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

Jun 15, 2026cs.LG

A Validated LBM Dataset and Pipeline for Surrogate Modeling of Turbulent 3D Obstructed Channel Flows

Evaluating neural operators for 3D turbulent flow requires validated datasets with physical benchmarks. We present a reproducible pipeline generating training data for 3D channel flows around generated geometries at Re=1,000-10,000. Our lattice Boltzmann solver with cumulant collision operators is rigorously verified against experimental measurements (Strouhal number, drag coefficients, turbulent fluctuations) with comprehensive grid convergence studies at resolution 1024x512x512. Building upon an established framework, this validated pipeline enables standardized surrogate model comparison. We outline planned systematic evaluation of Fourier Neural Operator and U-Net variants on forecasting, super-resolution, and error correction tasks, using physics-informed metrics to assess turbulent energy cascade representation. Future work will compare computational efficiency between numerical solvers and neural surrogates, exploring practical application. We seek community feedback on our validation approach, planned benchmark methodology, and evaluation priorities for neural operators in turbulent flows.

Lukas Schröder, Shubham Kavane, Harald Köstler

Chair of Computer Science 10 (System Simulation) Friedrich-Alexander-Universität Erlangen-Nürnberg

Neural Surrogate Modeling Synthetic Benchmark Generation Computational Fluid Dynamics

Jun 14, 2026physics.ins-det

GPT-Based Fast Simulation of CLAS12 Detector Hits via Conditional Autoregressive Generation

Modern particles physics experiments have demonstrated an increasing need for fast, high-fidelity detector simulation as detector components have improved and subsequent computational requirements approach the limits of available resources. Recently, deep generative models have emerged as a promising alternative to traditional Monte-Carlo methods, with recent works drawing inspiration from large language models (LLMs) and self-supervised next-token prediction methods. In this work, we present an application of a GPT-style autoregressive transformer as a fast surrogate model for the calorimeter inside the CLAS12 experiment at the Thomas Jefferson National Accelerator Facility. The model is conditioned on incident momentum and generates realistic detector hits autoregressively across all nine calorimeter layers as sequences of strip, ADC, and TDC tokens. We demonstrate that the model faithfully reproduces hit multiplicity, spatial distributions, energy deposits, and the energy-momentum response of the electromagnetic calorimeter. The generator achieves inference rates exceeding 700 events per second on a single GPU, providing a substantial speedup over traditional Geant4-based simulations while maintaining physics fidelity essential for high-luminosity experimental programs.

Cole Granger, James Giroux, Richard Tyson +2

William & Mary, Department of Data Science, Williamsburg, VA 23185, USA · University of Glasgow, School of Physics and Astronomy, Glasgow G12 8QQ,14 UK · Thomas Jefferson National Accelerator Facility, Newport News, VA 23606, USA +1

Neural Surrogate Modeling High-Energy Physics Conditional Generative Modeling Physics-Based Simulation

Jun 14, 2026cs.DC

Quantifying the Impact of Lossy Compression on Neural Generative Surrogate Modeling

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

Zhimin Li, Harshitha Menon, Charles Jekel +2

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

Neural Surrogate Modeling Surrogate Modeling

Jun 13, 2026physics.flu-dyn

ShipNet: A Geometric Deep Learning Surrogate for Real-Time Ship Hydrodynamics

Accurate prediction of hydrodynamic performance is central to ship design, yet high-fidelity computational fluid dynamics remains prohibitively expensive for large-scale parametric exploration. This motivates the development of data-driven surrogate models that provide rapid approximations to hydrodynamic predictions at substantially reduced cost. We present ShipNet, a geometric deep-learning surrogate that predicts both hull-surface pressure distributions and far-field free-surface wave patterns directly from hull geometry and speed. The network employs a regularized dynamic graph convolutional backbone on hull point clouds, with a multi-head decoder for simultaneous near-body pressure and free-surface elevation outputs. Training data consist of 420 inviscid free-surface simulations generated using a potential-flow panel method for two parent yacht hulls, each parameterized into 70 variants and evaluated at three speeds. ShipNet predicts per-point pressure coefficient and two-dimensional wave elevation map using a composite loss that combines point-wise regression and image-structure terms. On a geometry-held-out test set, ShipNet achieves R^2=0.98 for hull pressure and R^2=0.91 for wave fields. Inference requires approximately 0.15s per case, yielding over a 550x speedup relative to the potential-flow solver on conventional hardware. Limitations include the restricted geometry and speed ranges and the inviscid training data, while future work will extend the model to high-fidelity viscous simulations with physics-informed regularization.

Kirsten Odendaal, George Drakoulas

Maritime Research Insitute Netherlands Wageningen, Netherlands · Damen Research Gorinchem, Netherlands

Neural Surrogate Modeling Computational Fluid Dynamics

Jun 13, 2026cs.LG

Physics-conforming Latent Twins

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

Matthias Chung, Yutong Bu, Deepanshu Verma

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

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

Jun 12, 2026physics.flu-dyn

Multiscale Hypersonic Boundary Layer Reconstruction via Spectral Binning and Subdomain-wise Conditional Diffusion

We propose a multiscale probabilistic reconstruction framework for hypersonic Couette flow, where near-wall states are inferred from limited top-wall observations using conditional diffusion model. The boundary layer is divided into overlapping wall-normal subdomains, and a single height- and Mach-conditioned Elucidating Diffusion Model (EDM) is trained jointly for M=6,7,8 to sample velocity, density, pressure, and temperature fields conditioned on a top-wall boundary slice. A soft overlap inpainting strategy assembles subdomain predictions into full-volume reconstructions while maintaining inter-subdomain continuity and small-scale variability. To improve the spectral fidelity of the generated fields, we introduce a novel bounded binned spectral power (BSP) loss that preserves high-wavenumber content while remaining numerically stable across the diffusion noise schedule. Validation against direct numerical simulation data shows that the model recovers instantaneous structures, spectra, statistical profiles, correlations, and wall quantities across all training Mach numbers, while providing spatially structured uncertainty estimates. The reconstructed Mach-conditioned profiles also collapse under the Trettel-Larsson transformation, indicating consistency with compressibility scaling. These results establish the domain decomposed conditional diffusion model with a bounded binned spectral loss as an effective probabilistic surrogate for near-wall reconstruction in hypersonic wall-bounded turbulence.

