Neural Surrogate Modeling

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Overview

Neural surrogate modeling replaces repeated calls to expensive simulators with learned approximations of physical fields, system dynamics, or quantities of interest, making tasks such as design search, control, and Bayesian inference more practical. Common approaches include neural operators for PDE solution maps, graph neural networks for meshes and networks, reduced-order latent models, and physics-informed or hybrid models that combine learned components with governing equations. Researchers also use multi-fidelity training, active learning, and probabilistic models to reduce data needs and estimate uncertainty. A central challenge is that good one-step or in-distribution accuracy does not guarantee stable long rollouts, reliable extrapolation, physical consistency, or improved downstream decisions; classical solvers remain important when stringent accuracy and verification are required.

Latest papers

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418 papers45 papers in the last four weeks, down 15% on the four weeks before. 0.3% of all new papers.

May 14, 2026

A finite-element-inspired bipartite graph learned simulator for manufacturability assessment in large-deformation sheet forming

Explicit dynamic finite element (FE) simulations are widely used for large-deformation analysis but remain expensive for design-space exploration. In explicit FE analysis, nodal kinematics and element-level deformation measures evolve through a coupled node-element update process. An FE-inspired learned simulator can preserve this structure and learn nodal kinematics and elemental deformation on their native domains. Nodal displacement describes geometry evolution, while elemental thinning identifies local deformation and critical regions. Feeding both outputs back during rollout allows each field to inform subsequent updates of the other. This work proposes CAtt-BiGNN, a cross-attention-based bipartite graph neural network for coupled nodal-elemental learning. The bipartite graph encodes FE-guided state organisation and information flow without imposing equilibrium or constitutive constraints. Mesh nodes and elements are represented as distinct graph entities connected by directed node-element edges, enabling prediction of nodal displacement increments and elemental deformation on their native domains. An edge-aware cross-attention processor dynamically updates edge representations and weights messages using the receiving state and evolving local relations. For larger graphs, CAtt-BiUGNN uses separate nodal and elemental downsampling and upsampling to enhance long-range propagation while preserving their interaction across graph levels. The method is evaluated on dome-shaped cold-forming and corner-shaped hot-forming benchmarks. Comparisons with node-centred baselines, an FE-inspired hypergraph model, a Physics-Attention-based neural operator, a graph Transformer, and attention ablations show improved joint accuracy in nodal displacement and elemental thinning prediction during autoregressive rollout.

Yingxue Zhao, Haoran Li, Haosu Zhou +2

Dyson School of Design Engineering, Imperial College London, London, UK · NVIDIA, UK

Neural Surrogate ModelingGraph Neural NetworksFinite Element Method
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May 14, 2026

Real-time virtual circuits for plasma shape control via neural network emulators

Reliable position and shape control in tokamak plasmas requires accurate real-time regulation of several strongly coupled shape parameters. The control vectors that disentangle these couplings, referred to as virtual circuits (VCs), enable independent shape parameter control for a specific Grad--Shafranov (GS) equilibrium. Numerical calculation of VCs is not currently feasible in real time, therefore VCs are usually computed prior to each experiment, using a small number of reference GS equilibria sampled along the desired scenario trajectory, with each VC used to control the plasma within a preset time interval. While effective near the reference equilibrium, this approach can lead to degraded performance as the plasma departs from the reference equilibrium and/or from the desired trajectory, and it complicates the design of robust control strategies for rapidly evolving plasma configurations. In this paper, we construct neural-network-based emulators of plasma shape parameters from which VCs can be derived, to provide the MAST Upgrade (MAST-U) plasma control system with state-aware VCs in real-time. To do this, we develop an extensive library of over a million simulated GS equilibria, covering a substantial portion of the MAST-U operational space. These emulators provide differentiable functions whose gradients can be rapidly computed, enabling the derivation of accurate VCs for real-time shape control. We perform extensive verification of the emulated VCs by testing whether they disentangle the control problem. The neural-network-based approach delivers high accuracy and orthogonality across a diverse range of equilibria. This work establishes the physical validity of emulated VCs as a scalable and general alternative to schedules of precomputed VCs.

Alasdair Ross, George K. Holt, Kamran Pentland +7

STFC Hartree Centre, Sci-Tech Daresbury, Keckwick Lane, Daresbury, Warrington, WA4 4AD, United Kingdom · United Kingdom Atomic Energy Authority, Culham Campus, Abingdon, Oxfordshire, OX14 3DB, United Kingdom

Neural Surrogate ModelingFeedback ControlContinuous Control
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May 14, 2026

Scalable Solution of the Stochastic Multi-path Traveling Salesman Problem via Neural Networks

The multi-path Traveling Salesman Problem with stochastic travel costs arises in hybrid vehicle routing applications designed for Smart City and City Logistics, where multiple paths exist between each pair of locations. Travel times along these paths are typically affected by real-time traffic conditions and therefore modeled as stochastic. The objective of the problem is to determine a Hamiltonian tour that minimizes the expected total travel cost under uncertainty. In this work, we adopt a two-stage stochastic programming formulation. In the first stage, a predefined route specifying the sequence of locations to be visited is determined, while taking into consideration a second-stage recourse problem that selects the optimal path from the feasible set of alternative paths for each pair of locations, once real-time traffic conditions are realized. To reduce the computational burden imposed by the large number of scenarios required to capture travel time uncertainty, the innovation of this work is the integration of neural network-based surrogate models to approximate the expected value of the second-stage recourse problem. Different architectures and training strategies for the neural networks are proposed and analyzed, with performance evaluated in terms of computation time, solution quality, and generalization capability. Preliminary findings demonstrate the enhanced scalability and practical applicability of the approach for complex vehicle routing problems under uncertainty.

Xiaochen Chou, Ludovica Di Marco, Enza Messina

Department of Informatics, Systems and Communication, University of Milano-Bicocca, Viale Sarca 336, Milan, 20125, Italy.

