Surrogate Modeling

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21 papers in the last four weeks, up 200% on the four weeks before. 0.2% of all new papers.

Jul 13Week of Sep 28

Latest papers 139

Jul 6, 2026cs.LG

SMART: A Machine Learning and Monte Carlo Framework for Rapid Analysis of Stochastic Transistor Aging and Process Variation in Digital Circuits

As CMOS technology scales into the deep nanometer regime, digital circuit reliability is increasingly threatened by the combined stochastic effects of Bias Temperature Instability (BTI) and Process Variation (PV). Traditional reliability analysis methods, which rely on computationally intensive simulations or extensive lookup tables, fail to scale efficiently for large designs, creating a critical bottleneck in design space exploration. To address this, we propose SMART, a novel framework that integrates Machine Learning (ML) with Monte Carlo simulation to enable rapid, high-fidelity reliability analysis. SMART employs Random Forest regression to predict gate delay distributions directly, bypassing time-consuming atomic model parameter extractions. Crucially, the model utilizes Bayesian Optimization for automated hyperparameter tuning, ensuring maximum predictive robustness across diverse libraries. Experimental validation on ISCAS85 benchmark circuits demonstrates that SMART achieves a 94.54% reduction in analysis time compared to state-of-the-art methods, while maintaining a remarkable average accuracy error of just 1.63%. By shifting computational complexity to an offline training phase, the proposed framework offers a scalable, accurate solution for designing resilient, reliability-aware digital systems.

Arash Esshaghi, Siavash Es'haghi, Gholamreza Shahabadi +1

Department of Optimization and Mathematics, Payame Noor University, Tehran, Iran. · Department of Electrical and Computer Engineering, SR.C., Islamic Azad University, Tehran, Iran. · Department of Electrical Engineering, National University of Skills (NUS), Tehran, Iran +1

Surrogate Modeling Electronic Design Automation

Jul 5, 2026cs.LG

A Deep Learning-based surrogate model for Severe Accidents in nuclear reactors using ASTEC

Integral codes like the Accident Source Term Evaluation Code (ASTEC) are powerful tools to study the physics of Severe Accidents (SAs) in nuclear reactors. Real time SA simulators can also be helpful in training operators of nuclear plants to react correctly to malfunctions. However, SA simulators can take up to several days per simulation, making their use infeasible for real time applications. In this work we show how to speed up a SA simulator with a fast, Deep Learning based (DL), surrogate model (SM). The SM is built as a combination of a dimensionality reduction stage, via an AutoEncoder, and a time-stepping stage, via a Neural Ordinary Differential Equation. The data on which the SM is trained are obtained from the ASTEC simulator, by sampling a set of operator actions for station blackout (SBO) and loss-of-coolant accidents (LOCA). The objective of the developed SM is to approximate multiple spatio-temporal fields for the thermal-hydraulic physics, core degradation, and fission product release modules in ASTEC's vessel domain. The SM predicts simultaneously around

80

different physical variables (both scalar and fields), maintaining a stable autoregressive rollout up to

50

thousand time steps. In addition, the AutoEncoder achieves a dimensionality reduction by a factor of over

300

, which allows the SM to predict up to

40

hours of simulation in under a minute, both on CPU and GPU. This work is the first study of the capabilities and limits of DL based surrogate modeling in approximating the challenging, highly non-linear physics of ASTEC.

Alessandro Longhi, Danny Lathouwers, Zoltán Perkó

TU Delft · Department of Radiation Science and Technology · Delft, The Netherlands

Neural Surrogate Modeling Surrogate Modeling Physics-Based Simulation

Jul 2, 2026eess.SY

Koopman operator theory: fundamentals, control, and applications

The Koopman operator has gained considerable attention due to its ability to provide a global linear representation of highly complex dynamical systems. The operator describes nonlinear dynamics in a linear way through the lens of real- or complex-valued observable functions. Data-driven techniques, like extended dynamic mode decomposition (EDMD), kernel EDMD, and machine-learning methods, can be used to generate finite-dimensional approximations accompanied by finite-data error bounds. In this tutorial paper, we provide a concise introduction into Koopman operator theory and its use in systems and control. A particular focus is put on data-driven surrogate models, their extension to systems with inputs, and controller design using Koopman operator theory. Moreover, we demonstrate the key techniques, i.e., EDMD and Koopman MPC. To this end, we provide simulation studies including source code on GitHub to enable the interested reader to experience the Koopman operator in systems and control step by step.

Igor Mezić, Jorge Cortés, Karl Worthmann +2

Department of Mechanical Engineering, University of California, Santa Barbara, USA · Department of Mechanical and Aerospace Engineering, University of California, San Diego, USA · Optimization-based Control Group, TU Ilmenau, Germany +2

Surrogate Modeling Koopman Operator Learning Latent Dynamics Modeling Data-Driven Control

Jun 28, 2026cs.CV

Inpainting U-Net for seamless pedestrian-level wind prediction across urban morphologies

Pedestrian-level wind prediction is essential for urban design and wind-comfort assessment, but high-fidelity simulations such as LES remain computationally expensive for rapid evaluation. This study develops a two-stage U-Net framework for efficient prediction of time-averaged pedestrian-level wind speed over realistic urban morphologies. The model is trained and evaluated using the UrbanTALES dataset, which contains realistic city configurations under different approaching wind directions. In the first stage, a baseline U-Net model (M1) predicts wind fields patch-by-patch from normalised building height and fetch information. This formulation allows application to urban domains of arbitrary size, but independent patch inference can introduce discontinuities at patch boundaries. To address this, a second U-Net model (M2) is introduced as an inpainting-based refinement model. M2 uses a larger contextual window containing the initial M1 prediction and local morphology to reduce discontinuities using neighbouring flow information. During full-field inference, M2 is applied iteratively using a Gauss-Seidel scheme until convergence. Results show that M1 captures the main spatial distribution of pedestrian-level wind speed and performs well in low- and moderate-velocity regions, although high-velocity peaks are less accurate. M2 substantially reduces patch-boundary artefacts and improves spatial coherence. Across unseen urban cases, the framework reproduces mean velocity and spatial variability reasonably well, while maximum velocities remain underestimated. Overall, the proposed framework provides an efficient and flexible surrogate model for high-resolution pedestrian-level wind prediction across realistic urban morphologies.