Hojin Kim, Dibyajyoti Chakraborty, Takahiko Toki +2

School of Mechanical Engineering, Purdue University, West Lafayette, 47907, IN, USA · College of Information Sciences and Technology, Pennsylvania State University, University Park, 16802, PA, USA · Mathematics and Computer Science Division, Argonne National Laboratory, Lemont, 60439, IL, USA

Neural Surrogate Modeling Conditional Diffusion Models Computational Fluid Dynamics

Jun 11, 2026cs.LG

cAPM: Continual AI-Assisted Pace-Mapping with Active Learning

Ventricular tachycardia is a life-threatening rhythm disorder and a major cause of sudden cardiac death. Pace-mapping is a clinical procedure for identifying the intervention target during catheter ablation of VT. It requires clinicians to pace different sites in the ventricles and rapidly interpret the resulting electrocardiograms to determine where to pace next or whether a target site has been identified. Active learning AI models have been proposed to guide clinicians to the next pacing site, showing promise in reducing the number of pacing sites and improving the efficiency of pace-mapping. Existing methods require retraining each target without the ability to transfer knowledge across multiple VTs within the same patient or across patients. We introduce cAPM for continuous AI-assisted pace-mapping to capture and transfer knowledge accumulated from past pace-mapping data to reduce the number of pace-mapping data needed for future target VTs. This is made possible by a task-agnostic surrogate neural network that learns the mapping from pacing sites to 12-lead ECG morphology, an active-learning strategy that refines this surrogate model by selecting the most informative pacing site for each target, and a continual learning strategy to do so sequentially while retaining knowledge from prior targets. Evaluated on an in-silico testbed consisting of sequentially-presented localization tasks across different physiological conditions and ventricular geometries, cAPM with and without replay of past data samples achieved an 81% probability of localizing within clinical tolerance (5 mm accuracy) using 4.5 pace-mapping sites, compared to the state-of-the-art active-learning method achieving 38% probability using 13.7 pacing sites. These results provide a strong basis for preparing cAPM towards in-vivo preclinical and clinical studies where it can be used to guide pace-mapping.

Dylan O'Hara, Pradeep Bajracharya, Casey Meisenzahl +7

Rochester Institute of Technology, Rochester, New York, USA · Department of Biomedical Engineering, University of Utah, Salt Lake City, Utah, USA · Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, Utah, USA +5

Neural Surrogate Modeling Electrocardiography Active Learning

Jun 11, 2026cs.AR

BigPower: Hierarchical Source-Level Module Power Estimation for CPUs with Large Language Models

Accurate power estimation is important for understanding and optimizing CPU power behavior, yet practical workflows often rely on simulation-derived information or post-silicon analysis. In this work, we present BigPower, a hierarchical source-level surrogate model for fine-grained module-level power estimation during CPU design. BigPower leverages large language model-based representations together with architectural hierarchy, module connectivity, configuration parameters, and workload context to estimate module-level power consumption directly from source-level design information, without requiring additional simulation during inference. Experimental results in the open-source XiangShan processor family demonstrate practical fine-grained power estimation across diverse configurations and workloads, offering an efficient alternative to conventional simulation-based workflows.

Honghua Zhu, Chunjie Luo, Jianfeng Zhan

State Key Lab of Processors, Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China · University of Chinese Academy of Sciences, Beijing, China

Neural Surrogate Modeling

Jun 11, 2026cs.LG

A fully GPU-based workflow for building physics emulators of hypersonic flows

The ability to resolve complex physical phenomena with high fidelity and at low computational cost is central to addressing key challenges in modern engineering. A prime example lies in hypersonic flows, where the precise prediction of the full flowfield topology, in particular with respect to shock wave location and intensity, is critical. Yet supersonic and hypersonic flows continue to be a stumbling block for traditional reduced-order models and neural emulators that struggle to capture steep gradients in flow states with physical consistency in applications of industrial relevance. To that end, we introduce a fully GPU based workflow that integrates accelerated data generation with the training of neural emulators augmented by uncertainty quantification and physics-aware refinement. Our workflow is enabled by a differentiable high-fidelity solver (JAX-Fluids) which we employ for rapid dataset creation and residual-based improvement of the neural emulator to enhance physical consistency. Building on this framework, we first present a suite of model architectures and analyze their scaling behavior to expose their strengths and shortcomings. We then show that residual-based refinement enables training on cases where only mesh and input parameters are available, substantially reducing residuals and improving physical consistency. Together, differentiable simulation and residual-based refinement yield physics emulators that remain reliable beyond their training distribution, a key requirement for deploying surrogates in real-world engineering design loops.

