PDE Surrogate Modeling

PDE: Partial Differential Equation

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32 papers in the last four weeks, up 146% on the four weeks before. 0.3% of all new papers.

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Single-condition neural solvers encode transferable response spaces for parametric differential equations
Sep 14, 2026Wenbo Cao, Weiwei ZhangPDE Solving PDE Surrogate Modeling
Institute of AI for Industries, Chinese Academy of Sciences, Nanjing 211135, China · Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100190, China · School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China +2
Development and Validation of a Physics-Guided Machine Learning Extrapolation Framework Using a Classical Transient Diffusion Benchmark
Sep 9, 2026Ashutosh Yadav, Alok Dubey, Prodyut Ranjan Chakraborty +1PDE Surrogate Modeling OOD Generalization
Department of Mechanical Engineering, Indian Institute of Technology Jodhpur, Jodhpur 342030, India · Department of Aerospace Engineering, Indian Institute of Technology Jodhpur, Jodhpur 342030, India
ONE CYLinder: A Benchmark for Graph-Based Surrogate Modeling of Unsteady Bluff-Body Flows
Sep 8, 2026Théodore Michel, Antoine Campos, Alban Dujardin +3Surrogate Modeling PDE Surrogate Modeling
Mines Paris PSL University Centre for Material Forming (CEMEF) UMR CNRS, Sophia Antipolis, 06904, France
Selective boundary condition reduction via learned error gating
Sep 8, 2026Daniel Fernández, Dominik Penk, Dominik RiedelbauchPDE Surrogate Modeling Multifidelity Modeling
Chair for Dynamics, Control, Machine Learning, and Numerics (Alexander von Humboldt Professorship), Department of Mathematics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstraße, 91058 Erlangen, Germany. · Schaeffler Technologies AG & Co. KG, Industriestraße 1–3, Herzogenaurach, Germany.
Learning Metamaterial Eigenmodes with Wavelet-Encoded Fourier Neural Operators
Sep 8, 2026Han Zhang, Alexander Ogren, Cynthia Rudin +2Fourier Neural Operator PDE Surrogate Modeling
Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC, USA · Department of Mechanical Engineering, California Institute of Technology, Pasadena, CA, USA · Department of Electrical and Computer Engineering, Duke University, Durham, NC, USA
Structured Extrema Errors in Classical Surrogates for Viscous Burgers: A Physics-Consistent Interpretation
Sep 7, 2026Youssef OubariKernel Ridge Regression Surrogate Modeling
IMT Atlantique, France
Local gradient neural operator
Sep 7, 2026Baiming Zhang, Jinsong Tang, Ying Xu +2PDE Surrogate Modeling PDE Operator Learning
Zhejiang University · Nanjing University of Science and Technology · Hefei University of Technology
Distance-Aware Attention and Wall-Distance Expert Routing for Transformer-Based 3D Flow Prediction
Sep 7, 2026Sanghyeon Kim, Sunwoong Yang, Namwoo KangCross-Attention Mixture of Experts
Division of Future Vehicle Korea Advanced Institute of Science and Technology Daejeon, 34051, Republic of Korea · Department of Mechanical Engineering Hanyang University Ansan, 15588, Republic of Korea · Cho Chun Shik Graduate School of Mobility Korea Advanced Institute of Science and Technology Narnia Labs Daejeon, 34051, Republic of Korea
SurgeGen: A Hybrid Generative Diffusion Framework for Storm Surge Scenario Synthesis
Sep 3, 2026Shunan Zheng, John J. HasenbeinSurrogate Modeling PDE Surrogate Modeling
Operations Research and Industrial Engineering University of Texas at Austin Austin, TX, USA
Mesh-Native Physics-Informed Graph Surrogates for TCAD-in-the-Loop Design Space Exploration
Sep 2, 2026Leonid Popryho, Ayoub Sadeghi, Inna Partin-VaisbandPDE Surrogate Modeling Physics-Informed ML
University of Illinois Chicago · Chicago, IL, USA
Physics-Informed Neural Network Surrogate for Oxygen Vacancy Dynamics in epitaxial $\mathrm{SrTiO_3}$ on Si memristors via Dynamic Spectral Optimization
Sep 2, 2026Rodion Podorozhny, Nikoleta Theodoropoulou, Jelena TešićPDE Surrogate Modeling Materials Science
