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

CardsList

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

  1. System-Anchored Knee Estimation for Low-Cost Context Window Selection in PDE Forecasting

    Mar 26, 2026Wenshuo Wang, Fan ZhangNeural PDE SolversPDE 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

  2. Linear-Nonlinear Fusion Neural Operator for Partial Differential Equations

    Mar 25, 2026Heng Wu, Junjie Wang, Benzhuo LuPDE Operator LearningNeural Operators

    SKLMS, ICMSEC, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China · School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

  3. Pretrained Video Models as Differentiable Physics Simulators for Urban Wind Flows

    Mar 22, 2026Janne Perini, Rafael Bischof, Moab Arar +4Video Diffusion ModelsPDE Surrogate Modeling

    1Computational Design Lab, ETH Zurich, Switzerland · 2Tel Aviv University, Israel · 3Architecture and Building Systems, ETH Zurich, Switzerland +2

  4. Neural Galerkin Normalizing Flow for Transition Probability Density Functions of Diffusion Models

    Mar 19, 2026Riccardo Saporiti, Fabio NobileNormalizing FlowsNeural PDE Solvers

    CSQI, École Polytechnique Féderale de Lausanne, Switzerland

  5. Model Order Reduction of Cerebrovascular Hemodynamics Using POD_Galerkin and Reservoir Computing_based Approach

    Mar 19, 2026Rahul Halder, Arash Hajisharifi, Kabir Bakhshaei +1Reduced-Order ModelingPDE Surrogate Modeling

    Mathematics Area, mathLab, SISSA, via Bonomea 265, I-34136 Trieste, Italy · Biorobotics Institute, SMART Lab, Sant’Anna School of Advanced Studies, Pisa, Italy · Department of Computer Science, University of Pisa, Pisa, Italy

  6. UniFluids: Unified Neural Operator Learning with Conditional Flow-matching

    Mar 19, 2026Haosen Li, Qi Meng, Jiahao Li +4PDE Operator LearningPDE Surrogate Modeling

    Academy of Mathematics and Systems Science, Chinese Academy of Sciences · Microsoft Research Asia · Renmin University of China +1

  7. Gradient-Informed Temporal Sampling Improves Rollout Accuracy in PDE Surrogate Training

    Mar 18, 2026Wenshuo Wang, Fan ZhangTraining Data SelectionAdaptive Sampling

    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

  8. RHYME-XT: A Neural Operator for Spatiotemporal Control Systems

    Mar 18, 2026Marijn Ruiter, Miguel Aguiar, Jake Rap +2PDE Surrogate ModelingPDE Operator Learning

    Digital Futures and Division of Decision and Control Systems, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden. · Control Systems Group, EE Dept., Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

  9. A scalable neural bundle map for multiphysics prediction in lithium-ion battery across varying configurations

    Mar 17, 2026Zhiwei Zhao, Changqing Liu, Jie Lin +4Multiphysics SimulationNeural Surrogate Modeling

    College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China · School of Mechanical and Aerospace Engineering, Queen's University Belfast, Belfast BT9 5AH, UK

  10. pADAM: A Plug-and-Play All-in-One Diffusion Architecture for Multi-Physics Learning

    Mar 17, 2026Amirhossein Mollaali, Bongseok Kim, Christian Moya +1Physics-Informed Generative ModelingPDE Surrogate Modeling

    School of Mechanical Engineering, Purdue University, West Lafayette, 47906, IN, USA. · Department of Mathematics, Purdue University, West Lafayette, 47906, IN, USA.

  11. Physics-integrated neural differentiable modeling for immersed boundary systems

    Mar 17, 2026Chenglin Li, Hang Xu, Jianting Chen +1PDE Surrogate ModelingComputational Fluid Dynamics

    State Key Lab of Ocean Engineering, School of Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China · State Key Laboratory of Maritime Technology and Safety, Shanghai Ship and Shipping Research Institute Co., Ltd, Shanghai 200135, China.

  12. Physics-informed fine-tuning of foundation models for partial differential equations

    Mar 16, 2026Vlad Medvedev, Leon Armbruster, Christopher Straub +2PDE Foundation ModelsPDE Surrogate Modeling

    Department Modeling and Artificial Intelligence Fraunhofer Institute for Integrated Systems and Device Technology IISB Schottkystrasse 10, 91058 Erlangen, Germany

  13. A convolutional autoencoder and neural ODE surrogate modeling framework applied to transient counterflow flames

    Mar 16, 2026Mert Yakup Baykan, Weitao Liu, Mohammad Rafi Malik +4AutoencodersPDE Surrogate Modeling

    Department of Aerospace Engineering, KAIST, Daejeon, Republic of Korea · Clean Energy Research Platform (CERP), KAUST, Thuwal, Saudi Arabia · Institute for Reactive Flows (IRST), University of Stuttgart, Pfaffenwaldring 31, 70569 Stuttgart, Germany

  14. Deep Invertible Autoencoders for Dimensionality Reduction of Dynamical Systems

    Mar 13, 2026Nicolò Botteghi, Silke Glas, Christoph BruneAutoencodersPDE Surrogate Modeling

    1MOX Laboratory, Department of Mathematics, Politecnico di Milano, Milano, Italy · Department of Applied Mathematics, University of Twente, Enschede, Netherlands

  15. Parameterized Temporal Extrapolation of PDEs via Disentangled Latent Dynamics Manifold Fusion

    Mar 13, 2026Zhangyong Liang, Jihong Zhu, Huanhuan GaoLatent Dynamics ModelingPDE Solving