Neural Surrogate ModelingStochastic OptimizationTraveling Salesperson ProblemCombinatorial OptimizationVehicle Routing
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May 14, 2026

All-atomistic Transferable Neural Potentials for Protein Solvation

Implicit solvent models are widely used to decrease the number of solvent degrees of freedom and enable the calculation of solvation energetics without water molecules. However, its accuracy often falls short compared to explicit models. Recent advancements in neural potentials have shown promise in drug discovery, but transferability remains a persistent challenge. Here, we introduce the Protein Hydration Neural Network (PHNN), an implicit solvent model that extends analytical continuum solvation by learning transferable corrections to model parameters instead of applying post hoc adjustments to final energies. The model is explicitly designed to maximize data efficiency by leveraging physical priors embedded in the data. We demonstrate that PHNN improves accuracy relative to traditional analytical methods and maintains predictive accuracy on out-of-domain protein systems.

Rishabh Dey, Salvina Sharipova, Konstantin Popov

University of North Carolina at Chapel Hill - Eshelman School of Pharmacy

Neural Surrogate ModelingMachine Learning Interatomic Potentials
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May 14, 2026

Learning Scenario Reduction for Two-Stage Robust Optimization with Discrete Uncertainty

Two-Stage Robust Optimization (2RO) with discrete uncertainty is challenging, often rendering exact solutions prohibitive. Scenario reduction alleviates this issue by selecting a small, representative subset of scenarios to enable tractable computation. However, existing methods are largely problem-agnostic, operating solely on the uncertainty set without consulting the feasible region or recourse structure. In this paper, we introduce PRISE, a problem-driven sequential lookahead heuristic that constructs reduced scenario sets by evaluating the marginal impact of each scenario. While PRISE yields high-quality scenario subsets, each selection step requires solving multiple subproblems, making it computationally expensive at scale. To address this, we propose NeurPRISE, a neural surrogate model built on a GNN-Transformer backbone that encodes the per-scenario structure via graph convolution and captures cross-scenario interactions through attention. NeurPRISE is trained via imitation learning with a gain-aware ranking objective, which distills marginal gain information from PRISE into a learned scoring function for scenario ranking and selection. Extensive results on three 2RO problems show that NeurPRISE consistently achieves competitive regret relative to comprehensive methods, maintains strong calability with varying numbers of scenarios, and delivers 17-200x speedup over PRISE. NeurPRISE also exhibits strong zero-shot generalization, effectively handling instances with larger problem scales (up to 5x), more scenarios (up to 4x), and distribution shifts.

Tianjue Lin, Jianan Zhou, Jieyi Bi +4

Nanyang Technological University · Eindhoven University of Technology · Shandong University +1

Neural Surrogate ModelingRobust Optimization
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May 13, 2026

Mask-Morph Graph U-Net: A Generalisable Mesh-Based Surrogate for Crashworthiness Field Prediction under Large Geometric Variation

Nonlinear finite element crash simulations are accurate but computationally expensive, limiting their use in iterative design optimisation. Machine-learning surrogate models based on graph neural networks (GNNs) offer a faster alternative. Message-passing GNNs are widely used for mesh simulation, and their shared node and edge update functions are relatively generalisable across varying graph structures. By contrast, non-shareable edge-specific aggregation layers can capture nonlinear relationships more accurately but usually require fixed graph connectivity, which limits generalisability. This paper presents Mask-Morph Graph U-Net (MMGUNet), a practical approach to addressing the limitation of hierarchical Graph U-Net architectures that use edge-specific downsampling and upsampling layers. Fixed coarse graph connectivity is required for edge-specific layers. To retain this while improving spatial correspondence, the proposed method morphs the coarsened graph hierarchy to each input mesh using feature-aligned barycentric parameterisation before constructing cross-graph edges. It further applies node masking during supervised pretraining, followed by parameter-efficient fine-tuning in which high-parameter edge-specific layers are frozen. The proposed approach is evaluated in in-distribution, out-of-distribution, and cross-component transfer settings using mean Euclidean distance and maximum intrusion percentage error. Results show that coarse-graph morphing improves test accuracy relative to a fixed-coarse-graph baseline, while masked supervised pretraining reduces the train-test discrepancy and improves data efficiency during transfer. The proposed model also achieves lower prediction error compared with external baselines. These results demonstrate a practical route toward reusable, data-efficient mesh-based surrogate modelling for crashworthiness design exploration.

Haoran Li, Tobias Lehrer, Yingxue Zhao +5

Dyson School of Design Engineering, Imperial College London, London, UK · TUM School of Engineering and Design, Technical University of Munich, Munich, Germany · Faculty of Mechanical Engineering, OTH Regensburg, Regensburg, Germany +1

Neural Surrogate ModelingGraph Neural Networks
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May 13, 2026

Toward AI-Driven Digital Twins for Metropolitan Floods: A Conditional Latent Dynamics Network Surrogate of the Shallow Water Equations