Jingzi Huang, Claire E. Heaney, Tao Li +3

Department of Civil and Environmental Engineering, Imperial College London, London, SW7 2AZ, UK · Department of Earth Science and Engineering, Applied Modelling and Computation Group, Imperial College London, London, SW7 2AZ, UK

Surrogate Modeling U-Net

Jun 26, 2026cs.LG

RECAST: Model Reconstruction via Counterfactual-Aware Wasserstein Geometry under Limited Data

Counterfactual explanations (CFs) help understand machine learning models by identifying minimal input changes that would lead to alternative model outcomes. Recent work demonstrates their utility for reconstructing black-box models, enabling third-party auditing of opaque decision systems for fairness and accountability. Still, CF-based reconstruction may suffer from decision boundary shifts, overfitting, and restrictive assumptions requiring online query access to target platforms. We propose REconstruction via Counterfactual-Aware waSserstein opTimization (RECAST) under limited data and restricted access, a behavioral surrogate model based on Wasserstein barycentric prototypes. Our approach addresses decision boundary shifts by incorporating CFs as informative, though less representative, samples for both classes, maintaining high surrogate fidelity in low-sample regimes without requiring online access during reconstruction. To enhance fairness auditing, our method enables systematic group fairness diagnostics. Experiments on real-world datasets and various setups show that RECAST effectively achieves high fidelity and query efficiency, as well as stable results even when the access is limited and noisy.

Xuan Zhao, Lena Krieger, Zhuo Cao +3

IAS-8, Forschungszentrum Jülich, Germany · LMU Munich, Munich Center for Machine Learning (MCML), Germany · Department of Computer Science, Aarhus University, Denmark

Surrogate Modeling Model Extraction Attacks Black-Box Model Auditing

Jun 25, 2026cs.LG

Global Explanations for Multivariate Time Series Forecasting Models via $K$ -Order Markov Approximations

While many explainable AI (XAI) methods have been proposed, most are not designed for time-series forecasting models and often rely on the implicit assumption that timestamp features are independent. This assumption ignores the fundamental property of temporal dependence and can lead to explanations that violate the sequential and causal structure of the data. We introduce \textsc{KARMA}, a method for explaining time-series predictors by constructing a Markov surrogate model that captures the temporal dependencies learned by the predictor. Our approach revolves around three main aspects: identifying the minimal history length

K

that is predictively sufficient for the model, estimating the best-fitting

K

-order Markov transition kernel from the discretized history space, and a five-level global explanation hierarchy that can be derived from the Markov transition kernel, which we illustrate using real-world weather data (Beijing PM 2.5). We also certify using complex synthetic data with known true causal edges that KARMA (i) recovers the data causal structure as learned by the model via a controlled experiment and (ii) identifies temporal dependencies better than established attribution methods such as TimeSHAP.

Amadeo Tunyi

XITASO GmbH Austraße 35, 86153 Augsburg, Germany

Multivariate Time Series Forecasting Surrogate Modeling Explainable Time Series Forecasting Markov Models Time Series Forecasting Causal Interpretability

Jun 25, 2026cs.LG

Kolmogorov Arnold networks (KAN) for aerodynamic prediction: a comparison with MLPs and GNNs

Kolmogorov Arnold networks (KAN) have recently been introduced as a (deep) neural network architecture whose trainable parameters adapt the activation functions, instead of the coefficients of the affine transformations at the core of traditional architectures such as deep multilayer perceptrons (MLPs). This architecture builds on the Kolmogorov-Arnold theorem, which endows it with universal approximation properties. While the advent of KANs has been received with excitement, there is a current debate about the possible KAN supremacy over deep multilayer perceptrons (MLPs) for classic fields such as symbolic regression, generic-purpose machine learning, natural language processing or computer vision. Here we assess the performance of KANs --and its nuanced comparison against MLPs and graph neural networks (GNNs)-- in the realm of fluid dynamics surrogate modelling. To that aim, we consider the task of predicting the surface pressure distribution over subsonic and transonic airfoils, a canonical task in aerodynamics. Our results show that KAN models show good performance in predicting the whole pressure coefficients and is able to interpolate across Mach numbers and angles of attack, however its performance is comparable --marginally inferior-- to a suitably trained MLP, where best performance is achieved by a GNN at the expense or requiring lengthier training. While the optimal KAN model have typically much lower complexity than MLP and GNN --hence resulting in faster training--, we find that KANs suffer from training instabilities, and their performance is highly dependent on a proper hyperparameter optimisation.

Miguel Jaraiz, Fermin Gutierrez, Pablo Yeste +4

ETSIAE-UPM-School of Aeronautics, Universidad Politécnica de Madrid, Plaza Cardenal Cisneros 3, E-28040 Madrid, Spain · Center for Computational Simulation, Universidad Politécnica de Madrid, Campus de Montegancedo, Boadilla del Monte, 28660 Madrid, Spain · Institute for Cross-Disciplinary Physics and Complex Systems (IFISC, CSIC-UIB), 07122 Palma de Mallorca (Spain)

Multilayer Perceptrons Surrogate Modeling Kolmogorov-Arnold Networks Computational Fluid Dynamics

Jun 23, 2026physics.flu-dyn

A Physics-Informed Fourier-Wavelet Transformer for Multiscale Computational Fluid Dynamics Surrogate Modeling

Physics-informed surrogate models can accelerate computational fluid dynamics simulations. However, many existing methods reproduce global flow patterns more reliably than localized multiscale structures. This study presents a physics-informed Fourier-wavelet transformer for next-step velocity-field reconstruction in real-world flow benchmarks. The proposed formulation combines hybrid Fourier-wavelet spectral encoding with physics-biased self-attention based on partial differential equation residual diagnostics. It also uses self-supervised pretraining through Masked Physics Prediction and Equation Consistency Prediction. The experiments are conducted on two real benchmark cases: cylinder-wake flow and fluid-structure interaction. All approaches are evaluated under a shared local protocol and compared with spectral, transformer-based, operator-learning, and physics-informed neural-network baselines. On the cylinder-wake benchmark, the proposed model achieves the best aggregate accuracy, with an all-channel normalized mean-squared error of 0.05875 and an all-channel Pearson correlation coefficient of 0.97019. On the fluid-structure-interaction benchmark, it gives the lowest all-channel normalized mean-squared error of

2.70 \times 10^{-4}

, compared with

4.02 \times 10^{-4}

for the strongest baseline. Component-wise field comparisons and scale-separated diagnostics further show stronger recovery of localized wake structures, including near-body, wake-core, and far-wake features. The results demonstrate improved real-world flow reconstruction while maintaining a practical accuracy-cost tradeoff.

