Surrogate Modeling

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Overview

Surrogate modeling studies how to approximate costly simulators or opaque predictors so they can be queried, optimized, or interpreted more efficiently. Common approaches include Gaussian processes and reduced-order models, neural operators and other deep networks, and hybrid or multi-fidelity methods that combine cheap simulations with a smaller number of accurate ones; active learning can select the most useful new evaluations. Applications range from PDE and climate emulation to engineering design, control, Bayesian optimization, and explanations of black-box models. A central challenge is balancing speed and average prediction accuracy with reliable uncertainty estimates, physical consistency, and performance on unseen regimes or decisions.

Latest papers

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229 papers27 papers in the last four weeks, up 13% on the four weeks before. 0.2% of all new papers.

May 15, 2026

Multi-Fidelity Flow Matching: Cascaded Refinement of PDE Solutions

The source distribution in conditional flow matching is a design parameter that can be calibrated to data, not a default isotropic prior. We exploit this in Multi-Fidelity Flow Matching (MFFM), a cascade refinement framework for parametric PDE solutions: the source is calibrated to the empirical low-to-high-fidelity residual scale with local Gaussian-blur correlation, and the velocity network is conditioned on the low-fidelity solution. Conditioning makes the residual refinement problem substantially easier than unconditional field generation, while residual-calibrated source noise improves the flow-matching training geometry. A multi-resolution cascade applies the same construction independently between adjacent fidelities. After level-wise flow-matching pretraining, we fine-tune the composed cascade end-to-end with a deterministic one-step rollout, which makes one velocity evaluation per cascade level the optimized operating point at inference. The result is a learned analog of multigrid refinement that reaches the finest grid in LL deterministic network evaluations per query. We validate MFFM on eight benchmarks: two super-resolution problems and six spatiotemporal forecasting tasks from PDEBench, The Well, and the FNO Navier--Stokes dataset.

Sipeng Chen, Junliang Liu, Hewei Tang +1

Department of Computer Science, Florida State University · Department of Materials Science and Engineering, Florida State University · Hildebrand Department of Petroleum and Geosystems Engineering, The University of Texas at Austin

Surrogate ModelingConditional Flow MatchingPDE Surrogate ModelingMultifidelity Modeling
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May 15, 2026

CTF4Nuclear: Common Task Framework for Nuclear Fission and Fusion Models

The demand for clean energy is ever increasing, with new nuclear technologies presenting a complementary solution to renewable energies. However, designing and operating these systems is exceptionally difficult, given the complexity of the physical phenomena that interact to form the system dynamics. While high-fidelity simulations help to understand the non-linear, multi-physics interactions within a reactor, they are computationally expensive and rarely suitable for real-time applications. Furthermore, model-based approaches are inherently sensitive to simplifying assumptions required to derive their governing equations and parameters, leading to inevitable discrepancies with real-world measurements. In contrast, Machine Learning (ML) methods have the potential to generate reliable surrogate models which may be able to quickly predict the system's behaviour. However, the number of data-driven methods that can potentially be used for this task is large and diverse. In a safety-critical setting such as nuclear engineering, a fair comparison of different ML methods, and a clear understanding of their advantages and limitations, is of paramount importance. To address this, we introduce a Common Task Framework (CTF) for ML in nuclear engineering, building upon previous efforts in dynamical systems and seismology. This CTF considers a curated set of datasets from different nuclear and nuclear-adjacent systems. The CTF evaluates the performance of a method on 12 established metrics, alongside a new paradigm focused on system monitoring from sparse measurements only. We illustrate the framework by benchmarking standard ML baselines against these datasets, revealing current method limitations. Our vision is to replace ad hoc comparisons with standardized evaluations on hidden test sets, raising the bar for rigour and reproducibility in scientific ML for the nuclear industry.

Stefano Riva, Carolina Introini, Antonio Cammi +13

Autodesk Research, London, UK · Department of Energy, Nuclear Engineering Division, Politecnico di Milano, Milan, Italy · Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139 +10

Surrogate ModelingScientific ML
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May 14, 2026

Watch your neighbors: Training statistically accurate chaotic systems with local phase space information

Chaotic systems pose fundamental challenges for data-driven dynamics discovery, as small modeling errors lead to exponentially growing trajectory discrepancies. Since exact long-term prediction is unattainable, it is natural to ask what a good surrogate model for chaotic dynamics is. Prior work has largely focused either on reproducing the Jacobian of the underlying dynamics, which governs local expansion and contraction rates, or on training surrogate models that reproduce the ground-truth dynamics' long-term statistical behavior. In this work, we propose a new framework that aims to bridge these two paradigms by training surrogate dynamics models with accurate Jacobians and long-term statistical properties. Our method constructs a local covering of a chaotic attractor in phase space and analyzes the expansion and contraction of these coverings under the dynamics. The surrogate model is trained by minimizing the maximum mean discrepancy between the pushforward distributions of the coverings under the surrogate and ground-truth dynamics. Experiments show that our method significantly improves Jacobian accuracy while remaining competitive with state-of-the-art statistically accurate dynamics learning methods. Our code is fully available at https://anonymous.4open.science/r/neighborwatch.

Joon-Hyuk Ko, Andrus Giraldo, Deok-Sun Lee

Center for AI and Natural Sciences Korea Institute for Advanced Study Seoul, Korea 02455 · School of Computational Sciences Korea Institute for Advanced Study Seoul, Korea 02455

Surrogate ModelingNonlinear System IdentificationChaotic Dynamical Systems
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May 13, 2026

StampFormer: A Physics-Guided Material-Geometry-Coupled Multimodal Model for Rapid Prediction of Physical Fields in Sheet Metal Stamping

Traditional sheet metal forming relies on time-consuming and expensive Finite Element Analysis (FEA) for design validation, a process that significantly prolongs design cycles. While surrogate models offer faster iteration, current approaches have limitations: scalar-based methods cannot capture comprehensive field-based FEA results, while existing image-based models often ignore the critical role of material properties by focusing solely on geometry. To address this gap, we develop a physics-guided deep learning framework, namely StampFormer, which simultaneously uses component geometry and material stress-strain responses to predict FEA outcomes. The StampFormer framework uses three core components to process data. A Material-Augmented Geometric Network (MAGN) first fuses geometric and material data. This information is then integrated at various levels by a Hierarchical Material Embedding Injection Unit (HMEIU) before being processed by the primary network backbone, an adapted Swin-UNet. We evaluated our model on the stamping of a crossmember panel with two simulation datasets for steel and aluminium panels, and results demonstrate that StampFormer provides high-fidelity predictions of critical physical fields - including thinning, major strain, minor strain, plastic strain, and displacement - in under a second. Compared with ground truth FEA, our model achieved an average relative error of less than 8.5% on the four 2D fields and a mean squared error of less than 1.2 mm2 for the 3D displacement field. In summary, we introduce a practical and efficient framework that integrates multimodal information, namely geometry and material properties, to provide fast and accurate predictions, enabling designers to perform real-time manufacturability assessments.

