PDE Surrogate Modeling

PDE: Partial Differential Equation

PDE surrogate modeling studies how to approximate the mapping from physical conditions, geometry, and parameters to a PDE’s solution, reducing the cost of repeated simulations. Methods range from reduced-order models such as POD and latent dynamics to neural operators such as Fourier Neural Operators and DeepONets, as well as mesh-based graph networks, transformers, and generative models. Many approaches combine these learned models with physical structure, including conservation laws, symmetries, boundary conditions, and numerical solvers, to improve reliability and support inverse problems or design optimization. A central challenge is balancing speed with accuracy under new geometries or regimes, stable long rollouts, fine-scale fidelity, and calibrated uncertainty; whether a surrogate saves time overall depends on training and deployment costs as well as inference speed.

Latest papers

331 papers50 papers in the last four weeks, up 72% on the four weeks before. 0.3% of all new papers.

Late Fusion Neural Operators for Extrapolation Across Parameter Space in Partial Differential Equations
Apr 17, 2026Eva van Tegelen, Taniya Kapoor, George A. K. van Voorn +2Surrogate Modeling PDE Surrogate Modeling
Artificial Intelligence Group, Wageningen University and Research, Netherlands · Mathematical and Statistical Methods, Wageningen University and Research, Netherlands
FLARE: A Data-Efficient Surrogate for Predicting Displacement Fields in Directed Energy Deposition
Apr 17, 2026Kittipong Thiamchaiboonthawee, Ghadi Nehme, Ram Mohan Telikicherla +5Neural Surrogate Modeling Implicit Neural Representations
Massachusetts Institute of Technology, Cambridge, MA, USA · GE Vernova Advanced Research Center, Niskayuna, NY, USA
PINNACLE: An Open-Source Computational Framework for Classical and Quantum PINNs
Apr 17, 2026Shimon Pisnoy, Hemanth Chandravamsi, Ziv Chen +4Neural PDE Solvers PDE Surrogate Modeling
†Faculty of Mechanical Engineering, Technion Israel Institute of Technology, Haifa, Israel. · ‡Corresponding author. · §The Andrew and Erna Viterbi Faculty of Electrical & Computer Engineering, Technion Israel Institute of Technology, Haifa, Israel. +2
A Structure-Preserving Graph Neural Solver for Parametric Hyperbolic Conservation Laws
Apr 17, 2026Jiamin Jiang, Shanglin Lv, Jingrun ChenGraph Neural Networks Neural PDE Solvers
School of Artificial Intelligence and Data Science and Suzhou Institute for Advanced Research, University of Science and Technology of China, and Suzhou Big Data & AI Research and Engineering Center, China · School of Mathematical Sciences, University of Science and Technology of China, China · School of Mathematical Sciences and Suzhou Institute for Advanced Research, University of Science and Technology of China, and Suzhou Big Data & AI Research and Engineering Center, China
G-PARC: Graph-Physics Aware Recurrent Convolutional Neural Networks for Spatiotemporal Dynamics on Unstructured Meshes
Apr 16, 2026Jack T. Beerman, Tyler J. Abele, Mehdi Taghizadeh +6Neural PDE Solvers PDE Surrogate Modeling
School of Data Science, University of Virginia, Charlottesville, VA 22903, United States · Department of Engineering Systems and Environment, University of Virginia, Charlottesville, VA 22903, United States · Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, VA 22903, United States +1
Physics-Informed Machine Learning for Pouch Cell Temperature Estimation
Apr 16, 2026Zheng LiuNeural Surrogate Modeling PDE Surrogate Modeling
Department of Industrial and Manufacturing Systems Engineering University of Michigan-Dearborn Dearborn, USA
Non-intrusive Learning of Physics-Informed Spatio-temporal Surrogate for Accelerating Design
Apr 15, 2026Sudeepta Mondal, Soumalya SarkarPDE Surrogate Modeling Physics-Informed ML
Raytheon Technologies Research Center, 411 Silver Lane, East Hartford, CT 06108.
Nested Fourier-enhanced neural operator for efficient modeling of radiation transfer in fires
Apr 15, 2026Anran Jiao, Wengyao Jiang, Xiaoyi Lu +2Radiative Transfer PDE Surrogate Modeling