Somyajit Chakraborty, Ming Pan, Xizhong Chen

Shanghai Jiao Tong University, Department of Chemistry and Chemical Engineering 800 Dongchuan Road, Minhang District, Shanghai, 200240, China

Surrogate Modeling PDE Surrogate Modeling Wavelet Methods Physics-Informed ML Computational Fluid Dynamics

Jun 17, 2026physics.ao-ph

Optimal scenario design for climate emulation

As deep learning for physical systems continues to grow in popularity, efforts to improve generalizability have primarily focused on designing architectures that embed physical constraints. However, for machine-learning surrogate climate models (emulators), we show that the low structural diversity in existing scenarios commonly used to generate training data places a ceiling on predictive skill. Here, we examine whether training datasets themselves can be optimized to improve generalization. We introduce a method to create datasets that produce emulators capable of generalizing to new, structurally different scenarios absent from the training data. We use a differentiable Simple Climate Model (SCM) to calculate the sensitivity of emulator loss to perturbations in the training data, iteratively updating the training data to maximize emulator skill. For an SCM, training on one scenario optimized in this fashion outperforms an emulator trained on six standard ScenarioMIP pathways. We achieve this higher predictive skill despite training on a smaller dataset, finding that our emulator successfully isolates distinct physical behaviors of different climate forcing agents (e.g., greenhouse gases vs. aerosols) without single-forcing runs. We then demonstrate that scenarios optimized using an SCM, when used to drive an intermediate-complexity climate model, produce a training dataset that yields a more skillful emulator than training on ScenarioMIP outputs. Our results suggest that, in the compute-constrained environment of running full-scale climate models, generating a small number of dynamically rich scenarios provides greater marginal value for emulation and characterizing system responses than expanding the suite of traditional emissions pathways.

Christopher B. Womack, Shahine Bouabid, Andrei Sokolov +4

Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA, United States · Center for Sustainability Science and Strategy, Massachusetts Institute of Technology, Cambridge, MA, United States · Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA, United States +2

Surrogate Modeling Climate Modeling

Jun 16, 2026cs.LG

ThousandWorlds: A benchmark for climate emulation of potentially habitable exoplanets

The search for life beyond Earth will depend on detecting faint signatures in the atmospheres of potentially habitable exoplanets. Interpreting those signatures requires understanding the host planet's climate: the same molecule may signal life on one planet and abiotic chemistry on another. Global climate models (GCMs) provide this understanding, but individual runs can require up to millions of core-hours and substantial domain expert time. Machine-learning emulators could remove this bottleneck, but progress has been limited by the absence of a curated, multi-model exoclimate dataset. We introduce ThousandWorlds, an ML-ready benchmark for exoclimate emulation and for the broader regime of low-data, multi-simulator, parameter-to-field regression. The dataset contains approximately 1800 simulations from five GCMs, mapping eight planet parameters to 3D atmospheric fields including temperature, humidity, winds, clouds, and radiation. Three nested subsets define progressively harder challenges: single-simulator regression, multi-simulator regression with complete observations, and multi-simulator regression with structured missingness. We propose two evaluation protocols: one for ranking methods, and one that measures performance relative to the disagreement between GCMs themselves. We evaluate seven baselines spanning simple methods, deep learning, and Gaussian processes. GP-based methods perform best, suggesting that ThousandWorlds exposes a regime where off-the-shelf deep learning does not yet succeed. Data: https://doi.org/10.57967/hf/8695. Code: https://github.com/edstevenson/ThousandWorlds.

Edward T. Stevenson, Mei Ting Mak, Eric Wolf +4

University of Cambridge · University of Oxford · University of Colorado Boulder +3

Surrogate Modeling Climate Science Climate Modeling

Jun 16, 2026cs.AI

Surrogate Assisted Pedestrian Protection Design via a Foundation Model Orchestrated Workflow

AI-driven engineering workflows face particular challenges in crash safety design: unlike aerodynamics, crash events involve highly nonlinear contact dynamics, material nonlinearity, and discrete state transitions that are difficult to capture with data-driven surrogate models. To the best of our knowledge, we present the first foundation model--orchestrated workflow for crash safety design that enables surrogate-assisted exploration for pedestrian protection, reducing evaluation time from hours per CAE simulation to seconds. The workflow integrates four components: (1) a surrogate trained on CAE crash simulations to predict pedestrian leg injury metrics from design parameters, achieving an average

R^2=0.87

and providing distribution-free conformal prediction intervals; (2) multiobjective evolutionary search (NSGA-II) to discover diverse feasible parameter sets under user-specified constraints; (3) a morphing-based geometry generator that maps parameters to topology-preserving 3D shapes; and (4) a natural-language interface in which an LLM orchestrates the workflow and a vision--language model supports semantic comparison of generated designs. In an automotive front-bumper case study, the workflow produces 35 distinct safety-compliant alternatives from a single exploration, a process that would require weeks with conventional CAE iteration. These results suggest that foundation models can serve as integration layers between ML surrogates and physics-based simulation, helping bring AI capabilities to safety-critical engineering domains.

