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.

Jul 13Week of Sep 28

Latest papers 254

Oct 7, 2026cs.LG

NeuralBES: A Differentiable, Control-Aware Emulator for Scalable Building Energy Modeling

Demand-side flexibility i.e. forecasting, shifting, and curtailing residential energy loads, depends on thermal models trusted across millions of heterogeneous buildings. Existing tools force a hard tradeoff: high-fidelity physics simulators such as EnergyPlus are accurate but sequential and require per-building calibration, while purely data-driven sequence models scale but abandon the physical structure that makes their predictions trustworthy. We introduce NeuralBES (Building Energy Simulation), a differentiable emulator that resolves this tradeoff by parameterizing a resistance--capacitance (RC) based thermal model with a shared neural encoder: static building metadata such as floor area, vintage, and HVAC type is mapped to physically bounded capacitances, conductances, and equipment coefficients, which become the coefficients of a scalar linear recurrence solved via a log-space parallel scan, and a predictor--corrector loop closes the thermostat--temperature nonlinearity while preserving full-horizon gradient flow. Trained on the ResStock dataset across three climate zones, NeuralBES handles heterogeneous building archetypes, vintages, and climate zones within a single trained encoder, while black-box baselines produce statistically plausible but physically inconsistent trajectories. On the annual full-year rollout, NeuralBES is the only data-conditioned model that is simultaneously physics-valid and accurate to within 4 MAPE points of the strongest raw-error baseline, while operating at roughly an order of magnitude fewer parameters than the transformer and recurrent baselines; among physics-valid baselines at parameter parity it more than halves the MAPE of the grey-box RC alternative.

Ting-Yu Dai, Takuya Kurihana, Wing Yee Au +1

Fujitsu Research of America

Neural Surrogate Modeling Differentiable Physics

Oct 7, 2026cs.LG

PoreML: A Data-Driven Framework for Learning Multiphase Flow in Porous Media

Multiphase flow in porous microstructures is central to CO

_2

storage, fuel-cell operation, and flip-chip packaging. Predicting these flows remains challenging because wettability and complex pore geometry govern the nonlinear evolution of fluid interfaces. Machine learning holds substantial promise for advancing the field, but progress is constrained by scarce time-resolved 3D datasets and a lack of a unified workflow for training and evaluating models. To fill this critical gap, we introduce PoreML, an open-source framework unifying data generation, model training, and evaluation grounded in pore-scale physics. The framework comprises three core components. (a) A modern GPU-native lattice Boltzmann solver, validated against analytical solutions and published experiments, enables reproducible data generation. (b) A 3.3 TB dataset contains 560 simulation runs and 158,546 stored time steps across four application-driven scenarios. These trajectories span synthetic structures and geometries derived from micro-CT scans of real materials, covering diverse wetting conditions and viscosity ratios. (c) A unified learning framework evaluates one-step prediction and autoregressive rollouts. Its domain-specific evaluation protocols assess predictive accuracy and physical consistency. We evaluate five models of diverse architecture under these protocols. Two complementary challenges assess transfer to larger domains and from synthetic to micro-CT-derived structures. PoreML provides a shared foundation for machine-learning research on multiphase flow in porous media, with the aim of empowering the community to develop reliable predictive models and advance the field.

Chunyang Wang, Mingrui Zhang, Yuyan Zhang +5

Imperial College London · Stanford University · EarthFlow AI, Inc. +1

Neural Surrogate Modeling Computational Fluid Dynamics

Oct 7, 2026cs.LG

EC-EarthFlow: Probabilistic emulation of daily transient global climate model simulations with flow matching

We introduce EC-EarthFlow, a generative flow matching model that emulates simulations from the physical climate model EC-Earth3. The model is trained on transient simulations from EC-Earth3 (1950-2166, SSP2-4.5) to predict the day ahead temperature field from the previous days temperature as well as annual mean temperature. Predictions are made auto-regressively with rollout periods of between a month and an extended season. Using only this variable of interest, we are able to reproduce the daily variability, spatial patterns, annual cycle and long-term trend from EC-Earth3 at a substantially lower computational cost than the physical model. We demonstrate that EC-EarthFlow is stable for long inference periods, and that it can learn the physical relationships as simulated in EC-Earth3.

Kirien Whan, Nikolaj T. Mücke, Karin van der Wiel

KNMI, Utrechtseweg 297, De Bilt, 3731GA, The Netherlands · Scientific Computing, Centrum Wiskunde & Informatica, Science Park 123, Amsterdam, 1098XG, The Netherlands · Faculty of Civil Engineering and Geosciences, Delft University of Technology, Delft, The Netherlands +1

Climate Modeling Surrogate Modeling Neural Surrogate Modeling Probabilistic Forecasting

Oct 5, 2026cs.LG

Conditional Flow Matching for Single-Neuron Electrophysiology: Capturing Multimodal Responses Across Stimuli

Neurons of the brain exhibit a rich repertoire of electrophysiology dynamics with the same repeated stimulus eliciting very different voltage responses from the same cell. One common approach in biophysically detailed models is to capture this variability through ensembles of deterministic parametrizations, at a cost of hundreds of thousands of CPU hours. Existing machine learning surrogates inherit the same limitation, where a stimulus is mapped to a single voltage response. We address this challenge by learning a conditional generative model for single-neuron electrophysiology, using flow matching with a velocity field conditioned on the input current. On biophysically detailed models of two human cortical interneuron types, the generated responses closely reproduce the electrophysiological feature distributions, spike-time structure, and excitability profiles, even matching the experimental recordings from the corresponding human cortical neurons. Near the firing threshold, firing and non-firing responses coexist at the same stimulus amplitude, and at high amplitudes, ensembles may split into low- and high-firing modes near depolarization block. We show that our model recovers both modes in each case, while a neural operator baseline suppresses spiking near threshold and blurs the gap between modes at depolarization block.