AI-driven flood digital twins demand fast hydrodynamic surrogates for ensemble forecasting and observation assimilation. Yet even GPU-accelerated two-dimensional shallow water equation (SWE) solvers still require ∼55\sim 55 minutes per 9696-hour run on a ∼4.2\sim 4.2-million-active-cell metropolitan basin (the DesPlaines River basin at 30 m30\,\mathrm{m} resolution), making such workloads prohibitive at native resolution. We present the Conditional Latent Dynamics Network (CLDNet): a low-dimensional latent neural ODE driven by rainfall, paired with a coordinate-based decoder conditioned on static terrain (elevation, slope, Manning roughness) that reconstructs depth and discharge at arbitrary query points. Pointwise decoding decouples memory from grid size and handles irregular watersheds natively, enabling metropolitan-scale training on a single compute node and direct queries at exact gauge coordinates without raster snapping. We evaluate CLDNet on a synthetic 250,000250{,}000-cell Texas benchmark and on a new DesPlaines case study of 114114 real-rainfall StageIV storms whose reference simulator we validate against United States Geological Survey (USGS) gauges at the April2013 flood-of-record (Nash--Sutcliffe efficiency 0.570.57--0.940.94 on mean-recentered water-surface elevation). CLDNet roughly halves the relative root-mean-squared error of an unconditional baseline, outperforms regular-grid VAE--ConvLSTM and FNO baselines on the Texas benchmark (both presuppose a Cartesian grid and do not apply to the irregular Des~Plaines watershed), reaches a critical success index of ≈86%\approx 86\% at the 0.5 m0.5\,\mathrm{m} inundation threshold, and produces a full 9696-hour basin-wide forecast in ∼29\sim 29 seconds -- a ∼115×\sim 115\times speedup.

Phillip Si, Yuan Qiu, Omar Sallam +4

School of Computational Science and Engineering, Georgia Institute of Technology, 756 West Peachtree Street Northwest, Atlanta, 30308, GA, USA · Environmental Science Division, Argonne National Laboratory, 9700 S Cass Ave, Lemont, 60439, IL, USA

Digital TwinsPDE Surrogate ModelingFlood ForecastingNeural Surrogate ModelingSpatiotemporal ForecastingNeural ODEs+1
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May 13, 2026

Neural Surrogate Forward Modelling For Electrocardiology Without Explicit Intracellular Conductivity Tensor

Accurate forward modelling is essential for non-invasive cardiac electrophysiology, particularly in atrial fibrillation, where electrical activation is highly disorganised. Conventional physics-based forward models require explicit specification of intracellular conductivity tensors, which are not directly measurable in clinical practice and introduce structural modelling errors. This proof-of-concept study presents a deep learning approach that learns a direct mapping from left atrial intracellular electrical potentials to far-field ECGs without requiring explicit intracellular conductivity inputs at inference time. Despite training only on 74 subjects, the model achieved an R2 of 0.949 \pm 0.037, highlighting potential to reduce structural uncertainty and improve non-invasive AF assessment.

Shaheim Ogbomo-Harmitt, Cesare Magnetti, Jakub Grzelak +1

King’s College London, Floor 3, Lambeth Wing St Thomas’ Hospital Westminster Bridge Road, London, SE1 7EH · Floor 3, Lambeth Wing St Thomas’ Hospital Westminster Bridge Road, London, SE1 7EH · PhysicsX, 1 Leonard Circus, London EC2A 4DQ

Neural Surrogate ModelingElectrocardiography
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May 13, 2026

Local Inverse Geometry Can Be Amortized

Nonlinear inverse problems often trade inexpensive but fragile first-order updates against curvature-aware methods such as Gauss-Newton and Levenberg-Marquardt, which obtain stronger directions by repeatedly solving Jacobian-based linearized systems. We propose a learned alternative: amortize local inverse geometry into a reusable reverse operator. Our framework learns a bidirectional surrogate, Deceptron, and deploys it through D-IPG (Deceptron Inverse-Preconditioned Gradient), an iterative solver that pulls residual-corrected measurement-space proposals back to latent space. The key mechanism is a Jacobian Composition Penalty (JCP), which trains the reverse Jacobian to act as a local left inverse of the forward Jacobian; its runtime counterpart, RJCP, measures the same inverse-consistency error along optimization trajectories. We prove that D-IPG is first-order equivalent to damped Gauss-Newton under local pseudoinverse consistency, with deviation controlled by composition error and conditioning. Across seven PDE inverse-problem benchmarks, D-IPG outperforms standard baselines, achieves 94.8% mean success across the six-problem reliability suite, and reaches comparable or better recovery quality at up to 77x lower inference-time solve cost on the main benchmarks.

Aaditya L. Kachhadiya

Independent Researcher Surat, India

Neural Surrogate ModelingInference-Time OptimizationAmortized InferenceLearning to OptimizePDE Inverse Problems
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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

Keeping Score: Adaptive, Tuning-Free Loss Weighting for Score-Augmented Neural Ratio Estimation

Neural likelihood surrogates (e.g., Neural Ratio Estimation) for stochastic process models are commonly trained via probabilistic classification on simulated data, which forces a tradeoff between surrogate quality and training costs. For structured models where the exact score ∇θlog⁡p(x∣θ)\nabla_θ\log p(x \mid θ) is available, this information can be incorporated into training by augmenting the cross-entropy loss with a score-matching term. However, the optimal weighting of the two losses is not known a priori, and selecting it by hand requires expensive tuning that undercuts the computational savings. We propose an adaptive, tuning-free algorithm that sets the score loss weights during training based on loss gradients, adding minimal overhead to standard classifier training. We evaluate our approach on case studies involving network dynamics and spatial processes, demonstrating that it improves surrogate quality at a drastically lower computational cost than generating more training data. Notably, in some cases, our approach achieves downstream inference performance equivalent to a 10x increase in training data with less than a 1.1x increase in training time.

