate functions. Existing BO methods mostly rely on Gaussian process (GP) surrogate models and are not applicable to (doubly-stochastic) Gaussian Cox processes, where the observation process is modulated by a latent intensity function modeled as a GP. In this paper, we propose a novel maximum a posteriori inference of Gaussian Cox processes. It leverages the Laplace approximation and change of kernel technique to transform the problem into a new reproducing kernel Hilbert space, where it becomes more tractable computationally. It enables us to obtain both a functional posterior of the latent intensity function and the covariance of the posterior, thus extending existing works that often focus on specific link functions or estimating the posterior mean. Using the result, we propose a BO framework based on the Gaussian Cox process model and further develop a Nystr\"om approximation for efficient computation. Extensive evaluations on various synthetic and real-world datasets demonstrate significant improvement over state-of-the-art inference solutions for Gaussian Cox processes, as well as effective BO with a wide range of acquisition functions designed through the underlying Gaussian Cox process model.

A central challenge in gradient-free MCMC is designing algorithms that simultaneously bypass manual tuning, scale efficiently with dimension, and adapt to local target geometry. While adaptive strategies can auto-tune generic frameworks like random walk Metropolis, they offer slow, linear-order scaling of mixing times with dimension. Elliptical slice sampling (ESS) offers a promising alternative: it is tuning-free, adjusts to local geometry, and can achieve nearly dimension-free scaling under favorable conditions. However, its efficiency degrades rapidly if there is a mismatch between the target distribution and the distribution used to generate the ellipse-defining auxiliary variables, precluding its use in high-dimensional settings. We demonstrate that a careful synthesis of ESS and diminishing adaptation directly resolves these bottlenecks. The resulting adaptive generalized elliptical slice sampler (AGESS) self-corrects from a slow-mixing to a fast-mixing regime, while preserving ergodicity across a wide variety of target densities satisfying mild regularity conditions. The algorithm's utility is demonstrated across a broad collection of challenging applications, including generalized regression, deep Gaussian process surrogate modeling, and high-dimensional sparse regression. Together, our theoretical results and the case studies give evidence of the efficiency and robustness of AGESS across target distributions that are non-elliptical, non-differentiable, multi-modal, or high-dimensional.

We introduce a formal active learning methodology for guiding the placement of Lagrangian observers to infer time-dependent vector fields -- a key task in oceanography, marine science, and ocean engineering -- using a physics-informed spatio-temporal Gaussian process surrogate model. The majority of existing placement campaigns either follow standard `space-filling' designs or relatively ad-hoc expert opinions. A key challenge to applying principled active learning in this setting is that Lagrangian observers are continuously advected through the vector field, so they make measurements at different locations and times. It is, therefore, important to consider the likely future trajectories of placed observers to account for the utility of candidate placement locations. To this end, we present BALLAST: Bayesian Active Learning with Look-ahead Amendment for Sea-drifter Trajectories. We observe noticeable benefits of BALLAST-aided sequential observer placement strategies on both synthetic and high-fidelity ocean current models. In addition, we developed a novel GP inference method -- the Vanilla SPDE Exchange (VaSE) -- to boost the GP posterior sampling efficiency, which is also of independent interest.

Amid mounting concern about the reliability and credibility of machine learning research, we present a principled framework for making robust and generalizable claims: the multiverse analysis. Our framework builds upon the multiverse analysis (Steegen et al., 2016) introduced in response to psychology's own reproducibility crisis. To efficiently explore high-dimensional and often continuous ML search spaces, we model the multiverse with a Gaussian Process surrogate and apply Bayesian experimental design. Our framework is designed to facilitate drawing robust scientific conclusions about model performance, and thus our approach focuses on exploration rather than conventional optimization. In the first of two case studies, we investigate disputed claims about the relative merit of adaptive optimizers. Second, we synthesize conflicting research on the effect of learning rate on the large batch training generalization gap. For the machine learning community, the multiverse analysis is a simple and effective technique for identifying robust claims, for increasing transparency, and a step toward improved reproducibility.

We present a neural network emulator to constrain the thermal parameters of the intergalactic medium (IGM) at 5.4z6.0 using the Lyman-displaystylealpha (Lydisplaystylealpha) forest flux auto-correlation function. Our auto-differentiable JAX-based framework accelerates the surrogate model generation process using approximately 100 sparsely sampled Nyx hydrodynamical simulations with varying combinations of thermal parameters, i.e., the temperature at mean density T_{{0}}, the slope of the temperaturedisplaystyle-density relation displaystylegamma, and the mean transmission flux langle{F}{rangle}. We show that this emulator has a typical accuracy of 1.0% across the specified redshift range. Bayesian inference of the IGM thermal parameters, incorporating emulator uncertainty propagation, is further expedited using NumPyro Hamiltonian Monte Carlo. We compare both the inference results and computational cost of our framework with the traditional nearest-neighbor interpolation approach applied to the same set of mock Lyalpha flux. By examining the credibility contours of the marginalized posteriors for T_{{0}},gamma,and{langle}{F}{rangle} obtained using the emulator, the statistical reliability of measurements is established through inference on 100 realistic mock data sets of the auto-correlation function.

Bayesian optimization is a highly efficient approach to optimizing objective functions which are expensive to query. These objectives are typically represented by Gaussian process (GP) surrogate models which are easy to optimize and support exact inference. While standard GP surrogates have been well-established in Bayesian optimization, Bayesian neural networks (BNNs) have recently become practical function approximators, with many benefits over standard GPs such as the ability to naturally handle non-stationarity and learn representations for high-dimensional data. In this paper, we study BNNs as alternatives to standard GP surrogates for optimization. We consider a variety of approximate inference procedures for finite-width BNNs, including high-quality Hamiltonian Monte Carlo, low-cost stochastic MCMC, and heuristics such as deep ensembles. We also consider infinite-width BNNs and partially stochastic models such as deep kernel learning. We evaluate this collection of surrogate models on diverse problems with varying dimensionality, number of objectives, non-stationarity, and discrete and continuous inputs. We find: (i) the ranking of methods is highly problem dependent, suggesting the need for tailored inductive biases; (ii) HMC is the most successful approximate inference procedure for fully stochastic BNNs; (iii) full stochasticity may be unnecessary as deep kernel learning is relatively competitive; (iv) infinite-width BNNs are particularly promising, especially in high dimensions.

While few-step generative models have enabled powerful image and video generation at significantly lower cost, generic reinforcement learning (RL) paradigms for few-step models remain an unsolved problem. Existing RL approaches for few-step diffusion models strongly rely on back-propagating through differentiable reward models, thereby excluding the majority of important real-world reward signals, e.g., non-differentiable rewards such as humans' binary likeness, object counts, etc. To properly incorporate non-differentiable rewards to improve few-step generative models, we introduce TDM-R1, a novel reinforcement learning paradigm built upon a leading few-step model, Trajectory Distribution Matching (TDM). TDM-R1 decouples the learning process into surrogate reward learning and generator learning. Furthermore, we developed practical methods to obtain per-step reward signals along the deterministic generation trajectory of TDM, resulting in a unified RL post-training method that significantly improves few-step models' ability with generic rewards. We conduct extensive experiments ranging from text-rendering, visual quality, and preference alignment. All results demonstrate that TDM-R1 is a powerful reinforcement learning paradigm for few-step text-to-image models, achieving state-of-the-art reinforcement learning performances on both in-domain and out-of-domain metrics. Furthermore, TDM-R1 also scales effectively to the recent strong Z-Image model, consistently outperforming both its 100-NFE and few-step variants with only 4 NFEs. Project page: https://github.com/Luo-Yihong/TDM-R1

Vision language models (VLMs) typically pair a modestly sized vision encoder with a large language model (LLM), e.g., Llama-70B, making the decoder the primary computational burden during training. To reduce costs, a potential promising strategy is to first train the vision encoder using a small language model before transferring it to the large one. We construct small "surrogate models" that share the same embedding space and representation language as the large target LLM by directly inheriting its shallow layers. Vision encoders trained on the surrogate can then be directly transferred to the larger model, a process we call zero-shot grafting -- when plugged directly into the full-size target LLM, the grafted pair surpasses the encoder-surrogate pair and, on some benchmarks, even performs on par with full decoder training with the target LLM. Furthermore, our surrogate training approach reduces overall VLM training costs by ~45% when using Llama-70B as the decoder.

In computer-aided engineering design, the goal of a designer is to find an optimal design on a given requirement using the numerical simulator in loop with an optimization method. In this design optimization process, a good design optimization process is one that can reduce the time from inception to design. In this work, we take a class of design problem, that is computationally cheap to evaluate but has high dimensional design space. In such cases, traditional surrogate-based optimization does not offer any benefits. In this work, we propose an alternative way to use ML model to surrogate the design process that formulates the search problem as an inverse problem and can save time by finding the optimal design or at least a good initial seed design for optimization. By using this trained surrogate model with the traditional optimization method, we can get the best of both worlds. We call this as Surrogate Assisted Optimization (SAO)- a hybrid approach by mixing ML surrogate with the traditional optimization method. Empirical evaluations of propeller design problems show that a better efficient design can be found in fewer evaluations using SAO.

The task of locating first order saddle points on high-dimensional surfaces describing the variation of energy as a function of atomic coordinates is an essential step for identifying the mechanism and estimating the rate of thermally activated events within the harmonic approximation of transition state theory. When combined directly with electronic structure calculations, the number of energy and atomic force evaluations needed for convergence is a primary issue. Here, we describe an efficient implementation of Gaussian process regression (GPR) acceleration of the minimum mode following method where a dimer is used to estimate the lowest eigenmode of the Hessian. A surrogate energy surface is constructed and updated after each electronic structure calculation. The method is applied to a test set of 500 molecular reactions previously generated by Hermez and coworkers [J. Chem. Theory Comput. 18, 6974 (2022)]. An order of magnitude reduction in the number of electronic structure calculations needed to reach the saddle point configurations is obtained by using the GPR compared to the dimer method. Despite the wide range in stiffness of the molecular degrees of freedom, the calculations are carried out using Cartesian coordinates and are found to require similar number of electronic structure calculations as an elaborate internal coordinate method implemented in the Sella software package. The present implementation of the GPR surrogate model in C++ is efficient enough for the wall time of the saddle point searches to be reduced in 3 out of 4 cases even though the calculations are carried out at a low Hartree-Fock level.

When training deep learning models, the performance depends largely on the selected hyperparameters. However, hyperparameter optimization (HPO) is often one of the most expensive parts of model design. Classical HPO methods treat this as a black-box optimization problem. However, gray-box HPO methods, which incorporate more information about the setup, have emerged as a promising direction for more efficient optimization. For example, using intermediate loss evaluations to terminate bad selections. In this work, we propose an HPO method for neural networks using logged checkpoints of the trained weights to guide future hyperparameter selections. Our method, Forecasting Model Search (FMS), embeds weights into a Gaussian process deep kernel surrogate model, using a permutation-invariant graph metanetwork to be data-efficient with the logged network weights. To facilitate reproducibility and further research, we open-source our code at https://github.com/NVlabs/forecasting-model-search.

Directed energy deposition (DED) produces complex thermo-mechanical responses that can lead to distortion and reduced dimensional accuracy of a manufactured part. Thermo-mechanical finite element simulations are widely used to estimate these effects, but their computational cost and the complexity of accurately capturing DED physics limit their use in design iteration and process optimization. This paper introduces FLARE (Field Prediction via Linear Affine Reconstruction in wEight-space), a data-efficient surrogate modeling framework for predicting post-cooling displacement fields in DED from geometric and process parameters. We develop a predefined-geometry DED simulation workflow using an open-source finite element framework and generate a dataset of simulations with varying geometry, laser power, and deposition velocity. Each simulation provides full-field displacement, stress, strain, and temperature data throughout the manufacturing process. FLARE encodes each simulation as an implicit neural field and regularizes the corresponding neural-network weights so that they follow the affine structure of the input parameter space. This enables prediction of unseen parameter combinations by reconstructing network weights through affine mixing of training examples. On this DED benchmark, the method shows improved accuracy compared to baseline methods in both in-distribution and extrapolation settings. Although the present study focuses on DED displacement prediction, the proposed affine weight-space reconstruction framework offers a promising approach for data-efficient surrogate modeling of physical fields.

Global optimization of expensive, derivative-free black-box functions demands extreme sample efficiency and decision interpretability. While Large Language Models (LLMs) have shown broad capabilities, even state-of-the-art models remain limited in solving continuous black-box optimization tasks and struggle to maintain exploration-exploitation balance. We introduce GPTOpt, an optimization method that equips LLMs with continuous black-box optimization capabilities by fine-tuning Llama 3.1 8B on structured Bayesian optimization (BO) data, including surrogate model information. This provides an explainable framework calibrated to produce surrogate model outputs comparable to a Gaussian process, while keeping the advantages of flexible LLM-based optimization. On a variety of black-box optimization benchmarks, our model shows favorable performance compared to traditional optimizers and transformer-based alternatives, while providing important context and insight into the model's decisions.

Structural vibrations are a source of unwanted noise in engineering systems like cars, trains or airplanes. Minimizing these vibrations is crucial for improving passenger comfort. This work presents a novel design optimization approach based on guided flow matching for reducing vibrations by placing beadings (indentations) in plate-like structures. Our method integrates a generative flow matching model and a surrogate model trained to predict structural vibrations. During the generation process, the flow matching model pushes towards manufacturability while the surrogate model pushes to low-vibration solutions. The flow matching model and its training data implicitly define the design space, enabling a broader exploration of potential solutions as no optimization of manually-defined design parameters is required. We apply our method to a range of differentiable optimization objectives, including direct optimization of specific eigenfrequencies through careful construction of the objective function. Results demonstrate that our method generates diverse and manufacturable plate designs with reduced structural vibrations compared to designs from random search, a criterion-based design heuristic and genetic optimization. The code and data are available from https://github.com/ecker-lab/Optimizing_Vibrating_Plates.

Leveraging Large Language Models (LLMs) for recommendation has recently garnered considerable attention, where fine-tuning plays a key role in LLMs' adaptation. However, the cost of fine-tuning LLMs on rapidly expanding recommendation data limits their practical application. To address this challenge, few-shot fine-tuning offers a promising approach to quickly adapt LLMs to new recommendation data. We propose the task of data pruning for efficient LLM-based recommendation, aimed at identifying representative samples tailored for LLMs' few-shot fine-tuning. While coreset selection is closely related to the proposed task, existing coreset selection methods often rely on suboptimal heuristic metrics or entail costly optimization on large-scale recommendation data. To tackle these issues, we introduce two objectives for the data pruning task in the context of LLM-based recommendation: 1) high accuracy aims to identify the influential samples that can lead to high overall performance; and 2) high efficiency underlines the low costs of the data pruning process. To pursue the two objectives, we propose a novel data pruning method based on two scores, i.e., influence score and effort score, to efficiently identify the influential samples. Particularly, the influence score is introduced to accurately estimate the influence of sample removal on the overall performance. To achieve low costs of the data pruning process, we use a small-sized surrogate model to replace LLMs to obtain the influence score. Considering the potential gap between the surrogate model and LLMs, we further propose an effort score to prioritize some hard samples specifically for LLMs. Empirical results on three real-world datasets validate the effectiveness of our proposed method. In particular, the proposed method uses only 2% samples to surpass the full data fine-tuning, reducing time costs by 97%.