Cameron Schofield, Luca Ghafourpour, Philip H. Wong +2

University of Cambridge · Cedars-Sinai Medical Center · California Institute of Technology +1

Neural Surrogate Modeling Conditional Flow Matching Conditional Generative Modeling

Oct 5, 2026cs.LG

A Physics-Guided Transformer Framework for Electromigration Analysis in Multi-Segment Interconnects

As technology scales to smaller nodes, increasing current densities make electromigration (EM) one of the dominant reliability challenges in on-chip interconnects. Accurate transient stress analysis is needed to identify wires susceptible to EM degradation, but applying physics-based solvers across many interconnects remains computationally expensive. This paper proposes a physics-guided transformer framework for fast EM stress prediction in multi-segment interconnect lines. The framework converts each line into geometry- and DC-aware segment tokens and uses transformer attention to capture line-level context. A lightweight query decoder then predicts stress at selected locations and time instants. The model is trained with an objective that combines normalized supervised regression, linewise relative-

L_2

loss, and physics-guided continuity and terminal-flux terms. Experiments on IBM power grid benchmarks show that the proposed model achieves relative-

L_2

error below 8% and reaches up to 2459.68

\times

speedup compared with the matrix exponential~solver.

Pavlos Stoikos, Anuj Pathania, George Floros

Dept. of Electrical and Computer Engineering University of Thessaly, Greece · University of Amsterdam Amsterdam, The Netherlands · Dept. of Electronic and Electrical Engineering, Trinity College Dublin, Ireland

Neural Surrogate Modeling Transformer Physics-Informed ML

Oct 5, 2026quant-ph

Polynomial neural surrogates for designing photonic quantum experiments

Physics simulators can support the discovery of quantum experiments by predicting the states generated by experimental configurations. When these simulators are computationally expensive, repeated simulator calls can limit the search for experiments that generate a desired quantum state. Here, we develop a physics-inspired polynomial neural surrogate for PyTheus, a graph-based quantum-optics simulator, to predict quantum states and use it to design quantum experiments. Its polynomial activations are motivated by the relation between graph perfect matchings and the resulting state amplitudes. We train separate surrogate models for four-, six-, and eight-photon systems and show that they achieve higher prediction accuracy with fewer trainable parameters than standard multilayer perceptrons. We then use the trained surrogates for inverse design of GHZ, W, and linear-cluster states. For the larger systems, the surrogates also enable faster inverse design than direct optimization with PyTheus. These results suggest that incorporating the underlying physics into neural surrogates can provide an efficient approach to quantum experiment design.

Rohit Chaurasiya, Xuemei Gu

Institute of Condensed Matter Theory and Optics, Friedrich Schiller University Jena, Max-Wien-Platz 1, 07743 Jena, Germany

Neural Surrogate Modeling Polynomial Neural Networks Surrogate-Assisted Optimization Quantum State Preparation

Sep 30, 2026quant-ph

Neural Fourier Surrogates for Data Reuploading Quantum Neural Networks

For quantum machine learning, the exact boundary between classical and quantum advantage is still poorly understood. Direct comparison between quantum neural networks (QNNs) and existing classical models, which encompass fundamentally different function classes, often fails to provide broader insight into the difference between the two. Inspired by the techniques of Neural Quantum States and Random Fourier Features, this work introduces Neural Fourier Surrogates (NFS), a stochastic classical neural network architecture for efficiently learning coefficients over the same finite Fourier series support as quantum neural networks. Testing on a selection of tabular benchmark datasets, we find that NFS is an effective classifier architecture broadly competitive with established classical baselines, including a comparable Random Fourier Features model, and possessing comparable performance to data-reuploading QNNs; combined with additional analysis comparing the learned Fourier spectra of QNNs and NFS on synthetic data, these results establish NFS as a natural classical baseline for evaluating QNN performance.

Oliver Knitter, Jonathan Mei, Sang Hyub Kim +3

IonQ Inc., 4505 Campus Drive, College Park, MD 20740, USA.

Neural Surrogate Modeling Frequency-Domain Feature Learning Quantum Neural Networks

Sep 30, 2026cs.AI

PTNO: Training Neural Operators with Noisy Monte Carlo Estimates for Particle Transport Problems

Particle transport under multiple scattering is central to radiative transfer and plasma physics, yet high-fidelity Monte Carlo (MC) simulations must trace prohibitively many particles. Learning-based surrogates can amortize this cost, but typically train on expensive, well-converged MC solutions. We propose the Particle Transport Neural Operator (PTNO), a neural operator that learns particle transport surrogates directly from noisy, low-cost MC labels. Such labels pose two challenges: (1) high variance, which destabilizes standard supervised learning, and (2) a high dynamic range (HDR) spanning many orders of magnitude. For the first, we learn the solution operator from noisy labels of many configurations, amortizing MC cost and generalizing to unseen configurations. Because MC labels are unbiased, we show that the squared loss on them shares its minimizer with the loss on converged solutions, and our budget-allocation study over training scenes

M

, MC samples per render

N

, and independent renders per scene

K

shows that many noisy scenes beat fewer converged ones. For the second, a nonlinear transform such as the logarithm biases noisy supervision. Instead, PTNO keeps labels in physical space and enforces positivity with a softplus output layer that represents small values effectively. We further train with a pointwise relative

L_2

loss (PRelL2), the stop-gradient relative loss of HDR denoising and neural rendering, which normalizes each residual by the stop-gradient prediction instead of the noisy label. We demonstrate PTNO on neutron transport in fusion reactors and radiative transfer in participating media. On the two neutronics tasks, PTNO is

10^4

-

10^5\times

faster than converged MC on the same CPU and

10^3

-

10^5\times

cheaper than MC at matched accuracy; on the two radiative-transfer tasks, MC at matched accuracy costs

0.8

-

11\times

as much as PTNO.