Jiajie Luo, Mohamed Mohamed, Osama Hassan +8

Neural Surrogate ModelingSurrogate ModelingPhysics-Informed MLMultimodal Fusion
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May 12, 2026

Efficient Conditioning Why Pseudo Observation Batch Bayesian Optimization Works When It Does not

Constant Liar (CL), Kriging Believer (KB), and fantasy models are widely used for batch selection in parallel Bayesian Optimization, yet a unified theory explaining their effectiveness and conditions under which they fail has been lacking. We identify efficient conditioning as the key surrogate property the ability to update predictions in closed form when data is augmented. We prove that Gaussian Processes satisfy this requirement, producing provably distinct batch points with separation of order l, and that this holds for any acquisition function monotonically non decreasing in posterior uncertainty (EI, UCB, PI), with qualitatively similar behavior for Thompson Sampling. We unify CL, KB, and fantasy models as instances of a single conditioning mechanism differing only in the lie value distribution, and draw quantitative connections to Local Penalization (LP) and qualitative connections to Determinantal Point Processes (DPPs). To disentangle model structure from optimizer randomness, we introduce the Structural Diversity Diagnostic (SDD), a reusable methodology for testing surrogate compatibility. Experiments on Hartmann6D, Ackley 8D, Levy10D, and SVM hyperparameter tuning validate all theoretical predictions: CL or KBs implicit penalty matches or outperforms explicit LP greedy conditioning achieves convergence on par with joint qEI efficient conditioning extends to Multiquadric RBF networks; and parametric surrogates produce degenerate batches even when fully retrained (random forests), while neural networks regain diversity only at 15x the wall clock cost of GP conditioning. Robustness is confirmed across multiple initial datasets and under observation noise.

Kumbha Nagaswetha, Rabi Pathak

Surrogate ModelingBayesian OptimizationGaussian Processes
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May 11, 2026

Discovery of Interpretable Surrogates via Agentic AI: Application to Gravitational Waves

Fast surrogate models for expensive simulations are now essential across the sciences, yet they typically operate as black boxes. We present GWAgent, a large language model (LLM)-based workflow that constructs interpretable analytic surrogates directly from simulation data. Surrogate modeling is well suited to agentic workflows because candidate models can be quantitatively validated against ground-truth simulations at each iteration. As a demonstration, we build a surrogate for gravitational waveforms from eccentric binary black hole mergers. We show that providing the agent with a physics-informed domain ansatz substantially improves output model accuracy. The resulting analytic surrogate attains a median Advanced LIGO mismatch of 6.9×10−46.9\times10^{-4} together with an ∼8.4×\sim 8.4\times speedup in waveform evaluation, surpassing both symbolic regression and conventional machine learning baselines. Beyond producing an accurate model, the workflow identifies compact physical structure from the learned representation. As an astrophysical application, we use GWAgent to analyze the eccentricity of GW200129 and infer e20Hz=0.099−0.044+0.063e_{20\mathrm{Hz}}=0.099^{+0.063}_{-0.044}. These results show that validation-constrained agentic workflows can produce accurate, fast, and interpretable surrogates for scientific simulations and inference.

Tousif Islam, Digvijay Wadekar, Tejaswi Venumadhav +4

Kavli Institute for Theoretical Physics, University of California Santa Barbara, Kohn Hall, Lagoon Rd, Santa Barbara, CA 93106, USA. · Center for Gravitational Physics, University of Texas at Austin, Austin, TX 78712, USA. · Department of Physics, University of California at Santa Barbara, Santa Barbara, CA 93106, USA. +5

Surrogate ModelingGravitational-Wave AstronomyAgentic WorkflowsLarge Language Model-Guided Scientific Discovery
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May 11, 2026

Support-Proximity Augmented Diffusion Estimation for Offline Black-Box Optimization

Offline black-box optimization aims to discover novel designs with high property scores using only a static dataset, a task fundamentally challenged by the out-of-distribution (OOD) extrapolation problem. Existing approaches typically bifurcate into inverse methods, which struggle with the ill-posed nature of mapping scores to designs, and forward methods, which often lack the distributional expressivity to quantify uncertainty effectively. In this work, we propose SPADE (Support-Proximity Augmented Diffusion Estimation), a novel framework that reimagines forward surrogate modeling through the lens of conditional generative modeling. SPADE models the forward likelihood p(y|x) using a diffusion model, but with two critical enhancements to tailor it for optimization: (1) a Calibrated Diffusion Estimation module that enforces global consistency in statistical moments and pairwise rankings, and (2) a Support-Proximity Regularization mechanism that implicitly internalizes the data manifold constraint p(x) via kNN-based density estimation. Theoretically, we prove that our regularization is first-order equivalent to maximizing a Bayesian posterior with a valid design prior. Empirically, SPADE achieves state-of-the-art performance across Design-Bench tasks and an LLM data mixture optimization benchmark.

Yonghan Yang, Ye Yuan, Zipeng Sun +5

MBZUAI - Mohamed bin Zayed University of Artificial Intelligence · McGill University · Mila - Quebec AI Institute +1

Surrogate ModelingSurrogate-Assisted OptimizationBlack-Box OptimizationOOD Generalization
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May 11, 2026

Multifidelity Gaussian process regression for solving nonlinear partial differential equations

Solving nonlinear partial differential equations (PDEs) using kernel methods offers a compelling alternative to traditional numerical solvers. However, the performance of these methods strongly depends on the choice of kernel. In this work, as the available information is inherently multifidelity, we propose a kernel learning approach based on cokriging, leveraging empirical information from multifidelity simulations. In the first step, we fit a differentiable non-stationary kernel to an empirical kernel obtained from low-fidelity simulations. In the second step, we derive a high-fidelity kernel with estimated hyperparameters, and construct a corresponding high-fidelity mean using the multifidelity framework. These components can then be used within a Gaussian process framework for solving PDEs. Finally, we demonstrate the performance of the proposed physics-informed method on the Burgers' equation.