Large language models (LLMs) have shown remarkable instruction-following capabilities and achieved impressive performances in various applications. However, the performances of LLMs depend heavily on the instructions given to them, which are typically manually tuned with substantial human efforts. Recent work has used the query-efficient Bayesian optimization (BO) algorithm to automatically optimize the instructions given to black-box LLMs. However, BO usually falls short when optimizing highly sophisticated (e.g., high-dimensional) objective functions, such as the functions mapping an instruction to the performance of an LLM. This is mainly due to the limited expressive power of the Gaussian process (GP) which is used by BO as a surrogate to model the objective function. Meanwhile, it has been repeatedly shown that neural networks (NNs), especially pre-trained transformers, possess strong expressive power and can model highly complex functions. So, we adopt a neural bandit algorithm which replaces the GP in BO by an NN surrogate to optimize instructions for black-box LLMs. More importantly, the neural bandit algorithm allows us to naturally couple the NN surrogate with the hidden representation learned by a pre-trained transformer (i.e., an open-source LLM), which significantly boosts its performance. These motivate us to propose our INSTruction optimization usIng Neural bandits Coupled with Transformers (INSTINCT) algorithm. We perform instruction optimization for ChatGPT and use extensive experiments to show that INSTINCT consistently outperforms baselines in different tasks, e.g., various instruction induction tasks and the task of improving zero-shot chain-of-thought instructions. Our code is available at https://github.com/xqlin98/INSTINCT.

Controllable music generation methods are critical for human-centered AI-based music creation, but are currently limited by speed, quality, and control design trade-offs. Diffusion Inference-Time T-optimization (DITTO), in particular, offers state-of-the-art results, but is over 10x slower than real-time, limiting practical use. We propose Distilled Diffusion Inference-Time T -Optimization (or DITTO-2), a new method to speed up inference-time optimization-based control and unlock faster-than-real-time generation for a wide-variety of applications such as music inpainting, outpainting, intensity, melody, and musical structure control. Our method works by (1) distilling a pre-trained diffusion model for fast sampling via an efficient, modified consistency or consistency trajectory distillation process (2) performing inference-time optimization using our distilled model with one-step sampling as an efficient surrogate optimization task and (3) running a final multi-step sampling generation (decoding) using our estimated noise latents for best-quality, fast, controllable generation. Through thorough evaluation, we find our method not only speeds up generation over 10-20x, but simultaneously improves control adherence and generation quality all at once. Furthermore, we apply our approach to a new application of maximizing text adherence (CLAP score) and show we can convert an unconditional diffusion model without text inputs into a model that yields state-of-the-art text control. Sound examples can be found at https://ditto-music.github.io/ditto2/.

We propose a new uncertainty estimator for gradient-free optimisation of black-box simulators using deep generative surrogate models. Optimisation of these simulators is especially challenging for stochastic simulators and higher dimensions. To address these issues, we utilise a deep generative surrogate approach to model the black box response for the entire parameter space. We then leverage this knowledge to estimate the proposed uncertainty based on the Wasserstein distance - the Wasserstein uncertainty. This approach is employed in a posterior agnostic gradient-free optimisation algorithm that minimises regret over the entire parameter space. A series of tests were conducted to demonstrate that our method is more robust to the shape of both the black box function and the stochastic response of the black box than state-of-the-art methods, such as efficient global optimisation with a deep Gaussian process surrogate.

Aligning denoising generative models with human preferences or verifiable rewards remains a key challenge. While policy-gradient online reinforcement learning (RL) offers a principled post-training framework, its direct application is hindered by the intractable likelihoods of these models. Prior work therefore either optimizes an induced Markov decision process (MDP) over sampling trajectories, which is stable but inefficient, or uses likelihood surrogates based on the diffusion evidence lower bound (ELBO), which have so far underperformed on visual generation. Our key insight is that the ELBO-based approach can, in fact, be made both stable and efficient. By reducing surrogate variance and controlling gradient steps, we show that this approach can beat MDP-based methods. To this end, we introduce Variational GRPO (V-GRPO), a method that integrates ELBO-based surrogates with the Group Relative Policy Optimization (GRPO) algorithm, alongside a set of simple yet essential techniques. Our method is easy to implement, aligns with pretraining objectives, and avoids the limitations of MDP-based methods. V-GRPO achieves state-of-the-art performance in text-to-image synthesis, while delivering a 2times speedup over MixGRPO and a 3times speedup over DiffusionNFT.

Despite the success of reinforcement learning from human feedback (RLHF) in aligning language models, current reward modeling heavily relies on experimental feedback data collected from human annotators under controlled and costly conditions. In this work, we introduce observational reward modeling -- learning reward models with observational user feedback (e.g., clicks, copies, and upvotes) -- as a scalable and cost-effective alternative. We identify two fundamental challenges in this setting: (1) observational feedback is noisy due to annotation errors, which deviates it from true user preference; (2) observational feedback is biased by user preference, where users preferentially provide feedback on responses they feel strongly about, which creats a distribution shift between training and inference data. To address these challenges, we propose CausalRM, a causal-theoretic reward modeling framework that aims to learn unbiased reward models from observational feedback. To tackle challenge (1), CausalRM introduces a noise-aware surrogate loss term that is provably equivalent to the primal loss under noise-free conditions by explicitly modeling the annotation error generation process. To tackle challenge (2), CausalRM uses propensity scores -- the probability of a user providing feedback for a given response -- to reweight training samples, yielding a loss function that eliminates user preference bias. Extensive experiments across diverse LLM backbones and benchmark datasets validate that CausalRM effectively learns accurate reward signals from noisy and biased observational feedback and delivers substantial performance improvements on downstream RLHF tasks -- including a 49.2% gain on WildGuardMix and a 32.7% improvement on HarmBench. Code is available on our project website.

Bayesian optimization is an approach to optimizing objective functions that take a long time (minutes or hours) to evaluate. It is best-suited for optimization over continuous domains of less than 20 dimensions, and tolerates stochastic noise in function evaluations. It builds a surrogate for the objective and quantifies the uncertainty in that surrogate using a Bayesian machine learning technique, Gaussian process regression, and then uses an acquisition function defined from this surrogate to decide where to sample. In this tutorial, we describe how Bayesian optimization works, including Gaussian process regression and three common acquisition functions: expected improvement, entropy search, and knowledge gradient. We then discuss more advanced techniques, including running multiple function evaluations in parallel, multi-fidelity and multi-information source optimization, expensive-to-evaluate constraints, random environmental conditions, multi-task Bayesian optimization, and the inclusion of derivative information. We conclude with a discussion of Bayesian optimization software and future research directions in the field. Within our tutorial material we provide a generalization of expected improvement to noisy evaluations, beyond the noise-free setting where it is more commonly applied. This generalization is justified by a formal decision-theoretic argument, standing in contrast to previous ad hoc modifications.

Many state-of-the-art hyperparameter optimization (HPO) algorithms rely on model-based optimizers that learn surrogate models of the target function to guide the search. Gaussian processes are the de facto surrogate model due to their ability to capture uncertainty but they make strong assumptions about the observation noise, which might not be warranted in practice. In this work, we propose to leverage conformalized quantile regression which makes minimal assumptions about the observation noise and, as a result, models the target function in a more realistic and robust fashion which translates to quicker HPO convergence on empirical benchmarks. To apply our method in a multi-fidelity setting, we propose a simple, yet effective, technique that aggregates observed results across different resource levels and outperforms conventional methods across many empirical tasks.

Traditional scientific discovery relies on an iterative hypothesise-experiment-refine cycle that has driven progress for centuries, but its intuitive, ad-hoc implementation often wastes resources, yields inefficient designs, and misses critical insights. This tutorial presents Bayesian Optimisation (BO), a principled probability-driven framework that formalises and automates this core scientific cycle. BO uses surrogate models (e.g., Gaussian processes) to model empirical observations as evolving hypotheses, and acquisition functions to guide experiment selection, balancing exploitation of known knowledge and exploration of uncharted domains to eliminate guesswork and manual trial-and-error. We first frame scientific discovery as an optimisation problem, then unpack BO's core components, end-to-end workflows, and real-world efficacy via case studies in catalysis, materials science, organic synthesis, and molecule discovery. We also cover critical technical extensions for scientific applications, including batched experimentation, heteroscedasticity, contextual optimisation, and human-in-the-loop integration. Tailored for a broad audience, this tutorial bridges AI advances in BO with practical natural science applications, offering tiered content to empower cross-disciplinary researchers to design more efficient experiments and accelerate principled scientific discovery.

Advancements in high-computing devices increase the necessity for improved and new understanding and development of smart manufacturing factories. Discrete-event models with simulators have been shown to be critical to architect, designing, building, and operating the manufacturing of semiconductor chips. The diffusion, implantation, and lithography machines have intricate processes due to their feedforward and feedback connectivity. The dataset collected from simulations of the factory models holds the promise of generating valuable machine-learning models. As surrogate data-based models, their executions are highly efficient compared to the physics-based counterpart models. For the development of surrogate models, it is beneficial to have publicly available benchmark simulation models that are grounded in factory models that have concise structures and accurate behaviors. Hence, in this research, a dataset is devised and constructed based on a benchmark model of an Intel semiconductor fabrication factory. The model is formalized using the Parallel Discrete-Event System Specification and executed using the DEVS-Suite simulator. The time series dataset is constructed using discrete-event time trajectories. This dataset is further analyzed and used to develop baseline univariate and multivariate machine learning models. The dataset can also be utilized in the machine learning community for behavioral analysis based on formalized and scalable component-based discrete-event models and simulations.

Neural surrogates promise large speedups over classical solvers for physical dynamics but fail silently at sharp dynamical events such as shocks, fronts, and contact. We present hybrid neural world models for physical dynamics: a recipe for training and deploying multi-horizon surrogates in physical state space, where a single network with continuous horizon conditioning is trained with direct supervision against textbook reference solvers to predict any future state at horizon T in one forward pass. Although no part of the training data, loss function, or architecture supervises discontinuity location, the trained surrogate encodes it implicitly, recoverable from its forward passes alone as a per-trajectory error map that concentrates on shocks, fronts, and contacts, and stays small elsewhere. The map is competitive with or better than standard label-free baselines including deep ensembles, learned error heads, gradient-magnitude indicators, and locally-adaptive conformal prediction, while using only a single trained network and requiring no calibration set or governing-equation knowledge. The recipe supports two operating points. Mode 1 runs the surrogate alone for maximum throughput, with same-hardware CPU speedups of 26x to 72x against textbook solvers on the PDE environments. Mode 2 uses the error map to gate a reference-solver fallback, deferring uncertain trajectories and roughly halving the surrogate's residual error at the default operating point. The recipe applies without modification across reaction-diffusion, compressible Euler, and rigid-body collision dynamics.

In an industrial group like Safran, numerical simulations of physical phenomena are integral to most design processes. At Safran's corporate research center, we enhance these processes by developing fast and reliable surrogate models for various physics. We focus here on two technologies developed in recent years. The first is a physical reduced-order modeling method for non-linear structural mechanics and thermal analysis, used for calculating the lifespan of high-pressure turbine blades and performing heat analysis of high-pressure compressors. The second technology involves learning physics simulations with non-parameterized geometrical variability using classical machine learning tools, such as Gaussian process regression. Finally, we present our contributions to the open-source and open-data community.

Clinical trials or studies oftentimes require long-term and/or costly follow-up of participants to evaluate a novel treatment/drug/vaccine. There has been increasing interest in the past few decades in using short-term surrogate outcomes as a replacement of the primary outcome i.e., in using the surrogate outcome, which can potentially be observed sooner, to make inference about the treatment effect on the long-term primary outcome. Very few of the available statistical methods to evaluate a surrogate are applicable to settings where both the surrogate and the primary outcome are time-to-event outcomes subject to censoring. Methods that can handle this setting tend to require parametric assumptions or be limited to assessing only the restricted mean survival time. In this paper, we propose a non-parametric approach to evaluate a censored surrogate outcome, such as time to progression, when the primary outcome is also a censored time-to-event outcome, such as time to death, and the treatment effect of interest is the difference in overall survival. Specifically, we define the proportion of the treatment effect on the primary outcome that is explained (PTE) by the censored surrogate outcome in this context, and estimate this proportion by defining and deriving an optimal transformation of the surrogate information. Our approach provides the added advantage of relaxed assumptions to guarantee that the true PTE is within (0,1), along with being model-free. Finite sample performance of our estimators are illustrated via extensive simulation studies and a real data application examining progression-free survival as a surrogate for overall survival for patients with metastatic colorectal cancer.

Neural networks are a commonly used approach to replace physical models with computationally cheap surrogates. Parametric uncertainty quantification can be included in training, assuming that an accurate prior distribution of the model parameters is available. Here we study the common opposite situation, where direct screening or random sampling of model parameters leads to exhaustive training times and evaluations at unphysical parameter values. Our solution is to decouple uncertainty quantification from network architecture. Instead of sampling network weights, we introduce the model-parameter distribution as an input to network training via Markov chain Monte Carlo (MCMC). In this way, the surrogate achieves the same uncertainty quantification as the underlying physical model, but with substantially reduced computation time. The approach is fully agnostic with respect to the neural network choice. In our examples, we present a quantile emulator for prediction and a novel autoencoder-based ODE network emulator that can flexibly estimate different trajectory paths corresponding to different ODE model parameters. Moreover, we present a mathematical analysis that provides a transparent way to relate potential performance loss to measurable distribution mismatch.

Bayesian optimisation is a popular, surrogate model-based approach for optimising expensive black-box functions. Given a surrogate model, the next location to expensively evaluate is chosen via maximisation of a cheap-to-query acquisition function. We present an epsilon-greedy procedure for Bayesian optimisation in batch settings in which the black-box function can be evaluated multiple times in parallel. Our epsilon-shotgun algorithm leverages the model's prediction, uncertainty, and the approximated rate of change of the landscape to determine the spread of batch solutions to be distributed around a putative location. The initial target location is selected either in an exploitative fashion on the mean prediction, or -- with probability epsilon -- from elsewhere in the design space. This results in locations that are more densely sampled in regions where the function is changing rapidly and in locations predicted to be good (i.e close to predicted optima), with more scattered samples in regions where the function is flatter and/or of poorer quality. We empirically evaluate the epsilon-shotgun methods on a range of synthetic functions and two real-world problems, finding that they perform at least as well as state-of-the-art batch methods and in many cases exceed their performance.

Numerical simulations in climate, chemistry, or astrophysics are computationally too expensive for uncertainty quantification or parameter-exploration at high-resolution. Reduced-order or surrogate models are multiple orders of magnitude faster, but traditional surrogates are inflexible or inaccurate and pure machine learning (ML)-based surrogates too data-hungry. We propose a hybrid, flexible surrogate model that exploits known physics for simulating large-scale dynamics and limits learning to the hard-to-model term, which is called parametrization or closure and captures the effect of fine- onto large-scale dynamics. Leveraging neural operators, we are the first to learn grid-independent, non-local, and flexible parametrizations. Our multiscale neural operator is motivated by a rich literature in multiscale modeling, has quasilinear runtime complexity, is more accurate or flexible than state-of-the-art parametrizations and demonstrated on the chaotic equation multiscale Lorenz96.

To plan and optimize energy storage demands that account for Li-ion battery aging dynamics, techniques need to be developed to diagnose battery internal states accurately and rapidly. This study seeks to reduce the computational resources needed to determine a battery's internal states by replacing physics-based Li-ion battery models -- such as the single-particle model (SPM) and the pseudo-2D (P2D) model -- with a physics-informed neural network (PINN) surrogate. The surrogate model makes high-throughput techniques, such as Bayesian calibration, tractable to determine battery internal parameters from voltage responses. This manuscript is the first of a two-part series that introduces PINN surrogates of Li-ion battery models for parameter inference (i.e., state-of-health diagnostics). In this first part, a method is presented for constructing a PINN surrogate of the SPM. A multi-fidelity hierarchical training, where several neural nets are trained with multiple physics-loss fidelities is shown to significantly improve the surrogate accuracy when only training on the governing equation residuals. The implementation is made available in a companion repository (https://github.com/NREL/pinnstripes). The techniques used to develop a PINN surrogate of the SPM are extended in Part II for the PINN surrogate for the P2D battery model, and explore the Bayesian calibration capabilities of both surrogates.

