Neural Surrogate Modeling

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39 papers in the last four weeks, up 388% on the four weeks before. 0.4% of all new papers.

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Latest papers 254

Jul 31, 2026cs.LG

HERO: History-Enriched Rollout Training for Long-Horizon Autoregressive Neural Operators

Neural operators provide fast surrogates for time-dependent partial differential equations (PDEs) by applying a learned evolution operator recursively to its own predictions, but this autoregressive rollout feeds every prediction error back as input, so local errors accumulate. Existing rollout-training strategies reduce the mismatch between training inputs and self-generated states, yet their supervision still measures only the absolute discrepancy from the ground-truth trajectory. Such supervision is therefore uninformative about whether the operator has overcome the long-horizon failure behaviors it exhibited earlier during optimization. We propose history-enriched rollout training (HERO), which augments conventional absolute trajectory supervision with relative supervision derived from the model's optimization history. HERO ranks detached candidate rollouts from a periodically refreshed lagged operator, the current model, and a perturbed input by rollout error, spectral discrepancy, energy drift, and error growth, and selects the strongest failure trajectory as reference. This reference enters a margin-based objective as a fixed comparison baseline, inducing a bounded, sample-dependent reweighting of the ground-truth rollout gradient rather than an independent gradient direction, which we further analyze theoretically. Experiments on nine PDE benchmarks with spectral and attention-based backbones show that HERO consistently improves long-horizon accuracy, stable rollout length, and out-of-distribution robustness at no inference-time cost. These results indicate that history-enriched relative supervision is effective for stabilizing long-horizon autoregressive prediction.

Jiaquan Zhang, Shuxu Chen, Haifan Meng +6

School of Computer Science and Engineering, UESTC · Electronics and Information Convergence Engineering, KHU · Department of Mathematical Sciences, UOL +3

Neural Surrogate Modeling PDE Operator Learning Neural Operators

Jul 31, 2026nlin.CD

Extrapolating the emergence of Hamiltonian chaos with random-feature Hamiltonian neural networks

Machine learning of Hamiltonian dynamics has driven growing interest in Hamiltonian neural networks (HNNs), which encode Hamilton's equations of motion into the learning architecture. Despite this progress, it remains unknown whether such networks can predict dynamical regimes absent from their training data, in particular the broad chaotic sea that emerges beyond the observed parameter interval. We address this question using a parameter-aware random-feature Hamiltonian neural network (RF-HNN). Trained using data from only a small number of control-parameter values at which invariant tori dominate, the RF-HNN predicts autonomous long-time dynamics at unseen parameter values where mixed phase space develops and chaotic regions expand, with no data from that regime used in training or model selection. The method is demonstrated across four two-degree-of-freedom Hamiltonian families, including the Hénon-Heiles system. Using Poincaré-section geometry and finite-time Lyapunov exponents, we show that the RF-HNN reproduces the breakup of regular structures and the emergence and growth of chaotic regions, whereas conventionally trained HNNs with the same Hamiltonian structure remain too regular. These results show that what decides parameter extrapolation is not Hamiltonian structure alone but how the fitted Hamiltonian continues in the control parameter. To our knowledge, this is the first demonstration that a learned Hamiltonian can qualitatively extrapolate from predominantly regular dynamics into a broad chaotic sea absent from training.

Jaesung Choi

Center for Artificial Intelligence and Natural Sciences, Korea Institute for Advanced Study, Seoul 02455, Korea

Neural Surrogate Modeling Dynamical Systems Hamiltonian Neural Networks Chaotic Dynamical Systems Hamiltonian Dynamics

Jul 31, 2026stat.ML

Structured Neural Chaos: An Adaptive Surrogate Modeling Framework for Functional Uncertainty Quantification and Global Sensitivity Analysis

Variance-based global sensitivity analysis (GSA) plays a key role in uncertainty quantification by identifying the contributions of uncertain inputs to the variability of the model response. The repeated model evaluations required for these tasks are often prohibitively expensive; surrogate models provide an efficient alternative by constructing inexpensive approximations of the underlying system response. Constructing surrogate models that combine scalability and interpretability for systems with high-dimensional stochastic inputs and functional responses remains challenging, particularly when sensitivity estimates are required across spatial or temporal domains. Polynomial chaos expansion (PCE) provides an effective framework for uncertainty propagation and sensitivity analysis due to its orthogonal structure and direct relationship with variance-based sensitivity measures. However, PCE suffers from the curse of dimensionality, whose computational burden is amplified for problems with functional responses. In this work, we introduce the Structured Neural Chaos (sNC) expansion as a surrogate modeling framework for variance-based GSA, inspired by the interpretability and orthogonal structure of PCE. The proposed framework retains the interpretability of structured decompositions while leveraging the expressive power of neural networks. The sNC expansion mirrors a truncated functional ANOVA decomposition, where each interaction component admits a separable low-rank approximation whose basis functions and coefficients are parameterized by neural networks. The expansion is constructed sequentially, adaptively identifying the dominant modes within each ANOVA subspace and determining the effective complexity of the representation. The resulting structure enables the extraction of statistical and sensitivity quantities directly from the coefficients of the sNC expansion at negligible cost.

Isabel Corona Guevara, Yeping Hu

Department of Mathematical and Statistical Sciences, University of Colorado Denver, Denver, 80204, CO, USA · Computational Engineering Division, Lawrence Livermore National Laboratory, Livermore, 94550, CA, USA

Neural Surrogate Modeling Uncertainty Quantification

Jul 30, 2026physics.ao-ph

Rescene: band-limited stochastic forcing turns a frozen neural weather operator into a climate emulator

