PDE Solving

PDE: Partial Differential Equation

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19 papers in the last four weeks, up 111% on the four weeks before. 0.2% of all new papers.

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  1. An Interpretable Approach to PDE Solution Discovery via Structural Experience Distillation

    Oct 8, 2026Yunpeng Gong, Huolong Wu, Can Yang +1PDE SolvingSymbolic Regression

    School of Informatics, Xiamen University

  2. Gen-PINNs: Generative Adversarial Physics Informed Neural Networks for solving partial differential equations

    Oct 7, 2026Muhammad M. Akmal, Kamy Sepehrnoori, Michael J. PyrczPDE SolvingPhysics-Informed ML

    Hilderbrand Department of Petroleum and Geosystems Engineering, The University of Texas at Austin · Department of Earth and Planetary Sciences, The University of Texas at Austin

  3. Physics-Informed Neural Plasticity: PDE Solvers That Reshape Themselves

    Oct 7, 2026Chun-Wun Cheng, Bingcheng Hu, Angelica I. Aviles-RiveroNeural PDE SolversPDE Solving

    Shanghai Normal University · YMSC, Tsinghua University

  4. A Neural JKO Scheme for Hellinger-Kantorovich Gradient Flows via Monge-Growth Pairs

    Oct 6, 2026Geuntaek Seo, Cheolhyeong Kim, Hwijae Son +1Neural PDE SolversPDE Solving

    Department of Mathematics, Pohang University of Science and Technology · Samsung Electronics · Department of Mathematics, Konkuk University

  5. Geometry Meets Physics: Data-Efficient Pre-Training for Unstructured Neural PDE Solvers

    Oct 2, 2026Luis Medrano-Navarro, Giacomo Baldan, Qiang Liu +4Synthetic Data PretrainingNeural PDE Solvers

    Technical University of Munich · University of Stuttgart

  6. Kolmogorov-Arnold Networks for Free-Boundary Partial Differential Equations

    Oct 1, 2026Tan Phuong Dong LeNeural PDE SolversPDE Solving

    Department of Applied Mathematics, University of Waterloo, Canada · Department of Statistics and Actuarial Science, University of Waterloo, Canada

  7. Learning PDE Dynamics between Submanifolds Using Green's Observation Operators

    Oct 1, 2026Jan Tauberschmidt, Jephte Abijuru, Naukshatro Bose +5PDE SolvingPDE Surrogate Modeling

    German Research Center for Artificial Intelligence (DFKI), Kaiserslautern, Germany · Rheinland-Pfälzische Technische Universität (RPTU), Kaiserslautern, Germany · University of Manchester, Manchester, United Kingdom

  8. Cluster Attention Neural Operators for Solving Parametric Partial Differential Equations

    Sep 30, 2026Ming Zhong, Antonio Colanera, Gianluigi Rozza +1PDE SolvingAttention Mechanisms

    School of Advanced Interdisciplinary Sciences, University of Chinese Academy of Sciences, Beijing 100049, China. · State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China. · International School for Advanced Studies (SISSA), Trieste 34136, Italy. +1

  9. Neural Harmonic Measure Operator

    Sep 28, 2026Jinjin He, Sinan Wang, Yuchen Sun +1Neural PDE SolversPDE Solving

    Georgia Institute of Technology

  10. A Hybrid Iterative Deep Ritz Method for Elliptic Interface Problems

    Sep 23, 2026Tianhao Hu, Bangti Jin, Fengru Wang +1Neural PDE SolversPDE Solving

    Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong · Department of Mathematics & Scientific Computing Key Laboratory of Shanghai Universities, Shanghai Normal University, Shanghai 200234, China.

  11. GaussPDE: Graph-Based Partial Differential Equation-Driven Rendering for 3D Gaussian Splatting

    Sep 23, 2026Haoyuan Yue, Fengyuan Ye, Ziyin Li3D Gaussian SplattingPDE Solving

    Department of Physics, Westlake University, Hangzhou, China · The Chinese University of Hong Kong, Shenzhen, China · Department of Accounting, Xi’an Jiaotong-Liverpool University, Suzhou, China

  12. Cost-Accuracy Trade-offs: Neural Operator vs Classical Numerical Solver

    Sep 21, 2026Daniel Zhengyu Huang, Andrew M. StuartNeural Surrogate ModelingNeural PDE Solvers

    Beijing International Center for Mathematical Research, Center for Machine Learning Research, Peking University, Beijing, China · California Institute of Technology, Pasadena, CA

  13. Beyond PINNs: A Unified Gauss--Newton and Petrov--Galerkin Framework for Neural and Hybrid PDE Solvers

    Sep 17, 2026Nilo Schwencke, Roland MaierGauss-Newton OptimizationNeural PDE Solvers

  14. Amortizing Physics-Informed Neural Solvers via Graph Hypernetworks

    Sep 17, 2026Cheng Jing, Abhishek Verma, Kallol Bera +2Amortized InferenceMeta-Learning

    Arizona State University · Applied Materials Inc.