Fabian Paischer, Dylan Rubini, Deniz A. Bezgin +6

ELLIS Unit, Institute for Machine Learning, JKU Linz · EMMI AI, Linz · Chair of Aerodynamics and Fluid Mechanics, TU Munich, Germany

Neural Surrogate Modeling Physics-Informed ML Iterative Refinement Computational Fluid Dynamics

Jun 10, 2026cs.LG

PCA-Enhanced Adaptive NVAR Framework for High-Resolution Sea Surface Temperature Forecasting in the East Sea

Accurate forecasting of sea surface temperature (SST) in regional seas such as the East Sea is crucial for monitoring marine ecosystems, assessing climate risks, managing fisheries, and conducting naval operations. Traditional numerical ocean models provide reliable predictions but are computationally expensive and often unsuitable for real-time forecasting. Many deep learning methods also struggle with high-dimensional spatiotemporal ocean data and experience error accumulation over longer forecasting periods. This study builds on our previously proposed Adaptive Next-Generation Reservoir Computing (Adaptive NVAR) framework, initially introduced and tested on synthetic dynamical systems, and extends it to ocean forecasting. We present a reduced-order forecasting framework that combines Singular Value Decomposition (SVD) with Adaptive NVAR to predict SST dynamics in the East Sea. SST fields are compressed into a low-dimensional representation using SVD, which extracts dominant modes of ocean variability. Adaptive NVAR models the temporal evolution of these latent states, and the predicted states are reconstructed into SST forecasts. We evaluate the framework using regional ocean datasets and compare it with the standard NG-RC/NVAR. Results show that Adaptive NVAR consistently achieves lower forecasting errors across multiple prediction horizons. In addition, SVD reduces computational complexity, resulting in a fast and scalable framework suitable for real-time ocean forecasting.

Sherkhon Azimov, Susana López-Moreno, Eric Dolores-Cuenca +2

Department of Mathematics, Pusan National University, Republic of Korea · Humanoid Olfactory Display Center, Pusan National University, Republic of Korea · Industrial Mathematics Center, Pusan National University, Republic of Korea +3

Neural Surrogate Modeling Reservoir Computing Spatiotemporal Forecasting

Jun 10, 2026cs.LG

Scalable Deep Learning Framework for Global High-Resolution Land Use Reconstruction

Uncertainty in the terrestrial carbon cycle remains a major constraint in climate projections, partly driven by the uncertainties affecting the land surface representation and variability in Earth system models. To address this limitation, we present a data-driven framework AI4Land, for generating high-resolution historical reconstructions and future projections of key land surface variables. The framework follows a two-phase approach using a U-Net architecture. In the first phase, which is the focus of this work, it reconstructs annual land use and land cover by integrating coarse-resolution scenario data with static geophysical features. In a planned second phase, the resulting high-resolution maps will be used to predict dynamic biophysical variables, particularly leaf area index, at finer temporal scales. Trained on Earth observation data, the models learn to reproduce spatially explicit and physically consistent land surface patterns, extending temporal coverage to periods lacking direct observations. AI4Land was developed and trained on MareNostrum5, demonstrating how GPU-accelerated HPC infrastructure enables global-scale climate AI pipelines. The final product is a suite of open-source emulators designed for real-time coupling with digital twin platforms, such as those developed under the Destination Earth initiative. By delivering realistic and evolving land surface conditions on demand, this work aims to reduce critical uncertainties and improve the predictive power of next-generation climate simulations.

Amirpasha Mozaffari, Marina Castaño, Stefano Materia +7

Earth Science Department, Barcelona Supercomputing Center, Barcelona, 08034, Spain · AI Institute, Barcelona Supercomputing Center, Barcelona, 08034, Spain

Neural Surrogate Modeling Climate Science Climate Modeling

Jun 10, 2026cs.LG

Sparse probes and murky physics: a case study of interpretability challenges in a foundation model for continuum dynamics

Generative AI emulators are increasingly used in scientific domains where we already have strong theory, benchmarks, and physical intuition. This raises a central evaluation and interpretability question: when a foundation-style model can reproduce known continuum dynamics, what internal mechanism supports that behavior, is the internal behaviour consistent with known physics, and how does it relate to where the emulator succeeds or fails? We investigate a cross-domain foundation model for continuum dynamics, Walrus by Polymathic, using mechanistic interpretability guided by physical principles. We apply a sparse autoencoder (SAE) to probe a selected layer, and address the practical challenge of triaging a large feature set (over 20,000) using enstrophy as a physically grounded metric. As a deliberately simple testbed, we focus on shear flow and compare feature recruitment across multiple shear-flow setups, i.e. parameter values in the numerical simulation. Across setups we find evidence of piecewise consistency, with subsets of features recurring in similar roles, but this structure is intermittent and does not map cleanly onto standard physical decompositions. In parallel, direct comparisons between numerical simulation and the emulator reveal systematic output-level discrepancies, including regimes where energy/structures become too diffuse or too localized. We connect parts of these discrepancies to changes in specific SAE feature usage. Our work highlights open questions for scientific foundation models: how to robustly prioritize mechanistically meaningful features, how to separate stable structure from analysis artifacts (including single-layer and SAE limitations), and how to use established benchmarks to decide when "different" internal representations are genuinely informative rather than merely effective.

Katherine Rosenfeld, Maike Sonnewald

Gates Foundation · UC Davis

Neural Surrogate Modeling Mechanistic Interpretability Computational Fluid Dynamics

Jun 10, 2026cs.LG

Physics-Distilled Neural Network enabled by Large Language Models for Manufacturing Process-Property Predictive Modeling

Predicting process-property relationships in manufacturing is often challenged by high experimental costs and the limited interpretability of complex 'black-box' models. This paper proposes a novel knowledge distillation framework designed to achieve high-accuracy predictions in data-scarce scenarios. The framework integrates analytical physics priors, which are systematically extracted from scientific literature via Large Language Models, into a privileged teacher model. We employ a Graph-Masked Attention layer to capture the complex physical dependencies among input variables showing strict setpoints or a combination of static and high-frequency temporal signatures. This privileged knowledge is distilled into a lightweight student predictor for inference. The feasibility and robustness of the framework are evaluated through a comprehensive experiment across five diverse manufacturing processes. To ensure statistical reliability, given the small dataset sizes, a repeated K-fold cross-validation technique is employed to quantify model stability and generalization. Results indicate that the proposed framework consistently achieves high predictive accuracy across all evaluated domains. Most importantly, the architecture demonstrates significant fault tolerance by maintaining robust predictive performance even in scenarios where LLM-derived analytical priors are suboptimal or incomplete. Furthermore, the student predictor achieves an inference frequency exceeding 6000 Hz, which facilitates real-time edge deployment on standard industrial hardware. This work provides a scalable solution for bridging the gap between theoretical physics and real-time industrial monitoring in data-limited environments.