Fatima-Zahrae El-Boukkouri, Josselin Garnier, Olivier Roustant

Institut de Mathématiques de Toulouse, Université de Toulouse, INSA, Toulouse, 31077, France · CMAP, CNRS, Ecole polytechnique, Institut Polytechnique de Paris, Palaiseau, 91120, France

Surrogate ModelingPDE SolvingMultifidelity ModelingPhysics-Informed MLGaussian Process Regression
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May 7, 2026

Physics-based Digital Twins for Integrated Thermal Energy Systems Using Active Learning

Real-time supervisory control of thermal energy distribution systems requires digital twins that are accurate, interpretable, and uncertainty-aware, yet remain data and computationally efficient. High-fidelity simulations alone are costly, while purely data-driven surrogates often lack robustness. To address these challenges, this work proposes an active learning (AL) framework that couples system-level Modelica simulations with four simpler physics-informed and data-driven surrogate modeling approaches: deterministic Sparse Identification of Nonlinear Dynamics with Control (SINDyC), its probabilistic multivariate-Gaussian extension (MvG-SINDyC), feedforward neural network (FNN), and gated recurrent unit (GRU) network. Tailored to each surrogate, model-specific AL query strategies are employed, including Mahalanobis-distance sampling in coefficient space for MvG-SINDyC and error-based sampling in prediction space for SINDyC, FNN, and GRU, allowing the learning process to prioritize dynamically informative trajectories. The proposed approach is demonstrated on the glycol heat exchanger (GHX) subsystem of the Thermal Energy Distribution System (TEDS) at Idaho National Laboratory. Across key GHX outputs--the bypass mass flow rate m˙GHX\dot{m}_{\mathrm{GHX}} and heat transfer rate QGHXQ_{\mathrm{GHX}}-the AL framework achieves comparable predictive accuracy using as few as one-fifth of the simulation trajectories required by random sampling. Among the evaluated surrogates, the GRU achieves the highest predictive fidelity, while SINDyC remains the most computationally efficient and interpretable. The probabilistic MvG-SINDyC surrogate further enables uncertainty quantification and exhibits the largest computational gains under AL.

Umme Mahbuba Nabila, Paul Seurin, Linyu Lin +1

Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, MI 48109, United States · Nuclear Science & Technology Division, Idaho National Laboratory, Idaho Falls, ID 83415, United States · Department of Computer Science and Engineering, University of Michigan, Ann Arbor, MI 48109, United States

Surrogate ModelingSparse Identification of Nonlinear DynamicsNonlinear System IdentificationActive LearningPhysics-Informed MLDigital Twins
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May 6, 2026

Elicitation Matters: How Prompts and Query Protocols Shape LLM Surrogates under Sparse Observations

Large language models are increasingly used as surrogate models for low-data optimization, but their optimizer-facing prediction and its uncertainty remain poorly understood. We study the surrogate belief elicited from an LLM under sparse observations, showing that it depends strongly on prompt text and query protocol. We introduce an uncertainty-alignment criterion that measures whether model uncertainty tracks residual ambiguity among sample-consistent functions. Across controlled inference tasks and Bayesian optimization studies, we find that structural prompts act as effective priors, POINTWISE and JOINT querying induce different beliefs, and sequential evidence leads to non-monotonic, order-sensitive confidence updates. These effects change downstream acquisition decisions and regret, showing that elicitation protocol is part of the LLM surrogate specification, not a formatting detail.

Ge Lei, Samuel J. Cooper

Dyson School of Design Engineering Imperial College London Exhibition Road, London SW7 2AZ

Surrogate ModelingBayesian OptimizationLLM PromptingLarge Language Model-Guided OptimizationLLM Uncertainty Estimation
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May 5, 2026

Enabling Real-Time Training of a Wildfire-to-Smoke Map with Multilinear Operators

Wildfires are a major producer of fine particulate matter, impacting human health and the electrical grid. Accurately forecasting smoke impacts over long time scales incorporates fuel treatment strategies, natural fuel succession, and stochastic events like lightning strikes. However, predicting smoke for each fuel distribution with a forward simulation of a coupled fire-atmosphere model is computationally infeasible. Moreover, relatively simple fire models are tractable to run in many long-time scenarios but do not capture smoke transport. We use data-driven multilinear operators to predict a smoke concentration field from knowledge of the time since ignition for two quantities of interest: aerosol optical depth and smoke detection. Our method first computes the principal components of time-since-ignition and smoke concentration fields and then learns a map from powers of the input coefficients to the output coefficients. We apply our learned operator to smoke prediction in the Upper Rio Grande Watershed. After collecting training data, learning the approximation weights on a CPU takes less than 30 seconds, and each forward call takes less than 1 ms. On a proxy for aerosol optical depth, we obtain equal accuracy to Monte Carlo sampling with fewer than half as many coupled model calls. For smoke detection, we obtain an intersection-over-union (IoU) of 0.64 and an area under the receiver operating characteristic curve (AUC) of 0.95 on holdout data. Our method is significantly more accurate than the most similar published smoke classifier, which obtains an IoU and AUC of 0.15 and 0.61, respectively, on a 2015 bushfire in Australia.