Dept. of Computer Science, Texas State University, San Marcos, TX, USA · Dept. of Physics, Texas State University, San Marcos, TX, USA
Geometry-aware Latent Autoregressive Generative Model for PDEs in Complex Domains
Aug 31, 2026Zi Wang, Minghui Xu, Tapan MukerjiGraph Neural Networks Neural PDE Solvers
Department of Energy Science and Engineering Stanford University Stanford, CA 94305
Learning PDE Time-Stepping with Neural Cellular Automata
Aug 31, 2026Esha Saha, Hao WangNeural Cellular Automata PDE Solving
1Interdisciplinary Lab for Mathematical Ecology and Epidemiology (ILMEE) & The Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton (AB), T6G 2J5, Canada
Joint Spatiotemporal Spectral Neural Operators for Learning PDEs on Irregular Domains
Aug 30, 2026Abdolmehdi Behroozi, Chaopeng ShenPDE Surrogate Modeling PDE Operator Learning
Department of Civil and Environmental Engineering, Penn State University, University Park, PA 16802, USA
Sensitivity-Constrained Neural Operators for Data-Efficient Forward and Inverse Modeling of Partial Differential Equation Systems
Aug 30, 2026Abdolmehdi Behroozi, Chaopeng Shen, Daniel Kifer +1PDE Surrogate Modeling Jacobian Regularization
Department of Civil and Environmental Engineering, Penn State University, University Park, PA 16802, USA · School of Electrical Engineering and Computer Science, Penn State University, University Park, PA 16802, USA
The Frame Kernel Method for Multiscale Operator Learning
Aug 25, 2026Branden Frieden, Ryan Whitehead, M. Keith Ballard +2PDE Surrogate Modeling Kernel Methods
Kahlert School of Computing, University of Utah, Salt Lake City, UT 84112, USA. · U.S. Air Force Research Laboratory, Wright-Patterson AFB, OH 45433, USA.
Distillation of Foundation Models for Time-dependent PDEs
Aug 12, 2026Daniel Musekamp, Boshra Ariguib, Andrei Manolache +1Efficient Neural Network Inference PDE Surrogate Modeling
University of Stuttgart · University of Cologne · Bitdefender
RECAST: A Machine-Learning Framework for Correction and Super-Resolution of Coarse-Grid PDE Solvers
Aug 12, 2026Maryam Reza, Farbod FarajiNeural PDE Solvers PDE Solving
Independent Researcher · Department of Computing, Huxley Building, Imperial College London, London SW7 2RH, United Kingdom
FLARE++: Low-rank attention with dynamic attention routing
Aug 12, 2026Vedant Puri, Yongjie Jessica Zhang, Levent Burak KaraLow-Rank Attention PDE Surrogate Modeling
Department of Mechanical Engineering Carnegie Mellon University Pittsburgh, Pennsylvania, USA
Variational Parameter Calibration with Physics-Aware Latent-Space Surrogates
Aug 11, 2026Qiyao Zhou, Xujia Zhu, Pierre Joli +2Neural Surrogate Modeling Parameter Estimation
LMEE, UnivEvry, Université Paris-Saclay, Evry, France · L2S, Université Paris-Saclay, CNRS, CentraleSupéléc, Gif-sur-Yvette, France · CEREA, ENPC, EDF R&D, Institut Polytechnique de Paris, Île-de-France, France
Two-Step MV-DeepONet: Probabilistic Operator Learning for Uncertainty Propagation Driven by Random Input Fields
Aug 10, 2026Yupei Nie, Lei Wang, Jiasen LiuUncertainty Quantification PDE Surrogate Modeling
School of Mathematics and Physics, North China Electric Power University, Beijing 102206, P.R. China · School of Energy Power and Mechanical Engineering, North China Electric Power University, Beijing 102206, P.R. China
ADEx-FNO: A Unified Ambient-Domain Framework for Fourier Neural Operators on Varying Geometries
Aug 9, 2026Roberto Nuca, Giovanni Testa, Luca Galimberti +1Fourier Neural Operator PDE Surrogate Modeling
Computer, Electrical and Mathematical Sciences and Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia · Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano, Milan, Italy · Physical Science and Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia
Neural Operators for Immersed-Boundary Soft Swimmers Locomotion
Aug 7, 2026Mohammad Sadegh Eshaghi, Yizheng Wang, Navid Valizadeh +2PDE Surrogate Modeling Robot Locomotion