Yubo Cao, Xi Deng, Mengqi Xia +3

California Institute of Technology · Yale University · UK Atomic Energy Authority +1

Neural Surrogate Modeling Noisy-Label Learning Neural Operators

Sep 30, 2026cs.LG

Do Better Scores Mean Better Physics? Physics-Grounded Explanations for Sim2Real Neural Operators

Machine-learning surrogates accelerate physical simulation, but lower prediction error need not coincide with lower error in physically relevant flow statistics. We examine this question for flow around a NACA4418 airfoil using paired computational-fluid-dynamics simulations and experimental particle-image-velocimetry measurements. A mean-preserving input intervention removes velocity fluctuations from selected regions of observed flow histories. Across four neural operators, removing fluctuations from the most energetic 10% of valid observed cells changes forecasts more than equal-area random removal. Because the masks are not matched for removed fluctuation energy, this contrast measures sensitivity, not independent evidence of physical importance. Separately, a CNO has lower velocity-field error but substantially higher two-component fluctuation-energy error than the reference on both analysis subsets. An output attenuation stress test also demonstrates disagreement between benchmark errors and domain-summed fluctuation energy. These single-benchmark results motivate reporting complementary physical diagnostics alongside aggregate prediction scores; they do not establish counterfactual physical correctness.

Somyajit Chakraborty, Xizhong Chen

State Key Laboratory of Synergistic Chem-Bio Synthesis, Department of Chemical Engineering, School of Chemistry and Chemical Engineering, Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China

Neural Surrogate Modeling Explainable Artificial Intelligence Neural Operators Computational Fluid Dynamics

Sep 29, 2026cs.CE

SHIFT-Truck: A High-Fidelity Aerodynamics Dataset and Benchmark for Pickup Trucks

Pickup trucks account for 14% of new light-duty vehicles produced in the United States, yet are among the least aerodynamic. Their open cargo bed adds a flow absent from existing automotive aerodynamics datasets such as DrivAerML and SHIFT-SUV: the shear layer leaving the cab roof passes over a recirculating bed flow before separating again at the tailgate. The resulting drag lowers fuel efficiency, raises emissions and limits the range of electric trucks. Scale-resolved Computational Fluid Dynamics (CFD) is too costly for broad design exploration; neural surrogates can predict flow features at a fraction of that cost, provided they are trained on large-scale, high-fidelity, domain-specific data. We introduce SHIFT-Truck, the first such dataset for pickup trucks. It comprises 1,000 Spalart-Allmaras delayed detached-eddy simulations (SA-DDES) of a reference pickup geometry morphed across 17 shape parameters. Each case is run on a mesh of about 100 million cells at a Reynolds number of

1.4 \times 10^7

and released with time-averaged surface pressure, wall shear stress, volumetric pressure and velocity. The setup is verified by grid refinement and repeated runs, and checked against wind-tunnel measurements. We define geometry-grouped splits and benchmark four neural surrogates, DoMINO, GeoTransolver, AB-UPT and SMART, on surface and volume tracks. SHIFT-Truck also introduces controlled distribution shifts in the operating point, the input surface discretization and the vehicle archetype. Models with strong in-distribution performance can degrade substantially under these shifts: operating-condition changes expose failures to infer speed dependence, while tessellation and cross-vehicle shifts reveal markedly different robustness across architectures. SHIFT-Truck is thus a benchmark not only for surrogate accuracy but also for generalization across physical and numerical distributions.

Riddhiman Raut, Yin Yu, Aashwin Anand Mishra +4

Luminary, San Mateo, CA, USA · Department of Aeronautics and Astronautics, Stanford University, Stanford, CA, USA

Neural Surrogate Modeling Distribution Shift Robustness Computational Fluid Dynamics

Sep 29, 2026cs.AI

Stochastic World Models for Verifying Vision-Based Neural Feedback Systems

Verifying a vision-based neural feedback system requires a model of the observations its controller acts upon. Such a model must capture the variation the sensor produces, while remaining tractable for closed-loop analysis. Generative adversarial networks (GANs) have served as perception surrogates, but they are large, reproduce complex scenes poorly, and are hard to verify. We explore stochastic world models as a richer class of perception surrogates. We train a world model with physically grounded latents, built from operations that standard verifiers bound. It reproduces held-out frames more faithfully than GAN surrogates with up to 130 times as many parameters. To verify these surrogates, we develop a procedure that combines falsification, adaptive refinement, symbolic, and backward analyses. On an emergency braking benchmark with a GAN surrogate, our procedure resolves the entire state space, 38% of which the state-of-the-art verifier left unresolved. On the RGB version of the benchmark, where no verification results have previously been reported, our procedure resolves over 80% of the state space with a world model surrogate.

I. Samuel Akinwande, Mykel J. Kochenderfer, Clark Barrett

Department of Aeronautics and Astronautics, Stanford University · Department of Computer Science, Stanford University

Neural Surrogate Modeling Neural Network Verification World Model Learning World Models

Sep 29, 2026cs.AI

Accelerated surrogate dynamics for dynamical, stochastic system evolution

Dynamic simulations are an entrenched way of gaining insight into the evolution of system dynamics. Their computational cost however is often prohibitively high, especially in cases of stochastic frameworks. Machine learning algorithms are especially suited as simulation surrogates. Nevertheless, they face some very distinct limitations. Firstly, the sheer dimensionality of these systems, however, precludes the use of traditional time series models who struggle with high dimensional feature spaces. Additionally, traditional time series focus exclusively on either long or short range effects, causing local or global drift given enough time. In this paper, we propose a framework that addresses those limitations. Our framework combines a Variational Autoencoder, with a convolutional or graph basis that reduces the dimensionality of the system. This latent vector is propagated in time using a Temporal Fusion Transformer model, which includes both long range and short range effect encoding, as well as static covariate support. We test our framework on three distinct cases, to prove its robustness and in all three we have achieved practically identical to the simulation results at a fraction of the time. Further, our framework is flexible enough to be adapted to any new system and provides an inbuilt uncertainty quantification for targeted experiment design.