Zachary Morrow, Joseph Crockett, John D. Jakeman +1

Sandia National Laboratories 1515 Eubank Blvd SE, Albuquerque, NM 87123

Surrogate ModelingWildfire ForecastingSpatiotemporal ForecastingOperator Learning
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May 4, 2026

Multi-Fidelity Emulation of Atmospheric Correction Coefficients with Physics-Guided Kolmogorov-Arnold Networks

Atmospheric correction is a critical preprocessing step in optical remote sensing, but repeated high-fidelity radiative transfer simulations remain computationally expensive for dense look-up-table generation, sensitivity analysis, retrieval support, and operational preprocessing. This study presents a physics-aware multi-fidelity surrogate framework for emulating atmospheric correction coefficients using paired 6S and libRadtran simulations. Atmospheric and geometric states are sampled using Latin Hypercube Sampling, and both radiative transfer models are evaluated under matched conditions for Sentinel-2 bands using spectral-response-function-aware coefficient generation. The high-fidelity targets are path reflectance, total transmittance, and spherical albedo. A physics-guided Kolmogorov-Arnold Network, termed pKANrtm, receives the atmospheric state and low-fidelity 6S coefficients, predicts the residual relative to libRadtran, and reconstructs the high-fidelity coefficients. The pKANrtm model uses an Efficient-KAN architecture and is trained with a physics-consistency penalty applied in the original coefficient space. The proposed model is evaluated against state-of-the-art regression-based RTM surrogates. Across both standard and out-of-distribution evaluation settings, pKANrtm achieves the strongest overall predictive performance among the compared models. Runtime benchmarking demonstrates substantial acceleration relative to libRadtran, with GPU inference providing approximately four orders of magnitude single-sample speedup and batched inference reaching tens of thousands of samples per second. These results indicate that physics-aware multi-fidelity pKANrtm emulation provides an accurate, physically structured, and computationally efficient strategy for atmospheric correction coefficient generation.

Md Abdullah Al Mazid, Naphtali Rishe

Knight Foundation School of Computing and Information Sciences, Florida International University, Miami, FL 33199, USA

Surrogate ModelingRemote SensingKolmogorov-Arnold NetworksRadiative Transfer
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May 4, 2026

Multi-fidelity surrogates for mechanics of composites: from co-kriging to multi-fidelity neural networks

Composite materials exhibit strongly hierarchical and anisotropic properties governed by coupled mechanisms spanning constituents, plies, laminates, structures, and manufacturing history. This intrinsic complexity makes predictive modeling of composites expensive, because repeated experiments and high-fidelity simulations are needed to cover large design spaces of material, structure, and manufacturing. Multi-fidelity surrogate modeling addresses this challenge by combining abundant, less expensive data with limited high-accuracy data to recover reliable high-fidelity predictions. This review presents a structured overview of multi-fidelity modeling for composite mechanics, covering Gaussian-process or Kriging-based methods, including co-Kriging, coregionalization models, autoregressive formulations, nonlinear autoregressive Gaussian processes, multi-fidelity deep Gaussian processes, and multi-fidelity neural networks. Their distinctions are examined in terms of cross-fidelity correlation, discrepancy representation, uncertainty quantification, and scalability. Selected examples of their applications to composites are introduced according to the roles that multi-fidelity surrogates play in engineering problems, including forward prediction for rapid exploration of material design spaces, inverse optimization for composite parameter identification and design search under limited high-fidelity access, and workflow integration, where heterogeneous data sources, constraints, and validation requirements determine model utility. Open question discussions highlight recurring challenges specific to composites, such as regime-dependent fidelity gaps associated with nonlinear damage and manufacturing history, mismatches between simulations and experiments, and uncertainty propagation across multi-fidelity models.

Haizhou Wen, Elham Kiyani, Gang Li +3

Department of Mechanical Engineering, Clemson University, Clemson, SC 29634, USA · Division of Applied Mathematics, Brown University, Providence, RI 02912, USA · Center for Composite Materials, University of Delaware, Newark, DL 19716, USA +4

Surrogate ModelingSurrogate-Assisted OptimizationMultifidelity ModelingMaterials Science
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Apr 27, 2026

Generalizable Friction Coefficient Estimation via Material Embedding and Proxy Interaction Modeling

Accurately estimating friction coefficients between arbitrary material pairs is critical for robotics, digital fabrication, and physics-based simulation, but exhaustive pairwise testing scales quadratically with the number of materials. We introduce a proxy-based modeling framework that approximates any pairwise friction f(A,B)f(A,B) from a small, fixed set of proxy materials C=[c1,…,ck]C=[c_1,\dots,c_k] by learning a per-material embedding zA=g(f(A,c1),…,f(A,ck))z_A = g(f(A,c1),\dots,f(A,ck)) and a fusion function pp such that f(A,B)≈p(zA,zB)f(A,B)\approx p\big(z_A,z_B\big). We present deterministic and probabilistic realizations of gg and pp, procedures for selecting diverse proxy sets, and mechanisms for handling missing or noisy proxy measurements. The learned embeddings are compact, interpretable, and enable calibrated uncertainty estimates for downstream decision making. On simulated and measured friction datasets, our approach achieves high predictive accuracy, robust performance with partial observations, and substantial experimental savings by significantly reducing pairwise testing.

Zhendong Wang, Huamin Wang

Style3D Research Hangzhou, China

Surrogate ModelingMaterials Property Prediction
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Apr 26, 2026

WISE-FM:Operation-Aware, Engineering-Informed Foundation Model for Multi-Task Well Design

Deploying machine learning models across diverse well portfolios requires generalisation to wells with design parameters outside the training distribution. Current data-driven approaches to virtual flow metering (VFM) and bottomhole estimation typically treat each well independently or ignore the influence of well design on operational behaviour. We present WISE (Well Intelligence and Systems Engineering Foundation Model), a design-aware, physics-informed multi-task model that integrates three complementary mechanisms: Feature-wise Linear Modulation (FiLM) and cross-modal attention to condition operational embeddings on well design parameters; multi-task learning for simultaneous prediction of flow rates, bottomhole conditions, and flow regime classification; and structural mass conservation with soft physics constraints derived from well engineering principles. Evaluation on the ManyWells benchmark (2000 simulated wells, 10610^6 data points) demonstrates that design-aware models reduce VFM prediction error by up to 13×13\times compared to design-unaware baselines, and that physics constraints reduce negative flow predictions by 65%. Flow regime classification achieves 97.7% bottomhole accuracy, providing continuous well integrity monitoring without additional sensors. The methodology transfers to real operational data from five Equinor Volve producers (oil rate R2=0.89R^2 = 0.89, bottomhole pressure R2=0.98R^2 = 0.98, water rate R2=0.97R^2 = 0.97). The trained model additionally serves as a fast surrogate for integrity-aware well design optimisation over a 24-dimensional design space, with more than 1000×1000\times speedup over drift-flux simulations. These results demonstrate that design awareness, physics enforcement, and multi-task learning are essential and complementary ingredients for foundation models intended to operate across large well portfolios.