Scientific discovery often involves optimising expensive-to-evaluate objectives over vast, structured, and open-ended hypothesis spaces, such as molecules, protein sequences, and computer programs. Generative models such as large language models (LLMs) provide expressive priors over such spaces, but their likelihoods and self-assessments are unreliable proxies for the objectives and calibrated epistemic uncertainty, especially for novel candidates outside the observed data distribution. We introduce the Large Discovery Model (LDM), an empirically grounded recurrent architecture that couples a generative model with a Bayesian non-parametric reward surrogate model. The generative model proposes and refines candidate designs, while the surrogate predicts their performance and quantifies uncertainty, yielding an uncertainty-aware value that guides candidate generation, refinement, and selection. The discovery memory and the surrogate model are continually updated as each new experimental observation arrives. We evaluate LDM on three scenarios spanning different design modalities and objectives, including neural-network training, antibody design, and molecular optimisation. Compared to LLM-only reflection or traditional statistical search across these domains, LDM achieves a 2.4times greater reduction in validation BPB, an 18.2% relative decrease in binding energy, and more than 60% relative gains in molecular multi-objective performance. These results suggests that LDM could serve as a general-purpose discovery engine for effective search over open-ended hypothesis spaces.

This script offers an implementation-oriented introduction to deep learning methods for solving and estimating high-dimensional dynamic stochastic models in economics and finance. Its starting point is the curse of dimensionality: heterogeneous-agent economies, overlapping-generations models with aggregate risk, continuous-time models with occasionally binding constraints, climate-economy models, and macro-finance environments with many assets and frictions generate state and parameter spaces that strain classical tensor-product grid methods. The exposition is organized around four complementary methodologies. Deep Equilibrium Nets embed discrete-time equilibrium conditions into neural-network loss functions. Physics-Informed Neural Networks approximate continuous-time Hamilton--Jacobi--Bellman, Kolmogorov forward, and related partial differential equations. Deep surrogate models provide fast, differentiable approximations to expensive structural models, while Gaussian processes add a probabilistic layer that quantifies approximation uncertainty; together they support estimation, sensitivity analysis, and constrained policy design. Gaussian-process-based dynamic programming, combined with active learning and dimension reduction, extends value-function iteration to very large continuous state spaces. Applications span representative-agent and international real business cycle models, overlapping-generations and heterogeneous-agent economies, continuous-time macro-finance, structural estimation by simulated method of moments, and climate economics under uncertainty. Companion notebooks in TensorFlow and PyTorch invite hands-on experimentation. These notes are a deliberately subjective and inevitably incomplete snapshot of a rapidly evolving field, aimed at equipping PhD students and researchers to engage with this frontier hands-on.

We propose constrained causal Bayesian optimization (cCBO), an approach for finding interventions in a known causal graph that optimize a target variable under some constraints. cCBO first reduces the search space by exploiting the graph structure and, if available, an observational dataset; and then solves the restricted optimization problem by modelling target and constraint quantities using Gaussian processes and by sequentially selecting interventions via a constrained expected improvement acquisition function. We propose different surrogate models that enable to integrate observational and interventional data while capturing correlation among effects with increasing levels of sophistication. We evaluate cCBO on artificial and real-world causal graphs showing successful trade off between fast convergence and percentage of feasible interventions.

Resided at the intersection of multi-fidelity optimization (MFO) and Bayesian optimization (BO), MF BO has found a niche in solving expensive engineering design optimization problems, thanks to its advantages in incorporating physical and mathematical understandings of the problems, saving resources, addressing exploitation-exploration trade-off, considering uncertainty, and processing parallel computing. The increasing number of works dedicated to MF BO suggests the need for a comprehensive review of this advanced optimization technique. In this paper, we survey recent developments of two essential ingredients of MF BO: Gaussian process (GP) based MF surrogates and acquisition functions. We first categorize the existing MF modeling methods and MFO strategies to locate MF BO in a large family of surrogate-based optimization and MFO algorithms. We then exploit the common properties shared between the methods from each ingredient of MF BO to describe important GP-based MF surrogate models and review various acquisition functions. By doing so, we expect to provide a structured understanding of MF BO. Finally, we attempt to reveal important aspects that require further research for applications of MF BO in solving intricate yet important design optimization problems, including constrained optimization, high-dimensional optimization, optimization under uncertainty, and multi-objective optimization.

Genome-wide association study (GWAS) tests single nucleotide polymorphism (SNP) markers across the genome to localize the underlying causal variant of a trait. Because causal variants are seldom observed directly, a surrogate model based on genotyped markers are widely considered. Although many methods estimating the parameters of the surrogate model have been proposed, the connection between the surrogate model and the true causal model is yet investigated. In this work, we establish the connection between the surrogate model and the true causal model. The connection shows that population structure is accounted in GWAS by modelling the variant of interest and not the trait. Such observation explains how environmental confounding can be partially corrected using genetic covariates and why the previously claimed connection between PC correction and linear mixed models is incorrect.

Surrogate models are necessary to optimize meaningful quantities in physical dynamics as their recursive numerical resolutions are often prohibitively expensive. It is mainly the case for fluid dynamics and the resolution of Navier-Stokes equations. However, despite the fast-growing field of data-driven models for physical systems, reference datasets representing real-world phenomena are lacking. In this work, we develop AirfRANS, a dataset for studying the two-dimensional incompressible steady-state Reynolds-Averaged Navier-Stokes equations over airfoils at a subsonic regime and for different angles of attacks. We also introduce metrics on the stress forces at the surface of geometries and visualization of boundary layers to assess the capabilities of models to accurately predict the meaningful information of the problem. Finally, we propose deep learning baselines on four machine learning tasks to study AirfRANS under different constraints for generalization considerations: big and scarce data regime, Reynolds number, and angle of attack extrapolation.

Scientific Machine Learning (SciML) is concerned with the development of learned emulators of physical systems governed by partial differential equations (PDE). In application domains such as weather forecasting, molecular dynamics, and inverse design, ML-based surrogate models are increasingly used to augment or replace inefficient and often non-differentiable numerical simulation algorithms. While a number of ML-based methods for approximating the solutions of PDEs have been proposed in recent years, they typically do not adapt to the parameters of the PDEs, making it difficult to generalize to PDE parameters not seen during training. We propose a Channel Attention mechanism guided by PDE Parameter Embeddings (CAPE) component for neural surrogate models and a simple yet effective curriculum learning strategy. The CAPE module can be combined with neural PDE solvers allowing them to adapt to unseen PDE parameters. The curriculum learning strategy provides a seamless transition between teacher-forcing and fully auto-regressive training. We compare CAPE in conjunction with the curriculum learning strategy using a popular PDE benchmark and obtain consistent and significant improvements over the baseline models. The experiments also show several advantages of CAPE, such as its increased ability to generalize to unseen PDE parameters without large increases inference time and parameter count.

Offline optimization has recently emerged as an increasingly popular approach to mitigate the prohibitively expensive cost of online experimentation. The key idea is to learn a surrogate of the black-box function that underlines the target experiment using a static (offline) dataset of its previous input-output queries. Such an approach is, however, fraught with an out-of-distribution issue where the learned surrogate becomes inaccurate outside the offline data regimes. To mitigate this, existing offline optimizers have proposed numerous conditioning techniques to prevent the learned surrogate from being too erratic. Nonetheless, such conditioning strategies are often specific to particular surrogate or search models, which might not generalize to a different model choice. This motivates us to develop a model-agnostic approach instead, which incorporates a notion of model sharpness into the training loss of the surrogate as a regularizer. Our approach is supported by a new theoretical analysis demonstrating that reducing surrogate sharpness on the offline dataset provably reduces its generalized sharpness on unseen data. Our analysis extends existing theories from bounding generalized prediction loss (on unseen data) with loss sharpness to bounding the worst-case generalized surrogate sharpness with its empirical estimate on training data, providing a new perspective on sharpness regularization. Our extensive experimentation on a diverse range of optimization tasks also shows that reducing surrogate sharpness often leads to significant improvement, marking (up to) a noticeable 9.6% performance boost. Our code is publicly available at https://github.com/cuong-dm/IGNITE

Process supervision, i.e., evaluating each step, is critical for complex large language model (LLM) reasoning and test-time searching with increased inference compute. Existing approaches, represented by process reward models (PRMs), primarily focus on rewarding signals up to the current step, exhibiting a one-directional nature and lacking a mechanism to model the distance to the final target. To address this problem, we draw inspiration from the A* algorithm, which states that an effective supervisory signal should simultaneously consider the incurred cost and the estimated cost for reaching the target. Building on this key insight, we introduce BiRM, a novel process supervision model that not only evaluates the correctness of previous steps but also models the probability of future success. We conduct extensive experiments on mathematical reasoning tasks and demonstrate that BiRM provides more precise evaluations of LLM reasoning steps, achieving an improvement of 3.1% on Gaokao2023 over PRM under the Best-of-N sampling method. Besides, in search-based strategies, BiRM provides more comprehensive guidance and outperforms ORM by 5.0% and PRM by 3.8% respectively on MATH-500.

This paper studies the black-box optimization task which aims to find the maxima of a black-box function using a static set of its observed input-output pairs. This is often achieved via learning and optimizing a surrogate function with that offline data. Alternatively, it can also be framed as an inverse modeling task that maps a desired performance to potential input candidates that achieve it. Both approaches are constrained by the limited amount of offline data. To mitigate this limitation, we introduce a new perspective that casts offline optimization as a distributional translation task. This is formulated as learning a probabilistic bridge transforming an implicit distribution of low-value inputs (i.e., offline data) into another distribution of high-value inputs (i.e., solution candidates). Such probabilistic bridge can be learned using low- and high-value inputs sampled from synthetic functions that resemble the target function. These synthetic functions are constructed as the mean posterior of multiple Gaussian processes fitted with different parameterizations on the offline data, alleviating the data bottleneck. The proposed approach is evaluated on an extensive benchmark comprising most recent methods, demonstrating significant improvement and establishing a new state-of-the-art performance. Our code is publicly available at https://github.com/cuong-dm/ROOT.

Machine learning based surrogate models offer researchers powerful tools for accelerating simulation-based workflows. However, as standard datasets in this space often cover small classes of physical behavior, it can be difficult to evaluate the efficacy of new approaches. To address this gap, we introduce the Well: a large-scale collection of datasets containing numerical simulations of a wide variety of spatiotemporal physical systems. The Well draws from domain experts and numerical software developers to provide 15TB of data across 16 datasets covering diverse domains such as biological systems, fluid dynamics, acoustic scattering, as well as magneto-hydrodynamic simulations of extra-galactic fluids or supernova explosions. These datasets can be used individually or as part of a broader benchmark suite. To facilitate usage of the Well, we provide a unified PyTorch interface for training and evaluating models. We demonstrate the function of this library by introducing example baselines that highlight the new challenges posed by the complex dynamics of the Well. The code and data is available at https://github.com/PolymathicAI/the_well.

The aim of this study is to develop surrogate models for quick, accurate prediction of thrust forces generated through flapping fin propulsion for given operating conditions and fin geometries. Different network architectures and configurations are explored to model the training data separately for the lead fin and rear fin of a tandem fin setup. We progressively improve the data representation of the input parameter space for model predictions. The models are tested on three unseen fin geometries and the predictions validated with computational fluid dynamics (CFD) data. Finally, the orders of magnitude gains in computational performance of these surrogate models, compared to experimental and CFD runs, vs their tradeoff with accuracy is discussed within the context of this tandem fin configuration.

Recent years have seen a surge in deep learning approaches to accelerate numerical solvers, which provide faithful but computationally intensive simulations of the physical world. These deep surrogates are generally trained in a supervised manner from limited amounts of data slowly generated by the same solver they intend to accelerate. We propose an open-source framework that enables the online training of these models from a large ensemble run of simulations. It leverages multiple levels of parallelism to generate rich datasets. The framework avoids I/O bottlenecks and storage issues by directly streaming the generated data. A training reservoir mitigates the inherent bias of streaming while maximizing GPU throughput. Experiment on training a fully connected network as a surrogate for the heat equation shows the proposed approach enables training on 8TB of data in 2 hours with an accuracy improved by 47% and a batch throughput multiplied by 13 compared to a traditional offline procedure.

Offline optimization is an important task in numerous material engineering domains where online experimentation to collect data is too expensive and needs to be replaced by an in silico maximization of a surrogate of the black-box function. Although such a surrogate can be learned from offline data, its prediction might not be reliable outside the offline data regime, which happens when the surrogate has narrow prediction margin and is (therefore) sensitive to small perturbations of its parameterization. This raises the following questions: (1) how to regulate the sensitivity of a surrogate model; and (2) whether conditioning an offline optimizer with such less sensitive surrogate will lead to better optimization performance. To address these questions, we develop an optimizable sensitivity measurement for the surrogate model, which then inspires a sensitivity-informed regularizer that is applicable to a wide range of offline optimizers. This development is both orthogonal and synergistic to prior research on offline optimization, which is demonstrated in our extensive experiment benchmark.

Macro placement significantly affects a chip's post-route performance, power, and area (PPA). Most placement methods optimize half-perimeter wirelength (HPWL) as the primary objective. However, recent benchmarking shows a near-zero correlation between HPWL and post-route timing metrics such as the worst negative slack (WNS) and total negative slack (TNS). As a result, all six evaluated artificial intelligence (AI) placers degraded PPA relative to the hierarchical baseline. Recent efforts have tried to train cross-stage predictors to close this gap. However, existing methods focus on macro-only representations and use pre-route metrics as training labels. A label fidelity study of ten circuits at four design flow stages reveals that HPWL and pre-route timing poorly reflect final post-route timing rankings. In contrast, post-global-routing achieves the best balance between final timing fidelity and label generation cost-effectiveness. Based on this finding, PPAPlace is a timing-driven differentiable surrogate predicting post-route PPA from macro and standard-cell placements. The surrogate is a dual-stream predictor that combines graph attention over the chip netlist with spatial convolution over the placement grid. It is trained on post-global-routing labels. The predicted WNS and TNS gradients flow end-to-end back to cell coordinates. PPAPlace exploits these gradients in two ways: as a co-objective injected into an analytical placer's optimization loop (PPAPlace-CoOpt), and as a post-placement refinement step that adjusts macro positions via projected gradient descent (PPAPlace-Refine). On five ChiPBench test circuits excluded from training, PPAPlace improves average WNS and TNS by 22\% and 51\% over the hierarchical baseline while preserving power and routability, using the same predictor without test-circuit retraining. Code is available at https://github.com/ValleyC/PPAPlace.

Bayesian optimisation is a popular approach for optimising expensive black-box functions. The next location to be evaluated is selected via maximising an acquisition function that balances exploitation and exploration. Gaussian processes, the surrogate models of choice in Bayesian optimisation, are often used with a constant prior mean function equal to the arithmetic mean of the observed function values. We show that the rate of convergence can depend sensitively on the choice of mean function. We empirically investigate 8 mean functions (constant functions equal to the arithmetic mean, minimum, median and maximum of the observed function evaluations, linear, quadratic polynomials, random forests and RBF networks), using 10 synthetic test problems and two real-world problems, and using the Expected Improvement and Upper Confidence Bound acquisition functions. We find that for design dimensions ge5 using a constant mean function equal to the worst observed quality value is consistently the best choice on the synthetic problems considered. We argue that this worst-observed-quality function promotes exploitation leading to more rapid convergence. However, for the real-world tasks the more complex mean functions capable of modelling the fitness landscape may be effective, although there is no clearly optimum choice.