Osamu Ito, Akihiko Katagiri, Yoshikazu Nakagawa +3

Honda Motor Co., Ltd. Wako-shi, Saitama 351-0188, Japan

Surrogate Modeling Surrogate-Assisted Optimization Agentic Workflows

Jun 15, 2026stat.ML

Tight $L_\infty$ Sample Complexity for Low-Degree and Sparse Boolean Polynomials

Motivated by the optimization of bounded binary black-box functions, we study the problem of learning polynomial surrogates over the Boolean hypercube. To ensure that optimizing the surrogate yields good solutions for the underlying objective, we require uniform

L_\infty

-error guarantees rather than the usual

L_2

-type guarantees. We characterize the minimax sample complexity of uniform estimation under subgaussian noise for two classes of bounded polynomials. First, for polynomials of degree at most

d

on

n

variables, the sample complexity scales as

n^{d+1}

. Second, for

s

-sparse Fourier-Walsh polynomials with

s \leq n

, it scales as

ns^2

. These rates differ structurally from the noiseless setting, where uniform exact recovery scales as

n^d

and

ns

, respectively. Our lower bounds hold even for arbitrary adaptive learners, showing that the additional factors are intrinsic to the noisy cases. Standard Fourier-analysis tools for the

L_2

-norm do not naturally extend to the

L_\infty

-setting in a way that yields uniform guarantees. Our proofs overcome this difficulty by relying on suitably chosen auxiliary norms that serve as proxies for controlling the

L_\infty

-error. Together, our results provide a tight characterization of the sample complexity of learning optimization-safe polynomial surrogates.

Jasper van Doornmalen, Mathieu Molina, Victor Verdugo +1

Institute for Mathematical and Computational Engineering, Pontificia Universidad Católica de Chile, Chile · Blavatnik School of Computer Science and AI, Tel Aviv University, Israel · Institute for Mathematical and Computational Engineering, and Department of Industrial and Systems Engineering, Pontificia Universidad Católica de Chile, Chile

Surrogate Modeling Boolean Function Learning Sample Complexity

Jun 15, 2026cs.LG

Uncertainty Quantification of Engineering Structures by Polynomial Chaos Expansion and Multivariate Active Learning

In many engineering applications, a single high-fidelity model produces multiple quantities of interest (QoIs) under the same input parameters, e.g. finite element models of complex physical systems. To alleviate the high computational cost of direct model evaluations, surrogate models are widely used to construct efficient approximations of model responses. Naturally, the accuracy of surrogates strongly depends on the quality of the experimental design (ED). However, a single ED may not provide an adequate representation for all outputs simultaneously, especially when different outputs exhibit varying sensitivities to the input variables. A straightforward solution is to perform separate sampling for each output, but this results in increased sampling complexity and computational cost. From a statistical perspective, such an approach also ignores potential correlations among all outputs and may compromise data consistency. To address this issue, an adaptive sequential sampling method for constructing polynomial chaos expansion surrogate models is generalized for vector valued QoIs. The method sequentially selects new samples from a candidate pool based on their local contribution to the output variance, while balancing distance-based exploration of the input space and exploitation of aggregated variance information across all outputs. Its performance is compared with non-sequential Latin Hypercube Sampling through several numerical examples from engineering problems. Numerical results demonstrate that the proposed strategy improves both surrogate accuracy and stability, and provides a more reliable estimation of second-order statistics.

Qitian Lu, Jafar Jafari-Asl, Panagiotis Spyridis +1

Brno University of Technology, Brno, Czech Republic · University of Rostock, Rostock, Germany

Surrogate Modeling Uncertainty Quantification Adaptive Sampling

Jun 15, 2026stat.ME

Statistical Foundations of LLM-based A/B Testing: A Surrogacy Framework for Human Causal Inference

Organizations and researchers show increasing interest in using large language models (LLMs) in place of human participants in A/B tests, in the hope of experimenting faster and at lower cost. We study when a treatment effect estimated on LLM outcomes can recover the effect for the human population of interest. Distributional equivalence between LLM and human outcomes would make any standard estimator valid but is unrealistic. We therefore develop a statistical framework that adapts surrogate endpoint theory to LLMs, showing that calibrating LLM outcomes to human outcomes identifies the average treatment effect under surrogacy and comparability conditions that are jointly weaker than distributional equivalence. We present a falsification test for surrogacy and a bound on the worst-case bias from limited overlap between the LLM and human samples. We further show that the stochasticity inherent to LLMs can weaken surrogacy for identification while also introducing bias and variance during estimation, but that using an average over multiple LLM draws per unit as the surrogate mitigates these issues. Simulations validate the results, and an empirical application to the Upworthy Research Archive dataset shows that raw LLM outputs recover only 39% of the human treatment effect while nonparametric calibration closes the gap. A central takeaway is that A/B testing on LLM responses is correct only by assumption, whereas A/B testing on humans is correct by design, and that the required assumptions are hardest to justify precisely where LLMs promise the greatest benefit. We discuss the choice of LLM, prompting, and temperature as design variables, the compounded challenge posed by long-term outcomes, and how to size human pilot studies for validation.

Joel Persson, Mårten Schultzberg, Sebastian Ankargren

Spotify USA, Inc. New York, NY, USA · Spotify AB Stockholm, Sweden

Surrogate Modeling A/b Testing Causal Inference Generative AI Evaluation

Jun 15, 2026cs.CE

Graphical conditional generative modeling for digital twin modeling

Digital twin modeling, including control and data assimilation under model uncertainty, often faces an open-ended fidelity problem: adding variables, data streams, and time scales can indefinitely increase model complexity, ultimately producing systems that are difficult to maintain, validate, interpret, and use for stress or safety testing. As an alternative, one can seek parsimonious stochastic surrogate models built only on the variables needed to describe the relevant quantities of interest. We introduce a framework for discovering such variables from observational data by identifying which candidate inputs influence the full conditional law of a target quantity, rather than only its conditional mean. This distinction is essential in stochastic, coarse-grained, or partially observed systems, where dependencies may appear through changes in variability, tail behavior, multimodality, or uncertainty rather than through deterministic functional relationships. The framework couples conditional generative modeling, which learns the conditional distribution of the target given candidate inputs, with Gaussian-process-based analysis of variance (through kernel mode decomposition), which enables iterative pruning of non-influential inputs and interpretable structure discovery. In control settings, the resulting surrogate can be interpreted as a learned Markov decision process: the method identifies not only a transition model, but also the state, action, and memory variables needed to make the learned dynamics effectively Markovian. Across examples involving stochastic dynamical systems, missing variables, PDE control, reinforcement learning, and economic data, the discovered structures yield interpretable stochastic surrogates whose downstream performance is comparable to models trained on the full variable set.