Carine de Menezes Rebello, Anderson Rapello dos Santos, Idelfonso B. R. Nogueira

Department of Chemical Engineering, Norwegian University of Science and Technology (NTNU), Trondheim, Norway · Petróleo Brasileiro S.A. (PETROBRAS), Wells/Well Engineering, Rio de Janeiro, Brazil

Surrogate ModelingMulti-Task LearningPhysics-Informed ML
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Apr 24, 2026

Predicting Wind Loads on Container Ships in Harbor Environments through Multi-Fidelity Modeling

Modern container ships face higher wind loads due to increased windage areas, making accurate predictions of wind loads essential for mooring design. Existing empirical models, largely developed for container ships with smaller windage areas and simpler geometrical configurations than those of modern large-scale vessels, often lack accuracy and do not account for the influence of nearby structures. This study proposes a multi-fidelity surrogate modelling framework for the prediction of wind-load coefficients, combining empirical correlations with simplified and detailed CFD models for ships in open-sea and harbor environments. The approach relies on recursive co-kriging to consistently fuse information across fidelity levels, enabling accurate predictions at a reduced computational cost. A sensitivity analysis is used to identify the most influential geometric parameters, and the resulting reduced parameter space is explored through sequential sampling to efficiently construct the training database. The surrogate models are validated over a wide range of loading configurations and for two distinct harbor environments. The results demonstrate that the multi-fidelity approach significantly improves prediction accuracy compared to single-fidelity models, while substantially reducing the reliance on high-fidelity simulations. In particular, the proposed framework captures the dependence of wind loads on key geometric parameters and consistently outperforms traditional empirical correlations, providing a robust and efficient tool for engineering applications.

Matilde Fiore, Andrea Bresciani, Miguel Alfonso Mendez +1

Environmental and Applied Fluid Dynamics Department, von Karman Institute for Fluid Dynamics, Waterloosesteenweg 72, Sint-Genesius-Rode, B-1640, Belgium · Aero-Thermo-Mechanics Laboratory, École Polytechnique de Bruxelles, Université Libre de Bruxelles, Av. Franklin Roosevelt 50, Brussels, 1050, Belgium · Aerospace Engineering Research Group, Universidad Carlos III de Madrid, Av. de la Universidad 30, Leganés, 28911, Spain

Surrogate Modeling
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Apr 23, 2026

Neural surrogates for crystal growth dynamics with variable supersaturation: explicit vs. implicit conditioning

Simulations of crystal growth are performed by using Convolutional Recurrent Neural Network surrogate models, trained on a dataset of time sequences computed by numerical integration of Allen-Cahn dynamics including faceting via kinetic anisotropy. Two network architectures are developed to take into account the effects of a variable supersaturation value. The first infers it implicitly by processing an input mini-sequence of a few evolution frames and then returns a consistent continuation of the evolution. The second takes the supersaturation parameter as an explicit input along with a single initial frame and predicts the entire sequence. The two models are systematically tested to establish strengths and weaknesses, comparing the prediction performance for models trained on datasets of different size and, in the first architecture, different lengths of input mini-sequence. The analysis of point-wise and mean absolute errors shows how the explicit parameter conditioning guarantees the best results, reproducing with high-fidelity the ground-truth profiles. Comparable results are achievable by the mini-sequence approach only when using larger training datasets. The trained models show strong conditioning by the supersaturation parameter, consistently reproducing its overall impact on growth rates as well as its local effect on the faceted morphology. Moreover, they are perfectly scalable even on 256 times larger domains and can be successfully extended to more than 10 times longer sequences with limited error accumulation. The analysis highlights the potential and limits of these approaches in view of their general exploitation for crystal growth simulations.

Matteo Rigoni, Daniele Lanzoni, Francesco Montalenti +1

Dept. of Materials Science, University of Milano-Bicocca, 20125 Milano, Italy · Dept. of Physics, University of Genova, 16146 Genova, Italy

Neural Surrogate ModelingConvolutional RNNsSurrogate ModelingPDE Surrogate ModelingRecurrent Neural Networks
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Apr 22, 2026

Surrogate Functionals for Machine-Learned Orbital-Free Density Functional Theory

We introduce surrogate functionals: machine-learned energy functionals for orbital-free density functional theory (OF-DFT) which are defined not by universal fidelity to a physical reference, but merely by the requirement that density optimization with a fixed procedure yields the true ground-state density. Helpfully, training surrogate functionals requires only ground-state densities, no energies or gradients away from the ground state. We here propose a gradient-descent-improvement loss that guarantees exponential convergence of the density to the ground state, and combine it with an adaptive sampling scheme that concentrates learning around the optimization trajectories actually visited during inference. On the QM9 and QMugs benchmarks, surrogate functionals achieve density errors competitive with or improving upon the state of the art for fully supervised machine-learned OF-DFT, while eliminating the need for the O(N3)O(N^3) orthononormalization step required by prior work, yielding improved runtime scaling for larger systems.

Roman Remme, Fred A. Hamprecht

Interdisciplinary Center for Scientific Computing (IWR), Heidelberg University

Surrogate ModelingQuantum ChemistryAdaptive SamplingComputational Materials ScienceDensity Functional TheoryComputational Quantum Chemistry
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Apr 22, 2026

Surrogate modeling for interpreting black-box LLMs in medical predictions

Large language models (LLMs), trained on vast datasets, encode extensive real-world knowledge within their parameters, yet their black-box nature obscures the mechanisms and extent of this encoding. Surrogate modeling, which uses simplified models to approximate complex systems, can offer a path toward better interpretability of black-box models. We propose a surrogate modeling framework that quantitatively explains LLM-encoded knowledge. For a specific hypothesis derived from domain knowledge, this framework approximates the latent LLM knowledge space using observable elements (input-output pairs) through extensive prompting across a comprehensive range of simulated scenarios. Through proof-of-concept experiments in medical predictions, we demonstrate our framework's effectiveness in revealing the extent to which LLMs "perceive" each input variable in relation to the output. Particularly, given concerns that LLMs may perpetuate inaccuracies and societal biases embedded in their training data, our experiments using this framework quantitatively revealed both associations that contradict established medical knowledge and the persistence of scientifically refuted racial assumptions within LLM-encoded knowledge. By disclosing these issues, our framework can act as a red-flag indicator to support the safe and reliable application of these models.