Over the past few years, the rapid development of machine learning (ML) models for weather forecasting has produced deterministic models whose medium-range skill matches or exceeds that of the European Centre for Medium-Range Weather Forecasts (ECMWF)'s high-resolution forecast (HRES). However, when these models are integrated freely beyond the horizon they were trained for, they blow up, drift, or lose their seasonal cycle, and retraining them for stability is expensive. We therefore ask what can be recovered from a strictly frozen backbone. We present Rescene, a 0.4 M-parameter wrapper around a frozen 1.5 degree, 6-hourly vision-transformer operator, developed using ERA5 reanalysis data and comprising a deterministic "slow clock" (0.33 M) that blends the forecast toward a lead-aware day-of-year climatology and a generative head (0.06 M) that adds a spectrally shaped stochastic perturbation at every step. The performance evaluation demonstrates that the deterministic wrapper alone is stable for decades but collapses daily variability to 40% of ERA5. Adding the generative head restores 126% (Z500) and 130% (MSLP) of the observed daily variability with pattern correlations of 0.89 and 0.92, recovers 82% of the observed blocking frequency, keeps the ensemble calibrated (spread-skill ratio 0.78-0.97 from day 7 to day 90), and integrates for 100 years with no detectable drift (+0.008 +/- 0.014 K per century). Moreover, because the perturbation is band-limited to total wavenumber

k \le 20

, the small scales are never forced, yet realistic

k \ge 20

power is sustained: a direct decomposition of the 6-hourly energy budget shows that the frozen operator supplies 28 times more energy than the perturbation at

k \ge 40

, with a fractional growth rate 247 times larger at the grid scale than at planetary scales.

Minjong Cheon

Department of Computer Science and Engineering, Sejong University, Seoul, South Korea

Neural Surrogate Modeling Climate Modeling

Jul 30, 2026cond-mat.mtrl-sci

Deep Learning for Accelerated Long-Horizon Forecasting of Multicomponent Multiphase Microstructure Evolution in High-Entropy Alloys

Phase-field modeling provides a powerful approach for predicting microstructure evolution but becomes computationally prohibitive for multicomponent and multiphase systems over large spatial and temporal scales. This work presents an AE-GCN-LSTM surrogate framework for long-horizon forecasting of microstructure evolution in the multicomponent AlCrFeNi high-entropy alloy system containing coexisting BCC and FCC phases. A multi-head autoencoder compresses the four elemental concentration fields and phase-field order parameter into latent representations, which are formulated as graphs for learning their spatial and temporal evolution. The framework accurately forecasts microstructure evolution over horizons extending to 3,000,000 simulation timesteps. Its robustness is systematically evaluated under previously unseen conditions without retraining, fine-tuning, or parameter adaptation. These evaluations include variations in FCC precipitate size and initial position, microstructures containing one, two, and five FCC precipitates, and complex phase interactions involving precipitate merging and splitting. Although trained only on 100 x 100 computational domains containing a single nominal alloy composition, the framework is successfully transferred to larger 256 x 256 and 512 x 512 systems and to previously unseen AlCrFeNi compositions. Across the evaluated configurations, the model preserves the dominant phase morphology and compositional evolution while providing computational speedups ranging from approximately 7200 to 62300 relative to conventional phase-field simulations. These results demonstrate that latent graph-based AE-GCN-LSTM forecasting provides a scalable and computationally efficient surrogate for long-horizon simulation of multicomponent, multiphase microstructures and offers a promising foundation for high-throughput alloy design.

Hamidreza Razavi, Nele Moelans

Department of Materials Engineering, KU Leuven2026 Kasteelpark Arenberg 44 Bus 2450, 3001 Leuven, Belgium

Neural Surrogate Modeling Materials Science Spatiotemporal Forecasting

Jul 30, 2026cs.LG

Event-Structured Physics-Informed Neural Networks for Differentiable Critical Clearing Boundaries

Transient-stability assessment determines whether a power system can recover after a disturbance and is therefore essential to preventing generator trips and cascading outages. A key metric is the critical clearing time (CCT), which specifies the maximum time available to clear a fault before synchronism is lost. Reliable CCT estimation is challenging because complicated fault-clearing dynamics require repeated simulations over many fault severities and clearing times. We propose an event-structured physics-informed neural network (ES-PINN) that aligns its representation with the pre-fault, fault-on, and post-clearing swing dynamics and enforces exact state chaining across event interfaces. A smooth trajectory-induced stability margin defines a differentiable approximation of the CCT boundary, enabling accurate boundary extraction, local sensitivity analysis, and optional direct CCT prediction through a distilled readout. We further prove a local residual-to-trajectory-to-CCT error estimate, in which exact event chaining eliminates separate state-interface defect terms. Experiments on IEEE 9-, 14-, and 30-bus systems show that ES-PINN consistently improves held-out trajectory and stability-boundary accuracy over matched neural-surrogate baselines across mechanical and electrical contingencies with multiple clearing configurations. Additional full-network DAE validation, multi-fault experiments, and runtime analyses further demonstrate the effectiveness and computational efficiency of the proposed framework.

Baoli Hao, Chenxi Hu, Ming Zhong +1

Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA · Department of Computer Science, The Hang Seng University of Hong Kong, Sha Tin, Hong Kong · Department of Mathematics, University of Houston, Houston TX 77204, USA +1

Neural Surrogate Modeling Physics-Informed ML Power Systems

Jul 29, 2026astro-ph.IM

Emulating Cosmic Structure Formation with a Lagrangian Neural Cellular Automaton

Field-level inference of cosmological initial conditions from galaxy surveys requires a forward model that is simultaneously accurate in the non-linear regime, computationally efficient, and fully differentiable. Traditional N-body simulations are accurate but computationally prohibitive for iterative inference, while approximate solvers like Lagrangian Perturbation Theory (LPT) fail to capture the knotty halo-forming dynamics of the cosmic web at late times. We introduce the \textit{Lagrangian Neural Cellular Automaton} (LNCA), a hybrid deep learning framework that can be applied to emulate structure formation as a local, iterative dynamical process on a comoving lattice. Unlike standard Eulerian Convolutional Neural Networks (CNNs) which map fixed density fields, the LNCA operates in the Lagrangian frame, advecting the computational graph itself to follow the flow of mass. By training the network to learn only the \textit{residual} displacement corrections to the Zeldovich approximation, we achieve high-fidelity emulation of the non-linear physics while guaranteeing accuracy at large scales. We further constrain our model to produce complete trajectories, not just final states, by adopting an equivariant cellular automaton architecture, which recurrently iterates on its internal states to yield a dynamic history. The resulting model is strictly local, translationally and rotationally equivariant, and naturally supports continuous time integration, making it a reliable differentiable forward model for reconstructing the initial conditions of the universe from lightcone data. Our trained model supports percent-level precision in the power and cross spectra well into the non-linear regime (

k \lesssim 0.5 \, h \text{Mpc}^{-1}

), while requiring

\sim10^4

times fewer learned parameters than comparable models which take the form of an interpretable internal dynamic rule set.