Zongren Zou, Théo Bourdais, Ricardo Baptista +1

Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA, USA · Department of Statistical Sciences, University of Toronto, Toronto, Canada

Surrogate Modeling Digital Twins Conditional Generative Modeling

Jun 14, 2026cs.DC

Quantifying the Impact of Lossy Compression on Neural Generative Surrogate Modeling

Neural networks are used as generative surrogate models for scientific discovery, which are trainable approximations of scientific simulations. These models enable users to replace time-consuming numerical simulations with learned alternatives, providing quick solutions. However, high-fidelity generative surrogate models require massive training datasets, which can create storage and I/O challenges. Lossy compression is a promising way to reduce this burden, but compression errors may affect the model quality in subtle ways, making it challenging to quantify their impact. In this work, we examine how lossy compression of training data impacts the quality of generative surrogate models. We begin by characterizing the uncertainty inherent in training neural networks, showing that identical training configurations can produce different models. By exploiting this variability, we propose a method to estimate how much compression-induced error a surrogate model can tolerate without affecting its accuracy. Evaluation of two application simulations demonstrates that our approach significantly reduces memory/storage requirements and speeds up training while producing high-quality surrogate models. These results show that lossy compression saves data storage up to 23.7x and 39x with negligible impact on the quality of the surrogate model. Meanwhile, reducing the size of the training data set also enhances the data loading speed and reduces the training time by up to 3x.

Zhimin Li, Harshitha Menon, Charles Jekel +2

Department of Computer Science Vanderbilt University Nashville, United States · Center for Applied Scientific Computing Lawrence Livermore National Laboratory Livermore, United States · Computational Engineering Division Lawrence Livermore National Laboratory Livermore, United States +1

Neural Surrogate Modeling Surrogate Modeling

Jun 13, 2026cs.LG

Model Stealing Through the Lens of Model Multiplicity

Model stealing attacks, where adversaries create high-fidelity surrogate models, are a significant threat to the intellectual property of machine learning services. Conventional wisdom suggests these surrogates could provide adversaries with economic leverage comparable to the original service providers. This paper challenges this assumption by evaluating model stealing attacks beyond mere fidelity to the target model. Because query-based extraction provides only partial supervision of the target's input-output behavior, the surrogate is not uniquely identified: many near-optimal surrogates can achieve comparable fidelity while differing in deployment-relevant properties. Instead of performing a classic learning-based model stealing attack, we compute the Rashomon Set (i.e., the set of almost-equally-accurate models) of surrogate models, and evaluate its diversity using multiplicity metrics (ambiguity, discrepancy, and Rashomon Capacity) and group fairness metrics. Across tabular, medical imaging, and NLP tasks, our experiments on real-world datasets reveal that despite exhibiting similar fidelity to the target model, surrogate models can display significant variances in other critical performance metrics. These findings cast doubt on the presumed equivalence between high-fidelity surrogates and the target model in practical deployment scenarios.

Eliott Baltz, Satoshi Hara, Ulrich Aïvodji

§ÉTS, Mila : Montréal · ‡The University of Electro-Communications : Tokyo

Surrogate Modeling Model Extraction Attacks

Jun 13, 2026cs.LG

Physics-conforming Latent Twins

Surrogate models are central to scientific machine learning, where they enable fast prediction, simulation, inference, and control for complex physical systems. For time-dependent problems, however, accurate interpolation of training trajectories is not sufficient: reliable surrogates should also respect the conservation laws, invariants, admissibility conditions, and dissipative structures that give those trajectories physical meaning. We introduce Physics-conforming Latent Twins, a framework for learning latent surrogate solution operators whose dynamics satisfy selected physical principles by design. The method builds on the Latent Twin formulation by jointly learning an encoder, a decoder, and a latent flow map between arbitrary time-indexed states, while constraining the latent dynamics to preserve or dissipate prescribed structural quantities. We develop a constraint-transfer viewpoint that connects physical structure in the original state space with compatible constraints in latent space, and prove structure-preservation bounds showing how latent enforcement improves control of physical defects after decoding. We also derive algebraic conditions for latent flow maps that preserve linear and quadratic invariants or enforce dissipative inequalities. Numerical experiments on representative ODE and PDE benchmarks demonstrate improved constraint satisfaction, structural fidelity, and qualitative long-time behavior while maintaining accurate surrogate prediction.

Matthias Chung, Yutong Bu, Deepanshu Verma

Department of Mathematics, Emory University, 400 Dowman Drive, Atlanta, 30322, GA, USA · School of Mathematical and Statistical Sciences, Clemson University, 220 Parkway Drive, Clemson, 29634, SC, USA

Neural Surrogate Modeling Surrogate Modeling Latent Dynamics Modeling PDE Surrogate Modeling Physics-Informed ML

Jun 12, 2026physics.ao-ph

Regional Climate Model Emulation with Diffusion Approaches: What is the Added Value of Generative Machine Learning?

Emulators provide a cost-effective alternative to regional climate models (RCMs) by capturing their dynamical downscaling function. They link large-scale predictors simulated by global climate models (GCMs) to RCM-simulated high-resolution fields of the target variable, here precipitation. Machine learning methods, typically deep learning, are cheaper than running RCMs in computation time and energy. Among them, generative models are appealing because they can simulate ensembles of local high-resolution fields consistent with the predictors. This ensemble, which we call the uncertainty envelope, remains to be properly assessed for added value. Here, we make three contributions. First, we introduce ParamDiffusion, a new two-stage diffusion-based framework, and compare it with a state-of-the-art diffusion approach. Second, we expand standard validation through a comprehensive framework aligned with climate-science needs, examining specific precipitation events, including extremes. Third, within this framework, we assess the added value of diffusion approaches relative to deterministic methods. We intercompare four deep-learning models: a deterministic model designed to capture the precipitation tail; a parametric probabilistic model based on it; a recently proposed diffusion approach; and ParamDiffusion, which couples the parametric model with a diffusion model. Our results show that diffusion-based approaches reproduce climatological precipitation statistics with high skill, including distributional tails and spatially compounded extremes, while generating spatially detailed fields. However, none of the assessed models consistently accounts for the most extreme RCM-simulated events within its uncertainty envelope. Diffusion models are therefore promising for probabilistic RCM emulation, but progress is still required before they can reliably represent high-impact precipitation extremes.