Neural architecture search (NAS) faces a challenge in balancing the exploration of expressive, broad search spaces that enable architectural innovation with the need for efficient evaluation of architectures to effectively search such spaces. We investigate surrogate model training for improving search in highly expressive NAS search spaces based on context-free grammars. We show that i) surrogate models trained either using zero-cost-proxy metrics and neural graph features (GRAF) or by fine-tuning an off-the-shelf LM have high predictive power for the performance of architectures both within and across datasets, ii) these surrogates can be used to filter out bad architectures when searching on novel datasets, thereby significantly speeding up search and achieving better final performances, and iii) the surrogates can be further used directly as the search objective for huge speed-ups.

Process Reward Modeling (PRM) is critical for complex reasoning and decision-making tasks where the accuracy of intermediate steps significantly influences the overall outcome. Existing PRM approaches, primarily framed as classification problems, employ cross-entropy loss to independently evaluate each step's correctness. This method can lead to suboptimal reward distribution and does not adequately address the interdependencies among steps. To address these limitations, we introduce the Process Q-value Model (PQM), a novel framework that redefines PRM in the context of a Markov Decision Process. PQM optimizes Q-value rankings based on a novel comparative loss function, enhancing the model's ability to capture the intricate dynamics among sequential decisions. This approach provides a more granular and theoretically grounded methodology for process rewards. Our extensive empirical evaluations across various sampling policies, language model backbones, and multi-step reasoning benchmarks show that PQM outperforms classification-based PRMs. The effectiveness of the comparative loss function is highlighted in our comprehensive ablation studies, confirming PQM's practical efficacy and theoretical advantage.

Large Language Models (LLMs) are increasingly applied for Process Modeling (PMo) tasks such as Process Model Generation (PMG). To support these tasks, researchers have introduced a variety of Process Model Representations (PMRs) that serve as model abstractions or generation targets. However, these PMRs differ widely in structure, complexity, and usability, and have never been systematically compared. Moreover, recent PMG approaches rely on distinct evaluation strategies and generation techniques, making comparison difficult. This paper presents the first empirical study that evaluates multiple PMRs in the context of PMo with LLMs. We introduce the PMo Dataset, a new dataset containing 55 process descriptions paired with models in nine different PMRs. We evaluate PMRs along two dimensions: suitability for LLM-based PMo and performance on PMG. Mermaid achieves the highest overall score across six PMo criteria, whereas BPMN text delivers the best PMG results in terms of process element similarity.

Generative AI models have made significant progress in automating the creation of 3D shapes, which has the potential to transform car design. In engineering design and optimization, evaluating engineering metrics is crucial. To make generative models performance-aware and enable them to create high-performing designs, surrogate modeling of these metrics is necessary. However, the currently used representations of three-dimensional (3D) shapes either require extensive computational resources to learn or suffer from significant information loss, which impairs their effectiveness in surrogate modeling. To address this issue, we propose a new two-dimensional (2D) representation of 3D shapes. We develop a surrogate drag model based on this representation to verify its effectiveness in predicting 3D car drag. We construct a diverse dataset of 9,070 high-quality 3D car meshes labeled by drag coefficients computed from computational fluid dynamics (CFD) simulations to train our model. Our experiments demonstrate that our model can accurately and efficiently evaluate drag coefficients with an R^2 value above 0.84 for various car categories. Moreover, the proposed representation method can be generalized to many other product categories beyond cars. Our model is implemented using deep neural networks, making it compatible with recent AI image generation tools (such as Stable Diffusion) and a significant step towards the automatic generation of drag-optimized car designs. We have made the dataset and code publicly available at https://decode.mit.edu/projects/dragprediction/.

Bayesian parameter inference is useful to improve Li-ion battery diagnostics and can help formulate battery aging models. However, it is computationally intensive and cannot be easily repeated for multiple cycles, multiple operating conditions, or multiple replicate cells. To reduce the computational cost of Bayesian calibration, numerical solvers for physics-based models can be replaced with faster surrogates. A physics-informed neural network (PINN) is developed as a surrogate for the pseudo-2D (P2D) battery model calibration. For the P2D surrogate, additional training regularization was needed as compared to the PINN single-particle model (SPM) developed in Part I. Both the PINN SPM and P2D surrogate models are exercised for parameter inference and compared to data obtained from a direct numerical solution of the governing equations. A parameter inference study highlights the ability to use these PINNs to calibrate scaling parameters for the cathode Li diffusion and the anode exchange current density. By realizing computational speed-ups of 2250x for the P2D model, as compared to using standard integrating methods, the PINN surrogates enable rapid state-of-health diagnostics. In the low-data availability scenario, the testing error was estimated to 2mV for the SPM surrogate and 10mV for the P2D surrogate which could be mitigated with additional data.

With the increasing computational costs associated with deep learning, automated hyperparameter optimization methods, strongly relying on black-box Bayesian optimization (BO), face limitations. Freeze-thaw BO offers a promising grey-box alternative, strategically allocating scarce resources incrementally to different configurations. However, the frequent surrogate model updates inherent to this approach pose challenges for existing methods, requiring retraining or fine-tuning their neural network surrogates online, introducing overhead, instability, and hyper-hyperparameters. In this work, we propose FT-PFN, a novel surrogate for Freeze-thaw style BO. FT-PFN is a prior-data fitted network (PFN) that leverages the transformers' in-context learning ability to efficiently and reliably do Bayesian learning curve extrapolation in a single forward pass. Our empirical analysis across three benchmark suites shows that the predictions made by FT-PFN are more accurate and 10-100 times faster than those of the deep Gaussian process and deep ensemble surrogates used in previous work. Furthermore, we show that, when combined with our novel acquisition mechanism (MFPI-random), the resulting in-context freeze-thaw BO method (ifBO), yields new state-of-the-art performance in the same three families of deep learning HPO benchmarks considered in prior work.

Machine learning-based surrogate models have emerged as a powerful tool to accelerate simulation-driven scientific workflows. However, their widespread adoption is hindered by the lack of large-scale, diverse, and standardized datasets tailored to physics-based simulations. While existing initiatives provide valuable contributions, many are limited in scope-focusing on specific physics domains, relying on fragmented tooling, or adhering to overly simplistic datamodels that restrict generalization. To address these limitations, we introduce PLAID (Physics-Learning AI Datamodel), a flexible and extensible framework for representing and sharing datasets of physics simulations. PLAID defines a unified standard for describing simulation data and is accompanied by a library for creating, reading, and manipulating complex datasets across a wide range of physical use cases (gitlab.com/drti/plaid). We release six carefully crafted datasets under the PLAID standard, covering structural mechanics and computational fluid dynamics, and provide baseline benchmarks using representative learning methods. Benchmarking tools are made available on Hugging Face, enabling direct participation by the community and contribution to ongoing evaluation efforts (huggingface.co/PLAIDcompetitions).

Building local surrogates to accelerate stationary point searches on potential energy surfaces spans decades of effort. Done correctly, surrogates can reduce the number of expensive electronic structure evaluations by roughly an order of magnitude while preserving the accuracy of the underlying theory, with the gain depending on oracle cost, search distance, and the availability of analytical forces. We present a unified Bayesian optimization view of minimization, single-point saddle searches, and double-ended path searches: all three share one six-step surrogate loop and differ only in the inner optimization target and the acquisition criterion. The framework uses Gaussian process regression with derivative observations, inverse-distance kernels, and active learning, and we develop optional extensions for production use, including farthest-point sampling with the Earth Mover's Distance, MAP regularization, an adaptive trust radius, and random Fourier features for scaling. Accompanying pedagogical Rust code demonstrates that all three applications use the same Bayesian optimization loop, bridging the gap between theoretical formulation and practical execution.

Neural surrogates offer a promising route to accelerating computationally expensive simulations governed by partial differential equations across science and industry. Their practical deployment, however, is limited by unreliable predictions under out-of-distribution (OOD) conditions. We develop a solver-coupled surrogate-Newton framework that uses surrogate predictions as high-quality initial guesses for Newton-Krylov iterations, thereby combining rapid global flow-field prediction with high-accuracy numerical convergence at the terminal stage. On an OOD benchmark comprising geometries sampled from actual transonic airfoil optimization trajectories, the framework lowers the median residual L_2 ratio by over seven orders of magnitude while substantially reducing field and aerodynamic errors. In practical supercritical airfoil optimization, it improves online prediction reliability while achieving a 15.5-fold generation-level speedup over CFD. We further test the framework's extension to three dimensions using a flying-wing dataset. Together, these studies demonstrate the potential of surrogate-Newton coupling to deliver accurate, efficient and scalable steady CFD across industrial workflows.

The assessment of safety performance plays a pivotal role in the development and deployment of connected and automated vehicles (CAVs). A common approach involves designing testing scenarios based on prior knowledge of CAVs (e.g., surrogate models), conducting tests in these scenarios, and subsequently evaluating CAVs' safety performances. However, substantial differences between CAVs and the prior knowledge can significantly diminish the evaluation efficiency. In response to this issue, existing studies predominantly concentrate on the adaptive design of testing scenarios during the CAV testing process. Yet, these methods have limitations in their applicability to high-dimensional scenarios. To overcome this challenge, we develop an adaptive testing environment that bolsters evaluation robustness by incorporating multiple surrogate models and optimizing the combination coefficients of these surrogate models to enhance evaluation efficiency. We formulate the optimization problem as a regression task utilizing quadratic programming. To efficiently obtain the regression target via reinforcement learning, we propose the dense reinforcement learning method and devise a new adaptive policy with high sample efficiency. Essentially, our approach centers on learning the values of critical scenes displaying substantial surrogate-to-real gaps. The effectiveness of our method is validated in high-dimensional overtaking scenarios, demonstrating that our approach achieves notable evaluation efficiency.

Bayesian optimisation (BO) uses probabilistic surrogate models - usually Gaussian processes (GPs) - for the optimisation of expensive black-box functions. At each BO iteration, the GP hyperparameters are fit to previously-evaluated data by maximising the marginal likelihood. However, this fails to account for uncertainty in the hyperparameters themselves, leading to overconfident model predictions. This uncertainty can be accounted for by taking the Bayesian approach of marginalising out the model hyperparameters. We investigate whether a fully-Bayesian treatment of the Gaussian process hyperparameters in BO (FBBO) leads to improved optimisation performance. Since an analytic approach is intractable, we compare FBBO using three approximate inference schemes to the maximum likelihood approach, using the Expected Improvement (EI) and Upper Confidence Bound (UCB) acquisition functions paired with ARD and isotropic Matern kernels, across 15 well-known benchmark problems for 4 observational noise settings. FBBO using EI with an ARD kernel leads to the best performance in the noise-free setting, with much less difference between combinations of BO components when the noise is increased. FBBO leads to over-exploration with UCB, but is not detrimental with EI. Therefore, we recommend that FBBO using EI with an ARD kernel as the default choice for BO.

We introduced a novel method to solve Bayesian inverse problems governed by PDE equations with a hybrid two-level MCMC where we took advantage of the AI surrogate model speed and the accuracy of numerical models. We show theoretically the potential to solve Bayesian inverse problems accurately with only a small number of numerical samples when the AI surrogate model error is small. Several numerical experiment results are included which demonstrates the advantage of the hybrid method.

We propose Process-Aware Policy Optimization (PAPO), a method that integrates process-level evaluation into Group Relative Policy Optimization (GRPO) through decoupled advantage normalization, to address two limitations of existing reward designs. Outcome reward models (ORM) evaluate only final-answer correctness, treating all correct responses identically regardless of reasoning quality, and gradually lose the advantage signal as groups become uniformly correct. Process reward models (PRM) offer richer supervision, but directly using PRM scores causes reward hacking, where models exploit verbosity to inflate scores while accuracy collapses. PAPO resolves both by composing the advantage from an outcome component Aout, derived from ORM and normalized over all responses, and a process component Aproc, derived from a rubric-based PRM and normalized exclusively among correct responses. This decoupled design ensures that Aout anchors training on correctness while Aproc differentiates reasoning quality without distorting the outcome signal. Experiments across multiple model scales and six benchmarks demonstrate that PAPO consistently outperforms ORM, reaching 51.3% vs.\ 46.3% on OlympiadBench while continuing to improve as ORM plateaus and declines.

Recent advancements in large language models (LLMs) have been driven by their emergent reasoning capabilities, particularly through long chain-of-thought (CoT) prompting, which enables thorough exploration and deliberation. Despite these advances, long-CoT LLMs often exhibit suboptimal reasoning behaviors, such as overthinking and excessively protracted reasoning chains, which can impair performance. In this paper, we analyze reasoning processes through an optimization lens, framing CoT as a gradient descent procedure where each reasoning step constitutes an update toward problem resolution. Building on this perspective, we introduce RePro (Rectifying Process-level Reward), a novel approach to refine LLM reasoning during post-training. RePro defines a surrogate objective function to assess the optimization process underlying CoT, utilizing a dual scoring mechanism to quantify its intensity and stability. These scores are aggregated into a composite process-level reward, seamlessly integrated into reinforcement learning with verifiable rewards (RLVR) pipelines to optimize LLMs. Extensive experiments across multiple reinforcement learning algorithms and diverse LLMs, evaluated on benchmarks spanning mathematics, science, and coding, demonstrate that RePro consistently enhances reasoning performance and mitigates suboptimal reasoning behaviors.

In computational social science (CSS), researchers analyze documents to explain social and political phenomena. In most scenarios, CSS researchers first obtain labels for documents and then explain labels using interpretable regression analyses in the second step. One increasingly common way to annotate documents cheaply at scale is through large language models (LLMs). However, like other scalable ways of producing annotations, such surrogate labels are often imperfect and biased. We present a new algorithm for using imperfect annotation surrogates for downstream statistical analyses while guaranteeing statistical properties -- like asymptotic unbiasedness and proper uncertainty quantification -- which are fundamental to CSS research. We show that direct use of surrogate labels in downstream statistical analyses leads to substantial bias and invalid confidence intervals, even with high surrogate accuracy of 80-90%. To address this, we build on debiased machine learning to propose the design-based supervised learning (DSL) estimator. DSL employs a doubly-robust procedure to combine surrogate labels with a smaller number of high-quality, gold-standard labels. Our approach guarantees valid inference for downstream statistical analyses, even when surrogates are arbitrarily biased and without requiring stringent assumptions, by controlling the probability of sampling documents for gold-standard labeling. Both our theoretical analysis and experimental results show that DSL provides valid statistical inference while achieving root mean squared errors comparable to existing alternatives that focus only on prediction without inferential guarantees.

In agentic scientific machine learning (SciML), large language model (LLM) agents can discover surrogate models and select one by an automated score, typically an error metric. A low error, however, does not establish that the predicted fields satisfy the physics that matter for mechanics, such as boundary conditions, superposition, stiffness scaling, or causality. We introduce Physics-Audited Agentic SciML (PA-SciML), a verification-first workflow for agentic SciML discovery. The workflow fixes a scoring evaluator before search, derives reviewable machine-checkable physics requirements, checks each trained candidate on its outputs, and separately searches prescribed input ranges or measured load-history spans for high-violation cases without reference solution fields. A surrogate is reported as verified only under the stated checks. When enabled, the workflow also adds advisory numerical probes before training and tests one modeling change at a time to record which isolated edits are associated with score gains before reuse. In the reported computational-solid-mechanics numerical examples, the static elasticity run selects a surrogate with lower validation error than the error-only baseline while both selected models pass the common linear-elastic checks. In the transient elastodynamics run, an error-only baseline with similar mean error fails a stricter causality check by responding to future parts of the loading history, while the selected surrogate passes the stated checks. The main distinction is per-candidate physics evidence on predicted fields, not a richer aggregate score.