Cooper Jacobus, Beatriz Tucci, Oliver Philcox

Department of Physics, Stanford University, Stanford, CA 94305, USA · Kavli Institute for Particle Astrophysics and Cosmology, Stanford · Leinweber Institute for Theoretical Physics, Stanford

Neural Surrogate Modeling Neural Cellular Automata

Jul 28, 2026cs.LG

Recursive transformers for semiconductor thermo-mechanical reliability

Transformer-based surrogate models are increasingly used to replace expensive first-principles simulation in engineering design. But conventional transformer architectures are often over parameterized for the small, low-dimensional datasets typical of engineering design spaces, where large simulation data is expensive to generate. Under these conditions, excess parameter capacity leads to overfitting rather than improved accuracy, while also incurring unnecessary memory and compute overhead. This motivates a shift towards architectures that focus on additional compute rather than additional learnable parameters. This paper presents a hardware-aware evaluation of three recursive transformer paradigms for surrogate thermo-mechanical analysis of advanced packages: a)Tiny Recursive Model, b) our proposed Depth Recursive transformer, c) and a simple recursive transformer. We systematically compare their predictive performance (Recall, Mean Reciprocal Rank), parameter count, computational complexity (FLOPs), providing practical design guidelines for selecting recursive transformer architectures under resource-constrained scenarios. We validate this principle on two low-dimensional engineering prediction tasks: 1) thermo-mechanical reliability analysis of advanced semiconductor packages, where stress and warpage from thermal cycling must be evaluated repeatedly across a design-of-experiments sweep under costly finite element analysis (FEA). 2) Laplace PDE iterative numerical solver for capacitance field. Overall, recursive weight-sharing transformers provide an effective and generalizable trade-off between prediction accuracy, parameter efficiency, and computational cost for small data engineering surrogate modeling.

Kart-leong Lim

Institute of Microelectronics (IME), Agency for Science, Technology and Research (A*STAR), Singapore

Neural Surrogate Modeling PDE Surrogate Modeling Recurrent Transformers

Jul 27, 2026gr-qc

Fast, accurate, and differentiable: a neural-network surrogate for NRSur7dq4 precessing binary black hole waveforms

We present a neural network surrogate model that emulates the NRSur7dq4 gravitational waveform model for precessing binary black hole mergers. The surrogate decomposes the waveform into constituent quantities and trains an independent multilayer perceptron (MLP) for each. We validate the surrogate against NRSur7dq4 on 10,000 waveforms spanning its full parameter space (

1 \leq q \leq 4

,

|χ_{A,B}| \leq 0.8

). For representative total masses between 60 and 300

M_\odot

, median sky-averaged frequency-domain mismatches range from

8.0 \times 10^{-5}

to

1.7 \times 10^{-4}

, with 95th percentiles below

10^{-3}

. On an NVIDIA L40S GPU the JAX surrogate evaluates a single waveform in about 1 ms end-to-end, roughly 10 times faster than the LALSimulation C implementation of NRSur7dq4, and sustains about 140 times the LALSimulation throughput at batch size 64, making it well suited for both low-latency parameter-estimation samplers and large-scale waveform generation. The full NRSur7dq4 NN waveform-to-likelihood pipeline is implemented in JAX and is differentiable. This is the first neural-network surrogate of a precessing numerical-relativity waveform model to combine validated NR-faithful accuracy with a fully differentiable, GPU-accelerated inference pipeline, enabling gradient-based inference approaches via automatic differentiation including Fisher information matrices, GPU-accelerated nested sampling, gradient-based MCMC and importance sampling.

Michael Pürrer, Ashwin Girish, Lucy M. Thomas +2

Department of Physics, East Hall, University of Rhode Island, Kingston, RI 02881, USA · Institute for AI & Computational Research, Carothers Library, University of Rhode Island, Kingston, RI 02881, USA · 3TAPIR, California Institute of Technology, Pasadena, California 91125, USA +2

Neural Surrogate Modeling Gravitational-Wave Astronomy Differentiable Programming

Jul 27, 2026cs.LG

Perturbative-NeuSA: A Structured Spectral Framework for Time-Dependent PDEs

Neural spectral PDE solvers often learn an entire unresolved vector field even when an inexpensive approximate model can already capture most of the trajectory. Here we introduce Perturbative-NeuSA, a residual formulation that decomposes the target solution into a low-fidelity background and a high-resolution perturbation, so that only the unresolved dynamics is learned. Starting from the exact perturbation equation, the method combines a fixed spectral operator, a background-dependent correction, the background defect in the target PDE, and an optional neural closure. This construction makes the roles of physical structure and neural closure separately measurable. Across 2D Burgers, Klein-Gordon, and heterogeneous 2D wave equations, the deterministic structured solver outperforms the trained NeuSA baseline while requiring no neural-network training. The largest gains occur on Burgers, where the deterministic correction reduces training and extrapolation errors by factors of 24 and 44, respectively. In addition, a Klein-Gordon sweep over seven background resolutions shows that the effect of the closure is conditional: it improves a poor background by 3.6 times, becomes neutral at intermediate resolutions, and degrades a well-resolved background. For the wave equation, however, the closure provides an additional 18% reduction when the remaining residual is interface-localized. Multi-initial-condition diagnostics further show that the useful closure regime depends on the initial-condition spectrum and can disappear in extrapolation when structured correction already captures the dominant Burgers dynamics. Perturbative-NeuSA therefore reframes neural closure as a conditional, diagnosable correction governed by background fidelity, residual organization, and compatibility with the closure model.

