PDE Surrogate Modeling

PDE: Partial Differential Equation

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Overview

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

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

  1. Scalable Gaussian process modeling of parametrized spatio-temporal fields

    Feb 27, 2026Srinath Dama, Prasanth B. NairGaussian ProcessesGaussian Process Regression

    University of Toronto Institute for Aerospace Studies, 4925 Dufferin Street, Toronto, M3H 5T6, Ontario, Canada

  2. Agentic Exploration of PDE Spaces using Latent Foundation Models for Parameterized Simulations

    Feb 26, 2026Abhijeet Vishwasrao, Francisco Giral, Mahmoud Golestanian +8AI Agents for Scientific DiscoveryPhysics-Based Simulation

    University of Michigan · Universidad Polit´ecnica de Madrid · Purdue University +3

  3. Learning Physical Operators using Neural Operators

    Feb 26, 2026Vignesh Gopakumar, Ander Gray, Dan Giles +5PDE Surrogate ModelingPhysics-Informed Neural Operators

    UCL Centre for Artificial Intelligence · UK Atomic Energy Authority · LIX, CNRS, ´Ecole Polytechnique +2

  4. Surrogate models for Rock-Fluid Interaction: A Grid-Size-Invariant Approach

    Feb 25, 2026Nathalie C. Pinheiro, Donghu Guo, Hannah P. Menke +4Surrogate ModelingPDE Surrogate Modeling

    Applied Modelling and Computation Group, Department of Earth Science and Engineering, Imperial College London, London, SW7 2AZ UK · Institute of GeoEnergy Engineering, Heriot-Watt University, Edinburgh, EH14 1AS UK · Department of Civil and Environmental Engineering, Imperial College London, London, SW7 2AZ UK +2

  5. NESTOR: A Nested MOE-based Neural Operator for Large-Scale PDE Pre-Training

    Feb 25, 2026Dengdi Sun, Xiaoya Zhou, Xiao Wang +4Neural OperatorsPDE Surrogate Modeling

    School of Artificial Intelligence, Anhui University, Hefei, China · School of Computer Science and Technology, Anhui University, Hefei, China

  6. Structure-Aware Epistemic Uncertainty Quantification for Neural Operator PDE Surrogates

    Feb 24, 2026Haoze Song, Zhihao Li, Mengyi Deng +4Uncertainty QuantificationEpistemic Uncertainty

    The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, China · The Hong Kong University of Science and Technology, Hong Kong SAR, China

  7. Shape-informed cardiac mechanics surrogates in data-scarce regimes via geometric encoding and generative augmentation

    Feb 23, 2026Davide Carrara, Marc Hirschvogel, Francesca Bonizzoni +3Surrogate ModelingPDE Surrogate Modeling

    MOX Laboratory, Department of Mathematics, Politecnico di Milano, Milano, Italy · Division 2.2 Process Simulation, Bundesanstalt für Materialforschung und -prüfung (BAM), Berlin, Germany · Department of Mathematics, University of Trento, Trento, Italy

  8. SGNO: Spectral Generator Neural Operator for Long-Horizon PDE Prediction

    Feb 21, 2026Jiayi Li, Penghao Jiang, Baiyu Chen +5PDE Surrogate ModelingNeural Operators

  9. A Deep Surrogate Model for Robust and Generalizable Long-Term Blast Wave Prediction

    Feb 20, 2026Danning Jing, Xinhai Chen, Xifeng Pu +5Neural Surrogate ModelingSpatiotemporal Forecasting

    National Key Laboratory of Parallel and Distributed Computing, National University of Defense Technology, Changsha 410073, China · Laboratory of Digitizing Software for Frontier Equipment, National University of Defense Technology, Changsha 410073, China · College of Computer Science and Technology, National University of Defense Technology, Changsha 410073, China +2

  10. Multi-material Multi-physics Topology Optimization with Physics-informed Gaussian Process Priors

    Feb 19, 2026Xiangyu Sun, Shirin Hosseinmardi, Amin Yousefpour +1Topology OptimizationPhysics-Informed ML