Ge Song, Kiarash Naghavi Khanghah, Anandkumar Patel +2

School of Mechanical, Aerospace and Manufacturing Engineering, University of Connecticut, Storrs, CT 06269 · Department of Mechanical & Aerospace Engineering, Rutgers, the State University of New Jersey, Piscataway, NJ 08854

Neural Surrogate Modeling Materials Property Prediction Physics-Informed ML Knowledge Distillation

Jun 9, 2026cs.LG

COGENT: Continuous Graph Emulators with Neural Ordinary Differential Equations for Long-Term Physical Forecasting

In this work, we present COGENT, a continuous graph emulator with Neural Ordinary Differential Equations for long-term physical forecasting on irregular geospatial meshes. COGENT encodes a finite history of system states and associated forcing fields and external forcings with a graph-based history encoder, producing node-wise context vectors that capture both local spatial interactions and temporal evolution. These context vectors initialize and condition a latent Neural Ordinary Differential Equation whose dynamics are driven by interpolated future forcings and explicit relative rollout time. By modeling the forecast trajectory as a continuous latent dynamical system, COGENT can generate predictions at arbitrary future times rather than being restricted to a fixed temporal discretization. A residual decoder maps the resulting latent trajectories back to future physical states, enabling direct multi-step forecasting without repeatedly feeding predicted states back into the model. This formulation combines graph-based spatial representation, history-conditioned latent dynamics, and continuous-time rollout in a unified framework for mesh-based physical simulation emulation. In order to stabilize training with long-horizon supervision, we also propose effective rollout-horizon sampling and a progressive rollout-horizon scheduling strategy. We evaluate COGENT on transient ice-sheet simulations generated by the Ice-sheet and Sea-level System Model, demonstrating improved long-range stability over autoregressive graph baselines. These results suggest that continuous graph Neural ODEs provide a promising methodology for scalable physical forecasting on irregular geospatial meshes, particularly in applications that require stable long-horizon predictions and the ability to query system states at arbitrary times.

Zesheng Liu, Maryam Rahnemoonfar

Lehigh University · Bethlehem, Pennsylvania, USA

Neural Surrogate Modeling Long-Term Time Series Forecasting Spatiotemporal Forecasting Neural ODEs Spatiotemporal GNNs

Jun 9, 2026cs.CE

Non-linear mechanical field reconstruction coupling recurrent neural networks with physics-informed graph neural networks

Reconstructing local stress fields in heterogeneous microstructures under non-linear, history-dependent loading remains a major computational bottleneck in multi-scale simulations. We propose a coupled LSTM-GNN framework that links the temporal and spatial aspects of local stress field reconstruction. A Long Short-Term Memory network encodes macroscopic stress-strain sequences into a compact hidden state that captures the path-dependent constitutive response, while a physics-informed Graph Neural Network reconstructs the spatially-resolved stress field at each time step. We introduce a relative weighting strategy with linear warm-up to balance the data-driven reconstruction loss and a discrete divergence-based equilibrium penalty. This resolves the scale mismatch that prevents fixed-weight formulations from converging in the elasto-plastic regime. The model is trained on 10,000 non-proportional loading paths applied to a periodic plate-with-a-hole microstructure and von Mises elasto-plasticity. The model achieves three orders of magnitude speedup over finite element simulations and generalizes to loading sequences twice the training length, with 1.9% cumulative error. Because the graph relies on mesh connectivity instead of the specific element type, one trained surrogate can be applied directly without retraining to meshes with different element types and to both coarser and finer resolutions, while in all cases reproducing the high-fidelity quad-element FE field used during training. Indeed, the message passing characteristics inherent to GNN and MeshGraphNet architecture render the model mesh-agnostic. Analysis of the LSTM hidden states suggests a low-dimensional structure related to the internal state variables of the constitutive model.

Manuel Ricardo Guevara Garban, Yves Chemisky, Étienne Prulière +3

Univ. Bordeaux, CNRS, Bordeaux INP, I2M, UMR 5295, Talence, France · Univ. Bordeaux, CNRS, Bordeaux INP, LaBRI, UMR 5800, Talence, France · Institute of Mechanics and Fluid Dynamics, TU Bergakademie Freiberg, Freiberg, 09599, Germany +2

Neural Surrogate Modeling Structural Mechanics Physics-Informed ML Physics-Informed GNNs Spatiotemporal GNNs

Jun 9, 2026cs.LG

PL-KKT-hPINN: Enforcing Nonlinear Equality Constraints on Neural Networks via Piecewise-Linear Projection

While physics-informed neural networks (PINNs) have shown strong potential for process modeling, physical equations are only enforced as soft constraints during training, and thus, they do not guarantee constraint satisfaction at inference. We propose a framework, called piecewise-linear Karush--Kuhn--Tucker hard-constrained PINNs (PL-KKT-hPINNs), that strictly enforces nonlinear equality constraints through piecewise-linear projection. This extends the KKT-hPINN framewor, which exactly enforces linear equalities through the Karush--Kuhn--Tucker (KKT) conditions associated with orthogonally projecting neural network outputs onto the constraint feasible region. The method is demonstrated on a continuous stirred-tank reactor (CSTR) case study for both one and two inputs. Results show that PL-KKT-hPINN preserves predictive accuracy comparable to that of a standard neural network while achieving substantially lower constraint violations. In addition, the proposed model shows improved robustness in low-data regimes, yielding lower RMSE than the unconstrained neural network for limited training sample sizes. These results demonstrate that PL-KKT-hPINN provides a computationally efficient and physically consistent framework for surrogate modeling of nonlinear chemical engineering systems.