Changho Han, Songsoo Kim, Dong Won Kim +4

Medical Big Data Research Center, Seoul National University Medical Research Center, Seoul National University College of Medicine, Seoul, Republic of Korea · Department of Biomedical Systems Informatics, Yonsei University College of Medicine, Seoul, Republic of Korea. · Laboratory for Computational Physiology, Massachusetts Institute of Technology, Cambridge, MA 02139 +5

Surrogate ModelingLLM InterpretabilityDemographic Bias in Language ModelsMedical LLMs
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Apr 20, 2026

The High Explosives and Affected Targets (HEAT) Dataset

Artificial Intelligence (AI) surrogate models provide a computationally efficient alternative to full-physics simulations, but no public datasets currently exist for training and validating models of high-explosive-driven, multi-material shock dynamics. Simulating shock propagation is challenging due to the need for material-specific equations of state (EOS) and models of plasticity, phase change, damage, fluid instabilities, and multi-material interactions. Explosive-driven shocks further require reactive material models to capture detonation physics. To address this gap, we introduce the High-Explosives and Affected Targets (HEAT) dataset, a physics-rich collection of two-dimensional, cylindrically symmetric simulations generated using an Eulerian multi-material shock-propagation code developed at Los Alamos National Laboratory. HEAT consists of two partitions: expanding shock-cylinder (CYL) simulations and Perturbed Layered Interface (PLI) simulations. Each entry includes time series of thermodynamic fields (pressure, density, temperature), kinematic fields (position, velocity), and continuum quantities such as stress. The CYL partition spans a range of materials, including metals (aluminum, copper, depleted uranium, stainless steel, tantalum), a polymer, water, gases (air, nitrogen), and a detonating material. The PLI partition explores varied geometries with fixed materials: copper, aluminum, stainless steel, polymer, and high explosive. HEAT captures key phenomena such as shock propagation, momentum transfer, plastic deformation, and thermal effects, providing a benchmark dataset for AI/ML models of multi-material shock physics.

Bryan Kaiser, Kyle Hickmann, Sharmistha Chakrabarti +6

Los Alamos National Laboratory

Surrogate ModelingSynthetic Benchmark GenerationPhysics-Based Simulation
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Apr 20, 2026

Towards a Foundation-Model Paradigm for Aerodynamic Prediction in Three-dimensional Design

Accurate machine-learning models for aerodynamic prediction are essential for accelerating shape optimization, yet remain challenging to develop for complex three-dimensional configurations due to the high cost of generating training data. This work introduces a methodology for efficiently constructing accurate surrogate models for design purposes by first pre-training a large-scale model on diverse geometries and then fine-tuning it with a few more detailed task-specific samples. A Transformer-based architecture, AeroTransformer, is developed and tailored for large-scale training to learn aerodynamics. The methodology is evaluated on transonic wings, where the model is pre-trained on SuperWing, a dataset of nearly 30000 samples with broad geometric diversity, and subsequently fine-tuned to handle specific wing shapes perturbed from the Common Research Model. Results show that, with 450 task-specific samples, the proposed methodology achieves 0.36% error on surface-flow prediction, reducing 84.2% compared to training from scratch. The influence of model configurations and training strategies is also systematically studied to provide guidance on effectively training and deploying such models under limited data and computational budgets. To facilitate reuse, we release the datasets and the pre-trained models at https://github.com/tum-pbs/AeroTransformer. An interactive design tool is also built on the pre-trained model and is available online at https://webwing.pbs.cit.tum.de.

Yunjia Yang, Babak Gholami, Caglar Gurbuz +2

Technical University of Munich, Garching, D-85748, Germany · BMW Group, Bremer Str. 6, Munich, D-80788, Germany

Surrogate ModelingTransformerComputational Fluid Dynamics
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Apr 17, 2026

Late Fusion Neural Operators for Extrapolation Across Parameter Space in Partial Differential Equations

Developing neural operators that accurately predict the behavior of systems governed by partial differential equations (PDEs) across unseen parameter regimes is crucial for robust generalization in scientific and engineering applications. In practical applications, variations in physical parameters induce distribution shifts between training and prediction regimes, making extrapolation a central challenge. As a result, the way parameters are incorporated into neural operator models plays a key role in their ability to generalize, particularly when state and parameter representations are entangled. In this work, we introduce the Late Fusion Neural Operator, an architecture that disentangles learning state dynamics from parameter effects, improving predictive performance both within and beyond the training distribution. Our approach combines neural operators for learning latent state representations with sparse regression to incorporate parameter information in a structured manner. Across four benchmark PDEs including advection, Burgers, and both 1D and 2D reaction-diffusion equations, the proposed method consistently outperforms Fourier Neural Operator and CAPE-FNO. Late Fusion Neural Operators achieve consistently the best performance in all experiments, with an average RMSE reduction of 72.9% in-domain and 71.8% out-domain compared to the second-best method. These results demonstrate strong generalization across both in-domain and out-domain parameter regimes.

