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PDE: Partial Differential Equation

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23 papers in the last four weeks, up 109% on the four weeks before. 0.2% of all new papers.

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  1. 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

  2. An extended deep energy method for thermo-mechanical crack propagation

    Oct 7, 2026Han Zhang, Mehrisadat Makki Alamdari, Babak Shahbodagh +4Neural PDE SolversMaterials Science

    University of New South Wales, Sydney, NSW, Australia · Central Queensland University, Melbourne, VIC, Australia · Bauhaus-Universität Weimar, Weimar, Germany

  3. FOSLS-deRhaNN: native de Rham neural classes for H(div) and H(curl) with applications to first-order system least-squares neural network methods for partial differential equations

    Oct 6, 2026Shun ZhangNeural PDE SolversNeural Network Approximation Theory

    Department of Mathematics, City University of Hong Kong, Kowloon Tong, Hong Kong, China

  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. Singular parameters and missing limits in neural PDE solvers

    Oct 5, 2026Daniel FernándezNeural PDE SolversNeural Network Optimization

    Chair for Dynamics, Control, Machine Learning, and Numerics (Alexander von Humboldt Professorship), Department of Mathematics, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany.

  6. IGA-KAN: Isogeometric Analysis with Physics-Informed Closed-Form Kolmogorov-Arnold Networks for Forward and Inverse PDEs

    Oct 5, 2026Sima Naraghi, Kourosh Parand, Amirhossein Sadr +1Neural PDE SolversKolmogorov-Arnold Networks

    Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran · Department of Computer and Data Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran · Department of Cognitive Modeling, Institute for Cognitive and Brain Sciences, Shahid Beheshti University, Tehran, Iran +1

  7. Component-Level Evaluation of Adaptive PINN Training for CFD-Oriented Crystal Growth Simulation

    Oct 4, 2026Niruta Chapagain, Rohit Raj, Bertwin Kurisinkal Shine +1Neural PDE SolversPDE Surrogate Modeling

    University of Europe for Applied Sciences Potsdam, Germany · Vienna, Austria · Technische Universität Chemnitz Chemnitz, Germany +1

  8. 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

  9. 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

  10. Physics-Informed Method of Group Data Handling: Adaptive Construction of Functional Representations with an Application to the Navier-Stokes Equations

    Sep 30, 2026Mykhailo MininNeural PDE SolversPhysics-Informed ML

    JSC KIEP, Kyiv, Ukraine

  11. Warm-starting PDE solvers with any-dimensional machine learning

    Sep 30, 2026Wilson G. Gregory, George A. Kevrekidis, Ben Blum-Smith +1Neural PDE SolversPDE Surrogate Modeling

    Department of Statistics and Irving Institute for Cancer Dynamics, Columbia University · Division of Applied Mathematics, Brown University · Department of Applied Mathematics and Statistics, Johns Hopkins University

  12. PE-EK-PINN: Physics Embedding with Evolving Kernel for Scalable Physics-Informed Neural Networks

    Sep 29, 2026Huiwen Zhang, Feng Ye, Chu MaNeural PDE SolversPhysics-Informed ML

    Department of Electrical & Computer Engineering Madison, WI, 53706, USA

  13. Transolver-σσ: Joint Spectral-Physical Subspace Modeling for Neural PDE Solving

    Sep 29, 2026Haonan Shangguan, Hang Zhou, Haixu Wu +3Fourier Neural OperatorNeural PDE Solvers

    School of Software, BNRist, Tsinghua University · MIT CSAIL

  14. Neural Harmonic Measure Operator

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

    Georgia Institute of Technology

  15. GAC-PINN: Geometry-Adaptive and Constraint-Enhanced Physics-Informed Neural Networks

    Sep 28, 2026Yanxin Zhang, Yong Zhang, Houbiao LiNeural PDE SolversPhysics-Informed ML

    University of Electronic Science and Technology of China, Chengdu, 611731, Sichuan, China

  16. Physics-Informed Neural Networks for Depth-Averaged Avalanche Dynamics

    Sep 28, 2026Pradyumn Singh Sikarwar, Vishal Sharma, Gaurav BhutaniNeural PDE SolversPhysics-Informed ML

    School of Mechanical and Materials Engineering, Indian Institute of Technology Mandi, India

  17. Theory Guided and Interpretable Neural Operator Design for Partial Differential Equation Learning

    Sep 27, 2026Zeyuan Song, Zheyu JiangNeural PDE SolversNeural Network Interpretability

    Oklahoma State University Stillwater, OK 74078

  18. 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.

  19. 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

  20. 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

  21. Well-posedness of neural turbulence closures and tangent dissipation

    Sep 17, 2026Zhen Zhang, George Em KarniadakisNeural PDE SolversComputational Fluid Dynamics

    Division of Applied Mathematics, Brown University, Providence, RI 02912, USA

  22. 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

  23. Physics Informed Neural Network model for the dynamical study of Abdominal Aortic Aneurysm

    Sep 14, 2026Adrián Robles Arques, Martín Ruiz Fernandez, Javier Sanchis +2Neural PDE SolversPhysics-Informed ML

    Lucentia Research; Instituto Universitario de Investigación en Informática, Universidad de Alicante, Carr. San Vicent del Raspeig, Alicante, 03690, Comunidad Valenciana, España

  24. Physics-enriched neural solvers for transient ice-flow simulation

    Sep 14, 2026Thomas Gregov, Sebastian Rosier, Brandon Finley +2Neural Surrogate ModelingNeural PDE Solvers

    Institute of Earth Surface Dynamics, Universit´e de Lausanne, Lausanne, Switzerland · Department of Geography, Universität Zürich, Zürich, Switzerland

  25. 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

  26. A variational physics-informed graph neural network for heterogeneous solid mechanics

    Sep 10, 2026Aashay Rajan Yadav, Amiya Prakash Das, Ratna Kumar AnnabattulaNeural PDE SolversStructural Mechanics

    Mechanics of Materials Lab, Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, 600036, Tamil Nadu, India

  27. Solving the Elastic Wave Equation with Physics-Informed Neural Networks: A Robust and Critical Assessment

    Sep 7, 2026Davide Staub, Ben MoseleyNeural PDE SolversPhysics-Informed ML

    Department of Mathematics, ETH Zürich

  28. Latent-MoE: Domain-Aware Mixture-of-Experts for PDEs with Multi-Regime Physics

    Sep 7, 2026Hanwen Wang, Paris PerdikarisNeural PDE SolversPhysics-Informed ML

    Graduate Group of Applied Mathematics and Computational Science University of Pennsylvania Philadelphia, PA 19104 · Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania Philadelphia, PA 19104

  29. 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

  30. 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