Alexander Shen, Mikael Kuusela

Department of Statistics and Data Science Carnegie Mellon University Pittsburgh, PA 15213

Neural Surrogate ModelingSimulation-Based Inference
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May 12, 2026

When Does Equivariance Help? Canonical Alignment in Neural Fluid Surrogates

Neural surrogates can accelerate computational fluid dynamics (CFD) simulations by orders of magnitude, but practical deployment in engineering and healthcare applications requires architectures that scale to high-resolution meshes and learn effectively from limited data. Explicit equivariance offers a principled inductive bias, yet its accuracy benefits may depend on the prediction task and the distribution of anatomical orientations. We investigate this dependence across three hemodynamic benchmarks with different degrees of natural canonical alignment. To support this study, we introduce the Anchored-Branched Geometric Algebra Transformer (AB-GATr), an E(3)E(3)-equivariant surrogate that efficiently predicts coupled surface and volume quantities. Across these benchmarks, AB-GATr consistently outperforms the evaluated non-equivariant models, including variants trained with rotational augmentation, while achieving accuracy competitive with E(3)E(3)-equivariant LaB-GATr at substantially lower training cost. In comparison, rotational augmentation provides inconsistent benefits across architectures and can reduce accuracy. A controlled experiment on ShapeNet-Car shows that strong canonical alignment can favor non-equivariant models, but their accuracy generally deteriorates as training orientations broaden and can decline sharply under broader test rotations. We further investigate these patterns using extended symmetry-breaking diagnostics and probes of the predictive information associated with canonical alignment across all benchmarks. Together, these results support explicit equivariance for the evaluated hemodynamic tasks with natural orientation variation, while showing that its accuracy benefits depend on the task and orientation distribution.

Patryk Rygiel, Julian Suk, Kak Khee Yeung +2

Department of Applied Mathematics Technical Medical Centre Cardiovascular Health Technology Centre University of Twente · Department of Computer Science Munich Center for Machine Learning Technical University of Munich · Department of Surgery Amsterdam UMC, Location University of Amsterdam Atherosclerosis & Aortic diseases Amsterdam Cardiovascular Sciences

Neural Surrogate ModelingEquivariant Neural NetworksComputational Fluid Dynamics
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May 12, 2026

Crash Assessment via Mesh-Based Graph Neural Networks and Physics-Aware Attention

Full-vehicle crash simulations are computationally expensive, limiting their use in iterative design exploration. This work investigates learned hybrid surrogate models (MeshTransolver, MeshGeoTransolver, and MeshGeoFLARE) for predicting time-resolved structural deformation fields in an industrial lateral pole-impact benchmark. We evaluate whether neural surrogates can reproduce full-field crash kinematics with sufficient accuracy, spatial regularity, and structural plausibility for engineering interpretation. The proposed architectures combine local mesh message passing, geometry-aware global attention, and sparse contact-aware correction for autoregressive crash rollout. We compare mesh-based graph neural networks, attention-based geometric models, and hybrid architectures under a common training and hyperparameter configuration. The hybrid models capture both short-range structural interactions and long-range deformation patterns, while a sparse contact-aware variant assesses the effect of dynamic proximity interactions during rollout. On a 25-sample full-vehicle test set, the best hybrid model achieves a temporal mean root-mean-square error of 3.20 mm. While geometry-aware attention baselines are quantitatively competitive, qualitative side-view inspection shows they can introduce local spatial noise and deformation irregularities that complicate structural interpretation. In contrast, hybrid mesh-attention models provide the best balance between scalar accuracy, survival-space consistency, and physically interpretable displacement fields. These results suggest that crash surrogate assessment should combine global error metrics with downstream safety-relevant quantities and qualitative field inspection. The proposed methodology enables fast full-field predictions while preserving essential structural information for industrial crash-engineering analysis.

Gabriel Curtosi, Carlos Manuel Ruiz Ruiz, Fabiola Cavaliere +1

SEAT S.A., Barcelona, Spain · IDIADA Automotive Technology S.A., Santa Oliva, Spain

Neural Surrogate ModelingGraph Neural NetworksStructural MechanicsPhysics-Based Simulation
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May 11, 2026

Neural Statistical Functions

Classical deep learning typically operates on individual cases. Despite its success, real-world usage often requires repeated inference to estimate statistical quantities for complex decision-making tasks involving uncertainty or extreme-value analysis, resulting in substantial latency. We introduce neural statistical functions, a new family of models learned from pre-trained single-sample predictors and scattered data samples, which can directly infer statistics over continuous operating condition ranges without explicit sampling. By introducing the notion of prefix statistics, we transform and unify diverse statistical functions (e.g., integrals, quantiles, and maxima) into an interval-conditional framework, in which a principled identity between the prefix statistics and the individual-case regression serves as the learning objective. Neural statistical functions achieve strong performance in estimating essential statistics of complex physical processes, including accumulated energy in dynamical systems, quantiles of aerodynamic responses, and maximum stress in crash processes, while achieving up to a 100×\times reduction in model evaluations.

Daniel Xu, Yuxin Xie, Minghao Guo +2

Columbia University · MIT CSAIL

Neural Surrogate ModelingEfficient Neural Network Inference
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May 10, 2026

From Regression to Inference: Meta-Learning Predictors for Neural Architecture Search

Prediction-based approaches are widely used in neural architecture search (NAS), where a predictor estimates the performance of candidate architectures to guide selection. However, existing predictors are typically trained via supervised regression on limited samples, leading to overfitting and poor generalization to unseen architectures. In this work, we propose a fundamentally different formulation that models performance prediction as a conditional function inference problem using a Convolutional Neural Process (ConvNP) with meta-learning capabilities. Instead of fitting a fixed mapping to limited samples, our approach meta-learns to infer performance from partial observations by training with context-target splits across a group of synthesized tasks, explicitly optimizing for generalization under data scarcity and aligning the training procedure with the deployment setting in NAS. We further design simple yet effective meta-features for cell-based architectures and evaluate our method on NAS-Bench-101 and NAS-Bench-201. Extensive experiments show that our approach consistently improves top-K ranking quality and achieves the state-of-the-art architecture selection using limited samples.