We consider minimizing functions for which it is expensive to compute the (possibly stochastic) gradient. Such functions are prevalent in reinforcement learning, imitation learning and adversarial training. Our target optimization framework uses the (expensive) gradient computation to construct surrogate functions in a target space (e.g. the logits output by a linear model for classification) that can be minimized efficiently. This allows for multiple parameter updates to the model, amortizing the cost of gradient computation. In the full-batch setting, we prove that our surrogate is a global upper-bound on the loss, and can be (locally) minimized using a black-box optimization algorithm. We prove that the resulting majorization-minimization algorithm ensures convergence to a stationary point of the loss. Next, we instantiate our framework in the stochastic setting and propose the SSO algorithm, which can be viewed as projected stochastic gradient descent in the target space. This connection enables us to prove theoretical guarantees for SSO when minimizing convex functions. Our framework allows the use of standard stochastic optimization algorithms to construct surrogates which can be minimized by any deterministic optimization method. To evaluate our framework, we consider a suite of supervised learning and imitation learning problems. Our experiments indicate the benefits of target optimization and the effectiveness of SSO.

Mechanistic interpretability (MI) requires full access to model internals, yet the APIs for most widely deployed language models at best expose log-probabilities over output tokens. This creates a surrogate problem: when do measurements made on open models allow us to make claims about a closed model? We evaluate surrogate fidelity at the prediction, attribution, and representation levels. For binary classification tasks, log-odds provide an API-compatible scalar readout of the model's representation space, and leave-one-out attributions provide insight into model behavior. Across eleven models spanning four families (Llama, Qwen, GPT, and Gemini), we find that prediction fidelity substantially overstates attribution fidelity: models that agree on what the answer is often disagree on why. We document an access-validity inversion: white-box signals like attention patterns and perturbation magnitudes are highly stable across models but only weakly predictive of causal attributions, which black-box input ablations capture by design. Mechanistic insight does not automatically transfer to closed targets, and prediction-level agreement is insufficient to warrant such transfer. Code and results are available at https://github.com/facebookresearch/surrogate.

The existence of a plethora of language models makes the problem of selecting the best one for a custom task challenging. Most state-of-the-art methods leverage transformer-based models (e.g., BERT) or their variants. Training such models and exploring their hyperparameter space, however, is computationally expensive. Prior work proposes several neural architecture search (NAS) methods that employ performance predictors (e.g., surrogate models) to address this issue; however, analysis has been limited to homogeneous models that use fixed dimensionality throughout the network. This leads to sub-optimal architectures. To address this limitation, we propose a suite of heterogeneous and flexible models, namely FlexiBERT, that have varied encoder layers with a diverse set of possible operations and different hidden dimensions. For better-posed surrogate modeling in this expanded design space, we propose a new graph-similarity-based embedding scheme. We also propose a novel NAS policy, called BOSHNAS, that leverages this new scheme, Bayesian modeling, and second-order optimization, to quickly train and use a neural surrogate model to converge to the optimal architecture. A comprehensive set of experiments shows that the proposed policy, when applied to the FlexiBERT design space, pushes the performance frontier upwards compared to traditional models. FlexiBERT-Mini, one of our proposed models, has 3% fewer parameters than BERT-Mini and achieves 8.9% higher GLUE score. A FlexiBERT model with equivalent performance as the best homogeneous model achieves 2.6x smaller size. FlexiBERT-Large, another proposed model, achieves state-of-the-art results, outperforming the baseline models by at least 5.7% on the GLUE benchmark.

The lack of freely available standardized datasets represents an aggravating factor during the development and testing the performance of novel computational techniques in exposure assessment and dosimetry research. This hinders progress as researchers are required to generate numerical data (field, power and temperature distribution) anew using simulation software for each exposure scenario. Other than being time consuming, this approach is highly susceptible to errors that occur during the configuration of the electromagnetic model. To address this issue, in this paper, the limited available data on the incident power density and resultant maximum temperature rise on the skin surface considering various steady-state exposure scenarios at 10-90 GHz have been statistically modeled. The synthetic data have been sampled from the fitted statistical multivariate distribution with respect to predetermined dosimetric constraints. We thus present a comprehensive and open-source dataset compiled of the high-fidelity numerical data considering various exposures to a realistic source. Furthermore, different surrogate models for predicting maximum temperature rise on the skin surface were fitted based on the synthetic dataset. All surrogate models were tested on the originally available data where satisfactory predictive performance has been demonstrated. A simple technique of combining quadratic polynomial and tensor-product spline surrogates, each operating on its own cluster of data, has achieved the lowest mean absolute error of 0.058 {\deg}C. Therefore, overall experimental results indicate the validity of the proposed synthetic dataset.

Process Reward Models (PRMs) emerge as a promising approach for process supervision in mathematical reasoning of Large Language Models (LLMs), which aim to identify and mitigate intermediate errors in the reasoning processes. However, the development of effective PRMs faces significant challenges, particularly in data annotation and evaluation methodologies. In this paper, through extensive experiments, we demonstrate that commonly used Monte Carlo (MC) estimation-based data synthesis for PRMs typically yields inferior performance and generalization compared to LLM-as-a-judge and human annotation methods. MC estimation relies on completion models to evaluate current-step correctness, leading to inaccurate step verification. Furthermore, we identify potential biases in conventional Best-of-N (BoN) evaluation strategies for PRMs: (1) The unreliable policy models generate responses with correct answers but flawed processes, leading to a misalignment between the evaluation criteria of BoN and the PRM objectives of process verification. (2) The tolerance of PRMs of such responses leads to inflated BoN scores. (3) Existing PRMs have a significant proportion of minimum scores concentrated on the final answer steps, revealing the shift from process to outcome-based assessment in BoN Optimized PRMs. To address these challenges, we develop a consensus filtering mechanism that effectively integrates MC estimation with LLM-as-a-judge and advocates a more comprehensive evaluation framework that combines response-level and step-level metrics. Based on the mechanisms, we significantly improve both model performance and data efficiency in the BoN evaluation and the step-wise error identification task. Finally, we release a new state-of-the-art PRM that outperforms existing open-source alternatives and provides practical guidelines for future research in building process supervision models.

Current neural architecture search (NAS) strategies focus only on finding a single, good, architecture. They offer little insight into why a specific network is performing well, or how we should modify the architecture if we want further improvements. We propose a Bayesian optimisation (BO) approach for NAS that combines the Weisfeiler-Lehman graph kernel with a Gaussian process surrogate. Our method optimises the architecture in a highly data-efficient manner: it is capable of capturing the topological structures of the architectures and is scalable to large graphs, thus making the high-dimensional and graph-like search spaces amenable to BO. More importantly, our method affords interpretability by discovering useful network features and their corresponding impact on the network performance. Indeed, we demonstrate empirically that our surrogate model is capable of identifying useful motifs which can guide the generation of new architectures. We finally show that our method outperforms existing NAS approaches to achieve the state of the art on both closed- and open-domain search spaces.

The Dragonfly network, with its high-radix and low-diameter structure, is a leading interconnect in high-performance computing. A major challenge is workload interference on shared network links. Parallel discrete event simulation (PDES) is commonly used to analyze workload interference. However, high-fidelity PDES is computationally expensive, making it impractical for large-scale or real-time scenarios. Hybrid simulation that incorporates data-driven surrogate models offers a promising alternative, especially for forecasting application runtime, a task complicated by the dynamic behavior of network traffic. We present \ourmodel, a surrogate model that combines graph neural networks (GNNs) and large language models (LLMs) to capture both spatial and temporal patterns from port level router data. \ourmodel outperforms existing statistical and machine learning baselines, enabling accurate runtime prediction and supporting efficient hybrid simulation of Dragonfly networks.

Every call to an LLM classification endpoint produces a labeled input-output pair already retained in production logs. These pairs constitute a free, growing training set: a lightweight surrogate trained on them can absorb a significant portion of future traffic at near-zero marginal inference cost. The open questions are when the surrogate is reliable enough to deploy, what it handles versus defers, and how that boundary evolves as data accumulates. We introduce TRACER (Trace-based Adaptive Cost-Efficient Routing), an open-source system that trains ML surrogates on an LLM's own production traces and governs deployment through a parity gate: the surrogate is activated only when its agreement with the LLM exceeds a user-specified threshold α. To make the routing boundary transparent, TRACER generates interpretability artifacts describing which input regions the surrogate handles, where it plateaus, and why it defers. On a 77-class intent benchmark with a Sonnet 4.6 teacher, TRACER achieves 83-100% surrogate coverage depending on the quality target α; on a 150-class benchmark, the surrogate fully replaces the teacher. On a natural language inference task, the parity gate correctly refuses deployment because the embedding representation cannot support reliable separation. The system is available as open-source software.

An established way to improve the transferability of black-box evasion attacks is to craft the adversarial examples on an ensemble-based surrogate to increase diversity. We argue that transferability is fundamentally related to uncertainty. Based on a state-of-the-art Bayesian Deep Learning technique, we propose a new method to efficiently build a surrogate by sampling approximately from the posterior distribution of neural network weights, which represents the belief about the value of each parameter. Our extensive experiments on ImageNet, CIFAR-10 and MNIST show that our approach improves the success rates of four state-of-the-art attacks significantly (up to 83.2 percentage points), in both intra-architecture and inter-architecture transferability. On ImageNet, our approach can reach 94% of success rate while reducing training computations from 11.6 to 2.4 exaflops, compared to an ensemble of independently trained DNNs. Our vanilla surrogate achieves 87.5% of the time higher transferability than three test-time techniques designed for this purpose. Our work demonstrates that the way to train a surrogate has been overlooked, although it is an important element of transfer-based attacks. We are, therefore, the first to review the effectiveness of several training methods in increasing transferability. We provide new directions to better understand the transferability phenomenon and offer a simple but strong baseline for future work.

Complex multi-step reasoning tasks, such as solving mathematical problems or generating code, remain a significant hurdle for even the most advanced large language models (LLMs). Verifying LLM outputs with an Outcome Reward Model (ORM) is a standard inference-time technique aimed at enhancing the reasoning performance of LLMs. However, this still proves insufficient for reasoning tasks with a lengthy or multi-hop reasoning chain, where the intermediate outcomes are neither properly rewarded nor penalized. Process supervision addresses this limitation by assigning intermediate rewards during the reasoning process. To date, the methods used to collect process supervision data have relied on either human annotation or per-step Monte Carlo estimation, both prohibitively expensive to scale, thus hindering the broad application of this technique. In response to this challenge, we propose a novel divide-and-conquer style Monte Carlo Tree Search (MCTS) algorithm named OmegaPRM for the efficient collection of high-quality process supervision data. This algorithm swiftly identifies the first error in the Chain of Thought (CoT) with binary search and balances the positive and negative examples, thereby ensuring both efficiency and quality. As a result, we are able to collect over 1.5 million process supervision annotations to train a Process Reward Model (PRM). Utilizing this fully automated process supervision alongside the weighted self-consistency algorithm, we have enhanced the instruction tuned Gemini Pro model's math reasoning performance, achieving a 69.4\% success rate on the MATH benchmark, a 36\% relative improvement from the 51\% base model performance. Additionally, the entire process operates without any human intervention, making our method both financially and computationally cost-effective compared to existing methods.

Neural surrogates for partial differential equations (PDEs) have become popular due to their potential to quickly simulate physics. With a few exceptions, neural surrogates generally treat the forward evolution of time-dependent PDEs as a black box by directly predicting the next state. While this is a natural and easy framework for applying neural surrogates, it can be an over-simplified and rigid framework for predicting physics. In this work, we propose an alternative framework in which neural solvers predict the temporal derivative and an ODE integrator forwards the solution in time, which has little overhead and is broadly applicable across model architectures and PDEs. We find that by simply changing the training target and introducing numerical integration during inference, neural surrogates can gain accuracy and stability. Predicting temporal derivatives also allows models to not be constrained to a specific temporal discretization, allowing for flexible time-stepping during inference or training on higher-resolution PDE data. Lastly, we investigate why this new framework can be beneficial and in what situations does it work well.

Data-driven surrogate models improve the efficiency of simulating continuous dynamical systems, yet their autoregressive rollouts are often limited by instability and spectral blow-up. While global regularization techniques can enforce contractive dynamics, they uniformly damp high-frequency features, introducing a contraction-dissipation dilemma. Furthermore, long-horizon trajectory optimization methods that explicitly correct drift are bottlenecked by memory constraints. In this work, we propose Jacobian-Adaptive Weighting for Stability (JAWS), a probabilistic regularization strategy designed to mitigate these limitations. By framing operator learning as Maximum A Posteriori (MAP) estimation with spatially heteroscedastic uncertainty, JAWS dynamically modulates the regularization strength based on local physical complexity. This allows the model to enforce contraction in smooth regions to suppress noise, while relaxing constraints near singular features to preserve gradients, effectively realizing a behavior similar to numerical shock-capturing schemes. Experiments demonstrate that this spatially-adaptive prior serves as an effective spectral pre-conditioner, which reduces the base operator's burden of handling high-frequency instabilities. This reduction enables memory-efficient, short-horizon trajectory optimization to match or exceed the long-term accuracy of long-horizon baselines. Evaluated on the 1D viscous Burgers' equation, our hybrid approach improves long-term stability, shock fidelity, and out-of-distribution generalization while reducing training computational costs.

Despite recent advances in AI, the development of systems capable of executing complex, multi-step reasoning tasks involving multiple tools remains a significant challenge. Current benchmarks fall short in capturing the real-world complexity of tool-use reasoning, where verifying the correctness of not only the final answer but also the intermediate steps is important for evaluation, development, and identifying failures during inference time. To bridge this gap, we introduce ToolComp, a comprehensive benchmark designed to evaluate multi-step tool-use reasoning. ToolComp is developed through a collaboration between models and human annotators, featuring human-edited/verified prompts, final answers, and process supervision labels, allowing for the evaluation of both final outcomes and intermediate reasoning. Evaluation across six different model families demonstrates the challenging nature of our dataset, with the majority of models achieving less than 50% accuracy. Additionally, we generate synthetic training data to compare the performance of outcome-supervised reward models (ORMs) with process-supervised reward models (PRMs) to assess their ability to improve complex tool-use reasoning as evaluated by ToolComp. Our results show that PRMs generalize significantly better than ORMs, achieving a 19% and 11% improvement in rank@1 accuracy for ranking base and fine-tuned model trajectories, respectively. These findings highlight the critical role of process supervision in both the evaluation and training of AI models, paving the way for more robust and capable systems in complex, multi-step tool-use tasks.

Gravitational-wave approximants are essential for gravitational-wave astronomy, allowing the coverage binary black hole parameter space for inference or match filtering without costly numerical relativity (NR) simulations, but generally trading some accuracy for computational efficiency. To reduce this trade-off, NR surrogate models can be constructed using interpolation within NR waveform space. We present a 2-stage training approach for neural network-based NR surrogate models. Initially trained on approximant-generated waveforms and then fine-tuned with NR data, these dual-stage artificial neural surrogate (DANSur) models offer rapid and competitively accurate waveform generation, generating millions in under 20ms on a GPU while keeping mean mismatches with NR around 10^{-4}. Implemented in the bilby framework, we show they can be used for parameter estimation tasks.