Marco Jochum, Ioannis Kouroudis, Gohar Ali Siddiqui +3

Chair of Simulation of Nanosystems for Energy Conversion, Department of Electrical Engineering, TUM School of Computation, Information and Technology, Atomistic Modeling Center (AMC), Munich Data Science Institute (MDSI), Technical University of Munich, Hans-Piloty-Straße 1, 85748 Garching, Germany

Neural Surrogate Modeling Dynamical Systems Stochastic Linear Dynamical Systems Latent Dynamics Modeling

Sep 28, 2026cs.LG

Neural networks for spectral optimization

Given a functional dependent on the spectrum of a differential operator, we address the problem of finding a domain which optimizes this functional. PDE solvers might be used to tackle this optimization. It is however computationally expensive. We propose two neural network models which learn the spectrum directly from the geometry of the domain and can be used to optimize the domain from one or more eigenvalues. We investigate two representations. The first encodes the domain through Fourier coefficients and a light MLP, which is efficient on star-shaped geometries, achieving a precision of 0.2%. Through a rescaling of the coefficients the designed models satisfy the scaling law of the eigenvalues. Additionally, averaging the outputs of the trained surrogates over rotations and reflections induces invariance for these transformations. The second is a model that takes the landscape function, the indicator function and the gradient of the landscape function. A Gram-Schmidt process produces orthogonal eigenfunctions as output of the model along with the associated eigenvalues. The landscape model reaches 1% mean relative error on the first ten eigenvalues, compared with 4% for an FNO model. Replacing the landscape by an SDF worsened both prediction and optimization errors. The trained model also generalizes from synthetic shapes to domains given as classical image dataset. The resulting surrogates of both approaches recover classical spectral optima such as the disk for the first eigenvalue or the conjectured minima of higher eigenvalues. This confirms that our models produce accurate differentiable estimates of eigenvalues, which can be used in shape optimization problems involving spectral quantities.

Alexis de Villeroché, Beniamin Bogosel, Stéphane Breuils +2

Neural Surrogate Modeling

Sep 28, 2026cs.LG

FAST-Brain: A Flow-Aligned Spatio-Temporal Surrogate Brain Model

Modeling resting-state functional magnetic resonance imaging (rs-fMRI) data is crucial for understanding brain-wide neural activity. However, traditional methods struggle to capture complex temporal dynamics over long horizons, to account for the brain's anatomical spatial structure, and to model high-dimensional ambient signals that lie on a low-dimensional intrinsic subspace. We propose FAST-Brain, a unified flow-aligned spatio-temporal surrogate brain model that addresses all three challenges. At its core is a flow-aligned generative framework that directly predicts the clean blood-oxygen-level-dependent (BOLD) signal, paired with a graph convolutional network that captures spatial structural constraints and a Transformer that models long-range temporal dependencies. Theoretically, we show that under a low-dimensional subspace assumption, the approximation error of our model scales with the intrinsic dimension rather than the ambient dimension, which justifies our direct modeling of the BOLD signal. Extensive experiments on synthetic and Human Connectome Project datasets demonstrate that FAST-Brain achieves state-of-the-art performance in recovering functional connectivity, effective connectivity, and the implicit low-dimensional signal subspace.

Shucheng Liu, Changchun Shi, Kai Zhang +1

University of North Carolina at Chapel Hill · London School of Economics and Political Science

Neural Surrogate Modeling Functional Connectivity Generative Modeling Flow-Based Generative Modeling Neuroimaging Spatiotemporal GNNs+1

Sep 28, 2026cs.LG

CasEm: A Cascade Architecture for Long-Horizon Neural Emulation

Autoregressive neural emulators can drift or diverge over long rollouts despite accurate short-term predictions. We introduce Cascaded Emulation (CasEm), a one-way rollout architecture that augments an existing full-state backbone with an independently evolving model of physically specified aggregates. Its forecasts guide corrections to full-state predictions, without feedback from the backbone to the aggregate model. Effective guidance requires aggregates that cover substantial backbone error, remain accurately predictable, and support useful full-state corrections. We derive a finite-horizon error bound that clarifies these three factors and use empirical diagnostics to guide subsystem selection. Across four ODE/PDE benchmarks, CasEm reduces long-horizon rollout errors across diverse backbones and suppresses the trend toward error divergence in both diffusion tasks using Fourier neural operator backbones. In global climate emulation, CasEm with a regional total-water subsystem reduces 10-year full-state time-mean error by 66.6% and 46.3% for frozen ACE and Spherical DYffusion backbones, respectively, while adding less than 3% to inference time.

Zhaoyi Li, Jingtao Ding, Shihua Li

School of Automation, Southeast University · Beijing Zhongguancun Academy · Department of Earth System Science, Tsinghua University

Neural Surrogate Modeling PDE Surrogate Modeling

Sep 27, 2026cs.CE

Adapting neural operators for mechanics decisions under changing operating conditions

Neural operators can accelerate repeated nonlinear mechanics calculations, but their accuracy can deteriorate as operating conditions move beyond the training range. This work studies whether high-fidelity solutions acquired during use can be reused to adapt a neural operator and improve subsequent mechanics-based command selection. Two hard-magnetic soft-material systems are simulated using high-fidelity finite-element (FE) models, providing reference solutions for evaluating surrogate predictions and selected commands. A neural operator predicts deformation from known material, loading, and magnetic-field inputs, while an empirical error estimator determines which predictions may be used for command selection. Selected FE evaluations supplement these predictions, and their complete loading paths are retained for periodic updates of the neural operator and estimator. In both examples, the fixed operator loses substantial accuracy when stiffness and loading move outside the training range. Updates using 16 acquired paths recover much of the lost accuracy while preserving accuracy in the nominal regime. Under the same FE evaluation budget, the updated operators also improve command selection, although the benefit varies with the operating condition. Error estimation is less consistent, with inaccurate predictions sometimes accepted and accurate predictions rejected. These results demonstrate that reusing high-fidelity loading paths can extend the useful operating range of a neural operator. However, improved forward accuracy alone does not guarantee reliable prediction acceptance, highlighting prediction-specific error assessment as a separate requirement for trustworthy decision making.