Xianli Zhu, Jia Yin

School of Mathematical Sciences, Fudan University Shanghai, China

Neural Surrogate Modeling Neural PDE Solvers PDE Solving Spectral Methods

Jul 26, 2026math.NA

No Free Lunch in Flow Surrogates under Time-Varying Boundary Conditions: A Two-Regime Study

We test whether an architecture that succeeds on a simple flow regime also succeeds on a richer one, with each trained separately on each regime. We explore two transient flows under time-varying boundary conditions: the three-dimensional slurry film in chemical-mechanical planarisation (CMP), central to semiconductor manufacturing, and the two-dimensional Kármán vortex street (KVS). Eight surrogate models on one shared pipeline differ in whether they learn the full field or a latent representation, and in whether they predict in one shot or step by step. No single architecture wins both regimes. On the film, a one-shot full-field model reconstructs the cumulative wall shear stress to 2.7% relative error. On the wake, a latent autoregressive DeepONet retains 90% of the shedding power that direct and one-shot models damp to almost zero. The treatment of time decides the outcome. The self-sustained wake calls for autoregressive feedback and the boundary-driven film for a direct map. Pointwise RMSE hides the damped oscillation on the wake, compresses the sixfold lead on the film's process target, and picks the damped model under wake extrapolation. The evaluation scores five physical questions. Trained surrogates answer queries 10^3 to 10^4 times faster than the finite-element solver and pay off from the first query beyond the training set on the film and from the third on the wake. Neither the winning architecture nor its validation holds across regimes. The choice of surrogate should follow the dynamical character of the target flow, and its validation should resolve the failure modes.

Georg Winkler, Martin Stoll

Department of Mathematics, Chemnitz University of Technology, 09111, Chemnitz, Germany

Neural Surrogate Modeling PDE Surrogate Modeling Neural Operators Computational Fluid Dynamics Autoregressive Modeling

Jul 26, 2026cs.LG

Multimodal Auto-regressive Transformer Surrogate for Modeling Variable Operations and Quantifying Uncertainty in Geological Carbon Storage

The use of variable well perforation and injection strategies can improve the efficiency of geological carbon storage operations. We develop a new multimodal auto-regressive transformer surrogate to model these operations under geological uncertainty. A modified SEAM CO2 geomodel, which involves a faulted system with three stacked aquifers, is considered. The two injection wells are perforated in stages, from bottom to top, with the stage durations and individual well injection rates treated as control variables. The surrogate model processes three input modalities - the 3D geomodel, scalar parameters characterizing relative permeability functions, and control variables - through separate encoders. These are fused via self-attention in a transformer encoder, and a temporal decoder generates predictions auto-regressively through encoder-decoder cross-attention. The surrogate is trained, using 4000 GEOS flow simulations, to predict saturation and pressure at monitoring locations, total injected and mobile CO2 mass, and saturation footprints. For a new test set, involving randomly sampled geomodels and control variables, the surrogate achieves a median saturation MAE of 0.028 and median relative errors of 0.2-5% for the other quantities of interest. Importantly, it captures the switch from rate to bottom-hole-pressure control. The surrogate model is used within a hierarchical Markov chain Monte Carlo data assimilation procedure for a synthetic true model under three operational strategies. Substantial uncertainty reduction is achieved for key metaparameters, particularly the fault permeabilities. Posterior predictions for saturation footprints and total injected and mobile CO2 mass are also shown to be generally consistent with true model results.

Yifu Han, Louis J. Durlofsky

Department of Energy Science and Engineering, Stanford University, Stanford, CA, 94305, USA

Neural Surrogate Modeling Uncertainty Quantification Transformer PDE Surrogate Modeling

Jul 25, 2026cs.LG

Context-Aware Concept Distillation for Trustworthy Flood Prediction

Effective flood risk management relies on accurate forecasting, yet the "black box" nature of stateof-the-art Deep Learning models creates a barrier to trust and accountability in high-stakes public safety decisions. While existing Explainable AI (XAI) methods offer local attributions, they fail to provide the verifiable, operationally meaningful causal narratives required by disaster response authorities. To address this societal challenge, we propose Context-Aware Concept Distillation (CACD), a framework developed in collaboration with domain experts to distill opaque LSTMs into interpretable, hydrology-aware surrogate models. We introduce an unsupervised pipeline to discover a "Hydrological Language" and a Residual Hypernetwork that dynamically modulates these concepts based on static basin characteristics. Evaluated on 5,203 basins globally, our model achieves high fidelity (Median NSE 0.70), significantly outperforming black-box baselines (e.g., Multi Layer Perceptrons) on unseen future data. By demonstrating that human-interpretable concepts are sufficient to reconstruct flood dynamics, this work balances AI accuracy with the transparency required for responsible environmental decision-making.

Eli Levinkopf, Efrat Morin, Claudia V. Goldman

School of Computer Science and Engineering, The Hebrew University of Jerusalem, Israel · Institute of Earth Sciences, The Hebrew University of Jerusalem, Israel · Hebrew University Business School, The Hebrew University of Jerusalem, Israel

Neural Surrogate Modeling Explainable Artificial Intelligence Spatiotemporal Forecasting Knowledge Distillation Flood Forecasting

Jul 24, 2026physics.flu-dyn

Neptuna: A Comprehensive Machine Learning Framework for Benchmarking Complex Multiphase Flows

Compressible multiphase flows involving shocks and material interfaces arise in applications such as bubble collapse and droplet breakup, where strong nonlinear interactions produce complex interface deformation, mixing, and multiscale dynamics. Developing reliable machine learning surrogates for these flows remains challenging due to the simultaneous presence of compressibility, sharp discontinuities, and multiphase effects. In this work, we introduce the first large-scale benchmark specifically designed for shock-driven compressible multiphase flows, comprising 2.4 TB of high-fidelity 2D and 3D datasets featuring shock-induced bubble collapse and droplet breakup. We evaluate diverse surrogate model families on our benchmarking framework: Neptuna {https://github.com/tumaer/Neptuna}, including convolutional, spectral, transformer-based, and pre-trained PDE foundation models. Beyond standard MSE training, we investigate composite losses combining MSE with Sobolev, interface-aware, and structure-aware terms, together with adaptive loss balancing using SoftAdapt and GradNorm. Evaluation includes pointwise, spectral, feature-focused, structural, and physics-informed metrics. Results show that no single model performs best across all datasets and metrics, while composite losses significantly improve interface preservation and spectral fidelity. Among adaptive weighting strategies, SoftAdapt provides the most consistent improvements with almost no overhead compared to MSE-only training.