Department of Statistics and Data Science, Yale University, New Haven, CT 06511, USA · Department of Biostatistics, Yale University, New Haven, CT 06511, USA · FM, Research Division, Norwood, MA 02062, USA +1
AeTHERON: Autoregressive Topology-aware Heterogeneous Graph Operator Network for Fluid-Structure Interaction
Apr 15, 2026Sushrut KumarFluid-Structure Interaction PDE Surrogate Modeling
Department of Mechanical Engineering Johns Hopkins University Baltimore, MD 21218
AutoSurrogate: An LLM-Driven Multi-Agent Framework for Autonomous Construction of Deep Learning Surrogate Models in Subsurface Flow
Apr 13, 2026Jiale Liu, Nanzhe WangNeural Surrogate Modeling PDE Surrogate Modeling
School of Physics and Astronomy, The University of Edinburgh, Edinburgh, EH9 3FD, United Kingdom · Institute of GeoEnergy Engineering, School of Energy, Geoscience, Infrastructure and Society, Heriot-Watt University, Edinburgh, EH14 4AS, United Kingdom · Subsurface Energy Transition and Innovation Centre, Heriot-Watt University, Edinburgh, EH14 4AS, United Kingdom
SCNO: Spiking Compositional Neural Operator -- Towards a Neuromorphic Foundation Model for Nuclear PDE Solving
Apr 13, 2026Samrendra Roy, Souvik Chakraborty, Rizwan-uddin +1PDE Solving PDE Surrogate Modeling
University of Illinois Urbana-Champaign Department of Nuclear, Plasma & Radiological Engineering Urbana, IL, USA · Indian Institute of Technology Delhi Department of Applied Mechanics New Delhi, India · National Center for Supercomputing Applications Urbana, IL, USA
Meta-Learned Basis Adaptation for Parametric Linear PDEs
Apr 10, 2026Vikas Dwivedi, Monica Sigovan, Bruno SixouPDE Solving PDE Surrogate Modeling
CREATIS Biomedical Imaging Laboratory INSA, CNRS UMR 5220, Inserm, Université Lyon 1 Lyon 69621, France
Bias-Constrained Diffusion Schedules for PDE Emulations: Reconstruction Error Minimization and Efficient Unrolled Training
Apr 9, 2026Constantin Le Cleï, Nils Thuerey, Xiaoxiang ZhuDiffusion Models Autoregressive Diffusion
Technical University of Munich, Munich, Germany.
MENO: MeanFlow-Enhanced Neural Operators for Dynamical Systems
Apr 8, 2026Tianyue Yang, Xiao XueNeural Operators PDE Surrogate Modeling
Centre for Computational Science, University College London, London, United Kingdom
AE-ViT: Stable Long-Horizon Parametric Partial Differential Equations Modeling
Apr 7, 2026Iva Mikuš, Boris Muha, Domagoj VlahPDE Surrogate Modeling Reduced-Order Modeling
University of Zagreb Faculty of Electrical Engineering and Computer Science · University of Zagreb Faculty of Science Department of Mathematics
Operator Learning for Predicting Bulk Wave Parameters of Spectral Wave Models
Apr 7, 2026Shukai Cai, Sourav Dutta, Mark Loveland +4PDE Surrogate Modeling PDE Operator Learning
Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, 201 E 24th St, Austin, 78712, TX, USA · Information Technology Laboratory, U.S. Army Engineer Research and Development Center, MS, USA · Department of Mechanical Engineering and Technology Management, Norwegian University of Life Sciences, Ås, Norway +1
Real-Time Surrogate Modeling for Personalized Blood Flow Prediction and Hemodynamic Analysis
Apr 3, 2026Sokratis J. Anagnostopoulos, George Rovas, Vasiliki Bikia +3Neural Surrogate Modeling Clinical Prediction
Laboratory of Hemodynamics and Cardiovascular Technology, EPFL, Lausanne, Switzerland · Stanford DBDS and HAI, Stanford University, Palo Alto, USA · Medical School, National and Kapodistrian University of Athens, Athens, Greece
Toward an Operational GNN-Based Multimesh Surrogate for Fast Flood Forecasting
Apr 3, 2026Valentin Mercier, Serge Gratton, Lapeyre Corentin +1Flood Forecasting Neural Surrogate Modeling
Toulouse INP, IRIT, EPE UT · Université de Toulouse, INP, IRIT, Toulouse, France · IRIT, EPE UT, Toulouse INP +3
A Numerical Method for Coupling Parameterized Physics-Informed Neural Networks and FDM for Advanced Thermal-Hydraulic System Simulation
Apr 3, 2026Jeesuk Shin, Donggyun Seo, Sihyeong Yu +1Physics-Based Simulation PDE Surrogate Modeling
Division of Advanced Nuclear Engineering, Pohang University of Science and Technology, Pohang-si, Republic of Korea · Mueunjae School of Undergraduate Studies, Pohang University of Science and Technology, Pohang-si, Republic of Korea · Department of Quantum System Engineering, Jeonbuk National University, Jeonju-si, Republic of Korea