Prashant K. Jha, Koffi Enakoutsa, Ian Galloway +1

Department of Mechanical Engineering, South Dakota School of Mines and Technology, Rapid City, SD 57701, USA · Department of Mathematics, University of California, Los Angeles, Los Angeles, CA 90095, USA

Neural Surrogate Modeling Surrogate-Assisted Optimization Distribution Shift Operator Learning Neural Operators

Sep 27, 2026math.OC

DCEmbed: Scalable Optimization over Neural Surrogates

Neural surrogates can accelerate large-scale optimization by replacing expensive or intractable model components with efficient learned approximations, but solving the resulting embedded problems can remain prohibitively costly. For instance, standard exact encodings of neural networks with ReLU activations allow the problem to be solved by mixed-integer solvers, but add large numbers of binary variables to accommodate the nonlinearity of the activations, which can render the problem computationally prohibitive. To address this, we propose DCEmbed, a heuristic for optimization problems with embedded neural surrogates that leverages the difference-of-convex (DC) representation of the network and avoids adding activation binaries. Exploiting shared structure within the DC representation of a ReLU network, we derive a reduced-size, exact formulation for its convex components that can be embedded in optimization problems using just two linear inequalities and one continuous auxiliary variable per hidden neuron. Using this, the problem is solved via an iterative penalty convex-concave procedure, where only the concave portions of the neural terms are approximated at each stage. The original objective, constraints, and any discrete decisions are retained, allowing standard convex or mixed-integer optimization solvers to optimize the host and surrogate jointly at each iteration. In experiments on quadratic programs, mixed-integer resource allocation, and neural two-stage stochastic programming, our method demonstrates much faster progress toward high-quality feasible solutions than approaches using exact mixed-integer embeddings. In particular, DCEmbed achieves

4\times

lower normalized primal integral than the best exact baseline on the resource allocation problem, while in two-stage stochastic programming it reaches the global surrogate optimum

\sim 5\times

faster than Gurobi ML.

Akshay Sreekumar, Nicolas Christianson, Priya L. Donti +2

Stanford University Stanford, CA, USA · Johns Hopkins University Baltimore, MD, USA · Massachusetts Institute of Technology Cambridge, MA, USA

Neural Surrogate Modeling Surrogate-Assisted Optimization Nonconvex Optimization

Sep 27, 2026cs.AI

TopoMamba: A Load-Support Relation-Guided Multi-Directional State-Space Model for Topology Optimization

Deep learning has emerged as an efficient alternative for predicting high-performance material distributions in topology optimization. Existing methods struggle to accurately capture load-transfer information, limiting out-of-distribution generalization, while their model architectures often incur high computational costs. To address these challenges, this paper proposes TopoMamba, a topology prediction framework incorporating a load-support relation-guided multi-directional state-space model. Coupling physical fields with load-support relations enables more effective modeling of mechanical dependencies. A load-support relation-guided spatially adaptive fusion mechanism dynamically adjusts multi-directional scan features according to spatial conditions. Mamba is coupled with the solid isotropic material with penalty method to enhance structural mechanical performance while maintaining computational efficiency. Results on two-dimensional topology optimization benchmarks demonstrate that TopoMamba achieves superior topology prediction accuracy, out-of-distribution generalization, and computational efficiency over state-of-the-art models. The proposed load-support physics-guided framework enables efficient optimization of more complex structural systems.

Bin Lou, Yuxuan Cheng, Huaizhi Zong +2

State Key Laboratory of Fluid Power and Mechatronic Systems Zhejiang University Hangzhou

Neural Surrogate Modeling Topology Optimization

Sep 27, 2026cs.CE

Modelling non-linear aeroelastic loads in long-span bridges with extreme learning machines

Accurate modelling of aerodynamic loads is essential for predicting instabilities and ensuring the safety of long-span bridges. A methodology is introduced for modelling aerodynamic self-excited forces in bridge-deck cross-sections using extreme learning machines (ELMs). ELMs, as single-layer feedforward neural networks, offer efficient training and accurate predictions. Forced-oscillation datasets from computational fluid dynamics (CFD) or wind-tunnel experiments are used for training, enabling systematic data selection to capture non-linear aerodynamic behaviour often missed by semi-analytical approaches. Once trained, the model predicts self-excited loads for any arbitrary motion composed by frequencies and amplitudes within the training domain. Comparisons with analytical, semi-analytical, and CFD results show superior accuracy in capturing non-linear force components and close agreement for aerodynamic loads and flutter wind speeds. Training required about 1.1% of the time of a conventional neural network, and coupled flutter analysis runs in seconds, providing orders-of-magnitude speed-ups over CFD. These results indicate that ELM-based frameworks are accurate, practical, and efficient alternatives for modelling self-excited loads, particularly when preliminary CFD or wind-tunnel data are available. The presented approach offers a reliable data-driven technique for aeroelastic load modelling in long-span bridges.

Gledson Rodrigo Tondo, Samir Chawdhury, Sergio Andres Castro Giraldo +1

Bauhaus-Universität Weimar Weimar, Germany

Neural Surrogate Modeling

Sep 24, 2026cs.LG

Beyond Compression: Training Latent Representations for Stable Long-Horizon Rollout in Neural Surrogate Solvers

Latent neural surrogate solvers, or latent dynamics models, accelerate simulations of time-dependent physical systems by evolving a compressed latent space rather than resolving full-resolution fields directly. In principle this reduces computational cost and simplifies learning, but in practice errors often accumulate rapidly during long autoregressive rollouts, limiting predictive utility. We show that this instability does not stem from the latent representation itself, but arises when it is trained solely for reconstruction, producing representations poorly suited to long-horizon forecasting. We systematically evaluate training-level interventions that align latent representations with long-horizon rollout: Koopman operator learning and Hamming noise injection during autoencoder training to improve compression, together with noise injection and multi-step rollout fine-tuning to improve dynamics. Interventions that improve long-horizon rollout stability often degrade conventional training metrics, including reconstruction and one-step prediction accuracy. Collectively, these interventions reduce long-rollout error by approximately 40% and match or exceed the accuracy of full-resolution models on two physics benchmarks, while requiring 2 orders of magnitude fewer floating point operations and half the GPU memory. Applied to mesoscale crystal-plasticity simulations of high-cycle fatigue, the resulting surrogate achieves stable extrapolation over horizons orders of magnitude beyond those observed during training. More broadly, these results show that neural compression should be designed not merely to reduce dimensionality, but to restructure the solution space for stable dynamical evolution, a key requirement for reliable, efficient neural surrogates in scientific applications.