Liping Deng, MingQing Xiao

Department of Mathematics University of California, Riverside Riverside, CA 92507 USA · School of Mathematical and Statistical Sciences Southern Illinois University Carbondale Carbondale, IL 62901 USA

Neural Surrogate ModelingMeta-LearningNeural ProcessesNeural Architecture Performance PredictionNeural Architecture Search
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May 9, 2026

M3^3: Reframing Training Measures for Discretized Physical Simulations

Neural surrogate models for physical simulations are trained on discretized samples of continuous domains, where the induced empirical measure leads to uneven supervision, biasing optimization and causing spatial inconsistencies in physical fidelity. To mitigate this measure-induced bias, we propose M3^3 (Multi-scale Morton Measure), a scalable framework that balances training measures by partitioning space according to physical variation and allocating supervision across multiple scales. Applied to three industrial-scale datasets with diverse discretizations, M3^3 consistently improves predictions in the continuous physical domain, achieving up to 4.7×\times lower error in large-scale volumetric cases. These gains persist under aggressive subsampling (160M →\rightarrow 16M →\rightarrow 1.6M points), where M3^3-trained models outperform those trained on higher-resolution data, reducing physics-weighted relative L2L_2 error by 3--4×\times and the corresponding MSE by up to 13×\times. These results highlight data distribution as a key factor in operator learning and position M3^3 as a scalable, data-efficient approach for physically consistent modeling. Code is available at https://github.com/PhysDataRefine/M3.

Yuan Mei, Xingyu Song, Xiaowen Song +1

1Zhejiang University · *Visiting student at The University of Tokyo from Zhejiang University. · 2The University of Tokyo

Neural Surrogate ModelingAdaptive SamplingPDE Operator LearningPhysics-Based Simulation
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May 9, 2026

Inpainting physics: self-supervised learning for context-driven fluid simulation

Neural surrogate models for computational fluid dynamics (CFD) are typically trained as forward operators that map explicit problem specifications, such as geometry and boundary conditions, to solution fields. This ties the model to the conditioning variables seen during training and limits reuse under boundary-condition shifts or local geometry changes. We propose to reformulate steady CFD inference as an inpainting problem: instead of training on explicit boundary conditions, we learn a self-supervised prior over velocity fields and impose boundary constraints only during inference by fixing known regions such as inlet, outlet or unchanged regions from previous simulations. To scale this idea to large 3D meshes, we introduce a local neighbourhood tokeniser that represents high-resolution velocity fields as compact spatial latent tokens and train latent flow-matching and masked-autoencoder models on these tokens. On intracranial aneurysm hemodynamics, our method reconstructs full velocity fields from sparse boundary context, outperforms supervised neural surrogates under boundary-condition and dataset shift and enables local geometry editing by reusing unchanged simulation context. These results suggest that viewing CFD inference as context-conditioned inpainting can turn neural surrogates from task-specific predictors into reusable flow priors.

Jonas Weidner, Yeray Martin-Ruisanchez, Daniel Rueckert +2

AI for Image-Guided Diagnosis and Therapy, Technical University of Munich · Munich Center for Machine Learning (MCML) · AI in Healthcare and Medicine, Technical University of Munich +1

Neural Surrogate ModelingSelf-Supervised LearningComputational Fluid Dynamics
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May 8, 2026

Neural Operators as Efficient Function Interpolators

Neural operators (NOs) are designed to learn maps between infinite-dimensional function spaces. We propose a novel reframing of their use. By introducing an auxiliary base-space, any finite-dimensional function can be viewed as an operator acting by composition on functions of the base-space. Through a range of benchmarks on analytic functions of increasing complexity and dimensionality, we demonstrate that NOs can match or outperform standard multilayer perceptrons and Kolmogorov--Arnold Networks in accuracy while requiring significantly fewer parameters and training time. As a real-world application, we apply a two-dimensional Tensorized Fourier Neural Operator (TFNO) to the nuclear chart, learning a correction to state-of-the-art nuclear mass models as a partially observed residual field. A TFNO ensemble reaches a held-out root-mean-square error of 198.2 keV, placing it among the best recent neural-network approaches while retaining high parameter efficiency and short training times. More broadly, these results introduce NOs as a scalable framework for finite-dimensional function interpolation, from analytic benchmarks to structured scientific data.

Vasilis Niarchos, Angelos Sirbu, Sokratis Trifinopoulos

Department of Physics, CCTP and ITCP, University of Crete, 71303, Greece · Theoretical Physics Department, CERN, Geneva, Switzerland · Physik-Institut, Universität Zürich, 8057 Zürich, Switzerland

Neural Surrogate ModelingFourier Neural OperatorNeural Operators
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May 8, 2026

GNN for Structural Displacement Prediction

Accurate prediction of structural displacements under external loading is fundamental to structural health monitoring and seismic safety assessment. Although the finite element method (FEM) remains the prevailing approach because of its high accuracy, its considerable computational cost restricts its suitability for real-time monitoring applications. To address this limitation, this study proposes a data-driven framework based on Graph Neural Networks (GNNs), in which structural systems are represented as graphs with joints modeled as nodes and structural members as edges. By incorporating both geometric and mechanical properties into the graph representation, the proposed model learns the relationship between applied loads and structural responses directly from simulated data. A synthetic dataset was generated from a two-story frame structure using ANSYS, and both a conventional Neural Network (NN) and a GNN were trained for comparison. The results show that the proposed GNN framework predicts displacements and rotations with high accuracy and outperforms the NN model, demonstrating its potential as a fast and efficient alternative to traditional FEM-based analysis.