  15. Hybrid coupling with numerics-informed neural networks and the overlapping Schwarz alternating method

    Sep 15, 2026George Chumbipuma, Irina Tezaur, Alejandro Diaz +1Neural PDE SolversPDE Solving

    Rice University · Sandia National Laboratories

  16. Physics Informed Random Feature Neural Networks for Solving PDEs

    Sep 14, 2026Chi-An Chen, Chunyang Liao, Ming ZhongPDE SolvingRandom Feature Methods

    Department of Applied Mathematics, Mathematics, Illinois Institute of Technology, Chicago, IL, 60616 · Department of Mathematical Sciences, University of Arkansas, Fayetteville, AR, 72701 · Department of Mathematics, University of Houston, Houston, TX, 77204

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

    Sep 14, 2026Wenbo Cao, Weiwei ZhangPDE SolvingPDE 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

  18. Linearized PINN with pretrained nonlinear layers

    Sep 14, 2026Wenhao Chen, Alexandre M. TartakovskyEfficient Neural Network InferencePDE Solving

    Civil and Environmental Engineering Department University of Illinois Urbana-Champaign Urbana, IL 61801, USA · Pacific Northwest National Laboratory Richland, WA 99352, USA

  19. An explicit solution of the five-expert prediction PDE and the exact optimality set of COMB

    Sep 14, 2026Jeff Calder, Nadejda DrenskaPDE Solving

    School of Mathematics, University of Minnesota · Department of Mathematics, Louisiana State University

  20. Tackling Failure Modes of PINNs and PIKANs Using Conflict-Free Gradients

    Sep 13, 2026Sidharth S. Menon, Irina Tezaur, Ameya D. JagtapPDE SolvingGradient Interference

    Aerospace Engineering Department, Worcester Polytechnic Institute, Worcester, MA 01609, USA. · Sandia National Laboratories, 7011 East Ave, Livermore, CA 94550, USA.

  21. Attention Is All You Need (to Avoid Spurious Oscillations)

    Sep 11, 2026Jinyoung Jeong, Joseph B. Choi, Xinlun Cheng +3Neural PDE SolversPDE Solving

    School of Mechanical Engineering & IEDT, Kyungpook National University, Daegu, South Korea · School of Data Science, University of Virginia, Charlottesville, VA 22903, USA · Department of Mechanical Engineering, University of Iowa, Iowa City, Iowa 52242, USA +1

  22. Structured Extrema Errors in Classical Surrogates for Viscous Burgers: A Physics-Consistent Interpretation

    Sep 7, 2026Youssef OubariKernel Ridge RegressionSurrogate Modeling

    IMT Atlantique, France

  23. A Systematic Analysis of Automatic Differentiation versus Discretization-based Constraints for Physics-Informed PDE Solvers

    Sep 7, 2026Xing Guo, Hongwei Tang, Zewei Meng +3Automatic DifferentiationNeural PDE Solvers

    School of Systems Science and Engineering, Sun Yat-sen University, Guangzhou, China

  24. Residual neural networks overcome the curse of dimensionality for semilinear heat equations

    Sep 3, 2026Ilkhom Mukhammadiev, Diyora SalimovaNeural PDE SolversPDE Solving

    Department of Applied Mathematics, University of Freiburg, Germany

  25. Spectral Convergence of Random Feature Method in Multiple Dimensions

    Sep 3, 2026Pingbing Ming, Hao YuPDE SolvingRandom Feature Methods

  26. Learning Spectral-Like Mesh-Free Discretisations

    Sep 2, 2026Lucas Gerken Starepravo, Henry Broadley, Steven Lind +1PDE Solving

    School of Engineering, University of Manchester Manchester, UK · School of Engineering, Cardiff University Cardiff, UK

  27. DiffPDE: Masked Diffusion Language Models as PDE Solver

    Aug 31, 2026Wenxuan Guo, Yuyang Hong, Lubin Fan +4RL for Code GenerationMasked Diffusion Models

    School of Artificial Intelligence, University of Chinese Academy of Sciences · MAIS, Institute of Automation, Chinese Academy of Sciences · Independent Researcher

  28. Learning PDE Time-Stepping with Neural Cellular Automata

    Aug 31, 2026Esha Saha, Hao WangNeural Cellular AutomataPDE Solving

    1Interdisciplinary Lab for Mathematical Ecology and Epidemiology (ILMEE) & The Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton (AB), T6G 2J5, Canada

  29. RECAST: A Machine-Learning Framework for Correction and Super-Resolution of Coarse-Grid PDE Solvers

    Aug 12, 2026Maryam Reza, Farbod FarajiNeural PDE SolversPDE Solving

    Independent Researcher · Department of Computing, Huxley Building, Imperial College London, London SW7 2RH, United Kingdom

  30. Derivative Computation in PINNs: Automatic Differentiation, Finite Differences and Beyond

    Aug 11, 2026Maciej J. Mikulski, Tadeusz UhlAutomatic DifferentiationNeural PDE Solvers

    AGH University of Krakow