Andreas E. Robertson, Ashley T. Lenau, John D. Shimanek +5

Center for Integrated Nanotechnologies, Sandia National Laboratories, New Mexico, USA · Center for Computing Research, Sandia National Laboratories, Albuquerque, NM, USA · School of Engineering, Brown University, Providence, RI, USA +2

Neural Surrogate Modeling Latent Dynamics Modeling

Sep 24, 2026eess.SY

GridSFM: A Foundation Model for Solving AC Optimal Power Flow

We introduce GridSFM, a framework that combines a pretrained foundation model across grid topologies with physics-informed fine-tuning for solving AC Optimal Power Flow (AC-OPF) at scale. It is a

15

million parameter physics-inspired graph neural network pretrained across

54

topologies of

500

to

4{,}000

buses. Our model attains a

2.45\%

zero-shot generation-cost error on a

10{,}000

bus case held-out operating conditions with no degradation as system size grows. Building on this, we pair the pretrained backbone with a physics-informed fine-tuning design based on Newton's method for power flow. With only

100

solved instances, GridSFM adapts to unseen grids up to

10{,}000

buses. We show it out performs single topology, dedicated neural network models that are trained more data, both in terms of cost and solver iterations when deployed as warm starting points. In designing this foundation model, we overcome the fact that the feasible set for AC-OPF can be disconnected. This is an obstruction that prevents any continuous neural network from approximating the solution map. To do so, we lift the problem and relax its constraints with logarithmically penalized slacks. We prove that the resulting elastic feasible set is contractible, that the AC-OPF minimizers remain minimizers of the elastic problem above an explicit penalty threshold, and that projecting an approximate solution back onto the AC-OPF feasible set is well posed. We release all models, data, and code so that the community can build on a shared starting point for AC-OPF.

Luke Bhan, Weiwei Yang, Margaret Capetz +1

University of California, San Diego · Microsoft Research · University of Washington

Neural Surrogate Modeling Optimal Power Flow Physics-Informed GNNs Power Systems

Sep 24, 2026cs.CE

AFT Neural Function Approximators for 1D Nonlinear Force Laws

Nonlinear contacts and friction strongly influence the vibration response of assembled structures, but their accurate numerical treatment is computationally demanding. The harmonic balance method is widely used to compute periodic steady-state responses, yet the required alternating frequency-time scheme becomes costly for nonsmooth and hysteretic nonlinearities and must be repeated throughout the nonlinear solution process. Here we show that this procedure can be replaced by neural networks that directly map displacement Fourier coefficients to nonlinear force coefficients and provide the corresponding Jacobian through automatic differentiation. The surrounding solver and continuation algorithms remain unchanged for the computation of frequency response curves. The neural networks exclusively learn individual nonlinear elements rather than complete system responses. Physics-based nondimensionalization and phase normalization facilitate the learning process and enable a single trained network to cover a wide range of parameter combinations. Building on the cubic spring, unilateral spring, and Jenkins elements considered here, the approach points toward a reusable library of nonlinear-element surrogates that can be combined in arbitrary number and location within a mechanical system. By bypassing the iterative force evaluation in time domain, the method offers favorable computational scaling for high-resolution analyses and systems with many nonlinear elements.

Miriam Goldack, Johann Groß, Malte Krack +1

Technische Universität Berlin, Chair of Cyber-Physical Systems in Mechanical Engineering, Straße des 17. Juni 135, 10623 Berlin, Germany · University of Stuttgart, Institute of Aircraft Propulsion Systems, Pfaffenwaldring 6, 70569 Stuttgart, Germany

Neural Surrogate Modeling Dynamical Systems Structural Mechanics

Sep 24, 2026cs.CV

HGPTrans: Hierarchical Graph-Pooling Transolver for Automotive Aerodynamic Drag Coefficient Prediction

Accurate and rapid prediction of the aerodynamic drag coefficient (

C_D

) is essential for vehicle design, particularly during early-stage design, where many candidate geometries must be evaluated. Although computational fluid dynamics (CFD) provides reliable aerodynamic estimates, its high computational cost limits large-scale design exploration. This paper proposes the hierarchical graph-pooling Transolver (HGPTrans), which combines hierarchical graph pooling with Transolver-based attention to directly predict

C_D

from vehicle surface meshes. Motivated by the fact that vehicle aerodynamics depends on both local geometric features and long-range interactions among spatially distant surface regions, HGPTrans integrates three complementary components. Graph isomorphism convolutions encode discriminative local geometry, Transolver-style slice attention captures global interactions with linear computational complexity, and information-redundancy-aware hierarchical pooling progressively removes redundant nodes while preserving informative geometric structures. The model is trained and evaluated on the large-scale DrivAerNet and DrivAerNet++ datasets, where it achieves the lowest mean absolute error and mean squared error among the evaluated baselines. Its generalization capability is further assessed through transfer learning on a real-vehicle dataset containing both sedans and sport utility vehicles (SUVs), achieving relative

L_1

errors of 1.56% (sedans) and 2.12% (SUVs) with an inference time of approximately

0.293

s per vehicle. This corresponds to an acceleration of several orders of magnitude relative to high-fidelity CFD while keeping the predicted drag coefficients within a few percent of the CFD reference. Ablation studies confirm each component's contribution and reveal the effects of depth and pooling ratio.