Mikel N. Legasa, Antoine Doury, Achille Gellens +4

Laboratoire des Sciences du Climat et de l’Environnement (LSCE), CEA/CNRS/UVSQ, Universit´e Paris Saclay, UMR8212, 91191 Gif-sur-Yvette, France · CNRM, Universit´e de Toulouse, M´et´eo-France, CNRS, Toulouse, France · Institut Pierre-Simon Laplace (IPSL), FR636, Paris, France +1

Surrogate Modeling Precipitation Downscaling Climate Modeling Conditional Diffusion Models Climate Downscaling Diffusion Models

Jun 11, 2026cs.LG

Reliability of Probabilistic Emulation of Physical Systems

Two dominant approaches have emerged for generating probabilistic forecasts of physical systems: generative models, such as diffusion or flow matching; and ensembles of deterministic models with stochasticity injected, trained using the continuous ranked probability score (CRPS) loss. While both approaches have demonstrated strong predictive accuracy, the reliability of their uncertainties has not been systematically assessed. We address this gap by developing a framework to evaluate both approaches across diverse 2D spatiotemporal physical systems, under matched model size and computational budget. We assess the reliability of probabilistic emulation by inspecting the empirical coverage of predictive intervals, while also considering accuracy and computational efficiency metrics. CRPS-trained ensembles typically achieve more reliable uncertainties on both single-step prediction and autoregressive rollouts, demonstrating better coverage than the standard alternative of training generative models in a latent space. Moreover, the CRPS approach offers significantly faster inference. When generative models are trained in ambient rather than a compressed latent space, which is often infeasible for high-dimensional problems, they exhibit comparable coverage to CRPS-trained ensembles, though with substantially larger inference latency. In contrast, when CRPS-trained ensembles are trained in latent space they do not show a marked degradation in coverage with respect to ambient space. Both generative models and CRPS-trained ensembles demonstrate good predictive accuracy. To facilitate future research and application, we release AutoCast, a modular framework implementing both generative models and CRPS-trained ensembles, alongside AutoSim, a flexible dataset generation package for rapid prototyping.

Sam F. Greenbury, Radka Jersakova, Paolo Conti +4

The Alan Turing Institute · Autodesk Research · PhysicsX +3

Surrogate Modeling Probabilistic Forecasting Generative Modeling Spatiotemporal Forecasting Uncertainty Calibration

Jun 9, 2026cs.LG

SwiftCTS: Fast Cross-Design Prediction and Pareto Optimization of Clock Tree Metrics via Few-Shot Calibration

Clock Tree Synthesis (CTS) is a computationally expensive stage in the physical design flow, requiring iterative EDA tool invocations to navigate a vast configuration space for optimal power, wirelength, and timing skew. Existing machine learning approaches require computationally expensive retraining or fine-tuning cycles to adapt to unseen macro architectures and are architecturally mismatched to the millions of evaluations demanded by exhaustive combinatorial search. We present SwiftCTS, a physics-informed surrogate framework that addresses both limitations simultaneously. By coupling lightweight, physics-grounded statistical features with gradient-boosted ensembles, SwiftCTS trains in under five seconds on a CPU and delivers sub-millisecond inference without GPU support. To handle out-of-distribution (OOD) designs without retraining or fine-tuning, we introduce a K-shot multiplicative calibration mechanism that anchors predictions to just one or two physical reference runs, reducing power prediction error from 24.5% to 3.3% and wirelength error from 56.6% to under 1% on unseen macros. Integrating this engine with an evolutionary optimizer, SwiftCTS evaluates 100,000 CTS configurations in under ten seconds, yielding Pareto-optimal frontiers that are physically validated within the OpenROAD flow. Closed-loop validation confirms prediction errors below 0.5% for power and wirelength, and timing skew predictions within five picoseconds on an OOD benchmark, consistently outperforming default tool heuristics across all target metrics. Code publicly available at: https://github.com/BarsatKhadka/SwiftCTS

Barsat Khadka, Kawsher Roxy, Md Rubel Ahmed

The University of Southern Mississippi Hattiesburg, MS, USA · Intel Corporation Hillsboro, OR, USA · Louisiana Tech University Ruston, LA, USA

Surrogate Modeling Surrogate-Assisted Optimization Model Calibration Physics-Informed ML

Jun 9, 2026cs.LG

First-Order Trajectory Matching: Fast Ensemble Predictions of Chaotic, Turbulent, Stochastic Systems

We introduce First-Order Trajectory Matching (FTM), a surrogate-modeling method that learns the first-order local transport of probability mass from trajectories of stochastic systems. By matching the symmetric first-order motion of trajectories, FTM learns the probability current velocity, whose flow preserves time marginals to match ensemble averages, while also capturing current-like trajectory quantities such as fluxes, circulations, and barrier-crossing currents. FTM learns the current velocity directly from trajectories, avoiding drift, diffusion, and score estimation. Our stability analysis separates discretization error from sampling variance and shows that the one-step simulation-free FTM loss is stable when temporal resolution and sample size are properly balanced. Across stochastic dynamical systems and PDE examples, we empirically demonstrate that FTM provides trajectory-aware ensemble predictions at low, deterministic-rollout cost.