Solving the inverse problem is the key step in evaluating the capacity of a physical model to describe real phenomena. In medical image computing, it aligns with the classical theme of image-based model personalization. Traditionally, a solution to the problem is obtained by performing either sampling or variational inference based methods. Both approaches aim to identify a set of free physical model parameters that results in a simulation best matching an empirical observation. When applied to brain tumor modeling, one of the instances of image-based model personalization in medical image computing, the overarching drawback of the methods is the time complexity for finding such a set. In a clinical setting with limited time between imaging and diagnosis or even intervention, this time complexity may prove critical. As the history of quantitative science is the history of compression, we align in this paper with the historical tendency and propose a method compressing complex traditional strategies for solving an inverse problem into a simple database query task. We evaluated different ways of performing the database query task assessing the trade-off between accuracy and execution time. On the exemplary task of brain tumor growth modeling, we prove that the proposed method achieves one order speed-up compared to existing approaches for solving the inverse problem. The resulting compute time offers critical means for relying on more complex and, hence, realistic models, for integrating image preprocessing and inverse modeling even deeper, or for implementing the current model into a clinical workflow.

Data-driven surrogate models are an alternative to numerical homogenization of heterogeneous materials. In this contribution, a supervised learning approach is presented for predicting effective Lamé parameters of hyperelastic composites from low-dimensional microstructural descriptors. The data set is based on previously published numerical homogenization results for ensembles of two-phase stochastic microstructures generated by planar Boolean models, covering variations of inclusion shape, phase contrast, and area fraction; see Brändel, Brands, Maike, Rheinbach, Schröder, Schwarz and Stoyan (2022). A neural network is trained on combinations of scalar and curve-valued statistical descriptors, including the area fraction, a derived scalar shape descriptor τ, the two-point correlation function S_2(r), and the lineal-path function ell(z). Additional data representing limiting cases of the parameter space are incorporated to stabilize training and improve extrapolation behavior. The surrogate is evaluated by leave-one-grain-type-out cross-validation in order to assess generalization to unseen grain geometries. Numerical results demonstrate that additional descriptors can reduce relative errors. A predictor trained with τ and S_2(r) provides a compact representation with good quantitative accuracy and regular dense response behavior. Adding the lineal-path function ell(z) further reduces the error at the available data points, indicating that it is a promising additional descriptor; however, dense post-training response evaluations show that improved pointwise accuracy does not automatically guarantee physically admissible behavior between sampled parameter values. This motivates future work on physically constrained surrogate models, loss formulations, bounded output parametrizations, and a more systematic representation of curve-valued geometric descriptors.

Policy-based reinforcement learning algorithms are widely used in various fields. Among them, mainstream policy optimization algorithms such as TRPO and PPO introduce importance sampling into policy iteration, which allows the reuse of historical data. However, this can also lead to a high variance of the surrogate objective and indirectly affects the stability and convergence of the algorithm. In this paper, we first derived an upper bound of the surrogate objective variance, which can grow quadratically with the increase of the surrogate objective. Next, we proposed the dropout technique to avoid the excessive increase of the surrogate objective variance caused by importance sampling. Then, we introduced a general reinforcement learning framework applicable to mainstream policy optimization methods, and applied the dropout technique to the PPO algorithm to obtain the D-PPO variant. Finally, we conduct comparative experiments between D-PPO and PPO algorithms in the Atari 2600 environment, and the results show that D-PPO achieved significant performance improvements compared to PPO, and effectively limited the excessive increase of the surrogate objective variance during training.

Atmospheric retrieval determines the properties of an atmosphere based on its measured spectrum. The low signal-to-noise ratio of exoplanet observations require a Bayesian approach to determine posterior probability distributions of each model parameter, given observed spectra. This inference is computationally expensive, as it requires many executions of a costly radiative transfer (RT) simulation for each set of sampled model parameters. Machine learning (ML) has recently been shown to provide a significant reduction in runtime for retrievals, mainly by training inverse ML models that predict parameter distributions, given observed spectra, albeit with reduced posterior accuracy. Here we present a novel approach to retrieval by training a forward ML surrogate model that predicts spectra given model parameters, providing a fast approximate RT simulation that can be used in a conventional Bayesian retrieval framework without significant loss of accuracy. We demonstrate our method on the emission spectrum of HD 189733 b and find good agreement with a traditional retrieval from the Bayesian Atmospheric Radiative Transfer (BART) code (Bhattacharyya coefficients of 0.9843--0.9972, with a mean of 0.9925, between 1D marginalized posteriors). This accuracy comes while still offering significant speed enhancements over traditional RT, albeit not as much as ML methods with lower posterior accuracy. Our method is ~9x faster per parallel chain than BART when run on an AMD EPYC 7402P central processing unit (CPU). Neural-network computation using an NVIDIA Titan Xp graphics processing unit is 90--180x faster per chain than BART on that CPU.

De-identification of electronic health records (EHR) is a vital step towards advancing health informatics research and maximising the use of available data. It is a two-step process where step one is the identification of protected health information (PHI), and step two is replacing such PHI with surrogates. Despite the recent advances in automatic de-identification of EHR, significant obstacles remain if the abundant health data available are to be used to the full potential. Accuracy in de-identification could be considered a necessary, but not sufficient condition for the use of EHR without individual patient consent. We present here a comprehensive review of the progress to date, both the impressive successes in achieving high accuracy and the significant risks and challenges that remain. To best of our knowledge, this is the first paper to present a complete picture of end-to-end automatic de-identification. We review 18 recently published automatic de-identification systems -designed to de-identify EHR in the form of free text- to show the advancements made in improving the overall accuracy of the system, and in identifying individual PHI. We argue that despite the improvements in accuracy there remain challenges in surrogate generation and replacements of identified PHIs, and the risks posed to patient protection and privacy.

Expensive multi-objective optimization problems (EMOPs) are common in real-world scenarios where evaluating objective functions is costly and involves extensive computations or physical experiments. Current Pareto set learning methods for such problems often rely on surrogate models like Gaussian processes to approximate the objective functions. These surrogate models can become fragmented, resulting in numerous small uncertain regions between explored solutions. When using acquisition functions such as the Lower Confidence Bound (LCB), these uncertain regions can turn into pseudo-local optima, complicating the search for globally optimal solutions. To address these challenges, we propose a novel approach called SVH-PSL, which integrates Stein Variational Gradient Descent (SVGD) with Hypernetworks for efficient Pareto set learning. Our method addresses the issues of fragmented surrogate models and pseudo-local optima by collectively moving particles in a manner that smooths out the solution space. The particles interact with each other through a kernel function, which helps maintain diversity and encourages the exploration of underexplored regions. This kernel-based interaction prevents particles from clustering around pseudo-local optima and promotes convergence towards globally optimal solutions. Our approach aims to establish robust relationships between trade-off reference vectors and their corresponding true Pareto solutions, overcoming the limitations of existing methods. Through extensive experiments across both synthetic and real-world MOO benchmarks, we demonstrate that SVH-PSL significantly improves the quality of the learned Pareto set, offering a promising solution for expensive multi-objective optimization problems.

The spatiotemporal resolution of Partial Differential Equations (PDEs) plays important roles in the mathematical description of the world's physical phenomena. In general, scientists and engineers solve PDEs numerically by the use of computationally demanding solvers. Recently, deep learning algorithms have emerged as a viable alternative for obtaining fast solutions for PDEs. Models are usually trained on synthetic data generated by solvers, stored on disk and read back for training. This paper advocates that relying on a traditional static dataset to train these models does not allow the full benefit of the solver to be used as a data generator. It proposes an open source online training framework for deep surrogate models. The framework implements several levels of parallelism focused on simultaneously generating numerical simulations and training deep neural networks. This approach suppresses the I/O and storage bottleneck associated with disk-loaded datasets, and opens the way to training on significantly larger datasets. Experiments compare the offline and online training of four surrogate models, including state-of-the-art architectures. Results indicate that exposing deep surrogate models to more dataset diversity, up to hundreds of GB, can increase model generalization capabilities. Fully connected neural networks, Fourier Neural Operator (FNO), and Message Passing PDE Solver prediction accuracy is improved by 68%, 16% and 7%, respectively.

In recent years, large language models have greatly improved in their ability to perform complex multi-step reasoning. However, even state-of-the-art models still regularly produce logical mistakes. To train more reliable models, we can turn either to outcome supervision, which provides feedback for a final result, or process supervision, which provides feedback for each intermediate reasoning step. Given the importance of training reliable models, and given the high cost of human feedback, it is important to carefully compare the both methods. Recent work has already begun this comparison, but many questions still remain. We conduct our own investigation, finding that process supervision significantly outperforms outcome supervision for training models to solve problems from the challenging MATH dataset. Our process-supervised model solves 78% of problems from a representative subset of the MATH test set. Additionally, we show that active learning significantly improves the efficacy of process supervision. To support related research, we also release PRM800K, the complete dataset of 800,000 step-level human feedback labels used to train our best reward model.

Vision-language models (VLMs) are increasingly explored as visual critics, reward generators, and failure detectors in robotic manipulation. These roles implicitly require models to judge not only final task success, but also how a manipulation execution is physically and temporally progressing. However, existing evaluations fail to test whether VLMs possess fine-grained process understanding. To address this gap, we present RoboProcessBench, a benchmark for process-aware understanding in vision-language robotic manipulation. RoboProcessBench decomposes such capability into two complementary dimensions, static monitoring and dynamic reasoning, instantiated as 12 diagnostic question families covering phase, contact, motion, coordination, primitive-local progress, temporal order, outcome, and primitive-level transitions. Built from physically grounded execution traces, the curated benchmark corpus ProcessData contains \textasciitilde 58k question-answer pairs across 260 manipulation tasks, which is further split into ProcessData-SFT and ProcessData-Eval for post-training and evaluation purposes. Extensive evaluation of various VLMs on ProcessData-Eval reveals broad limitations across 12 diagnostic task families, suggesting current models still lack robust process-aware understanding of manipulation executions. But with ProcessData-SFT, the post-trained Qwen2.5-VL-7B and InternVL-3-8B exhibit consistent gains on local state, motion, progress, and primitive-aware cues. These results demonstrate that RoboProcessBench serves as both an evaluation benchmark and a learnable supervision source for developing VLMs capable of monitoring and evaluating robotic manipulation processes. Project webpage: https://processbench-2026.github.io/RoboProcessBench-Web/{https://processbench-2026.github.io}.

Recent advancements in large language models (LLMs) have substantially enhanced their mathematical reasoning abilities. However, these models still struggle with complex problems that require multiple reasoning steps, frequently leading to logical or numerical errors. While numerical mistakes can be largely addressed by integrating a code interpreter, identifying logical errors within intermediate steps is more challenging. Moreover, manually annotating these steps for training is not only expensive but also labor-intensive, requiring the expertise of professional annotators. In our study, we introduce an innovative approach that bypasses the need for process annotations (from human or GPTs) by utilizing the Monte Carlo Tree Search (MCTS) framework. This technique automatically generates both the process supervision and the step-level evaluation signals. Our method iteratively trains the policy and value models, leveraging the capabilities of a well-pretrained LLM to progressively enhance its mathematical reasoning skills. Furthermore, we propose an efficient inference strategy-step-level beam search, where the value model is crafted to assist the policy model (i.e., LLM) in navigating more effective reasoning paths, rather than solely relying on prior probabilities. The experimental results on both in-domain and out-of-domain datasets demonstrate that even without GPT-4 or human-annotated process supervision, our AlphaMath framework achieves comparable or superior results to previous state-of-the-art methods.

In this paper we develop a dynamic form of Bayesian optimization for machine learning models with the goal of rapidly finding good hyperparameter settings. Our method uses the partial information gained during the training of a machine learning model in order to decide whether to pause training and start a new model, or resume the training of a previously-considered model. We specifically tailor our method to machine learning problems by developing a novel positive-definite covariance kernel to capture a variety of training curves. Furthermore, we develop a Gaussian process prior that scales gracefully with additional temporal observations. Finally, we provide an information-theoretic framework to automate the decision process. Experiments on several common machine learning models show that our approach is extremely effective in practice.

Information-seeking is a core capability for AI agents, requiring them to gather and reason over tool-generated information across long trajectories. However, such multi-step information-seeking tasks remain challenging for agents backed by language models. While process reward models (PRMs) can guide agents by ranking candidate steps at test-time, existing PRMs, designed for short reasoning with binary judgment, cannot capture richer dimensions of information-seeking steps, such as tool interactions and reasoning over tool outputs, nor handle the rapidly growing context in long-horizon tasks. To address these limitations, we introduce PRInTS, a generative PRM trained with dual capabilities: (1) dense scoring based on the PRM's reasoning across multiple step quality dimensions (e.g., interpretation of tool outputs, tool call informativeness) and (2) trajectory summarization that compresses the growing context while preserving essential information for step evaluation. Extensive evaluations across FRAMES, GAIA (levels 1-3), and WebWalkerQA (easy-hard) benchmarks on multiple models, along with ablations, reveal that best-of-n sampling with PRInTS enhances information-seeking abilities of open-source models as well as specialized agents, matching or surpassing the performance of frontier models with a much smaller backbone agent and outperforming other strong reward modeling baselines.

Large Language Models (LLMs) have shown promising capabilities for solving Operations Research (OR) problems. While reinforcement learning serves as a powerful paradigm for LLM training on OR problems, existing works generally face two key limitations. First, outcome reward suffers from the credit assignment problem, where correct final answers can reinforce flawed reasoning. Second, conventional discriminative process supervision is myopic, failing to evaluate the interdependent steps of OR modeling holistically. To this end, we introduce StepORLM, a novel self-evolving framework with generative process supervision. At its core, StepORLM features a co-evolutionary loop where a policy model and a generative process reward model (GenPRM) iteratively improve on each other. This loop is driven by a dual-feedback mechanism: definitive, outcome-based verification from an external solver, and nuanced, holistic process evaluation from the GenPRM. The combined signal is used to align the policy via Weighted Direct Preference Optimization (W-DPO) and simultaneously refine the GenPRM. Our resulting 8B-parameter StepORLM establishes a new state-of-the-art across six benchmarks, significantly outperforming vastly larger generalist models, agentic methods, and specialized baselines. Moreover, the co-evolved GenPRM is able to act as a powerful and universally applicable process verifier, substantially boosting the inference scaling performance of both our own model and other existing LLMs.

This paper introduces a novel surrogate modeling framework for aerodynamic applications based on Neural Fields. The proposed approach, MARIO (Modulated Aerodynamic Resolution Invariant Operator), addresses non parametric geometric variability through an efficient shape encoding mechanism and exploits the discretization-invariant nature of Neural Fields. It enables training on significantly downsampled meshes, while maintaining consistent accuracy during full-resolution inference. These properties allow for efficient modeling of diverse flow conditions, while reducing computational cost and memory requirements compared to traditional CFD solvers and existing surrogate methods. The framework is validated on two complementary datasets that reflect industrial constraints. First, the AirfRANS dataset consists in a two-dimensional airfoil benchmark with non-parametric shape variations. Performance evaluation of MARIO on this case demonstrates an order of magnitude improvement in prediction accuracy over existing methods across velocity, pressure, and turbulent viscosity fields, while accurately capturing boundary layer phenomena and aerodynamic coefficients. Second, the NASA Common Research Model features three-dimensional pressure distributions on a full aircraft surface mesh, with parametric control surface deflections. This configuration confirms MARIO's accuracy and scalability. Benchmarking against state-of-the-art methods demonstrates that Neural Field surrogates can provide rapid and accurate aerodynamic predictions under the computational and data limitations characteristic of industrial applications.