Fateme Mohammad Mohammadi, Hector Budman, Joshua L. Pulsipher

Department of Chemical Engineering University of Waterloo, 200 University Ave W, Waterloo, ON N2L 3G1, Canada

Neural Surrogate Modeling Constrained Optimization Physics-Informed ML

Jun 8, 2026cs.LG

OnlyDense: Reduced-Order Modeling for Lagrangian simulation

In science and engineering, Lagrangian simulation methods such as Smooth Particle Hydrodynamics (SPH) or Material Point Method (MPM) are often employed to study the behavior of dynamic systems. However, these methods can be prohibitively computationally expensive, particularly when simulating multi-scale spatial or temporal phenomena, e.g., void growth and coalescence within macro-scale geometries, structural failure of spacecraft components resulting from hypervelocity impact of space debris particles, etc. In contrast to graph-based methods, where the state of the system is understood as a discrete set of particles, we propose a learning framework for scalable representation and dynamics modeling of massive particle systems by treating the system state as a function and its evolution as a trajectory in Hilbert space. Rather than representing the state as a discrete set of particles or embedding it in a nonlinear latent manifold, we approximate the state space with a linear subspace spanned by learned neural basis functions. This parameterization enables direct projection to obtain latent coefficients and explicit access to the basis functions, avoiding optimization over a nonlinear latent space. The resulting representation admits a natural interpretation: latent variables correspond to coefficients in Hilbert space, and basis functions correspond to spatial modes, analogous to Proper Orthogonal Decomposition. The framework thus unifies classical projection-based reduced-order modeling with modern deep learning, while remaining invariant to the number of discretization points. Experiments on large-scale SPH simulations with over one million particles, including dynamic events with extreme deformation and fragmentation, demonstrate that the proposed method accurately reconstructs and predicts dynamics, achieving an R

^2

score above

0.99

with as few as

32

basis functions.

Tu Do, Shannon Ryan, Santu Rana

A2I2, Deakin University, Geelong, Victoria, Australia

Neural Surrogate Modeling Reduced-Order Modeling Physics-Based Simulation

Jun 6, 2026cs.LG

Mesh Graph Neural Network Framework for Accelerating Finite Element Simulation for Arbitrary Geometries

Finite element analysis (FEA) is essential for structural design but remains computationally expensive, particularly when evaluating multiple design iterations or load scenarios. Machine learning surrogate models offer a promising alternative, yet most approaches struggle with a critical limitation: generalizing across varying geometries. This work presents a mesh graph network (MGN) for predicting von Mises stress fields in 2D structural components with arbitrary hole geometries. Unlike traditional machine learning approaches that use absolute node coordinates as features, the proposed model builds on existing MGN frameworks that encode node types (e.g., fixed boundary, free surface, hole edge), relative edge features (distance between neighbors), and global features (applied load). This architecture is inherently translation- and rotation-invariant, enabling generalization to unseen geometries without retraining. The MGN was trained on 11 plate geometries under 20 load conditions and evaluated on 7 unseen geometries and 3 unseen loads. In the most favorable case, the model achieves

R^2 \geq 0.97

on an unseen geometry and unseen load, compared to

R^2 \approx 0.01

--

0.86

for conventional models (Random Forest, Gradient Boosting , K-Nearest Neighbors) trained on identical data. However, even in less favorable cases, the MGN model still outperforms conventional models. This work extends the mesh-based simulation framework of Pfaff et al. (arXiv:2010.03409) to structural mechanics, demonstrating that graph neural networks can serve as efficient surrogates for finite element analysis across varying geometries.

Josiah D. Kunz, Kamal Choudhary

Illinois College, Jacksonville, IL, USA · Department of Materials Science and Engineering, Whiting School of Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA

Neural Surrogate Modeling Graph Neural Networks Structural Mechanics PDE Surrogate Modeling Finite Element Method

Jun 5, 2026cs.LG

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

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

Ryan Missel, Xiajun Jiang, Linwei Wang

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

Jun 4, 2026cs.LG

Learned Response-Field Inertia Operator for HEC-RAS 2D Water-Surface Elevation Prediction

This article presents a cross-dataset evaluation of learned native-cell surrogate models for solver-consistent water-surface elevation (WSE) prediction in HEC-RAS 2D. To avoid raster remapping error and information-access confounding, surrogates are evaluated directly on the original nonuniform computational cells under an explicit policy that separates static project inputs, current hydraulic state, project-input forcing, calibration-derived quantities, and future solver-output targets. We introduce the Learned Response-Field Inertia Operator (LRFIO), a no-forcing, increment-based learned surrogate that calibrates an inertial response operator from solved HEC-RAS trajectories and deploys the retained operator through closed-form native-cell rollout. LRFIO evaluates a base-case-first response hierarchy consisting of persistence, global calibrated inertia, and segmented response-field inertia. Segmentation, residual correction, and neuralized inertia are treated as learnable modeling choices, with added complexity retained only when validation evidence justifies its cost. Evaluated across four diverse HEC-RAS 2D benchmarks, LRFIO retains different response structures for different domains, demonstrating adaptive learned complexity. The selector audit shows controlled complexity with a maximum validation regret of 4.30%. During deployment, retained rollout times range from 0.003 s to 0.242 s, and the Beaver Bayou measured-solve comparison gives an estimated 2.75 x 10^4 horizon-normalized speedup over HEC-RAS. These results indicate that the current native-cell increment is a strong solver-conditioned predictive scaffold and that added response-field, neural, or spatial complexity should be retained only when empirically justified.