Harish Ramachandran, Björn Kimpel, Thomas Paula +3

Technical University of Munich

Neural Surrogate Modeling PDE Surrogate Modeling Computational Fluid Dynamics

Jul 23, 2026physics.comp-ph

Cycle-Consistent and Uncertainty-Aware Neural Surrogates for Tokamak Edge Plasmas

The boundary and divertor plasma govern how a tokamak exhausts power and particles, setting heat fluxes, target conditions, and the onset of detachment. Predicting these quantities is essential for operating current and future devices, but edge simulations that resolve them are too slow for parameter scans, optimization, or real-time control. Machine-learning surrogates offer a fast alternative, yet most are forward-only: they cannot recover input parameters from observations or assess the reliability of their predictions. We introduce a cycle-consistent neural surrogate for edge plasmas, combining a conditional U-Net forward model with an optimization-based inverse method built on the frozen forward network. The forward model maps five control parameters to two-dimensional plasma-state fields on the SOLPS-ITER mesh; the inverse method enforces consistency between forward and inverse predictions, a self-supervised quality check needing no ground-truth labels at inference. An ensemble of multilayer perceptrons also predicts electron temperature and density profiles at the outboard midplane and divertor targets, with uncertainty estimates that flag where more simulations are needed. The forward model achieves normalized root-mean-square errors below 2.6% and Pearson correlations above 0.95 for all fields. Cycle-consistency regularization raises the average cyclical

R^2

from 0.59 to 0.99 without degrading forward accuracy and enables recovery of the core fueling rate; all five control parameters are recovered with Pearson

r\ge0.97

. A

k

-d tree warm start yields a database completion rate above 95%, versus roughly 30% outright failures when cold-started. With about

4\times10^6

parameters, the model produces full 2D predictions in milliseconds, five to six orders of magnitude faster than SOLPS-ITER, enabling real-time control, parameter scans, uncertainty analysis, and digital twins.

Abdourahmane Diaw, Sebastian De Pascuale, Jae-Sun Park +3

Fusion Energy Division, Oak Ridge National Laboratory, Oak Ridge, TN 37932, USA · DIFFER - Dutch Institute for Fundamental Energy Research, De Zaale 20, 5612 AJ Eindhoven, the Netherlands

Neural Surrogate Modeling PDE Surrogate Modeling Consistency Regularization Inverse Problems

Jul 23, 2026physics.flu-dyn

Explainable quantum-compressed machine learning for complex fluid flows

Machine-learning surrogates of physical systems face a paradox: explainable models facing the challenge of expressivity to capture complex nonlinear flows, whereas expressive deep surrogates match high-fidelity simulations only through massive parameterisations that turn the learned dynamics into a black box. Here, we introduce quantum-compressed machine learning (QCML), which resolves this tension by compressing the latent propagator of a flow surrogate from

524{,}288

trainable parameters to no more than

8

. This parameter reduction brings the learned dynamical law to the parameter scale of a physical constitutive relation rather than a black-box neural network, making the surrogate directly interpretable and controllable without sacrificing expressivity. The compression is realised by a structured quantum circuit whose unitary propagator constrains the latent spectrum to the unit circle exactly and by construction, replacing exponential error growth with linear accumulation over autoregressive rollouts. Classical regularisation only approximates this constraint: even a quantum-inspired classical baseline penalised towards unitarity collapses within one Lyapunov time on turbulent channel flow, whereas QCML remains stable over the full rollout. Shared phase and coupling angles parameterising the circuit correspond directly to modal frequencies and inter-mode interactions, giving the learned dynamics a physical interpretation in spectral space. On two patient-specific cardiovascular benchmarks, the structured QCML propagator matches the predictive accuracy of its classical counterpart on surface pressure spectra, pressure drop, and wall shear stress. These results establish QCML as a working component of scientific machine learning and a concrete contribution towards practical quantum advantage in real-world prediction.

Xiao Xue, Maida Wang, Mingyang Gao +2

Centre for Computational Science, University College London, London, UK · Leibniz Supercomputing Centre of the Bavarian Academy of Sciences and Humanities, Boltzmannstraße 1, 85748 Garching, Germany · Centre for Advanced Research Computing, University College London, London, UK

Neural Surrogate Modeling Interpretable ML Quantum Machine Learning Computational Fluid Dynamics

Jul 22, 2026physics.flu-dyn

Label-Free Finite-Volume-Residual Training of Attention Graph Neural Networks for Coupled Thermo-Fluid Fields

Neural surrogates are widely used in scientific machine learning for fast prediction of three-dimensional (3D) thermo-fluid fields. However, generating training data using conventional numerical solvers often incurs substantial computational and storage costs. We propose to train an attention graph neural network by minimizing the finite-volume method (FVM) residuals of the governing equations. These residuals are evaluated directly on the mesh, requiring no labeled data. We evaluate the trained surrogates against computational fluid dynamics (CFD) references and a data-supervised baseline across four scenarios. On the two steady-state benchmarks, the FVM-loss model achieves an all-field normalized root-mean-square error (nRMSE) of 2.3-2.8%. It demonstrates close agreement with the CFD references, including the buoyancy-energy coupling. On the two parametric transient cases, the FVM-loss model outperforms the supervised baseline in terms of accuracy, while avoiding the data-generation cost entirely. These results indicate that the FVM loss can provide a practical training signal for neural surrogates and reduce the model development cost.

Tianyu Li, Zhiwei Cao, Qingang Zhang +3

Interdisciplinary Graduate Programme, Nanyang Technological University, Singapore, Singapore. · School of Future Technology, Fuzhou University, Fuzhou, China. · College of Computing and Data Science, Nanyang Technological University, Singapore, Singapore. +2

Neural Surrogate Modeling Graph Neural Networks PDE Solving Physics-Informed ML Physics-Informed GNNs Computational Fluid Dynamics

Jul 22, 2026cs.LG

AI-Driven Surrogate Models for Predicting Electrode-Scale Discharge Behavior in Lithium-Ion Batteries

Physics-based simulations are essential for understanding the electrode-scale discharge behavior of lithium-ion batteries (LIBs) but suffer from prohibitive computational costs. To address this, we introduce a novel deep learning surrogate pipeline based on the Swin3D Transformer to predict spatiotemporal discharge dynamics directly from volumetric data. Our approach integrates two key innovations: Gaussian Positional Encoding (GPE), which enhances spatial feature representation by adapting to the complex geometry of electrode microstructures, and a specialized Temporal Encoding module to capture non-linear timeseries evolution. Experimental validation on an Electrochemical Simulation (ES) dataset demonstrates that our pipeline significantly outperforms state-of-the-art point cloud baselines in prediction accuracy. Furthermore, the proposed method reduces the computational overhead by orders of magnitude, providing a scalable and efficient framework for high-throughput battery design and optimization.