Eva van Tegelen, Taniya Kapoor, George A. K. van Voorn +2

Artificial Intelligence Group, Wageningen University and Research, Netherlands · Mathematical and Statistical Methods, Wageningen University and Research, Netherlands

Surrogate ModelingPDE Surrogate ModelingOOD GeneralizationPDE Operator LearningNeural Operators
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Apr 15, 2026

Interpretable and Explainable Surrogate Modeling for Simulations: A State-of-the-Art Survey and Perspectives on Explainable AI for Decision-Making

The simulation of complex systems increasingly relies on sophisticated but fundamentally opaque computational black-box simulators. Surrogate models play a central role in reducing the computational cost of complex systems simulations across a wide range of scientific and engineering domains. Notwithstanding, they inevitably inherit and often exacerbate this black-box nature, obscuring how input variables drive physical responses. Conversely, Explainable Artificial Intelligence (XAI) offers powerful tools to unpack these models. Yet, XAI methods struggle with engineering-specific constraints, such as highly correlated inputs, dynamical systems, and rigorous reliability requirements. Consequently, surrogate modeling and XAI have largely evolved as distinct fields of research, despite their strong complementarity. To reconnect these approaches, this state-of-the-art survey provides a structured perspective that maps existing XAI techniques onto the various stages of surrogate modeling workflows for design and exploration. To ground this synthesis, we draw upon illustrative applications across both equation-based simulations and agent-based modeling. We survey a broad spectrum of techniques, highlighting their strengths for revealing interactions and supporting human comprehension. Finally, we identify pressing open challenges, including the explainability of dynamical systems and the handling of mixed-variable systems, and propose a research agenda to make explainability a core, embedded element of simulation-driven workflows from model construction through decision-making. By transforming opaque emulators into explainable tools, this agenda empowers practitioners to move beyond accelerating simulations to extracting actionable insights from complex system behaviors.

Pramudita Satria Palar, Paul Saves, Muhammad Daffa Robani +6

Faculty of Mechanical and Aerospace Engineering, Institut Teknologi Bandung, Jl. Ganesha 10, Bandung, 15414, West Java, Indonesia. · IRIT, Université Toulouse Capitole, Toulouse, 31000,France. · AwanTunai, Urban Suites, 3 Hullet Road, Singapore, 229158, Singapore, Singapore. +2

Surrogate ModelingExplainable Artificial Intelligence
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Apr 13, 2026

Parametric Interpolation of Dynamic Mode Decomposition for Predicting Nonlinear Systems

We present parameter-interpolated dynamic mode decomposition (piDMD), a parametric reduced-order modeling framework that embeds known parameter-affine structure directly into the DMD regression step. Unlike existing parametric DMD methods which interpolate modes, eigenvalues, or reduced operators and can be fragile with sparse training data or multi-dimensional parameter spaces, piDMD learns a single parameter-affine Koopman surrogate reduced order model (ROM) across multiple training parameter samples and predicts at unseen parameter values without retraining. We validate piDMD on fluid flow past a cylinder, electron beam oscillations in transverse magnetic fields, and virtual cathode oscillations -- the latter two being simulated using an electromagnetic particle-in-cell (EMPIC) method. Across all benchmarks, piDMD achieves accurate long-horizon predictions and improved robustness over state-of-the-art interpolation-based parametric DMD baselines, with less training samples and with multi-dimensional parameter spaces.

Ananda Chakrabarti, Haitham H. Saleh, Indranil Nayak +3

Department of Electrical and Computer Engineering, The Ohio State University, Columbus, OH 43210, USA · ElectroScience Laboratory, The Ohio State University, Columbus, OH 43212, USA · SLAC National Accelerator Laboratory, Stanford University, Menlo Park, CA 94025, USA +1

Reduced-Order ModelingDynamic Mode DecompositionSurrogate Modeling
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Apr 13, 2026

Limited Perfect Monotonical Surrogates constructed using low-cost recursive linkage discovery with guaranteed output

Surrogates provide a cheap solution evaluation and offer significant leverage for optimizing computationally expensive problems. Usually, surrogates only approximate the original function. Recently, the perfect linear surrogates were proposed that ideally represent the original function. These surrogates do not mimic the original function. In fact, they are another (correct) representation of it and enable a wide range of possibilities, e.g., discovering the optimized function for problems where the direct transformation of the encoded solution into its evaluation is not available. However, many real-world problems can not be represented by linear models, making the aforementioned surrogates inapplicable. Therefore, we propose the Limited Monotonical Perfect Surrogate (LyMPuS), which overcomes this difficulty and enables the comparison of two solutions that differ by a single variable. Our proposition is suitable for limiting the cost of expensive local search procedures. The proposed surrogate is parameterless and can be trained on the fly without any separate surrogate-building step. It uses only the necessary fitness evaluations, and the already-paid costs are not wasted when the model is updated. Finally, it offers low-cost missing-linkage detection and low-cost linkage discovery, guaranteed to find a missing dependency in no more than 2⌈log⁡2(n)⌉2\lceil\log_2(n)\rceil steps.

M. W. Przewozniczek, F. Chicano, R. Tinós +1

Wroclaw Univ. of Science and Techn. Wroclaw, Poland · ITIS Software, University of Málaga Málaga, Spain · University of São Paulo Ribeirão Preto, Brazil

Surrogate ModelingSurrogate-Assisted Optimization
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Apr 8, 2026

Lecture notes on Machine Learning applications for global fits

These lecture notes provide a comprehensive framework for performing global statistical fits in high-energy physics using modern Machine Learning (ML) surrogates. We begin by reviewing the statistical foundations of model building, including the likelihood function, Wilks' theorem, and profile likelihoods. Recognizing that the computational cost of evaluating model predictions often renders traditional minimization prohibitive, we introduce Boosted Decision Trees to approximate the log-likelihood function. The notes detail a robust ML workflow including efficient generation of training data with active learning and Gaussian processes, hyperparameter optimization, model compilation for speed-up, and interpretability through SHAP values to decode the influence of model parameters and interactions between parameters. We further discuss posterior distribution sampling using Markov Chain Monte Carlo (MCMC). These techniques are finally applied to the B±→K±ννˉB^\pm \to K^\pm ν\barν anomaly at Belle II, demonstrating how a two-stage ML model can efficiently explore the parameter space of Axion-Like Particles (ALPs) while satisfying stringent experimental constraints on decay lengths and flavor-violating couplings.

Jorge Alda

Dipartimento di Fisica e Astronomia “Galileo Galilei”, Università degli Studi di Padova and INFN Sezione Padova, via Marzolo 8 35129 Padova, Italy. · Centro de Astropartículas y Física de Altas Energías (CAPA), Pedro Cerbuna 12 50009 Zaragoza, Spain.