Edward Holmberg, Elias Ioup, Md Meftahul Ferdaus +2

Canizaro Livingston Gulf States Center for Environmental Informatics, Department of Computer Science, The University of New Orleans, New Orleans, LA 70148, USA · Center for Geospatial Sciences, Naval Research Laboratory, Mississippi, USA · Ocean Sciences Division, Naval Research Laboratory, Mississippi, USA

Neural Surrogate Modeling PDE Surrogate Modeling Spatiotemporal Forecasting Computational Fluid Dynamics

Jun 4, 2026cs.AI

Integrating Mechanistic and Data-Driven Models for Neurological Disorders through Differentiable Programming

Advances in computational modeling, neuroimaging, and artificial intelligence are revolutionizing the modeling of neurological disorders for improved diagnostics, prognosis, and treatment planning. Mechanistic models provide valuable scientific insight into the disorders, but in practice they are often simplified with assumptions or computationally expensive and slow to solve. However, while purely data driven approaches provide speed and scalability, they require large, high quality data to train and generally suffer from interpretability and generalization issues. This perspective paper presents a structured overview of hybrid modeling strategies, which combine deep learning models with physics based solvers, and are categorized into parallel, series, and parallel-series architectures. Three main approaches that have been emphasized are residual modeling for missing or incomplete physics, Neural Ordinary Differential Equations (NODEs) for continuous time dynamics approximation, and solver in the loop that accelerates traditional solvers with neural approximations. These hybrid models integrate the governing differential equation based formulations and deep learning to characterize the evolution of neurological disorders, and promise advanced personalized neurological modeling. In addition, the study explores and proposes different hybrid configurations to improve diagnosis accuracy, predict disease progression, and inform treatment strategies across a range of neurological disorders. These capabilities outperform standalone mechanistic or purely data driven approaches, making hybrid modeling a powerful tool, especially in applications involving modeling the progression and treatment responses in neurological conditions such as brain tumors, Alzheimer's disease, and stroke.

Shah Pallav Dhanendrakumar, Saikat Pal, Sitikantha Roy

Department of Applied Mechanics, Indian Institute of Technology Delhi, New Delhi-110016, India · Yardi School of Artificial Intelligence, Indian Institute of Technology Delhi, New Delhi-110016, India

Neural Surrogate Modeling Differentiable Programming Physics-Informed ML

Jun 3, 2026cs.NE

U-Net-Accelerated Quality-Diversity Optimization for Climate-Adaptive Urban Layouts

Optimizing urban layouts for climate adaptation requires balancing building density with cold-air ventilation. Because physics-based climate simulations are computationally expensive, planners typically evaluate fewer than ten manual designs. \gls{qd} algorithms offer a way to systematically illuminate the design space, but they require surrogate models to be practical. In this paper, we replace a slow, regulatory physics simulator with a spatial deep-learning surrogate (U-Net) inside an offline MAP-Elites loop. We systematically compare this spatial approach with a traditional \gls{gp} surrogate across different training-data strategies (quasi-random Sobol sampling vs.\ active \gls{qd} bootstrapping). Our results reveal that scalar \gls{gp} surrogates fail catastrophically when trained on random samples, requiring expensive, actively generated \gls{qd} archives to generalize. In contrast, the spatial inductive bias of the U-Net allows it to learn the underlying physics mapping robustly (

R^2 = 0.996

), completely independent of the training data source. This allows offline \gls{qd} optimization to achieve highly accurate fitness rankings (

ρ= 0.994

) using only a one-time batch of random training samples. The resulting pipeline, deployed in the open-source OpenSKIZZE tool, generates thousands of diverse, climate-evaluated building layouts in under ten minutes.

Alexander Hagg, Tania Guerrero, Dirk Reith

Institute of Technology, Resource and Energy-efficient Engineering (TREE) Bonn-Rhein-Sieg University of Applied Sciences Sankt Augustin, 53757, Germany · Fraunhofer Institute for Algorithms and Scientific Computing (SCAI), Sankt Augustin, Germany

Neural Surrogate Modeling Surrogate-Assisted Optimization Urban Planning Quality-Diversity Optimization

Jun 2, 2026math.OC

Nonlocal Mean Field Schrödinger Bridge with Learned Interactions

The Schrödinger Bridge Problem connects an initial distribution to a terminal one along a minimum-energy stochastic process. Its mean-field extension, the Mean-Field Schrödinger Bridge, governs interacting populations whose dynamics and costs depend on the collective distribution. When these interactions are nonlocal, their direct evaluation scales quadratically with the population size, making large ensembles intractable within FBSDE-based solvers. We replace these terms with neural surrogates in state and time, trained on empirical interaction values along sampled trajectories and embedded in a four-stage alternating scheme that updates the forward and backward potentials and the surrogates in turn, while preserving forward--backward consistency and the prescribed endpoint marginals. We derive Grönwall-type stability bounds quantifying how surrogate errors propagate to the generated trajectories under a small-gain condition. On crowd-navigation and high-dimensional opinion-dynamics benchmarks, the surrogates reproduce the trajectories obtained with exact evaluation at reduced training cost. The advantage is most significant when the interaction is a nonlinear functional of the measure, such as the normalized bounded-confidence drift, for which random-batch subsampling is biased and unstable whereas the learned surrogate remains accurate.

Daisuke Inoue, Dante Kalise, Mathieu Laurière

Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom. · Shanghai Frontiers Science Center of Artificial Intelligence and Deep Learning, NYU-ECNU Institute of Mathematical Sciences, NYU Shanghai, Shanghai 200126, People’s Republic of China.