    Department of Mechanical and Aerospace Engineering, University of California, Irvine · Department of Civil and Environmental Engineering, University of California, Irvine

  11. Flowers: A Warp Drive for Neural PDE Solvers

    Feb 17, 2026Till Muser, Alexandra Spitzer, Matti Lassas +2Neural PDE SolversPDE Surrogate Modeling

    Department of Mathematics and Computer Science, University of Basel, Basel, Switzerland · Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland · Simons Chair in Computational and Applied Mathematics and Earth Science, Rice University, Houston, TX, USA

  12. Learning Data-Efficient and Generalizable Neural Operators via Fundamental Physics Knowledge

    Feb 16, 2026Siying Ma, Mehrdad M. Zadeh, Mauricio Soroco +3PDE Surrogate ModelingNeural Operators

    Simon Fraser University · Georgia Institute of Technology

  13. PDE foundation models are skillful AI weather emulators for the Martian atmosphere

    Feb 16, 2026Johannes Schmude, Sujit Roy, Liping Wang +10PDE Foundation ModelsWeather Forecasting

    IBM Research · NASA Marshall Space Flight Center, Huntsville, Al, USA · Earth System Science Center, University of Alabama in Huntsville, Al, USA +1

  14. Adjoint-based shape optimization of a ship hull using a Conditional Variational Autoencoder (CVAE) assisted propulsion surrogate model

    Feb 16, 2026Moloud Arian Maram, Georgios Bletsos, Thanh Tung Nguyen +3PDE Surrogate ModelingComputational Fluid Dynamics

    J.M. Voith SE & Co. KG, Alexanderstrasse 2, Heidenheim, 89522, Baden-Württemberg, Germany · Institute for Fluid Dynamics and Ship Theory, Hamburg University of Technology, Am Schwarzenberg-Campus 4, Hamburg, 21073, Germany

  15. Solving Inverse Parametrized Problems via Finite Elements and Extreme Learning Networks

    Feb 16, 2026Erik Burman, Mats G. Larson, Karl Larsson +1PDE Surrogate ModelingPDE Inverse Problems

  16. GenPANIS: A Latent-Variable Generative Framework for Forward and Inverse PDE Problems in Multiphase Media

    Feb 16, 2026Matthaios Chatzopoulos, Phaedon-Stelios KoutsourelakisPDE Inverse ProblemsPhysics-Informed Generative Modeling

    Technical University of Munich, Professorship of Data-driven Materials Modeling, School of Engineering and Design, Boltzmannstr. 15, 85748 Garching, Germany · Munich Data Science Institute (MDSI - Core member), Garching, Germany

  17. Stabilizing Physics-Informed Consistency Models via Structure-Preserving Training

    Feb 10, 2026Che-Chia Chang, Chen-Yang Dai, Te-Sheng Lin +2Physics-Informed Generative ModelingPDE Surrogate Modeling

    Institute of Artificial Intelligence Innovation National Yang Ming Chiao Tung University Hsinchu, Taiwan · Department of Applied Mathematics National Yang Ming Chiao Tung University Hsinchu, Taiwan · Department of Applied Mathematics National Yang Ming Chiao Tung University Hsinchu, Taiwan National Center for Theoretical Sciences National Taiwan University Taipei, Taiwan

  18. Transolver-3: Scaling Up Transformer Solvers to Industrial-Scale Geometries

    Feb 4, 2026Hang Zhou, Haixu Wu, Haonan Shangguan +4Efficient Neural Network InferenceNeural PDE Solvers

    School of Software, BNRist, Tsinghua University, China.