Bo Liu, Fengli Zhang, Qiuli Luo +2

Institute of Auto Engineering, BYD Auto Industry Co., Ltd., Shenzhen, China

Neural Surrogate Modeling Graph Neural Networks

Sep 23, 2026physics.ao-ph

HClimRep-Ocean: A Global Ocean Emulator on an Unstructured Mesh

Machine-learning (ML) emulators for atmospheric processes have advanced rapidly in recent years, transforming weather forecasting. Although early ML ocean forecasting models now exist, they remain less developed than their atmospheric counterparts. Unlike the atmosphere, much of the ocean's kinetic energy resides in mesoscale eddies whose characteristic spatial scales are approximately an order of magnitude smaller than those of comparable atmospheric features. Moreover, complex coastlines, narrow straits, and ice-covered seas make boundary representation a central challenge that atmospheric models do not face. Consequently, numerical ocean simulations commonly use locally refined or even completely unstructured meshes. However, their data-driven counterparts have so far been built around latitude-longitude grids. We present HClimRep-Ocean, an ocean emulator that operates directly on the native unstructured mesh of FESOM2. The emulator is trained on a 209-year AWI-CM3 control integration and is run without atmospheric forcing, receiving the atmospheric state only at initialisation time, which isolates the predictability carried by the ocean state itself. Skill is strongly field-dependent: for currents, HClimRep-Ocean outperforms every reference at 30 day forecast, whereas for temperature and salinity a damped-anomaly persistence forecast remains the more accurate estimator. This behaviour is physically interpretable: current variability is largely geostrophic and internally generated, whereas sea-surface temperature and salinity fluctuations are driven by atmospheric forcing through weather state. Evaluated independently on the OceanBench benchmark, a reanalysis-trained variant of HClimRep-Ocean achieves the lowest RMSE against GLORYS reanalysis among all assessed systems, confirming the competitiveness of the native-mesh approach.

Kacper Nowak, Aleksei Koldunov, Nikolay Koldunov +7

Alfred Wegener Institute, Helmholtz Centre for Polar and Marine Research, Bremerhaven, Germany · Forschungszentrum Jülich GmbH, Jülich Supercomputing Center, Jülich, Germany · Karlsruhe Institute of Technology, Karlsruhe, Germany +3

Neural Surrogate Modeling Climate Modeling Spatiotemporal Forecasting

Sep 23, 2026cs.LG

Probabilistic and Geometry Aware Neural Surrogate of Scrape Off Layer Plasma Simulations

Fast surrogates for tokamak boundary-plasma simulation are typically deterministic regressors mapping a global operating point to a flattened vector of cell values. Near the divertor detachment transition the steady state is not reliably single-valued. A point estimate must average over qualitatively different plasma states, and it arrives with no statement of confidence. Moreover, the flattened vector representation discards the geometric structure of the SOLPS-ITER mesh. This work addresses both problems. We unroll the curvilinear mesh into three fixed-size image tensors whose layout preserves cell adjacency and inverts exactly, letting a convolutional network act on the geometry without loss of information. A conditional flow matching model, well suited to highly sensitive systems, is then trained on this representation. The result is an efficient, scalable surrogate that captures multiple plausible outcomes even at sensitive operating points. Along a gas-puff scan, the predictive distribution splits into a hot and a cold mode across an early regime transition. A further check on synthetic data with an injected bifurcation of known size confirms the model recovers both branches rather than their average.

Gabriele Gianuzzo, Stefan Dasbach, Fleur Hendriks +2

Eindhoven University of Technology · DIFFER

Neural Surrogate Modeling Surrogate Modeling Conditional Generative Modeling

Sep 23, 2026cs.CE

KATOsuper: Surrogate-accelerated neural topology optimization with sensitivity-consistent Fourier neural operators

Topology optimization (TO) remains computationally intensive due to repeated finite element analysis (FEA) evaluations required at each iteration. While neural network-based surrogates offer potential acceleration, existing approaches often suffer from gradient inconsistency between predicted objectives and sensitivities, leading to optimization instability. This work presents KATOsuper, an objective-agnostic framework that couples neural-reparameterized topology optimization with a Sensitivity-Consistent Fourier Neural Operator (SC-FNO). The framework employs the forward_split architecture, which derives deployed sensitivities via automatic differentiation through the predicted objective field and thereby preserves consistency between the predicted objective and the gradient used for optimization. The case studies include three 2D benchmark problems and three 3D structures considering compliance or stress minimization. A physics-informed multi-channel input encoding with Fourier position embedding enables resolution-invariant learning, supporting zero-shot extrapolation beyond the training resolution, with useful performance at moderate scaling factors and topology-preserving exploration at up to 64x without retraining. The framework extends to 3D through KATO3D, featuring novel KANConv3D blocks with learnable B-spline activations. KATOsuper demonstrates 15--110x deployment-time speedup over MATLAB baselines while maintaining competitive optimality, with the clearest gains observed in complex 3D and stress-optimization cases. The insight that sensitivity direction matters more than magnitude enables robust optimization even with approximate physics evaluation, extensible to other differentiable physics-driven design objectives.

Shengyu Yan, Jasmin Jelovica

Department of Mechanical Engineering, The University of British Columbia, 6250 Applied Science Ln, Vancouver, V6T 1Z4, Canada · Department of Civil Engineering, The University of British Columbia, 6250 Applied Science Ln, Vancouver, V6T 1Z4, Canada

Neural Surrogate Modeling Topology Optimization Surrogate Modeling Fourier Neural Operator Surrogate-Assisted Optimization

Sep 22, 2026cs.LG

Towards Hierarchical GNNs for multi-grid power flow: generalization across operating scenarios

Hierarchical latent communication improves the generalization of a multi-grid power-flow model to new operating scenarios. The module exchanges information through two reduced graphs within a GENCO-based corrective network. We compare Kron-derived transports, a same-anchor Quotient construction and a flat backbone in preliminary trainings of 200 epochs on three grid topologies, with three initialization seeds per model. Evaluation uses 200 newly generated, preselected scenarios per grid. On the training topologies, Kron reduces the macro family-balanced voltage error from 5.660 +- 0.899 to 0.851 +- 0.110: an 85.0% reduction relative to Flat GENCO and 31.0% relative to Quotient, which reaches 1.235 +- 0.225. Both hierarchical models outperform a per-bus mean fitted on training solutions on every training topology in all three seeds. These results demonstrate generalization across operating scenarios within the studied topologies, with one set of learned parameters shared across grids. Evaluation on two additional topologies distinguishes this achievement from cross-topology generalization: the current models do not yet outperform the fitted reference in that calibrated- transfer setting. This preprint presents the architecture and preliminary evidence for hierarchical communication as a component of multi-grid power-flow learning, with generalization to unseen topologies as the next development objective.