Neural Surrogate Modeling Schrödinger Bridges Mean-Field Theory

Jun 2, 2026cs.LG

Validation-Gated Multi-Agent Governance for Online Adaptation of Thermal-Hydraulic Surrogate Models under Operating-Regime Shift

Artificial-intelligence surrogates can support second-by-second thermal-hydraulic forecasting, but models selected and frozen offline may become condition-locked once deployed outside their pretraining envelope. This study develops a guarded continual-adaptation framework for experimental thermal-hydraulic loop data in which role-separated agents - Monitor, Diagnosis, Adaptation, Safety-Auditor, and Orchestrator - diagnose error signatures, prioritize candidate model families, and review promotions, while deterministic champion-challenger gates and background shadow learning retain final authority over model replacement. Seven surrogate families were screened by blocked three-fold cross-validation, and a temporal Fourier neural operator was selected as the initial champion for 60-s-history-to-10-s-trajectory forecasting on two held-out transients, with three seeds per adaptive mode. Static deployment gave a channel-averaged MAE of 7.06 and a 56.8% warning-exceedance ratio; rule-based adaptation reduced MAE to 6.54, whereas shadow refresh alone remained close to Static. The MA-Full mode, in which the role-separated multi-agent council reviews every evaluated stream step, achieved the lowest mean error, 5.72, and 35.8% exceedance, corresponding to a 19.0% improvement over Static. Paired bootstrap intervals against Static excluded zero, although intervals among adaptive modes overlapped and the six paired units limit broad statistical claims. Validated promotions from the neural operator to Transformer and graph neural network indicate that logged, gate-controlled adaptation can support auditable surrogate evolution while deterministic gates retain deployment authority.

Doyeong Lim, Seungyoon Lee, In Cheol Bang

Department of Nuclear Engineering, Ulsan National Institute of Science and Technology (UNIST), Ulsan, 44919, Republic of Korea

Neural Surrogate Modeling Continual Test-Time Adaptation Time Series Forecasting AI Agent Governance

Jun 2, 2026cs.LG

Rethinking Neural Width for Alternating Current Optimal Power Flow Proxies

Deep learning proxies for Alternating Current Optimal Power Flow (ACOPF) lack systematic methods for determining architectural size. This paper conducts a constructive thought experiment to answer a fundamental inquiry: how wide must a neural network be to almost accurately approximate the ACOPF manifold? We introduce a Loss-Guided Neural Densification (LG-ND) algorithm that incrementally discovers necessary capacity by expanding only when the current deep neural network topology fails to improve further. Empirical results across various IEEE systems show that LG-ND achieves performance parity with literature baselines using up to ten times fewer neurons per layer. Such architectural minimalism is critical for the formal verification required in safety-critical grid operations.

Dhruvi Khandelwal, Anurag Basistha, Ayushi Jolotia +1

Department of Electrical Engineering, National Institute of Technology Kurukshetra, India. · Indraprastha Institute of Information Technology Delhi, India. · Department of Electrical Engineering, Indian Institute of Technology Roorkee, India.

Neural Surrogate Modeling Optimal Power Flow Constrained Optimization Neural Network Approximation Theory Neural Architecture Search Neural Network Expressivity

Jun 2, 2026cs.LG

Will Accurate Fields Mislead Photonic Design? FromGlobal Accuracy to Port Readout

Neural field surrogates can accelerate photonic design loops, but a surrogate that looks accurate in global field error can still mis-rank candidate devices when the final decision depends on localized output-port readouts. This risk is acute in propagation-dominated MMI splitters and couplers, where port power, splitting, phase, and coupling are determined by accumulated modal interference and output-window aggregation rather than by average field similarity alone. We study this field-to-design mismatch through a Field/Mediator/Readout view that separates dense complex-field error from propagation-profile and output-window errors before port aggregation. To align the surrogate with this chain, we propose PaNO, a propagation-aligned neural operator that keeps the full-field prediction interface while organizing latent states around local boundary structure, transverse modal content, axial propagation, and cross-mode interaction. We also evaluate PaNO-R2, an output-aware feedback variant for residual field components near the port region. On a 15-wavelength tunable

3{\times}3

MMI benchmark with 4608 held-out fields, PaNO lowers NeurOLight's port-power error from 0.2018 to 0.0739 despite slightly higher cMAE, showing that global field accuracy alone is not sufficient for design-relevant readout fidelity. PaNO-R2 attains the best cMAE, propagation-profile error, output-profile error, and port-power error, reducing NeurOLight's port-power and output-profile errors by 72.7% and 72.5%.

Yitian Zhang, Yonghong chen, Youming Chen +6

Sun Yat-sen University · The Hong Kong University of Science and Technology (Guangzhou)

Neural Surrogate Modeling Physics-Based Simulation Neural Operators

Jun 1, 2026cs.LG

Gradient-based optimization of nuclear criticality experiments using neural surrogate eigenvalue sensitivities

The validation of advanced nuclear reactor designs and fuel concepts will require the design of new critical experiments with high neutronic similarity to the target technology. Neutronic similarity can be quantified by the correlation coefficient

c_k

, which captures the shared bias in

k_\text{eff}

induced by uncertainties in nuclear data. Generally, a

c_k\geq0.9

is needed for an experiment to be sufficiently similar to a target technology. In this work, a physics-informed deep neural network is trained to predict the neutronic sensitivity of grid-based critical experiment geometries. The differentiability of the neural network is used to enable gradient-based design optimization of new experiment geometries to maximize

c_k

with the sensitivity profile of a target technology. This approach allows for optimization over the combinatorial design space of potential material combinations within the grid, moving beyond traditional parametric optimization approaches. The method is applied to the validation of the TN-Americas TN-LC transportation cask with HALEU fuel, for which existing critical experiment coverage is limited. This application is shown to produce experiment geometries achieving

c_k

scores of 0.97757, 0.81324, and 0.93276 for three configurations of interest.