Mengda Xing, Jean-Marie Lagniez, Alejandro Franco

CRIL, UA · CRIL, UMR 8188, Université d’Artois, Rue Jean Souvraz SP 18, F-62307 Lens Cedex, France · LRCS +1

Neural Surrogate Modeling Materials Science Lithium-Ion Batteries

Jul 21, 2026cs.LG

Thermodynamics-Informed Input Reparameterization for Neural Prediction of Real-Fluid Thermodynamic Properties in Supercritical Combustion

Real-fluid thermodynamic property evaluation is a major computational cost in supercritical combustion simulations. In the enthalpy-based pressure-correction formulation, the closure evaluates temperature T, density

ρ

, and compressibility coefficient

ψ

from the solver state (h,p,Y) through enthalpy-temperature inversion and repeated real-fluid equation-of-state evaluations. Neural-network surrogates offer fixed-cost inference, but direct mapping from (h,p,Y) to

(T,ρ,ψ)

must capture the enthalpy-temperature relation and non-ideal equation-of-state response, resulting in a complex regression problem. This work introduces a thermodynamics-informed input reparameterization strategy, termed target-aligned input reparameterization (TAIR). TAIR replaces the raw enthalpy coordinate of each property network with a target-matched thermodynamic coordinate: the temperature network uses a temperature estimate obtained by inverting a constant-

c_p

ideal-gas mixture enthalpy approximation, whereas the density and compressibility networks use an ideal-gas density estimate. These algebraic transformations use only solver-available variables and species constants, guiding the networks to learn real-fluid departures from ideal-gas baselines rather than reconstructing the full closure from raw enthalpy. The method is assessed using supercritical methane-oxygen counterflow flame data against a raw-input baseline and target-inconsistent cross-reparameterization controls. TAIR reduces held-out RMSE by factors of about 1.5, 2.0, and 7.5 for T,

ρ

, and

ψ

, respectively. For an unseen strain-rate flame within the augmented thermodynamic envelope, the corresponding factors are 3.6, 14.5, and 6.0. The target-inconsistent controls perform worse, indicating that the gains arise from thermodynamically matched input design rather than generic preprocessing.

Haoze Zhang, Han Li, Ke Xiao +3

State Key Laboratory of Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, China · AI for Science Institute (AISI), Beijing 100080, China

Neural Surrogate Modeling Computational Fluid Dynamics

Jul 21, 2026cs.LG

Deep learning-based prediction of time-resolved adhesive forces in viscoelastic Hertzian contacts

Fast prediction of the response of adhesive soft viscoelastic contacts represents a current challenge in soft robotics and for gripping and manipulation tasks. Determining the complete time-resolved force trajectory requires full numerical simulations, whose computational cost is strongly parameter-dependent, making them impractical for real-time application or design-optimization loops. In this work, we overcome this limitation by training a scalar-conditioned, stateful, sequence-to-sequence deep learning model to predict the full force evolution from a prescribed displacement history for both short- and long-range adhesion regimes. The data set spans four orders of magnitude in loading and unloading rates and includes varied dwell times, with the Tabor parameter ranging from

0.2

to

3.2

. To enable learning across these heterogeneous time scales, we introduce a fixed-measurement-step (FMS) representation that converts variable-length trajectories into fixed-length sequences while preserving their physical-time information. Different architectures were trained, including long short-term memory (LSTM) networks, temporal convolutional neural (TCN) networks, and time-distributed dense layers with three different Tabor-conditioning mechanisms. The models were compared using global waveform and error metrics. We found that the best-performing model has an LSTM architecture with concatenated conditioning, which achieves a held-out mean-squared error of

5.0\times10^{-4}

, a median pull-off-force error of

\approx2.2\%

, and a median hysteresis error of

\approx1.1\%

. For the held-out protocols, the model predicts a complete force trajectory with a median inference time of

0.16

s. The model is tested across unseen parameter combinations and against analytical limiting cases, providing a rapid surrogate for repeated numerical evaluations with potential use in control-oriented applications.

Ali Maghami, Merten Stender, Michele Ciavarella +1

Neural Surrogate Modeling

Jul 20, 2026cs.LG

A Continual Validation, Updating, and Decision-Making Framework for Self-Adaptive Digital Twins via Robust Model Predictive Control: A Case Study in Additive Manufacturing

Digital Twins rely on surrogate models to mirror physical systems in real time, yet these models can degrade as operating conditions evolve, a phenomenon known as concept drift. Maintaining surrogate fidelity under drift, particularly when models must also capture aleatoric uncertainty, remains an open challenge. Existing adaptive frameworks lack principled mechanisms for detecting when updates are needed, for efficiently adapting models from limited streaming data, and for certifying that updates genuinely improve predictive performance. Here we present an adaptive Digital Twin framework that integrates a Fisher score--based multivariate drift detector, Low-Rank Adaptation (LoRA) for parameter-efficient continual learning, and a Mann--Whitney

U

test for online statistical validation. The framework monitors surrogate-model confidence via Fisher score vectors, triggers targeted fine-tuning of fewer than 1% of model parameters upon drift detection, and statistically certifies predictive improvement before deploying the updated surrogate. Applied to a stochastic linear system and a directed energy deposition additive manufacturing process as case studies, the framework successfully detects distributional shifts with short delays and restores both predictive accuracy and uncertainty quantification under abrupt and incremental drift. These results establish a statistically rigorous and computationally tractable pathway for sustaining the trustworthiness of neural-network--based Digital Twins throughout their operational life cycle.