Hung-Fu Chang, Tzu-Kang Lin, Yung-Li Cheng

R. B. Annis School of Engineering University of Indianapolis Indianapolis United States · Department of Civil Engineering National Yang Ming Chiao Tung University Hsinchu Taiwan

Neural Surrogate ModelingGraph Neural NetworksStructural Health Monitoring
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May 8, 2026

CarCrashNet: A Large-Scale Dataset and Hierarchical Neural Solver for Data-Driven Structural Crash Simulation

Crash simulation is a cornerstone of modern vehicle development because it reduces the need for costly physical prototypes, accelerates safety-driven design iteration, and increasingly supports virtual testing workflows. At the same time, modeling structural crash mechanics remains exceptionally challenging: the response is governed by nonlinear contact, large deformation, material plasticity, failure, and complex multi-body interactions evolving over space and time on high-resolution finite-element meshes. In this work, we introduce CarCrashNet, a public high-fidelity open-source benchmark for data-driven structural crash simulation. CarCrashNet combines component-scale and full-vehicle simulations in a multi-modal format, including more than 14,000 bumper-beam pole-impact simulations with varying geometry, materials, and boundary conditions, together with 825 full-vehicle crash simulations built from three industry-standard vehicle models of increasing structural complexity: Dodge Neon, Toyota Yaris, and Chevrolet Silverado. To establish the reliability of the benchmark, we validate our open-source finite-element workflow based on OpenRadioss against both experimental crash data and the commercial solver Ansys LS-DYNA. We also introduce CrashSolver, a machine-learning model designed for full-vehicle crash prediction from high-resolution finite-element crash data. We further perform extensive benchmarking across the released datasets and evaluate CrashSolver against state-of-the-art geometric deep learning and transformer-based neural solvers. Our results position CarCrashNet as a foundation for reproducible research in structural simulation, crashworthiness modeling, and AI-driven virtual crash testing. The dataset is available at https://github.com/Mohamedelrefaie/CarCrashNet.

Mohamed Elrefaie, Dule Shu, Matthew Klenk +1

Department of Mechanical Engineering MIT Cambridge, MA, USA · Future Product Innovation Toyota Research Institute Los Altos, CA, USA

Neural Surrogate ModelingStructural MechanicsSynthetic Benchmark GenerationPhysics-Based Simulation
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May 7, 2026

Physics-Based Flow Matching for Full-Field Prediction of Silicon Photonic Devices

Designing photonic integrated circuits requires accurate electromagnetic field simulations, which remain computationally expensive even for simple device geometries. We present PIC-Flow, a generative neural surrogate that predicts electromagnetic field distributions for photonic devices given their geometry and operating wavelength as an alternative to costly finite-difference time-domain (FDTD) simulations. Our approach combines three key ideas: (i) conditional flow matching as the generative framework, learning a velocity field that transports Gaussian noise to physically valid field solutions; (ii) a real-valued U-Net operating on split real and imaginary field channels; and (iii) physics-constrained training through a Helmholtz residual loss enforcing ∇2Ez+k02εEz=0\nabla^2 E_z + k_0^2 \varepsilon E_z = 0. We introduce an interface-aware masking scheme for the Helmholtz residual that excludes dielectric boundary pixels where finite-difference stencil errors dominate, yielding a physically meaningful compliance metric. The data set consists of 22,500 ground-truth FDTD simulations split evenly between multimode interferometers, Y-branches, and directional couplers at λ=1.55 μλ=1.55\,μm in an 80/10/10 split between training, validation, and test sets. We evaluate ablations on the network against the held out test devices and also show that the model generalizes to held out device classes such as S-bends, tapers, and cascaded Y-branches. Rather than a drop-in replacement for FDTD, this work establishes a foundation that, with broader data coverage, more compute, and further training optimization, could scale toward broadband, device-agnostic field prediction with dramatically improved runtime for rapid design-space exploration of complex photonic devices and circuits.

Joseph Quaratiello, Anthony Rizzo

Thayer School of Engineering, Dartmouth College, Hanover, NH 03755

Neural Surrogate ModelingPhysics-Informed ML
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May 7, 2026

BRICKS: Compositional Neural Markov Kernels for Zero-Shot Radiation-Matter Simulation

We introduce a new strategy for compositional neural surrogates for radiation-matter interactions, a key task spanning domains from particle physics through nuclear and space engineering to medical physics. Exploiting the locality and the Markov nature of particle interactions, we create a next-particle prediction kernel using hybrid discrete-continuous transformer models based on Riemannian Flow Matching on product manifolds. The model generates variable-sized typed sets of particles and radiation side effects that are the result of the interaction of an incident particle with a material volume. The resulting kernel can be composed to simulate unseen large-scale material distributions in a zero-shot manner. Unlike mechanistic simulators, our model is designed to be differentiable, provides tractable likelihoods for future downstream applications. A significant computational speed-up on GPU compared to CPU-bound mechanistic simulation is observed for single-kernel execution. We evaluate the model at the kernel level and demonstrate predictive stability over multi-round autoregressive rollouts. We additionally release a novel 20M-event radiation-matter interaction dataset for further research.

Richard Hildebrandt, Evangelos Kourlitis, Baran Hashemi +7

Technical University of Munich · Max-Planck Institute for Mathematics in the Sciences, Leipzig, Germany · SLAC National Accelerator Laboratory +3

Neural Surrogate ModelingRiemannian Flow MatchingGenerative ModelingPhysics-Based Simulation
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May 7, 2026

Geometric Kolmogorov--Arnold Network (GeoKAN)

We introduce Geometric Kolmogorov--Arnold Networks (GeoKANs), a family of geometry-aware KAN-type models in which approximation is carried out in learned, geometry-adapted coordinates rather than in fixed Euclidean input coordinates. GeoKAN achieves this by learning a diagonal Riemannian metric that warps the input before basis expansion and feature mixing. The learned metric provides a geometric inductive bias through local length scaling and volume distortion, and in physics-informed settings it also affects the differential structure seen by the model. Within this framework, we develop three main variants, namely GeoKAN-NNMetric, GeoKAN-γγ, and LM-KAN. For LM-KAN, we further consider three basis-specific versions, LM-KAN-RBF, LM-KAN-Wav, and LM-KAN-Fourier. These variants allow us to study geometry-aware KAN models both as general function approximators and as surrogates in physics-informed learning. By stretching regions with rapid variation and compressing smoother regions, GeoKAN reallocates representational resolution in a task-dependent manner, allowing the model to place capacity where it is most needed. As a result, GeoKAN is well suited to sharp, stiff, localized, and strongly non-uniform regimes arising in scientific machine learning and differential-equation problems.