Neural networks excel as function approximators, but their complexity often obscures the types of functions they learn, making it difficult to explain their behavior. To address this, the linearity score lambda(f) is introduced, a simple and interpretable diagnostic that quantifies how well a regression network's output can be mimicked by a linear model. Defined as the R^2 value between the network's predictions and those of a trained linear surrogate, lambda(f) measures linear decodability: the extent to which the network's behavior aligns with a structurally simple model. This framework is evaluated on both synthetic and real-world datasets, using dataset-specific networks and surrogates. High lambda(f) scores reliably indicate alignment with the network's outputs; however, they do not guarantee accuracy with respect to the ground truth. These results highlight the risk of using surrogate fidelity as a proxy for model understanding, especially in high-stakes regression tasks.

Reinforcement learning (RL) has become a promising paradigm for optimizing Retrieval-Augmented Generation (RAG) in complex reasoning tasks. However, traditional outcome-based RL approaches often suffer from reward sparsity and inefficient credit assignment, as coarse-grained scalar rewards fail to identify specific erroneous steps within long-horizon trajectories. This ambiguity frequently leads to "process hallucinations", where models reach correct answers through flawed logic or redundant retrieval steps. Although recent process-aware approaches attempt to mitigate this via static preference learning or heuristic reward shaping, they often lack the on-policy exploration capabilities required to decouple step-level credit from global outcomes. To address these challenges, we propose ProRAG, a process-supervised reinforcement learning framework designed to integrate learned step-level supervision into the online optimization loop. Our framework consists of four stages: (1) Supervised Policy Warmup to initialize the model with a structured reasoning format; (2) construction of an MCTS-based Process Reward Model (PRM) to quantify intermediate reasoning quality; (3) PRM-Guided Reasoning Refinement to align the policy with fine-grained process preferences; and (4) Process-Supervised Reinforcement Learning with a dual-granularity advantage mechanism. By aggregating step-level process rewards with global outcome signals, ProRAG provides precise feedback for every action. Extensive experiments on five multi-hop reasoning benchmarks demonstrate that ProRAG achieves superior overall performance compared to strong outcome-based and process-aware RL baselines, particularly on complex long-horizon tasks, validating the effectiveness of fine-grained process supervision. The code and model are available at https://github.com/lilinwz/ProRAG.

Deep-learning survival models for electronic health record (EHR) data are hard to compare across papers because the upstream preprocessing step, which includes cohort definition, time discretisation, missingness handling, and censoring rules, is typically undocumented and inconsistent. A reported difference in concordance between two mortality models can therefore reflect any of these choices rather than a modelling contribution. We present SurvBench, an open-source preprocessing pipeline that converts raw PhysioNet exports into model-ready tensors for survival analysis. SurvBench covers four critical-care databases (MIMIC-IV, eICU, MC-MED, HiRID) and four input modalities: time-series vitals and laboratory values, static demographics, International Classification of Diseases (ICD) codes, and radiology report embeddings. Every preprocessing decision is controlled through YAML configuration. Imputation, scaling, and feature filtering are fit on the training fold only. Missingness is recorded as a binary mask alongside each feature tensor. The pipeline handles single-risk endpoints (in-hospital and in-ICU mortality) and competing-risks endpoints (a three-way emergency-department admission pathway, with home discharge treated as administrative censoring). We also provide support for harmonised cross-dataset external validation between eICU and MIMIC-IV. SurvBench is publicly available at https://github.com/munibmesinovic/SurvBench, providing a robust platform that future deep-learning EHR survival work, especially nascent multi-modal approaches, can be measured against under matched preprocessing.

Step-by-step verifiers -- also known as process reward models (PRMs) -- are a key ingredient for test-time scaling. PRMs require step-level supervision, making them expensive to train. This work aims to build data-efficient PRMs as verbalized step-wise reward models that verify every step in the solution by generating a verification chain-of-thought (CoT). We propose ThinkPRM, a long CoT verifier fine-tuned on orders of magnitude fewer process labels than those required by discriminative PRMs. Our approach capitalizes on the inherent reasoning abilities of long CoT models, and outperforms LLM-as-a-Judge and discriminative verifiers -- using only 1% of the process labels in PRM800K -- across several challenging benchmarks. Specifically, ThinkPRM beats the baselines on ProcessBench, MATH-500, and AIME '24 under best-of-N selection and reward-guided search. In an out-of-domain evaluation on a subset of GPQA-Diamond and LiveCodeBench, our PRM surpasses discriminative verifiers trained on the full PRM800K by 8% and 4.5%, respectively. Lastly, under the same token budget, ThinkPRM scales up verification compute more effectively compared to LLM-as-a-Judge, outperforming it by 7.2% on a subset of ProcessBench. Our work highlights the value of generative, long CoT PRMs that can scale test-time compute for verification while requiring minimal supervision for training. Our code, data, and models will be released at https://github.com/mukhal/thinkprm.

Data-driven surrogate models are increasingly adopted to accelerate vehicle design. However, open-source multi-fidelity datasets and empirical guidelines linking dataset size to model performance remain limited. This study investigates the relationship between training data size and prediction accuracy for a graph neural network (GNN) based surrogate model for aerodynamic field prediction. We release an open-source, multi-fidelity aerodynamic dataset for double-delta wings, comprising 2448 flow snapshots across 272 geometries evaluated at angles of attack from 11 (degree) to 19 (degree) at Ma=0.3 using both Vortex Lattice Method (VLM) and Reynolds-Averaged Navier-Stokes (RANS) solvers. The geometries are generated using a nested Saltelli sampling scheme to support future dataset expansion and variance-based sensitivity analysis. Using this dataset, we conduct a preliminary empirical scaling study of the MF-VortexNet surrogate by constructing six training datasets with sizes ranging from 40 to 1280 snapshots and training models with 0.1 to 2.4 million parameters under a fixed training budget. We find that the test error decreases with data size with a power-law exponent of -0.6122, indicating efficient data utilization. Based on this scaling law, we estimate that the optimal sampling density is approximately eight samples per dimension in a d-dimensional design space. The results also suggest improved data utilization efficiency for larger surrogate models, implying a potential trade-off between dataset generation cost and model training budget.

Given a sample of size N, it is often useful to select a subsample of smaller size n<N to be used for statistical estimation or learning. Such a data selection step is useful to reduce the requirements of data labeling and the computational complexity of learning. We assume to be given N unlabeled samples {{boldsymbol x}_i}_{ile N}, and to be given access to a `surrogate model' that can predict labels y_i better than random guessing. Our goal is to select a subset of the samples, to be denoted by {{boldsymbol x}_i}_{iin G}, of size |G|=n<N. We then acquire labels for this set and we use them to train a model via regularized empirical risk minimization. By using a mixture of numerical experiments on real and synthetic data, and mathematical derivations under low- and high- dimensional asymptotics, we show that: (i)~Data selection can be very effective, in particular beating training on the full sample in some cases; (ii)~Certain popular choices in data selection methods (e.g. unbiased reweighted subsampling, or influence function-based subsampling) can be substantially suboptimal.

Process Reward Models (PRMs) have emerged as a promising approach to enhance the reasoning quality of Large Language Models (LLMs) by assigning fine-grained scores to intermediate reasoning steps within a solution trajectory. However, existing PRMs predominantly adopt a unidirectional left-to-right (L2R) evaluation paradigm, which limits their ability to leverage global context, making it challenging to verify the consistency of earlier steps based on later ones. In light of these challenges, we propose a novel bidirectional evaluation paradigm, named Bidirectional Process Reward Model (BiPRM). BiPRM seamlessly incorporates a parallel right-to-left (R2L) evaluation stream alongside the conventional L2R flow, enabling later reasoning steps to help assess earlier ones in real time. Notably, the built-in R2L evaluation is implemented solely through prompt modifications that reverse the original reasoning trajectory, without any additional parameters or inference latency introduced. This ensures BiPRM remains both efficient and broadly compatible with existing PRM studies. We conduct extensive experiments on two mathematical reasoning benchmarks using samples generated by three different policy models. Our method, BiPRM, is evaluated across three backbones and three distinct PRM objectives. Across all settings, BiPRM consistently outperforms unidirectional baselines, achieving up to a 31.9% improvement in stepwise reward evaluation. Generally, our results highlight BiPRM's effectiveness, robustness, and general applicability, offering a promising new direction for process-based reward modeling.

The work focuses on gathering high-fidelity and low-fidelity numerical simulations data using Nektar++ (Solver based on Applied Mathematics) and XFOIL respectively. The utilization of the higher polynomial distribution in calculating the Coefficient of lift and drag has demonstrated superior accuracy and precision. Further, Co-kriging Data fusion and Adaptive sampling technique has been used to obtain the precise data predictions for the lift and drag within the confined domain without conducting the costly simulations on HPC clusters. This creates a methodology to quantifying uncertainty in computational fluid dynamics by minimizing the required number of samples. To minimize the reliability on high-fidelity numerical simulations in Uncertainty Quantification, a multi-fidelity strategy has been adopted. The effectiveness of the multi-fidelity deep neural network model has been validated through the approximation of benchmark functions across 1-, 32-, and 100-dimensional, encompassing both linear and nonlinear correlations. The surrogate modelling results showed that multi-fidelity deep neural network model has shown excellent approximation capabilities for the test functions and multi-fidelity deep neural network method has outperformed Co-kriging in effectiveness. In addition to that, multi-fidelity deep neural network model is utilized for the simulation of aleatory uncertainty propagation in 1-, 32-, and 100 dimensional function test, considering both uniform and Gaussian distributions for input uncertainties. The results have shown that multi-fidelity deep neural network model has efficiently predicted the probability density distributions of quantities of interest as well as the statistical moments with precision and accuracy. The Co-Kriging model has exhibited limitations when addressing 32-Dimension problems due to the limitation of memory capacity for storage and manipulation.

We present extensive empirical evidence showing that current Bayesian simulation-based inference algorithms can produce computationally unfaithful posterior approximations. Our results show that all benchmarked algorithms -- (Sequential) Neural Posterior Estimation, (Sequential) Neural Ratio Estimation, Sequential Neural Likelihood and variants of Approximate Bayesian Computation -- can yield overconfident posterior approximations, which makes them unreliable for scientific use cases and falsificationist inquiry. Failing to address this issue may reduce the range of applicability of simulation-based inference. For this reason, we argue that research efforts should be made towards theoretical and methodological developments of conservative approximate inference algorithms and present research directions towards this objective. In this regard, we show empirical evidence that ensembling posterior surrogates provides more reliable approximations and mitigates the issue.

Model merging has emerged as an effective approach to combine multiple single-task models into a multitask model. This process typically involves computing a weighted average of the model parameters without any additional training. Existing model-merging methods focus on enhancing average task accuracy. However, interference and conflicts between the objectives of different tasks can lead to trade-offs during the merging process. In real-world applications, a set of solutions with various trade-offs can be more informative, helping practitioners make decisions based on diverse preferences. In this paper, we introduce a novel and low-compute algorithm, Model Merging with Amortized Pareto Front (MAP). MAP efficiently identifies a Pareto set of scaling coefficients for merging multiple models, reflecting the trade-offs involved. It amortizes the substantial computational cost of evaluations needed to estimate the Pareto front by using quadratic approximation surrogate models derived from a pre-selected set of scaling coefficients. Experimental results on vision and natural language processing tasks demonstrate that MAP can accurately identify the Pareto front, providing practitioners with flexible solutions to balance competing task objectives. We also introduce Bayesian MAP for scenarios with a relatively low number of tasks and Nested MAP for situations with a high number of tasks, further reducing the computational cost of evaluation.

Bayesian optimization has attracted huge attention from diverse research areas in science and engineering, since it is capable of efficiently finding a global optimum of an expensive-to-evaluate black-box function. In general, a probabilistic regression model is widely used as a surrogate function to model an explicit distribution over function evaluations given an input to estimate and a training dataset. Beyond the probabilistic regression-based methods, density ratio estimation-based Bayesian optimization has been suggested in order to estimate a density ratio of the groups relatively close and relatively far to a global optimum. Developing this line of research further, supervised classifiers are employed to estimate a class probability for the two groups instead of a density ratio. However, the supervised classifiers used in this strategy are prone to be overconfident for known knowledge on global solution candidates. Supposing that we have access to unlabeled points, e.g., predefined fixed-size pools, we propose density ratio estimation-based Bayesian optimization with semi-supervised learning to solve this challenge. Finally, we show the empirical results of our methods and several baseline methods in two distinct scenarios with unlabeled point sampling and a fixed-size pool, and analyze the validity of our methods in diverse experiments.

This paper puts forward an integrated microstructure design methodology that replaces the common existing design approaches: 1) reconstruction of microstructures, 2) analyzing and quantifying material properties, and 3) inverse design of materials using deep-learned generative and surrogate models. The long-standing issue of microstructure reconstruction is well addressed in this study using a new class of state-of-the-art generative model, the diffusion-based generative model (DGM). Moreover, the conditional formulation of DGM for guidance to the embedded desired material properties with a transformer-based attention mechanism enables the inverse design of multifunctional composites. A convolutional neural network (CNN)-based surrogate model is utilized to analyze the nonlinear material behavior to facilitate the prediction of material properties for building microstructure-property linkages. Combined, these generative and surrogate models enable large data processing and database construction that is often not affordable with resource-intensive finite element method (FEM)-based direct numerical simulation (DNS) and iterative reconstruction methods. An example case is presented to demonstrate the effectiveness of the proposed approach, which is designing mechanoluminescence (ML) particulate composites made of europium and dysprosium ions. The results show that the inversely-designed multiple ML microstructure candidates with the proposed generative and surrogate models meet the multiple design requirements (e.g., volume fraction, elastic constant, and light sensitivity). The evaluation of the generated samples' quality and the surrogate models' performance using appropriate metrics are also included. This assessment demonstrates that the proposed integrated methodology offers an end-to-end solution for practical material design applications.

Medical care follows complex clinical pathways that extend beyond isolated physician-patient encounters, emphasizing decision-making and transitions between different stages. Current benchmarks focusing on static exams or isolated dialogues inadequately evaluate large language models (LLMs) in dynamic clinical scenarios. We introduce CP-Env, a controllable agentic hospital environment designed to evaluate LLMs across end-to-end clinical pathways. CP-Env simulates a hospital ecosystem with patient and physician agents, constructing scenarios ranging from triage and specialist consultation to diagnostic testing and multidisciplinary team meetings for agent interaction. Following real hospital adaptive flow of healthcare, it enables branching, long-horizon task execution. We propose a three-tiered evaluation framework encompassing Clinical Efficacy, Process Competency, and Professional Ethics. Results reveal that most models struggle with pathway complexity, exhibiting hallucinations and losing critical diagnostic details. Interestingly, excessive reasoning steps can sometimes prove counterproductive, while top models tend to exhibit reduced tool dependency through internalized knowledge. CP-Env advances medical AI agents development through comprehensive end-to-end clinical evaluation. We provide the benchmark and evaluation tools for further research and development at https://github.com/SPIRAL-MED/CP_ENV.

Learning in Gaussian Process models occurs through the adaptation of hyperparameters of the mean and the covariance function. The classical approach entails maximizing the marginal likelihood yielding fixed point estimates (an approach called Type II maximum likelihood or ML-II). An alternative learning procedure is to infer the posterior over hyperparameters in a hierarchical specification of GPs we call Fully Bayesian Gaussian Process Regression (GPR). This work considers two approximation schemes for the intractable hyperparameter posterior: 1) Hamiltonian Monte Carlo (HMC) yielding a sampling-based approximation and 2) Variational Inference (VI) where the posterior over hyperparameters is approximated by a factorized Gaussian (mean-field) or a full-rank Gaussian accounting for correlations between hyperparameters. We analyze the predictive performance for fully Bayesian GPR on a range of benchmark data sets.