Shreya Jha, Timo Schorlepp, Nicholas Geissler +2

Courant Institute of Mathematical Sciences, New York University

Dynamical Systems Surrogate Modeling Stochastic Linear Dynamical Systems PDE Surrogate Modeling Probabilistic Forecasting

Jun 8, 2026cs.LG

In-Context Learning for Latent Space Bayesian Optimization

Bayesian optimization (BO) is a central tool for sample-efficient design, and latent-space Bayesian optimization (LSBO) extends it to structured objects such as molecules and proteins. In parallel, tabular foundation models such as TabPFN and TabICL now achieve state-of-the-art regression performance and are increasingly used as BO surrogates. Because their Bayesian behavior is induced by large synthetic pretraining collections, the composition of this pretraining distribution is crucial. LSBO creates a distinctive mismatch: the induced map from latent code to objective value differs markedly from the regression tasks used to train current in-context models. We address this mismatch by complementing the pretraining stage of tabular foundation model surrogates with synthetic optimization tasks defined on the latent space of a molecular VAE. The continued-pretraining objective features a regularizer that anchors the model to the original checkpoint, preserving its broad regression prior while avoiding overspecialization to the adaptation tasks. On held-out molecular optimization benchmarks, the resulting model achieves strong performance, supporting the relevance of LSBO-specific adaptation for in-context surrogates.

Tuan A. Vu, Harri Lähdesmäki, Julien Martinelli

Aalto University

Synthetic Data Pretraining Molecular Optimization Surrogate Modeling Bayesian Optimization Latent Space Optimization Tabular ICL

Jun 8, 2026cs.LG

Machine-Learning Emulation of Satellite Greenhouse Gas Retrievals: Stability over Time

Retrieval algorithms are used to estimate atmospheric concentrations of greenhouse gases (GHGs), such as carbon dioxide (CO2) and methane (CH4), by solving inverse problems from high-spectral-resolution satellite radiance measurements. However, these algorithms are computationally expensive, which makes real-time estimation at scale difficult. Machine-learning models have therefore been proposed as fast emulators of retrieval algorithms. Most existing studies, however, evaluate them only on test data from the same period as the training data. We study the stability over time of such emulators using data from the Greenhouse Gases Observing SATellite (GOSAT). We show that prediction accuracy generally deteriorates when the test period moves away from the training period. We also show that including time as an input feature substantially improves XCH4 prediction for Lasso and neural-network models. Among the methods considered, a simple Lasso model performs as well as or better than more complex methods such as neural networks, and yields more stable predictions over time. We further validate the results using the Total Carbon Column Observing Network (TCCON), a ground-based observation network. On the TCCON-matched dataset, the time-augmented Lasso achieves errors against TCCON that are comparable to the disagreement between GOSAT and TCCON for both XCO2 and XCH4.

Nugzar Gognadze, Motonobu Kanagawa, Yu Someya +1

Data Science Department, EURECOM, 450 Route des Chappes, Biot, 06410, France

Surrogate Modeling Distribution Shift Remote Sensing Temporal Distribution Shift

Jun 5, 2026cs.LG

Temporal Coverage over Density: Parsimonious Training-Set Design for ML Climate Downscaling

High-resolution regional climate simulations provide critical information for climate impacts assessments but remain computationally expensive, motivating the development of machine-learning downscalers and emulators. A key challenge is determining how limited high-resolution simulations should be distributed across a changing climate trajectory to capture both forced climate response and internal variability. Using the CESM2 Large Ensemble over the western United States, we compare three training-year selection strategies under fixed data budgets: a contiguous block of historical years, years drawn from both the beginning and end of the simulation period, and years distributed throughout the full climate trajectory. Including both historical and future years consistently outperforms training on historical years alone, demonstrating the importance of exposing downscaling models to climate states outside the historical record and highlighting limitations of stationarity assumptions common in statistical downscaling. Training on years distributed throughout the full climate trajectory performs best overall, indicating that broad sampling of internal variability provides additional information beyond exposure to the forced climate response alone. Models trained on temporally distributed subsets more successfully reproduce variability in unseen ensemble members while retaining strong performance across a wide range of climate diagnostics. Even when trained on only one-tenth of the available high-resolution years, temporally distributed models remain highly competitive with full-data training. These results suggest that, under fixed computational budgets, broad sampling of climate states is more valuable than temporal continuity when allocating scarce high-resolution simulations. The findings provide practical guidance for regional climate downscaling and large-ensemble projection workflows.

Karandeep Singh, Stefan Rahimi, Chad W. Thackeray +2

Atmospheric and Oceanic Sciences, University of California, Los Angeles, CA, USA · Department of Atmospheric Science, University of Wyoming, WY, USA

Surrogate Modeling Climate Science Training Data Selection Climate Modeling Climate Downscaling

Jun 5, 2026cs.LG

CoMetaPNS: Continually Meta-learning Personalized Neural Surrogates for Cardiac Electrophysiology Simulations

Personalized virtual heart simulations face challenges in model personalization and computational cost. While neural surrogates offer state-of-the-art solutions, they typically address either efficient personalization or training generalizable models. Recent work reframes this by learning the process of personalizing a surrogate using limited subject-specific context data, through few-shot generative modeling with set-conditioned surrogates and meta-learned amortized inference. These methods, however, assume a static and diverse training distribution with known task identifiers. When new data becomes available, they require costly retraining with all prior data to avoid catastrophic forgetting - a phenomena where the model forgets earlier tasks when trained on new ones. This is a major limitation in clinical settings where often unlabeled data arrives sequentially and full retraining is infeasible. This paper presents a new continual meta-learning framework to achieve personalized neural surrogates able to not only continually integrate information but also identify whether incoming data stems from a known or unknown dynamics source. By leveraging a continual Bayesian Gaussian Mixture Model over a memory buffer, our framework can infer the identifiers and relationships of data over time - required for effective meta-learning. Empirical results on synthetic cardiac data demonstrate superior simulation forecasting, computational scalability, and resilience to catastrophic forgetting compared to existing baselines.