    National Center for Applied Mathematics, Tianjin University, Tianjin, 300072, PR China · School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an, 710072, China · School of Mechanical and Aerospace Engineering, Jilin University, Changchun, 130025, China

  16. Adaptive Diffusion Posterior Sampling for Data and Model Fusion of Complex Nonlinear Dynamical Systems

    Mar 13, 2026Dibyajyoti Chakraborty, Hojin Kim, Romit MaulikPDE Surrogate ModelingChaotic Time-Series Prediction

    College of Information Sciences and Technology, Pennsylvania State University, University Park, 16802, PA, USA · School of Mechanical Engineering, Purdue University, West Lafayette, 47907, IN, USA

  17. Physics-informed neural operator for parametric phase-field modelling of interfacial degradation and microstructural evolution

    Mar 10, 2026Nanxi Chen, Airong Chen, Rujin MaPhysics-Informed Neural OperatorsPDE Surrogate Modeling

    College of Civil Engineering, Tongji University, Shanghai 200092, China

  18. Graph-Instructed Neural Networks for parametric problems with varying boundary conditions

    Mar 9, 2026Francesco Della Santa, Sandra Pieraccini, Maria StrazzulloPDE Surrogate ModelingNeural PDE Solvers

    Department of Mathematical Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Turin, Italy · Gruppo Nazionale per il Calcolo Scientifico INdAM, Piazzale Aldo Moro 5, 00185, Rome, Italy

  19. Wiener Chaos Expansion based Neural Operator for Singular Stochastic Partial Differential Equations

    Mar 9, 2026Dai Shi, Luke Thompson, Andi Han +3Stochastic PDEsPDE Surrogate Modeling

    University of Cambridge · University of Sydney · Chinese Academy of Science

  20. Tau-BNO: Brain Neural Operator for Tau Transport Model

    Mar 9, 2026Nuutti Barron, Heng Rao, Urmi Saha +6Neural Surrogate ModelingPDE Surrogate Modeling

    Department of Radiology and Biomedical Imaging, University of California San Francisco, USA · College of Computer Science and Engineering, Northeastern University, China · Department of Computer Science, Wake Forest University, USA +1

  21. Generative prediction of laser-induced rocket ignition with dynamic latent space representations

    Mar 8, 2026Tony Zahtila, Ettore Saetta, Murray Cutforth +3Neural Surrogate ModelingPDE Surrogate Modeling

    Center for Turbulence Research, Stanford University, USA · University of Naples Federico II, Italy

  22. Prediction of Steady-State Flow through Porous Media Using Machine Learning Models

    Mar 6, 2026Jinhong Wang, Matei C. Ignuta-Ciuncanu, Ricardo F. Martinez-Botas +1Porous Media FlowPDE Surrogate Modeling

    Department of Mechanical Engineering, Imperial College London, South Kensington Campus, London, SW7 2AZ, , United Kingdom

  23. Towards Efficient and Stable Ocean State Forecasting: A Continuous-Time Koopman Approach

    Mar 5, 2026Rares Grozavescu, Pengyu Zhang, Mark Girolami +1Spatiotemporal ForecastingPDE Surrogate Modeling

    Department of Engineering, University of Cambridge, Cambridge, UK · Alan Turing Institute, London, UK · INRIA, Paris, France

  24. Hierarchical Inference and Closure Learning via Adaptive Surrogates for ODEs and PDEs

    Mar 4, 2026Pengyu Zhang, Arnaud Vadeboncoeur, Alex Glyn-Davies +1PDE Inverse ProblemsPDE Surrogate Modeling

    Department of Engineering, University of Cambrdige, 7a JJ Thomson Ave, Cambridge, CB3 0FA, UK · The Alan Turing Institute, 96 Euston Rd., London, NW1 2DB, UK

  25. From Complex Dynamics to DynFormer: Rethinking Transformers for PDEs

    Mar 3, 2026Pengyu Lai, Yixiao Chen, Dewu Yang +3PDE Surrogate ModelingNeural Operators

    School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai, 200240, China

  26. Accelerating PDE Surrogates via RL-Guided Mesh Optimization

    Mar 2, 2026Yang Meng, Ruoxi Jiang, Zhuokai Zhao +3PDE Surrogate ModelingData-Efficient Learning

    UChicago · Fudan University · UAlbany

  27. Probabilistic Retrofitting of Learned Simulators

    Mar 2, 2026Cristiana Diaconu, Miles Cranmer, Richard E. Turner +2Surrogate ModelingPDE Surrogate Modeling

    The Polymathic AI Collaboration · University of Cambridge · Alan Turing Institute

  28. DGNet: Discrete Green Networks for Data-Efficient Learning of Spatiotemporal PDEs

    Mar 2, 2026Yingjie Tan, Quanming Yao, Yaqing WangNeural PDE SolversPDE Surrogate Modeling

    Qiuzhen College, Tsinghua University · Department of Electronic Engineering, Tsinghua University · Beijing Institute of Mathematical Sciences and Applications

  29. Neural Latent Arbitrary Lagrangian-Eulerian Grids for Fluid-Solid Interaction

    Feb 28, 2026Shilong Tao, Zhe Feng, Shaohan Chen +3Fluid-Structure InteractionPhysics-Based Simulation

    School of Computer Science, Peking University · Global Innovation Exchange, Tsinghua University · School of Electrical and Computer Science, University of Southampton

  30. KROM: Kernelized Reduced Order Modeling

    Feb 27, 2026Aras Bacho, Jonghyeon Lee, Houman OwhadiPDE Surrogate ModelingReduced-Order Modeling

    Department of Computing and Mathematical Sciences, Caltech, CA, USA.