Carmine Delle Femine, Leire Garin Atxaga, Asier Diaz-Iglesias +3

Vicomtech Foundation, Department of Energy, Basque Research and Technology Alliance (BRTA), Donostia/San Sebastián, Spain · Department of Languages and Information Systems, University of the Basque Country (UPV/EHU), Donostia/San Sebastián, Spain

Neural Surrogate Modeling Graph Neural Networks Power Systems

Sep 22, 2026cs.LG

DeepFEAv2: Deep Learning for Transient Finite Element Analysis Beyond Structured Meshes

Finite Element Analysis (FEA) is widely used for transient mechanical simulations, but its high computational cost limits real-time and high-resolution applications. Deep learning surrogate models can reduce this cost; however, many existing approaches are restricted to steady-state prediction or cannot jointly predict Node- and Element-based Outputs (NEO) over time. The state-of-the-art DeepFEA framework has addressed these issues but remains limited to structured finite element (FE) meshes. To overcome this limitation, this study proposes DeepFEAv2, a deep learning surrogate framework that enables prediction of transient FEA simulations across different FE mesh topologies and element types. The main contributions of DeepFEAv2 are: (a) a module that uses the FE connectivity matrix to organize input features by element and arrange them into an input sequence guided by the mesh topology; (b) a novel neural network architecture designed to process the input sequence and jointly predict NEO over time; and (c) a FEA-informed optimization strategy for regularizing these NEO predictions. DeepFEAv2 was evaluated on structured and unstructured 3D linear elastic datasets, as well as on a pressure-driven aortic valve dataset. DeepFEAv2 achieved R^2 values up to 0.99 and normalized errors as low as 0.38%. Compared with DeepFEA, it achieved up to 38.0% relative increase in R^2 and up to 87.1% reduction in normalized error. DeepFEAv2 also performed inference up to three orders of magnitude faster than traditional FEA. These results demonstrate that DeepFEAv2 can efficiently model transient FEA simulations across increasingly complex FE settings, providing a scalable surrogate framework for transient FEA.

Georgios Triantafyllou, Panagiotis G. Kalozoumis, Dimitris K. Iakovidis

Department of Computer Science and Biomedical Informatics, University of Thessaly, 2-4 Papasiopoulou st. 35131, Lamia, Greece

Neural Surrogate Modeling Finite Element Method

Sep 21, 2026cs.LG

Predictive Uncertainty for Neural CAE Surrogates

Neural surrogates can substantially accelerate computer-aided engineering (CAE) workflows, but their use in design requires uncertainty estimates that remain meaningful across varying geometries, spatial prediction fields, and engineering quantities of interest. We investigate how established uncertainty quantification (UQ) approaches behave when adapted to geometry-conditioned neural surrogates. We compare one closed-form and two sampling-based approaches-a Gaussian process (GP)-based method, concrete Monte Carlo (MC) dropout, and deep ensembles-and evaluate them on three large, industry-relevant CAE datasets for external aerodynamics and crash dynamics. We examine whether predicted uncertainties have credible magnitudes, identify locations with larger prediction errors, respond to unfamiliar inputs, and remain informative for derived engineering quantities. On the DrivAerStar dataset, where all three methods are compared, each generally assigns higher uncertainty to locations with larger prediction errors, and validation-based rescaling brings interval coverage close to nominal on a disjoint in-distribution test set. Results on AirFRANS and automotive crash also show useful error ranking and interval estimates, but the relative performance of the methods changes with the dataset and evaluation criterion. UQ methods and evaluation metrics should therefore be selected based on the intended downstream CAE decision.

Kaustubh Tangsali, Mohammad Amin Nabian, Kelvin Lee +2

NVIDIA

Neural Surrogate Modeling Uncertainty Quantification Uncertainty Calibration

Sep 21, 2026math.NA

Cost-Accuracy Trade-offs: Neural Operator vs Classical Numerical Solver

Neural operators are data-driven models that learn mappings from inputs that parameterize partial differential equations, such as spatially varying coefficients, initial conditions, forcing terms, boundary conditions, or geometries, to solution fields or quantities of interest. Once trained, they can serve as surrogates for classical numerical solvers in many-query settings that require repeated evaluations for varying inputs. We address the question of when, and then why, neural operator surrogates outperform classical numerical solvers, in terms of cost for a given accuracy. We focus on the post-training, many-query limit, in which data-acquisition and training costs are treated as fixed and fully amortized. Even in this deliberately favorable regime for neural operators, there are regimes in which classical solvers outperform the surrogate models. We compare the cost-accuracy performance of neural operator surrogates and classical numerical solvers through a reproducible benchmark study comparing neural operators with problem-matched classical solvers on representative problems in computational science and engineering, focusing on prediction error, per-query floating-point cost, and wall-clock runtime. Neural operators are most competitive at low-to-moderate accuracy requirements. Their floating-point cost advantage depends strongly on the problem structure, arising when they avoid temporal or nonlinear iterations or predict a reduced quantity of interest rather than a full solution field. Additional wall-clock speedups result from dense tensor operations that are well suited to modern hardware. As the target accuracy is tightened, achieving the required accuracy with neural operators becomes increasingly challenging, and classical solvers outperform surrogates in this regime; thus classical solvers will remain important for verification and high-accuracy computation.

Daniel Zhengyu Huang, Andrew M. Stuart

Beijing International Center for Mathematical Research, Center for Machine Learning Research, Peking University, Beijing, China · California Institute of Technology, Pasadena, CA

Neural Surrogate Modeling Neural PDE Solvers PDE Solving Neural Operators