  19. SFO: Learning PDE Operators via Spectral Filtering

    Jan 23, 2026Noam Koren, Rafael Moschopoulos, Kira Radinsky +1PDE Surrogate ModelingPDE Operator Learning

    Department of Computer Science Technion - Israel Institute of Technology · Department of Computer Science Princeton University

  20. PGOT: A Physics-Geometry Operator Transformer for Complex PDEs

    Dec 29, 2025Zhuo Zhang, Xi Yang, Ying Miao +5Neural PDE SolversPDE Surrogate Modeling

    National University of Defense Technology · Peking University · National University of Singapore +2

  21. Spectral Embedding via Chebyshev Bases for Robust DeepONet Approximation

    Dec 9, 2025Muhammad Abid, Omer SanPDE Surrogate ModelingPDE Operator Learning

    Department of Mechanical and Aerospace Engineering, University of Tennessee, Knoxville, TN 37996, USA.

  22. Efficient Generative Transformer Operators For Million-Point PDEs

    Dec 4, 2025Armand Kassaï Koupaï, Lise Le Boudec, Patrick GallinariPDE Surrogate ModelingTransformer Neural Operator

    Sorbonne Université, CNRS, ISIR, 75005 Paris, France · Criteo AI Lab, Paris, France

  23. Conditional Clifford-Steerable CNNs for PDE Modeling

    Oct 15, 2025Bálint László Szarvas, Maksim ZhdanovDynamic ConvolutionPDE Surrogate Modeling

    University of Amsterdam · 2AMLab.

  24. A Flow-rate-conserving CNN-based Domain Decomposition Method for Blood Flow Simulations

    Sep 19, 2025Simon Klaes, Axel Klawonn, Natalie Kubicki +4PDE SolvingPDE Surrogate Modeling

    Department of Mathematics and Computer Science, University of Cologne, Germany · Center for Data and Simulation Science, University of Cologne, Germany · Institute for Advanced Simulation (IAS-2), Forschungszentrum Jülich, Germany +1

  25. Blending data and physics for reduced-order modeling of systems with spatiotemporal chaotic dynamics

    Jul 21, 2025Alex Guo, Michael D. GrahamReduced-Order ModelingChaotic Time-Series Prediction

    Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison WI 53706, USA

  26. DPG loss functions for learning parameter-to-solution maps by neural networks

    Jun 23, 2025Pablo Cortés Castillo, Wolfgang Dahmen, Jay GopalakrishnanPDE SolvingPDE Surrogate Modeling

  27. Surrogate Modeling of 3D Rayleigh-Benard Convection with Equivariant Autoencoders

    May 19, 2025Fynn Fromme, Hans Harder, Christine Allen-Blanchette +1AutoencodersPDE Surrogate Modeling

    Lamarr Institute for Machine Learning and Artificial Intelligence and Karlsruhe Institute of Technology · Lamarr Institute for Machine Learning and Artificial Intelligence and Department of Computer Science at Paderborn University · Department of Mechanical and Aerospace Engineering Center for Statistics and Machine Learning Princeton University +1

  28. Latent Evolution Operator (LEO): State-to-State Forecasting of Parametric PDEs

    May 14, 2025Khalid Rafiq, Wenjing Liao, Aditya G. NairPDE Surrogate ModelingPDE Operator Learning

    Department of Mechanical Engineering, University of Nevada, Reno, Reno, USA · School of Mathematics, Georgia Institute of Technology, Atlanta, USA

  29. Fast localized urban microclimate emulator: wind and temperatures in unseen urban morphologies

    Mar 25, 2025Shaoxiang Qin, Theodore Potsis, Dongxue Zhan +3PDE Surrogate ModelingComputational Fluid Dynamics

    Department of Building, Civil and Environmental Engineering, Cetner Zero Energy Building Studies, Concordia University, Montreal, Canada · School of Computer Science, McGill University, Montreal, Canada · Mohamed bin Zayed University of Artificial Intelligence, Abu Dhabi, United Arab Emirates

  30. Residuals Are Not Enough: Limits of Physics-Informed Pre-Training for Scientific Foundation Models

    Mar 24, 2025Serge Kotchourko, Amin Totounferoush, Michael W. Mahoney +1PDE Surrogate ModelingPhysics-Informed ML

    University of Stuttgart, Germany · ICSI, LBNL, and University of California, Berkeley, USA