Surrogate ModelingHigh-Energy Physics
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Apr 8, 2026

Graph Neural ODE Digital Twins for Control-Oriented Reactor Thermal-Hydraulic Forecasting Under Partial Observability

Real-time supervisory control of advanced reactors requires accurate forecasting of plant-wide thermal-hydraulic states, including locations where physical sensors are unavailable. Meeting this need calls for surrogate models that combine predictive fidelity, millisecond-scale inference, and robustness to partial observability. In this work, we present a physics-informed message-passing Graph Neural Network coupled with a Neural Ordinary Differential Equation (GNN-ODE) to addresses all three requirements simultaneously. We represent the whole system as a directed sensor graph whose edges encode hydraulic connectivity through flow/heat transfer-aware message passing, and we advance the latent dynamics in continuous time via a controlled Neural ODE. A topology-guided missing-node initializer reconstructs uninstrumented states at rollout start; prediction then proceeds fully autoregressively. The GNN-ODE surrogate achieves satisfactory results for the system dynamics prediction. On held-out simulation transients, the surrogate achieves an average MAE of 0.91 K at 60 s and 2.18 K at 300 s for uninstrumented nodes, with R2R^2 up to 0.995 for missing-node state reconstruction. Inference runs at approximately 105 times faster than simulated time on a single GPU, enabling 64-member ensemble rollouts for uncertainty quantification. To assess sim-to-real transfer, we adapt the pretrained surrogate to experimental facility data using layerwise discriminative fine-tuning with only 30 training sequences. The learned flow-dependent heat-transfer scaling recovers a Reynolds-number exponent consistent with established correlations, indicating constitutive learning beyond trajectory fitting. The model tracks a steep power change transient and produces accurate trajectories at uninstrumented locations.

Akzhol Almukhametov, Doyeong Lim, Rui Hu +1

Department of Nuclear Engineering, Texas A&M University, College Station, TX 77843, USA · Argonne National Laboratory, Nuclear Science and Engineering Division, USA

Surrogate ModelingDigital TwinsPhysics-Informed GNNsNeural ODEs
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Apr 7, 2026

GS-Surrogate: Deformable Gaussian Splatting for Parameter Space Exploration of Ensemble Simulations

Exploring ensemble simulations is increasingly important across many scientific domains. However, supporting flexible post-hoc exploration remains challenging due to the trade-off between storing the expensive raw data and flexibly adjusting visualization settings. Existing visualization surrogate models have improved this workflow, but they either operate in image space without an explicit 3D representation or rely on neural radiance fields that are computationally expensive for interactive exploration and encode all parameter-driven variations within a single implicit field. In this work, we introduce GS-Surrogate, a deformable Gaussian Splatting-based visualization surrogate for parameter-space exploration. Our method first constructs a canonical Gaussian field as a base 3D representation and adapts it through sequential parameter-conditioned deformations. By separating simulation-related variations from visualization-specific changes, this explicit formulation enables efficient and controllable adaptation to different visualization tasks, such as isosurface extraction and transfer function editing. We evaluate our framework on a range of simulation datasets, demonstrating that GS-Surrogate enables real-time and flexible exploration across both simulation and visualization parameter spaces.

Ziwei Li, Rumali Perera, Angus Forbes +5

The Ohio State University · NVIDIA · Oak Ridge National Laboratory

Scientific VisualizationSurrogate Modeling3D Gaussian Splatting
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Apr 3, 2026

From Model-Based Screening to Data-Driven Surrogates: A Multi-Stage Workflow for Exploring Stochastic Agent-Based Models

Systematic exploration of Agent-Based Models (ABMs) is challenged by the curse of dimensionality and their inherent stochasticity. We present a multi-stage pipeline integrating the systematic design of experiments with machine learning surrogates. Using a predator-prey case study, our methodology proceeds in two steps. First, an automated model-based screening identifies dominant variables, assesses outcome variability, and segments the parameter space. Second, we train Machine Learning models to map the remaining nonlinear interaction effects. This approach automates the discovery of unstable regions where system outcomes are highly dependent on nonlinear interactions between many variables. Thus, this work provides modelers with a rigorous, hands-off framework for sensitivity analysis and policy testing, even when dealing with high-dimensional stochastic simulators.

Paul Saves, Matthieu Mastio, Nicolas Verstaevel +1

IRIT, Université Toulouse Capitole, Toulouse, France

Sensitivity AnalysisAgent-Based ModelingSurrogate Modeling
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Apr 2, 2026

Variational LSTM with Augmented Inputs: Nonlinear Response History Metamodeling with Aleatoric and Epistemic Uncertainty

Uncertainty propagation in high-dimensional nonlinear dynamic structural systems is pivotal in state-of-the-art performance-based design and risk assessment, where uncertainties from both excitations and structures, i.e., the aleatoric uncertainty, must be considered. This poses a significant challenge due to heavy computational demands. Machine learning techniques are thus introduced as metamodels to alleviate this burden. However, the "black box" nature of Machine learning models underscores the necessity of avoiding overly confident predictions, particularly when data and training efforts are insufficient. This creates a need, in addition to considering the aleatoric uncertainty, of estimating the uncertainty related to the prediction confidence, i.e., epistemic uncertainty, for machine learning-based metamodels. We developed a probabilistic metamodeling technique based on a variational long short-term memory (LSTM) with augmented inputs to simultaneously capture aleatoric and epistemic uncertainties. Key random system parameters are treated as augmented inputs alongside excitation series carrying record-to-record variability to capture the full range of aleatoric uncertainty. Meanwhile, epistemic uncertainty is effectively approximated via the Monte Carlo dropout scheme. Unlike computationally expensive full Bayesian approaches, this method incurs negligible additional training costs while enabling nearly cost-free uncertainty simulation. The proposed technique is demonstrated through multiple case studies involving stochastic seismic or wind excitations. Results show that the calibrated metamodels accurately reproduce nonlinear response time histories and provide confidence bounds indicating the associated epistemic uncertainty.

Manisha Sapkota, Min Li, Bowei Li

Department of Civil, Environmental, and Construction Engineering, Texas Tech University, 2500 Broadway St, Lubbock 79409, TX, USA · Department of Civil and Environmental Engineering, Rensselaer Polytechnic Institute, 110 8th Street, Troy 12180, NY, USA · National Wind Institute, Texas Tech University, 1009 Canton Ave, Lubbock 79409, TX, USA

Surrogate ModelingUncertainty PropagationLong Short-Term Memory NetworksEpistemic UncertaintyStructural MechanicsAleatoric Uncertainty
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