Will Savage, Logan Burnett, Dean Price

Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, 60 Vassar St., Cambridge, 02139, MA, US

Neural Surrogate Modeling

Jun 1, 2026cs.LG

On the Generalization in Topology Optimization via Sensitivity-Conditioned Bernoulli Flow Matching

Surrogate models for topology optimization (TO) exhibit highly variable out-of-distribution (OOD) generalization under distribution shifts such as changing loads or boundary conditions, yet the source of this variability remains unclear. We hypothesize that OOD performance is governed by how much information the conditioning signal preserves about the adjoint sensitivity (reduced gradient) that drives classical TO. Modeling the TO pipeline as a causal Markov chain, the Data Processing Inequality establishes that, under this abstraction, the sensitivity field is an information-theoretically optimal conditioning signal for topology prediction. However, computing exact adjoint sensitivities can be expensive or unavailable in practice; we observe that certain physical fields can approximate sensitivities through monotone transformations. To formalize this, we introduce \textbf{pseudo-sensitivities} to characterize which fields enable generalization versus those that are information-poor. We then show that a sensitivity-conditioned Bernoulli flow-matching generator empirically confirms these predictions: conditioning on sensitivities yields state-of-the-art OOD performance, while increasingly distant physical fields degrade toward raw parameter conditioning. Results hold across structural TO benchmarks under load shifts and our new CFD-TO dataset under boundary-condition shifts such as multi-outlet configurations. Code and datasets are available at https://tum-pbs.github.io/topotransformer/ .

Mohammad Rashed, Duarte F. Valoroso Madeira, Babak Gholami +3

School of Computation, Information and Technology, Technical University of Munich, Germany · BMW AG, Munich, Germany · Munich Center for Machine Learning, Munich, Germany. +1

Neural Surrogate Modeling Topology Optimization OOD Generalization Sensitivity Analysis

Jun 1, 2026cs.LG

Hybrid Neural Ordinary Differential Equations for Data-Efficient Polymerization Modeling with Incomplete Kinetics

Accurate prediction of polymerization dynamics is essential for process design, control, and optimization. Yet, purely mechanistic models require labor-intensive parameterization of partially characterized kinetics, while purely data-driven models demand large, diverse datasets that are costly to obtain, particularly in early-design stages. We propose a hybrid Neural Ordinary Differential Equation (NODE) framework for data-efficient modeling of free-radical polymerization. Using batch polymerization of methyl methacrylate (MMA) as a case study, the mechanistic mass balances are retained explicitly, and only the partially-characterized effective radical concentration governing monomer consumption is learned from data through a neural network surrogate, while established reactions such as initiator decomposition, propagation, and termination remain physically modeled. The hybrid NODE is evaluated against a discrete-time feedforward neural network and a purely data-driven NODE under sparse data conditions, with models trained on as few as ten measurements under both regular and irregular sampling. The hybrid NODE consistently achieves lower prediction errors and more physically consistent extrapolations than both purely data-driven baselines. In a generalization scenario with noisy data and unseen operating conditions, the hybrid NODE achieves an RMSE of 0.013, compared to 0.31 for the data-driven NODE and 0.68 for the discrete-time model, demonstrating that learning only a closure term rather than the full dynamics is sufficient for reliable prediction under limited data availability.

Marah Almanasreh, Alexander Mitsos, Eike Cramer

RWTH Aachen University, Process Systems Engineering (AVT.SVT), 52074 Aachen, Germany · JARA-CSD, 52425 Jülich, Germany · Energy Systems Engineering (ICE-1), Forschungszentrum Jülich, 52425 Jülich, Germany +1

Neural Surrogate Modeling Materials Science Neural ODEs Data-Efficient Learning

Jun 1, 2026eess.IV

PINNOCHIO: Physics-Informed Neural Network for Coupled Hyperelastic Interface-Volume Simulation in Orthognathic Surgery

Predicting patient-specific facial soft-tissue deformation is critical for iterative orthognathic surgery planning. However, current computational methods face a strict accuracy-efficiency trade-off: high-fidelity Finite Element Methods (FEM) are computationally prohibitive, whereas pure deep learning models often produce biomechanically inconsistent results. While Physics-Informed Neural Networks (PINNs) offer a promising avenue, learning the complex heterogeneous mechanics of bone--soft-tissue interactions with only partial clinical supervision (i.e., outer facial surfaces) remains highly unstable. To overcome these challenges, we present PINNOCHIO, a novel physics-informed framework for facial soft-tissue simulation. PINNOCHIO introduces a hybrid sequential decomposition that explicitly decouples discontinuous bone--soft-tissue interface movements from continuous volumetric hyperelastic deformation. This structural separation enables stable training and facilitates a physics-enabled sim-to-real adaptation strategy, ensuring internal biomechanical consistency without requiring volumetric ground truth. Evaluated on a 40-patient clinical cohort, PINNOCHIO outperforms existing baselines in both surface accuracy and physical validity. Furthermore, it achieves a substantial speedup over FEM, successfully resolving the accuracy-efficiency trade-off to provide a highly reliable and practical tool for interactive surgical planning.

Jungwook Lee, Daeseung Kim, Kevin Gu +6

Department of Biomedical Engineering and Center for Biotechnology and Interdisciplinary Studies, Rensselaer Polytechnic Institute, Troy, NY 12180, USA · Department of Oral and Maxillofacial Surgery, Houston Methodist Research Institute, Houston, TX 77030, USA · Department of Neurosurgery, Baylor College of Medicine, Houston, TX 77030, USA

Neural Surrogate Modeling Hyperelasticity Physics-Informed ML