Process reward models (PRMs) offer fine-grained, step-level evaluations that facilitate deeper reasoning processes in large language models (LLMs), proving effective in complex tasks like mathematical reasoning. However, developing PRMs is challenging due to the high cost and limited scalability of human-annotated data. Synthetic data from Monte Carlo (MC) estimation is a promising alternative but suffers from a high noise ratio, which can cause overfitting and hinder large-scale training. In this work, we conduct a preliminary study on the noise distribution in synthetic data from MC estimation, identifying that annotation models tend to both underestimate and overestimate step correctness due to limitations in their annotation capabilities. Building on these insights, we propose Self-Denoising Monte Carlo Annotation (SCAN), an efficient data synthesis and noise-tolerant learning framework. Our key findings indicate that: (1) Even lightweight models (e.g., 1.5B parameters) can produce high-quality annotations through a self-denoising strategy, enabling PRMs to achieve superior performance with only 6% the inference cost required by vanilla MC estimation. (2) With our robust learning strategy, PRMs can effectively learn from this weak supervision, achieving a 39.2 F1 score improvement (from 19.9 to 59.1) in ProcessBench. Despite using only a compact synthetic dataset, our models surpass strong baselines, including those trained on large-scale human-annotated datasets such as PRM800K. Furthermore, performance continues to improve as we scale up the synthetic data, highlighting the potential of SCAN for scalable, cost-efficient, and robust PRM training.

We introduce Agent Process Reward Models (AgentPRM), a simple and scalable framework for training LLM agents to continually improve through interactions. AgentPRM follows a lightweight actor-critic paradigm, using Monte Carlo rollouts to compute reward targets and optimize policies. It requires minimal modifications to existing RLHF pipelines, making it easy to integrate at scale. Beyond AgentPRM, we propose InversePRM, which learns process rewards directly from demonstrations without explicit outcome supervision. We also explore key challenges and opportunities, including exploration, process reward shaping, and model-predictive reasoning. We evaluate on ALFWorld benchmark, show that small 3B models trained with AgentPRM and InversePRM outperform strong GPT-4o baselines, and analyze test-time scaling, reward hacking, and more. Our code is available at: https://github.com/sanjibanc/agent_prm.

Autonomous research systems increasingly make the scientific workflow executable: agents can propose ideas, run code, inspect results, and draft papers. But executable workflows do not by themselves produce research judgment. We analyze where current systems lose trial experience: weak evidence becomes prose, pilot signals become broad claims, memory remains textual, and recurring process failures do not change later behavior. We introduce Sibyl-AutoResearch, a self-evolving AutoResearch framework built around Scientific Trial-and-Error Harnesses. A harness lets agents run bounded trials, preserve positive and negative outcomes, and route lessons into later planning, validation, claim scope, scheduling, critique, writing, and harness repair. We formalize this through two auditable conversion units: trial-to-behavior conversion, which links trial signals to later research actions, and trial-to-harness-behavior conversion, which links recurring process failures to system updates. We implement the framework in SIBYL, a file-backed autonomous research system that exposes the state, roles, memory, gates, and artifact traces needed to inspect these conversion paths. A retrospective audit identifies eight high-confidence conversion events, with a median latency of one iteration and a maximum latency of three iterations. A recovered-failure registry further shows how five naturally occurring failure classes, including duplicate results, stale numbers, and unsupported statistics, were blocked, downgraded, or routed into later repair. These traces do not establish a comparative performance claim; they show that the proposed conversion units are recoverable from realistic autonomous-research workspaces. The SIBYL framework and system are available at https://github.com/Sibyl-Research-Team/AutoResearch-SibylSystem.

Optimization problems with nonlinear cost functions and combinatorial constraints appear in many real-world applications but remain challenging to solve efficiently compared to their linear counterparts. To bridge this gap, we propose SurCo that learns linear text{Sur}rogate costs which can be used in existing text{Co}mbinatorial solvers to output good solutions to the original nonlinear combinatorial optimization problem. The surrogate costs are learned end-to-end with nonlinear loss by differentiating through the linear surrogate solver, combining the flexibility of gradient-based methods with the structure of linear combinatorial optimization. We propose three SurCo variants: SurCo-zero for individual nonlinear problems, SurCo-prior for problem distributions, and SurCo-hybrid to combine both distribution and problem-specific information. We give theoretical intuition motivating SurCo, and evaluate it empirically. Experiments show that SurCo finds better solutions faster than state-of-the-art and domain expert approaches in real-world optimization problems such as embedding table sharding, inverse photonic design, and nonlinear route planning.

Designing urban spaces that provide pedestrian wind comfort and safety requires time-resolved Computational Fluid Dynamics (CFD) simulations, but their current computational cost makes extensive design exploration impractical. We introduce WinDiNet (Wind Diffusion Network), a pretrained video diffusion model that is repurposed as a fast, differentiable surrogate for this task. Starting from LTX-Video, a 2B-parameter latent video transformer, we fine-tune on 10,000 2D incompressible CFD simulations over procedurally generated building layouts. A systematic study of training regimes, conditioning mechanisms, and VAE adaptation strategies, including a physics-informed decoder loss, identifies a configuration that outperforms purpose-built neural PDE solvers. The resulting model generates full 112-frame rollouts in under a second. As the surrogate is end-to-end differentiable, it doubles as a physics simulator for gradient-based inverse optimization: given an urban footprint layout, we optimize building positions directly through backpropagation to improve wind safety as well as pedestrian wind comfort. Experiments on single- and multi-inlet layouts show that the optimizer discovers effective layouts even under challenging multi-objective configurations, with all improvements confirmed by ground-truth CFD simulations.

Recent years have seen considerable advancements in multi-step reasoning with Large Language Models (LLMs). The previous studies have elucidated the merits of integrating feedback or search mechanisms during model inference to improve the reasoning accuracy. The Process-Supervised Reward Model (PRM), typically furnishes LLMs with step-by-step feedback during the training phase, akin to Proximal Policy Optimization (PPO) or reject sampling. Our objective is to examine the efficacy of PRM in the inference phase to help discern the optimal solution paths for multi-step tasks such as mathematical reasoning and code generation. To this end, we propose a heuristic greedy search algorithm that employs the step-level feedback from PRM to optimize the reasoning pathways explored by LLMs. This tailored PRM demonstrated enhanced results compared to the Chain of Thought (CoT) on mathematical benchmarks like GSM8K and MATH. Additionally, to explore the versatility of our approach, we develop a novel method to automatically generate step-level reward dataset for coding tasks and observed similar improved performance in the code generation tasks. Thus highlighting the robust nature of our reward-model-based approach to inference for reasoning tasks.

The remarkable performance of models like the OpenAI o1 can be attributed to their ability to emulate human-like long-time thinking during inference. These models employ extended chain-of-thought (CoT) processes, exploring multiple strategies to enhance problem-solving capabilities. However, a critical question remains: How to intelligently and efficiently scale computational resources during testing. This paper presents the first comprehensive study on the prevalent issue of overthinking in these models, where excessive computational resources are allocated for simple problems with minimal benefit. We introduce novel efficiency metrics from both outcome and process perspectives to evaluate the rational use of computational resources by o1-like models. Using a self-training paradigm, we propose strategies to mitigate overthinking, streamlining reasoning processes without compromising accuracy. Experimental results show that our approach successfully reduces computational overhead while preserving model performance across a range of testsets with varying difficulty levels, such as GSM8K, MATH500, GPQA, and AIME.

The inspiral, merger, and ringdown of Massive Black Hole Binaries (MBHBs) is one the main sources of Gravitational Waves (GWs) for the future Laser Interferometer Space Antenna (LISA), an ESA-led mission in the implementation phase. It is expected that LISA will detect these systems throughout the entire observable universe. Robust and efficient data analysis algorithms are necessary to detect and estimate physical parameters for these systems. In this work, we explore the application of Sequential Neural Likelihood, a simulation-based inference algorithm, to detect and characterize MBHB GW signals in synthetic LISA data. We describe in detail the different elements of the method, their performance and possible alternatives that can be used to enhance the performance. Instead of sampling from the conventional likelihood function, which requires a forward simulation for each evaluation, this method constructs a surrogate likelihood that is ultimately described by a neural network trained from a dataset of simulations of the MBHB signals and noise. One important advantage of this method is that, given that the likelihood is independent of the priors, we can iteratively train models that target specific observations in a fraction of the time and computational cost that other traditional and machine learning-based strategies would require. Because of the iterative nature of the method, we are able to train models to obtain qualitatively similar posteriors with less than 2\% of the simulator calls that Markov Chain Monte Carlo methods would require. We compare these posteriors with those obtained from Markov Chain Monte Carlo techniques and discuss the differences that appear, in particular in relation with the important role that data compression has in the modular implementation of the method that we present. We also discuss different strategies to improve the performance of the algorithms.

Time-dependent partial differential equations (PDEs) are ubiquitous in science and engineering. Recently, mostly due to the high computational cost of traditional solution techniques, deep neural network based surrogates have gained increased interest. The practical utility of such neural PDE solvers relies on their ability to provide accurate, stable predictions over long time horizons, which is a notoriously hard problem. In this work, we present a large-scale analysis of common temporal rollout strategies, identifying the neglect of non-dominant spatial frequency information, often associated with high frequencies in PDE solutions, as the primary pitfall limiting stable, accurate rollout performance. Based on these insights, we draw inspiration from recent advances in diffusion models to introduce PDE-Refiner; a novel model class that enables more accurate modeling of all frequency components via a multistep refinement process. We validate PDE-Refiner on challenging benchmarks of complex fluid dynamics, demonstrating stable and accurate rollouts that consistently outperform state-of-the-art models, including neural, numerical, and hybrid neural-numerical architectures. We further demonstrate that PDE-Refiner greatly enhances data efficiency, since the denoising objective implicitly induces a novel form of spectral data augmentation. Finally, PDE-Refiner's connection to diffusion models enables an accurate and efficient assessment of the model's predictive uncertainty, allowing us to estimate when the surrogate becomes inaccurate.

Knowledge distillation is a model compression technique in which a compact "student" network is trained to replicate the predictive behavior of a larger "teacher" network. In logit-based knowledge distillation, it has become the de facto approach to augment cross-entropy with a distillation term. Typically, this term is either a KL divergence that matches marginal probabilities or a correlation-based loss that captures intra- and inter-class relationships. In every case, it acts as an additional term to cross-entropy. This term has its own weight, which must be carefully tuned. In this paper, we adopt a choice-theoretic perspective and recast knowledge distillation under the Plackett-Luce model by interpreting teacher logits as "worth" scores. We introduce "Plackett-Luce Distillation (PLD)", a weighted list-wise ranking loss. In PLD, the teacher model transfers knowledge of its full ranking of classes, weighting each ranked choice by its own confidence. PLD directly optimizes a single "teacher-optimal" ranking. The true label is placed first, followed by the remaining classes in descending teacher confidence. This process yields a convex and translation-invariant surrogate that subsumes weighted cross-entropy. Empirically, across CIFAR-100, ImageNet-1K, and MS-COCO, PLD achieves consistent gains across diverse architectures and distillation objectives, including divergence-based, correlation-based, and feature-based methods, in both homogeneous and heterogeneous teacher-student pairs.

Temporal credit assignment in reinforcement learning is often approached by introducing value estimates at multiple discount factors. A natural next step is to let the actor dynamically route among these temporal heads, using either differentiable attention or heuristic uncertainty weights. This paper argues that such routing can create a numerical shortcut rather than a reliable temporal abstraction. We study this issue in a controlled PPO setting on LunarLander-v2, using the environment as a visual sandbox for diagnosing failure modes. First, we formalize Surrogate Objective Hacking: a differentiable softmax router exposed to the PPO surrogate receives a direct gradient toward advantage heads that are numerically favorable for the current update, even when this routing change does not correspond to improved physical control. Because unnormalized advantages at different discount factors have different effective scales, this creates a scale-discrepancy vulnerability. Second, we identify the Paradox of Temporal Uncertainty in gradient-free error-based routing: short-horizon heads can receive the largest routing share because their prediction targets are easier, even when they are less aligned with delayed task success. As a structural response, we study Target Decoupling: the critic may retain multi-timescale auxiliary heads, but the actor is updated only with the long-horizon advantage. Target Decoupling is not presented as a broad performance booster; in this run set it removes the exploitable actor-side routing pathway and improves the observed worst-seed return. Code is available at https://github.com/ben-dlwlrma/Representation-Over-Routing.

Simulations of turbulent flows in 3D are one of the most expensive simulations in computational fluid dynamics (CFD). Many works have been written on surrogate models to replace numerical solvers for fluid flows with faster, learned, autoregressive models. However, the intricacies of turbulence in three dimensions necessitate training these models with very small time steps, while generating realistic flow states requires either long roll-outs with many steps and significant error accumulation or starting from a known, realistic flow state - something we aimed to avoid in the first place. Instead, we propose to approach turbulent flow simulation as a generative task directly learning the manifold of all possible turbulent flow states without relying on any initial flow state. For our experiments, we introduce a challenging 3D turbulence dataset of high-resolution flows and detailed vortex structures caused by various objects and derive two novel sample evaluation metrics for turbulent flows. On this dataset, we show that our generative model captures the distribution of turbulent flows caused by unseen objects and generates high-quality, realistic samples amenable for downstream applications without access to any initial state.

Physics-informed neural networks (PINNs) are emerging as popular mesh-free solvers for partial differential equations (PDEs). Recent extensions decompose the domain, applying different PINNs to solve the equation in each subdomain and aligning the solution at the interface of the subdomains. Hence, they can further alleviate the problem complexity, reduce the computational cost, and allow parallelization. However, the performance of the multi-domain PINNs is sensitive to the choice of the interface conditions for solution alignment. While quite a few conditions have been proposed, there is no suggestion about how to select the conditions according to specific problems. To address this gap, we propose META Learning of Interface Conditions (METALIC), a simple, efficient yet powerful approach to dynamically determine the optimal interface conditions for solving a family of parametric PDEs. Specifically, we develop two contextual multi-arm bandit models. The first one applies to the entire training procedure, and online updates a Gaussian process (GP) reward surrogate that given the PDE parameters and interface conditions predicts the solution error. The second one partitions the training into two stages, one is the stochastic phase and the other deterministic phase; we update a GP surrogate for each phase to enable different condition selections at the two stages so as to further bolster the flexibility and performance. We have shown the advantage of METALIC on four bench-mark PDE families.

Long-form generation is crucial for academic writing papers and repo-level code generation. Despite this, current models, including GPT-4o, still exhibit unsatisfactory performance. Existing methods that utilize preference learning with outcome supervision often fail to provide detailed feedback for extended contexts. This shortcoming can lead to content that does not fully satisfy query requirements, resulting in issues like length deviations, and diminished quality. In this paper, we propose enhancing long-form generation by incorporating process supervision. We employ Monte Carlo Tree Search to gather stepwise preference pairs, utilizing a global memory pool to maintain consistency. To address the issue of suboptimal candidate selection, we integrate external critiques to refine and improve the quality of the preference pairs. Finally, we apply step-level DPO using the collected stepwise preference pairs. Experimental results show that our method improves length and quality on long-form generation benchmarks, with almost lossless performance on general benchmarks across various model backbones.