A Multimodal Vision Transformer-based Modeling Framework for Prediction of Fluid Flows in Energy Systems
Apr 2, 2026Kiran Yalamanchi, Shivam Barwey, Ibrahim Jarrah +1Computational Fluid Dynamics PDE Surrogate Modeling
Transportation and Power Systems Division, Argonne National Laboratory, Lemont, IL, USA
PI-JEPA: Label-Free Surrogate Pretraining for Coupled Multiphysics Simulation via Operator-Split Latent Prediction
Apr 1, 2026Brandon Yee, Pairie KohMultiphysics Simulation PDE Surrogate Modeling
Physics Lab, Yee Collins Research Group · Graduate School of Business, Stanford University
Performance of Neural and Polynomial Operator Surrogates
Apr 1, 2026Josephine Westermann, Benno Huber, Thomas O'Leary-Roseberry +1Surrogate Modeling PDE Surrogate Modeling
Heidelberg University · The Ohio State University
Deep Learning-Accelerated Surrogate Optimization for High-Dimensional Well Control in Stress-Sensitive Reservoirs
Apr 1, 2026Mahammad Valiyev, Jodel Cornelio, Behnam JafarpourSurrogate-Assisted Optimization Optimal Control
University of Southern California
Predicting Wave Reflection and Transmission in Heterogeneous Media via Fourier Operator-Based Transformer Modeling
Mar 31, 2026Zhe Bai, Hans JohansenPDE Surrogate Modeling Surrogate Modeling
AMCR Division, Lawrence Berkeley National Lab, Berkeley, USA
Derived Fields Increase the Recoverable Information in Budgeted Neural PDE Surrogate
Mar 31, 2026Wenshuo Wang, Fan ZhangPDE Surrogate Modeling Neural Surrogate Modeling
School of Future Technology, South China University of Technology, China · State Key Laboratory of Ocean Sensing & Ocean College, Zhejiang University, China · Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, USA
Learning noisy phase transition dynamics from stochastic partial differential equations
Mar 31, 2026Luning Sun, Van Hai Nguyen, Shusen Liu +2Stochastic PDEs PDE Surrogate Modeling
Lawrence Livermore National Laboratory, Livermore, CA, 94550,USA · The University of Texas at Austin, Austin, TX, 78712, USA
FluidFlow: a flow-matching generative model for fluid dynamics surrogates on unstructured meshes
Mar 30, 2026David Ramos, Lucas Lacasa, Fermín Gutiérrez +2PDE Surrogate Modeling Computational Fluid Dynamics
ETSIAE-UPM-School of Aeronautics, Universidad Politécnica de Madrid, Plaza Cardenal Cisneros 3, E-28040 Madrid, Spain · Institute for Cross-Disciplinary Physics and Complex Systems (IFISC, CSIC-UIB), 07122 Palma de Mallorca (Spain) · Center for Computational Simulation, Universidad Politécnica de Madrid, Campus de Montegancedo, Boadilla del Monte, 28660 Madrid, Spain
Koopman-based surrogate modeling for reinforcement-learning-control of Rayleigh-Benard convection
Mar 30, 2026Tim Plotzki, Sebastian PeitzRL Control PDE Surrogate Modeling
TU Dortmund University & Lamarr Institute for Machine Learning and Artificial Intelligence, Dortmund, Germany
Sparse Autoencoders as a Steering Basis for Phase Synchronization in Graph-Based CFD Surrogates
Mar 28, 2026Yeping Hu, Ruben Glatt, Shusen LiuComputational Fluid Dynamics PDE Surrogate Modeling
Computational Engineering Division Lawrence Livermore National Laboratory Livermore, CA 94550 · Center for Applied Scientific Computing Lawrence Livermore National Laboratory Livermore, CA 94550
Anchored-Branched Steady-state WInd Flow Transformer (AB-SWIFT): a metamodel for 3D atmospheric flow in urban environments
Mar 26, 2026Armand de Villeroché, Rem-Sophia Mouradi, Vincent Le Guen +5Neural Surrogate Modeling PDE Surrogate Modeling
CEREA, ENPC, EDF R&D, Institut Polytechnique de Paris, Île-de-France, France · EDF R&D, Île-de-France, France · SINCLAIR AI Laboratory, Saclay, Île-de-France, France +1

Apr 17, 2026J/K move · Enter open · S save

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

Eva van Tegelen, Taniya Kapoor, George A. K. van Voorn, Peter van Heijster+1

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

Surrogate Modeling PDE Surrogate Modeling OOD Generalization PDE Operator Learning Neural Operators

Open paper AskPDF arXiv

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