Abhijit Sen, Bikram Keshari Parida, Giridas Maiti +2

Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, USA. · Institute of Applied Geosciences, Karlsruhe Institute of Technology, Karlsruhe 76131, Germany.

Neural Surrogate ModelingMetric LearningKolmogorov-Arnold Networks
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May 6, 2026

Hierarchical Multi-Fidelity Learning for Predicting Three-Dimensional Flame Wrinkling and Turbulent Burning Velocity

High-fidelity experimental characterization of turbulent premixed flames remains limited by the cost and complexity of advanced diagnostics, particularly under elevated pressures and intense turbulence where measurements of coupled flame morphology and burning dynamics are sparse. Here, we develop a hierarchical multi-fidelity neural network framework (MuFiNNs) to address this challenge by integrating sparse high-fidelity experimental data with structured low-fidelity representations encoding dominant physical trends. The framework combines hierarchical low-fidelity construction with nonlinear multi-fidelity correction to learn coupled geometric and reactive flame behavior while recovering discrepancies that simplified models alone cannot capture. The methodology is applied to expanding turbulent premixed flames to predict three-dimensional flame wrinkling dynamics and turbulent mass burning velocity across varying fuels, pressures, and turbulence intensities. Using experimentally informed low-fidelity trend models with sparse high-fidelity measurements, MuFiNNs accurately reconstruct observed flame behavior, enable interpolation across unseen operating conditions, and demonstrate robust extrapolation beyond the training domain. Importantly, the framework remains effective in noisy, weakly structured, or experimentally inaccessible regimes where conventional data-driven approaches often fail. These results show that hierarchical multi-fidelity learning provides a scalable and physically grounded strategy for predictive combustion modeling in data-limited regimes. More broadly, this work establishes multi-fidelity scientific machine learning as a practical framework for extracting physically meaningful predictive models from sparse experiments, particularly for instability-dominated and turbulence-sensitive reactive flows where high-fidelity data acquisition is demanding.

Saghar Zolfaghari, Yu Xie, Junfeng Yang +1

Department of Mechanical and Industrial Engineering, Northeastern University, Boston, MA 02115, USA · School of Mechanical Engineering, University of Leeds, Leeds, UK

Neural Surrogate ModelingMultifidelity ModelingComputational Fluid Dynamics
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May 6, 2026

Full-chip CMP modelling based on Fully Convolutional Network leveraging White Light Interferometry

As time-to-market is crucial in the Integrated Circuit (IC) industry, speeding up layout manufacturability verifi-cation is essential. Chemical-Mechanical Polishing (CMP) plays a vital role in IC fabrication but is significantly influenced by Layout-Dependent Effects (LDE). An accurate and efficient CMP model enables design teams to correct surface unevenness before fabrication, reducing costs and accelerating the design phase. However, existing models often rely on Density Step Height (DSH) modeling, which is time-consuming for calibration and requires substantial hardware resources for fine-grained predictions. In this paper, we propose combining the advantages of two surface analysis techniques, White Light Interfer-ometry (WLI) and Atomic Force Microscopy (AFM), to train a deep learning model. This model aims to predict full-chip post-CMP nanotopography with nanometer-scale accuracy. Our deep learning model is based on a Convolutional Neural Network (CNN) and follows a two-step pipeline. The model is trained on each technique separately, resulting in a detailed full-chip CMP model.

Jules Exbrayat, Renan Bouis, Elie Sezestre +4

Univ. Grenoble Alpes, CEA, Leti, F-38000 Grenoble, France

Neural Surrogate ModelingSemiconductor Manufacturing
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May 6, 2026

Reduced-order Neural Modeling with Differentiable Simulation for High-Detail Tactile Perception

Tactile perception is key to dexterous manipulation, yet simulating high-resolution elastomer deformation remains computationally prohibitive. Finite element methods (FEM) deliver high fidelity but demand costly remeshing, while Material Point Methods (MPM) suffer from heavy particle-memory tradeoffs. We propose a {reduced-order neural simulation framework} that couples coarse-grained MPM dynamics with an implicit neural decoder to reconstruct sub-particle tactile details from compact latent states. The framework learns a continuous deformation manifold from paired high- and low-resolution simulations, enabling physically consistent, differentiable inference. Compared to the TacIPC, our method achieves over 65% faster simulation and {40% lower memory usage}, while maintaining better geometric fidelity. In tactile rendering and 3D surface reconstruction, our methods further improve accuracy by 25% and produce realistic depth images and surface mesh within a faster inference speed. These results demonstrate that the proposed reduced-order neural model enables high-detail, physically grounded tactile simulation with substantial efficiency gains for robotic interaction and optimization.

Yuhu Guo, Zhikai Shen, Jiasheng Qu +4

The University of Manchester, UK · The Chinese University of Hong Kong, Hong Kong SAR, China · University of Leeds, UK +1

Neural Surrogate ModelingMaterial Point MethodReduced-Order ModelingDifferentiable PhysicsTactile Sensing for Robotic ManipulationDeformable Object Simulation
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May 6, 2026

Counter-Dyna: Data-Efficient RL-Based HVAC Control using Counterfactual Building Models

Model-based reinforcement learning (MBRL) offers a promising approach for data-efficient energy management in buildings, combining the strengths of predictive modeling and reinforcement learning. While previous MBRL methods applied to HVAC control have reduced training data requirements, they still require several months of interaction with the building to learn a satisfactory control policy. A key reason is that existing surrogate models attempt to predict the entire state-space, including weather and electricity prices that are unaffected by control actions, or completely ignore these variables. Addressing these issues, we propose Counter-Dyna, a method that enhances the data-efficiency of Dyna, an MBRL method. We create data-efficient counterfactual surrogate models (CSM) by leveraging invariances in the state-space. Using a CSM in Dyna speeds up RL training measured in environment interaction data compared to previous results. In comparison with previous state-of-the-art that used 6-12 months of environment interactions, our method needs only 5 weeks. We evaluate our method in a large simulation study using the literature standard BOPTEST framework and proximal policy algorithm (PPO) as the RL algorithm. Our results show cost-saving potentials of 5.3% to 17.0% in a hypothetical deployment scenario. Our work is a significant step towards making real-world deployment of RL algorithms in HVAC control practically viable.