Ryan Missel, Xiajun Jiang, Linwei Wang

Neural Surrogate Modeling Surrogate Modeling Meta-Learning Physics-Based Simulation Catastrophic Forgetting

Jun 5, 2026cs.LG

Decision-Aware Evaluation of Physics-Informed Surrogates

Physics-informed machine learning is often assessed by curve error, although engineering use depends on downstream decisions: ranking candidates, avoiding infeasible designs and limiting regret. We introduce pinn-gym, an open benchmark for material-conditioned lattice design that couples a transparent reduced-order crush-and-impact oracle with five printable polymer cards, dimensionless force-response targets and a protocol spanning curve fidelity, physical admissibility, top-k retrieval and mass regret. Across per-material, pooled and cross-material settings, low nRMSE is frequently insufficient to identify useful design selections. Physics-informed losses alter trade-offs rather than monotonically improving all metrics, and dimensionless conditioning improves comparability without making transfer symmetric. The benchmark is not a certified material model; within the released oracle, candidate generator and material cards, pinn-gym provides a reproducible testbed for evaluating PIML surrogates as decision systems rather than curve predictors alone.

Daniel Cieślak, Andrzej Czyżewski

Gdańsk University of Technology, Gdańsk, Poland

Surrogate Modeling Benchmark Design Physics-Informed ML Computational Materials Science

Jun 4, 2026cs.RO

3D Underwater Path Planning via Generative Flow Field Surrogates

Autonomous underwater vehicle (AUV) launch and recovery (LAR) into the hull of an advancing host platform requires traversal of a complex, three-dimensional propeller wake whose hydrodynamic structure cannot be characterised by a uniform current model. High-fidelity Reynolds-Averaged Navier-Stokes (RANS) Computational Fluid Dynamics (CFD) simulations resolve this structure with sufficient accuracy for path planning, but their computational cost renders them impractical for onboard use. We address this gap by integrating two conditional generative adversarial network (cGAN) architectures -- a regularised PatchGAN and a 2D3DGAN with self-attention -- as drop-in replacements for RANS CFD data within a three-dimensional, energy-weighted A* path planning framework. Both generators are driven by a hierarchical pipeline that synthesises full

128^3

voxel flow field volumes from scalar operating condition inputs alone, with end-to-end inference times of approximately 28-146

μ

s, compared to hours for a single RANS computation. We benchmark all four environmental knowledge levels: uniform current, ground-truth CFD, PatchGAN, and 2D3DGAN~SA across 19,800 independently generated trajectories spanning 550 distinct flow conditions. Full CFD wake knowledge reduces energy expenditure by 5.7-12.5% and high-velocity wake-core encounters by up to 77.8% relative to uniform-current planning, with both benefits scaling with operating severity. The cGAN surrogates recover approximately 45-60% of the CFD energy benefit and high-velocity cell avoidance benefit while operating at inference speeds compatible with edge device use. These results provide the first systematic quantification of the downstream path planning value of cGAN-predicted hydrodynamic fields in a three-dimensional maritime robotics application.

Zachary Cooper-Baldock, Paulo E. Santos, Russell S. A. Brinkworth +1

Flinders University · PrioriAnalytica

Surrogate Modeling Underwater Robotics Motion Planning Autonomous Underwater Navigation Generative Adversarial Networks

Jun 3, 2026cs.LG

Data-efficient flood depth prediction through domain-aware coreset selection and tabular foundation models

Near-real-time flood depth prediction demands surrogate models that are accurate, fast, and transferable across watersheds. Supervised surrogates can match physics-based simulators in accuracy but need millions of training rows per watershed and cannot extrapolate beyond their original mesh. We propose a domain-aware coreset construction pipeline that conditions a tabular foundation model at inference time. The pipeline stratifies storms by return period and most-affected watershed, then samples hexagons with a target-aware spatial selector. With 0.7% of the per-watershed training pool, the model attains a mean

R^2

of 0.663 across nine Houston-area watersheds, within 98.5% of the supervised reference (

R^2

= 0.673). It transfers to held-out watersheds without task-specific retraining, staying ahead of a coreset-trained supervised baseline. On real storms it exceeds the supervised reference on a far out-of-distribution case and trails it on a mostly in-distribution one. Domain-aware coreset construction lets tabular foundation models deliver data-efficient, watershed-transferable flood predictions without per-watershed training.

Lipai Huang, Adithi Srinath, Manas Singh +2

Urban Resilience.AI Lab, Zachry Department of Civil and Environmental Engineering, Texas A&M University, College Station, TX, USA · Department of Computer Science and Engineering, Texas A&M University, College Station, TX, USA · Resilitix Intelligence LLC, Houston, TX, USA +1

Surrogate Modeling OOD Generalization Coreset Selection Spatiotemporal Forecasting Flood Forecasting

Jun 2, 2026hep-ex

CaloTrilogy: Toward a Breakthrough in One-Step, End-to-End, Physics-Guided Shower Generation for Modern Calorimeters

High-precision calorimeter simulation at current and future colliders imposes rapidly growing computational demands, motivating the development of machine-learning surrogates for traditional Monte Carlo tools such as Geant4. Flow matching and diffusion-based generative models have become leading approaches for high-dimensional fast simulation because of their sample quality, but typically require

{\cal O}(100)

function evaluations at inference and often rely on auxiliary networks to constrain global observables, compromising streamlined end-to-end generation. We introduce a unified framework that improves the balance between speed, shower quality, and physics fidelity. The method combines: (i) an average velocity field integrator that enables sampling in one or a few evaluations; (ii) a learned generative prior in shower space, constructed from data rather than random noise; and (iii) physics-guided loss terms that impose inductive biases on key observables during training. These elements are training time regularizers, preserving end-to-end inference with no additional cost. With only one or a few evaluation steps, the model achieves shower quality competitive with state-of-the-art flow and diffusion approaches, tested on several public high granularity calorimeter datasets. The results demonstrate inter-layer shower structure consistent with the underlying physics, providing a strong candidate for future fast simulation workflows.

Cheng Jiang, Sitian Qian, Kevin Pedro +3

School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom · Department of Physics, University of Wisconsin-Madison, Madison, WI 53706, USA · Fermi National Accelerator Laboratory, Batavia, IL 60510, USA +2

Physics-Informed Generative Modeling Flow Matching Surrogate Modeling One-Step Generative Modeling Physics-Informed ML Physics-Based Simulation