Chair of Computational Science and Simulation Technology, Institute of Photonics, Department of Mathematics and Physics, Leibniz University Hannover, Germany · Department of Engineering Mechanics, Tsinghua University, Beijing, China · Institute of Structural Mechanics, Bauhaus-Universität Weimar, Germany
From Points to Edges: Edge-Conditioned Spectral Operators for Physics-Sensitive PDE Learning
Aug 7, 2026Zhentao Tan, Ruijie Quan, Yi YangPDE Surrogate Modeling PDE Operator Learning
Collaborative Innovation Center of Artificial Intelligence (CCAI), Zhejiang University, China
Kastor: An efficient fine-tuning strategy for generative emulation of PDE simulations
Aug 6, 2026Guillaume Couairon, Alexis Jacq, Yu-Han Wu +4Surrogate Modeling Fine-Tuning
Google DeepMind
Discrete energy as an exact label-free training objective for finite-element surrogates
Aug 5, 2026Ruifeng Cao, Xidan SongSurrogate Modeling Structural Mechanics
The University of Manchester · The University of Manchester, Manchester, United Kingdom · Wuhan University +1
Continual-Learning Physics-Informed Neural Networks for Parameterized Partial Differential Equations
Aug 5, 2026Xujia Chen, Xinyue Hu, Letian Chen +2PDE Surrogate Modeling Replay-Based Continual Learning
Department of Automation, Tsinghua University, Beijing, 100084, China
Conformal risk control for model-form uncertainty in parametric non-intrusive reduced-order models
Aug 4, 2026Edgar Jaber, Rémy Vallot, Thibault Dairay +1Uncertainty Quantification PDE Surrogate Modeling
CB, ENS Paris Saclay · Université Paris-Saclay, CNRS, ENS Paris-Saclay, Centre Borelli, Gif-sur-Yvette, 91190, France · CB, Michelin +3
Modeling Unknown Nonlocal PDE Systems via Flow Map Learning
Aug 1, 2026Zhongshu Xu, Ying Li, Yanzhi Zhang +1PDE Surrogate Modeling Flow Map Learning
Department of Mathematics, The Ohio State University, Columbus, OH 43210, USA. · Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409, USA.
Geometry-aware Incremental Neural Operator for Long-Horizon PDE prediction
Jul 31, 2026Jiaquan Zhang, Shuxu Chen, Haifan Meng +6PDE Surrogate Modeling PDE Operator Learning
School of Information and Software Engineering, UESTC · Electronics and Information Convergence Engineering, KHU · School of Computer Science and Engineering, UESTC +4

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Single-condition neural solvers encode transferable response spaces for parametric differential equations

Wenbo Cao, Weiwei Zhang

Institute of AI for Industries, Chinese Academy of Sciences, Nanjing 211135, China · Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100190, China · School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China+2

PDE Solving PDE Surrogate Modeling Active Learning Transfer Learning PDE Operator Learning

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Operator learning for parametric partial differential equations (PDEs) typically builds global models over prescribed domains, requiring cross-condition data or costly physics-constrained training. Here we show that the output Jacobian of a neural solution model trained at one condition defines a reusable response space for cross-condition solution variations. We introduce Linearized Subspace Transfer (LST) to exploit this space and recover target solutions by minimizing the target PDE-system residual over response-space coordinates. Because any single response space has finite coverage, Active Transfer Modeling (ATM) uses post-transfer residuals as coverage indicators to selectively acquire response spaces from additional single-condition models. Across six systems, single-condition response spaces supported cross-condition transfer, with enrichment improving accuracy when added spaces expanded representation capacity. Relative to evaluated physics-informed operator baselines, ATM reduced error and offline construction cost, with orders-of-magnitude accuracy gains in representative cases and millisecond-to-second target adaptation. These results establish neural solvers as reusable local parametric models.

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