Jan Marco Ruiz de Vargas, Fabian Raisch, Zoltan Nagy +2

Technical University of Munich Munich, Germany · Technical University of Applied Sciences Rosenheim Rosenheim, Germany · Eindhoven University of Technology Eindhoven, Netherlands +1

Neural Surrogate ModelingBuilding Energy ManagementFeedback ControlSample-Efficient RLModel-Based RLHeating, Ventilation, and Air Conditioning Control
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May 6, 2026

Geometry-Aware Neural Optimizer for Shape Optimization and Inversion

Geometry is central to PDE-governed systems, motivating shape optimization and inversion. Classical pipelines conduct costly forward simulation with geometry processing, requiring substantial expert effort. Neural surrogates accelerate forward analysis but do not close the loop because gradients from objectives to geometry are often unavailable. Existing differentiable methods either rely on restrictive parameterizations or unstable latent optimization driven by scalar objectives, limiting interpretability and part-wise control. To address these challenges, we propose Geometry-Aware Neural Optimizer (GANO), an end-to-end differentiable framework that unifies geometry representation, field-level prediction, and automated optimization/inversion in a single latent-space loop. GANO encodes shapes with an auto-decoder and stabilizes latent updates via a denoising mechanism, and a geometry-informed surrogate provides a reliable gradient pathway for geometry updates. Moreover, GANO supports part-wise control through null-space projection and uses remeshing-free projection to accelerate geometry processing. We further prove that denoising induces an implicit Jacobian regularization that reduces decoder sensitivity, yielding controlled deformations. Experiments on three benchmarks spanning 2D Helmholtz, 2D airfoil, and 3D vehicles show state-of-the-art accuracy and stable, controllable updates, achieving up to +55.9% lift-to-drag improvement for airfoils and ~7% drag reduction for vehicles.

Guoze Sun, Tianya Miao, Haoyang Huang +4

Gaoling School of Artificial Intelligence, Renmin University of China

Neural Surrogate ModelingGeometric Representation LearningConstrained OptimizationDifferentiable Optimization
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May 5, 2026

Capabilities of Auto-encoders and Principal Component Analysis of the Reduction of Microstructural Images; Application on the Acceleration of Phase-Field Simulations

In this work, a data-driven framework based on Phase-Field simulations data is proposed to highlight the capabilities of neural networks to ensure accurate low dimensionality reduction of simulated microstructural images and to provide time-series analysis. The dataset was indeed constructed from high-fidelity Phase-Field simulations. Analyses demonstrated that the association of auto-encoder neural networks and principal component analyses leads to ensure efficient and significant dimensionality reduction: 1/196 of reduction ratio with more than 80% of accuracy. These findings give insight to apply analyses on data from the latent dimension. Application of Long Short Term Memory (LSTM) neural networks showed the possibility of making next frame predictions; that makes possible the acceleration of Phase-Field simulation without the need of high computing resources. We discussed the application of such a framework on various areas of research. Different methods are proposed from the conducted analyses, in order to ensure dimensionality reduction, including auto-encoders, principal component analysis and Artificial Neural Networks, and time-series analysis, including LSTM and Gated Recurrent Unit (GRU).

Seifallah Fetni, Thinh Quy Duc Pham, Truong Vinh Hoang +4

University of Liège, UEE Research Unit, MSM division, allée de la Découverte, 9 B52/3, B 4000 Liège, Belgium · Chair of Mathematics for Uncertainty Quantification, RWTH-Aachen University, 52056 Aachen, Germany · Institute of Strategy Development, Thu Dau Mot University, 75100 Binh Duong Province, Viet Nam

Neural Surrogate ModelingAutoencodersDimensionality Reduction
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May 5, 2026

Model synthesis and identifiability analysis of stiff chemical reaction systems with inVAErt networks

We consider the problem of learning data-driven replicas for stiff systems of ordinary differential equations arising in chemical kinetics that can be evaluated with high computational efficiency. We first focus on training emulators for families of reaction equations under varying reaction rates, using conditional residual networks or long-short term memory architectures. We then apply a recently proposed data-driven framework known as ``inVAErt networks'' to address the ill-posed inverse problem of inferring reaction rates, integration time, and possibly initial conditions from a target set of species concentrations - a problem that has received relatively little attention in the literature. The proposed approach is demonstrated on chemical systems with reversible and irreversible kinetics, spanning 2 to 20 differential equations, 3 to 20 chemical species, and 3 to 25 reaction rate parameters. Relative root mean squared errors produced by the proposed emulators range from 10−510^{-5} for lower-dimensional systems to 10−410^{-4} and 10−310^{-3} for an air pollution model and a hydrogen-air reaction system, respectively. Manifolds of non-identifiable reaction rates recovered by the proposed approach can be analytically verified for simple systems and are consistent with local identifiability analysis in higher dimensions.

Sreejata Dey, Guoxiang Grayson Tong, Jonathan F. MacArt +1

Department of Applied and Computational Mathematics and Statistics, University of Notre Dame · Department of Pediatrics, Stanford University · Department of Aerospace and Mechanical Engineering, University of Notre Dame

Neural Surrogate ModelingParameter IdentifiabilityNonlinear System Identification
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