Yi-Ping Chen, Ying-Kuan Tsai, Vispi Karkaria +3

Department of Mechanical Engineering, Northwestern University · Department of Industrial Engineering and Management Science, Northwestern University

Neural Surrogate Modeling Concept Drift Online Continual Learning Digital Twins

Jul 19, 2026cs.CV

Visible-Light Imaging Diagnosis of Neutral Particle Emission Tomography in the Tokamak Divertor: An Efficient Transformer-based Surrogate Model

Nuclear fusion has made significant progress in recent years and is expected to become one of the most important pathways to addressing global energy challenges. This paper focuses on observing plasma using visible-light cameras, analyzing its spatio-temporal motion cues, and predicting the two-dimensional spatial distribution of light intensity, aiming to provide a foundational basis for future scientific experiments using deep neural networks. Specifically, we propose Delta-InvFormer, a novel backbone network centered on a differential Transformer. The key insight is that by taking consecutive video frames as input, we can better capture the dynamics of the plasma. Moreover, spatial and temporal differential self-attention effectively mitigates interference from noisy signals, ensuring high-quality feature extraction. These features are then fused into a compact and informative representation, which is fed into a decoder network to predict the distribution. Based on real experimental data collected from the Experimental Advanced Superconducting Tokamak (EAST) large-scale scientific facility, our results demonstrate that the proposed model not only significantly accelerates traditional methods for distribution prediction but also achieves competitive reconstruction accuracy. The source code of this paper will be released on https://github.com/Event-AHU/OpenFusion

Xiao Wang, Hao Si, Qiang Chen +8

School of Computer Science and Technology, Anhui University, Hefei 230601, China. · Institute of Plasma Physics, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei 230031, China. · School of Artificial Intelligence, Anhui University, Hefei 230601, China.

Neural Surrogate Modeling Transformer Efficient ViTs Computed Tomography

Jul 18, 2026cs.LG

On the Potential of Graph Neural Networks as Metamodels for Supply Chain Optimization: Dataset, Architectures, and Directions

Graph Neural Networks (GNNs) have emerged as a powerful, differentiable class of learning models for graph-structured systems. Their ability to generalize across topologies opens the prospect of a surrogate for combined structural and parametric optimization, which classical metamodels cannot offer. Supply chains are a natural target, yet the use of GNN surrogates for supply chain problems is largely unexplored. This paper lays the foundation, presents initial steps, and discusses key research directions. As a foundation, we formulate the problem and create a large public training dataset of programmatically generated supply chain graphs with input parameters and steady-state performance metrics obtained using our SupplyNetPy simulation library. As initial steps, we explore GNN architectures that work well as surrogates for node- and network-level predictions, and analyze their accuracy-compute trade-off against simulation. Most importantly, we outline the exciting directions this opens, namely gradient-based optimization over topology, fast design-space exploration, and sensitivity analysis.

Tushar Lone, Neha Karanjkar

School of Mathematics and Computer Science, Indian Institute of Technology Goa, Ponda, Goa, INDIA

Neural Surrogate Modeling Topology Optimization Combinatorial Optimization Supply Chain Management

Jul 18, 2026cs.AI

A Research Prototype for Closed-Loop Generative Design of Customized Foot Orthoses via Semantic-Physics Alignment

Translating unstructured clinical prescriptions into patient-specific foot orthoses (FOs) is hindered by a semantic-physical misalignment: high-level clinical intent is not mapped deterministically onto the 3D geometric parameters of the orthosis, and existing design workflows remain dependent on manual expertise with no instantaneous biomechanical validation. We present TANS-FO, a research prototype-a modular pipeline with closed-loop feedback for computational design automation of customized FOs, not a clinically validated therapeutic device. A Text-Aligned Neural Surrogate (TANS) uses cross-attention to project clinical-text embeddings onto a continuous lattice-density field, while a Graph Neural Network (GNN) surrogate predicts plantar stress in real time as a substitute for Finite Element Analysis (FEA). The framework is anchored on the open-access PicoFoot-5K anthropometric database (5,230 subjects; 30+ anatomical parameters). Under standardized quasi-static loading, the GNN surrogate agrees with an Abaqus reference solver (R^2 = 0.94), and the full pipeline synthesizes manufacturing-ready lattice insoles within minutes. On the Male 18-40 cohort, the proposed system attains a surrogate-predicted peak-pressure reduction of 34.7% over parametric CAD, with a fit error of 0.42 mm. Separately, an exploratory feasibility observation (n = 12; 2-week follow-up; no control group) using VAS pain reporting indicates short-term comfort improvement (VAS 6.4 -> 2.1), but this data is explicitly classified as preliminary observational evidence only-not evidence of clinical efficacy.

Rui Wang, Byungwon Min, Suxing Liu

Department of IT Engineering, Mokwon University, Daejeon 35349, South Korea · Shanghai Artificial Intelligence Generative Design Technology Co., Ltd., Shanghai 200000, China · School of Digital Arts, Jiangxi Arts & Ceramics Technology Institute, Jingdezhen 333001, China

Neural Surrogate Modeling Conditional Generative Modeling

Jul 17, 2026cs.RO

Learning a System-Level Surrogate for Hydraulic Excavators: A Simulation-to-Real LSTM Approach

Developing autonomous hydraulic excavators is constrained by limited access to physical machines and the high cost of real-world experimentation. This paper proposes a simulation-to-real framework for learning a system-level digital surrogate using Long Short-Term Memory (LSTM) networks. Instead of modeling internal dynamics, the excavator is treated as an input-output operator, and the surrogate is trained to reproduce its closed-loop behavior under identical control inputs. The approach is first validated in a MuJoCo simulation environment and then transferred to a real excavator. To address measurement inconsistencies in real-world data, a consistency-aware state estimation method based on adaptive Kalman filtering is introduced. Experimental results demonstrate that the learned surrogate achieves high fidelity in both angular velocity and long-horizon trajectory reproduction under closed-loop autoregressive evaluation. These results confirm that the proposed model can serve as a drop-in surrogate for both simulation and physical systems, enabling scalable and efficient development of excavation automation algorithms.

Shuai Wang, Shen Wang, Qiang Wang +4

National Engineering Research Center of Mobile Network Technologies, Beijing University of Posts and Telecommunications, Beijing 100876, China · Yaowu (Shenzhen) Technology Co., Ltd., Shenzhen 518052, China

Neural Surrogate Modeling Robotic Construction Surrogate Modeling Sim-to-Real Transfer Ensemble Kalman Filtering

Jul 16, 2026math.NA

Subgrid-Scale Parameterization in Burgers' Equation Using Structure-Preserving Neural Networks and Entropy Variables

We present a machine learning approach for developing subgrid-scale (SGS) parametrizations in coarse simulations of partial differential equations. We utilize structure-preserving neural networks and entropy variables to learn subgrid fluxes in coarse simulations of the Burgers' equation. In particular, we employ a decoupled neural network architecture explicitly separating the subgrid corrections into two distinct components: a conservative Flux Potential network and an Eddy Viscosity network. We demonstrate that this reduced-order framework maintains high physical fidelity, accurately reproducing the energy spectrum, spatial and temporal correlation functions, and dynamical characteristics of the full-scale system. Furthermore, we show that our approach is robust and applicable to parameters outside the training regime.

Aijaz Nazir, Ilya Timofeyev

Dept. of Mathematics, University of Houston, Houston, TX 77204

Neural Surrogate Modeling PDE Solving Computational Fluid Dynamics

Jul 15, 2026cs.CE

Accounting for Hysteresis and Eddy Currents in Finite Element Simulations of Ferromagnetic Laminated Cores using a Recurrent Neural Network

Incorporating hysteresis and eddy currents into finite element simulations of laminated-core electrical machines is computationally challenging. Resolving the fields inside the laminations at each integration point and at every nonlinear iteration leads to computational costs several orders of magnitude higher than anhysteretic simulations, making such approaches impractical for design applications. Conversely, simplified models accounting only for magnetic saturation are becoming increasingly inadequate as electrical machine topologies and operating conditions grow in complexity. In this context, machine learning surrogate modeling has emerged as a promising alternative, offering efficient and accurate approximations of complex electromagnetic behaviors. In this paper, a recurrent neural network is trained as a surrogate of a laminated-core material model for an isotropic laminated core, and is integrated into realistic two-dimensional magnetodynamic finite element simulations based on a magnetic vector potential formulation. The proposed approach achieves excellent agreement with the reference laminated-core model while limiting the computational cost to about twice that of an anhysteretic simulation. By training the recurrent neural network on a sufficiently diverse set of artificially generated magnetic field sequences designed to mimic those encountered in electrical machine simulations, the proposed approach can be readily applied across a wide range of finite element simulations. Furthermore, the trained surrogate model is provided as a standalone component that can be easily incorporated into existing computational frameworks. It is publicly available at https://gitlab.onelab.info/getdp/lamnet.

Florent Purnode, Louis Denis, François Henrotte +2

Department of Electrical Engineering and Computer Science, University of Liege, Belgium

Neural Surrogate Modeling PDE Surrogate Modeling

Jul 15, 2026cs.LG

Microstructure-Conditioned Surrogate Models for Graded Multiscale Optimization of Mycelium Composites

Emerging sustainable materials increasingly rely on engineered hierarchy and microstructure to achieve control of their properties and mechanical behavior. Optimizing these materials with controllable microstructures requires efficient multiscale simulations. Data-driven surrogate models for the microscale can accelerate multiscale simulations, but require large amounts of data even for a fixed microstructure. When a range of microstructures is considered, as is the case in multiscale optimization, even more data is needed to train a surrogate. To overcome this challenge, we condition a hybrid physics-data surrogate on microstructural variables using a hypernetwork. This approach enables accurate predictions of multiscale mechanical behavior for a mycelium-woodchip composite material, even when trained on small datasets. The conditioned surrogate makes multiscale simulations of functionally graded structures tractable, and we validate it against a full FE^2 simulation. We optimize a graded multiscale disk, and reduce the peak stress by 42% compared to one with a random microstructure. Then, we go one step further, conditioning the network directly on manufacturing variables that can have a complex influence on the microstructure. This is a practical route to engineer the microscale for desired macroscale behavior. This contribution highlights the benefits of microarchitectured structures and demonstrates how conditioned surrogate models enable their multiscale optimization, which will accelerate the development and design of future sustainable materials and structures.

J. Storm, I. B. C. M. Rocha, S. Schyck +2

SLIMM Lab, Faculty of Civil Engineering and Geosciences, Delft University of Technology, P.O. Box 5048, Delft, 2600GA, Zuid-Holland, The Netherlands · Shaping Matter Lab, Faculty of Aerospace Engineering, Delft University of Technology, Delft, Zuid-Holland, The Netherlands

Neural Surrogate Modeling Surrogate Modeling Surrogate-Assisted Optimization Structural Mechanics Computational Materials Science

Jul 15, 2026math.NA

Approximation of solutions of parameter-dependent problems by residual neural networks

We develop a convergent scheme to train neural networks involving analytic activation functions based on gradient flows. Convergence properties are guaranteed by Lojasiewicz theory. The main advantage of this approach is its simplicity of implementation. The coefficients of the network are approximated by solving a system of ordinary differential equations. We test the method by constructing residual neural network approximations of solutions of parametric problems. The dependence of the solutions of simple ordinary differential equations on a few parameters is correctly reproduced. The solutions of inverse problems involving wave constraints which depend on a few parameters can be reasonably approximated, even in regions in which the problem is severely ill posed.

Ana Carpio

Universidad Complutense de Madrid, Spain

Neural Surrogate Modeling Neural Network Optimization Neural Network Approximation Theory

Jul 14, 2026physics.comp-ph

Towards end-to-end optimization in multimaterial 3D printing

Multimaterial 3D printing enables the fabrication of functionally graded components, but optimizing their spatial material distribution alongside structural topology remains a formidable challenge due to high-dimensional design spaces and complex constitutive modeling. This paper presents an end-to-end computational framework integrating sparsified physics-augmented neural networks with finite-element-based topology optimization. By extracting closed-form, composition-aware hyperelastic constitutive laws from experimental data, this approach facilitates exact symbolic differentiation via the adjoint state method implemented with FEniCSx, efficiently circumventing the bottlenecks of applying neural network constitutive models. This pipeline is deployed on soft robotic gripper applications, demonstrating continuous composition optimization for highly anisotropic contact responses, and the concurrent optimization of macroscopic topology and material distribution under non-failure stretch constraints. This methodology could replace laborious empirical prototyping, establishing interpretable machine-learning models as practical, robust design primitives for advanced multimaterial additive manufacturing.

Xue-Ling Luo, Steven Yang, Jingye Tan +3

Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY, USA · Department of Aerospace & Mechanical Engineering, University of Southern California, Los Angeles, CA, USA · Department of Materials Science and Engineering, Technion - Israel Institute of Technology, Haifa, Israel +1

Neural Surrogate Modeling Topology Optimization