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. Efficient Weak-Entropy PINN for Solving Hyperbolic Conservation Laws

    Aug 11, 2026Qi Gao, Kuang Huang, Xuan DiNeural PDE SolversPDE Solving

    Department of Civil Engineering and Engineering Mechanics, Columbia University · Department of Mathematics, The Chinese University of Hong Kong · Center for Smart Cities, Data Science Institute, Columbia University

  2. Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing

    Aug 10, 2026Konrad Kleinberg, Thomas KruseNeural PDE SolversPDE Solving

    Department of Mathematics & Informatics, University of Wuppertal, Germany

  3. Quantum-Classical Physics-Informed Kolmogorov-Arnold Networks for Solving Fuzzy Differential Equations

    Aug 9, 2026Xiang Rao, Yuxuan ShenPDE SolvingHybrid Quantum-Classical ML

    1. School of Petroleum Engineering, Yangtze University, Wuhan 430100, China · 2. College of Future Technology, Yangtze University, Wuhan 430100, China · 3. School of Computer Science, Yangtze University, Jingzhou 434023, China +2

  4. Explicit and Stable Pseudospectral Time-Domain Method for the Föppl-von Kármán Equations

    Aug 6, 2026Victor Zheleznov, Stefan BilbaoPDE SolvingStructural Mechanics

    Acoustics and Audio Group, University of Edinburgh, Edinburgh, UK · STMS (UMR9912), IRCAM, CNRS, Sorbonne Universit´e, Paris, France

  5. Adaptive Quantum Physics-Informed Neural Networks for Differential Equations with Applications to Fluid Dynamics

    Aug 1, 2026Fabio Pereira dos Santos, Renato Portugal, Júlio de Castro Vargas Fernandes +1PDE SolvingHybrid Quantum-Classical ML

    Coordination of Mathematical and Computational Methods National Laboratory of Scientific Computing Av. Getúlio Vargas, 333 - Quitandinha, Petrópolis - RJ, 25651-075 · Center for Computation and Technology - Louisiana State University, 888 S. Stadium Dr., Baton Rouge, LA 70808, USA

  6. Reflected diffusion, no-flux continuity equations and confined Lagrangian flows in bounded domains

    Jul 30, 2026Rama ContDynamical SystemsStochastic Differential Equations

  7. Learning features from Newton's algorithm: a way to accelerate nonlinear parametrized PDE solvers

    Jul 30, 2026Rémy Vallot, Florian de Vuyst, Thibault Dairay +1PDE SolvingPDE Surrogate Modeling

    CB, Michelin · Centre Borelli UMR 9010, ENS Paris-Saclay, Université Paris-Saclay, CNRS, France · Michelin, Centre de Recherche de Ladoux, Cébazat, France +4

  8. Fractional Parabolic Partial Differential Equations in Anisotropic Spectral Barron Spaces: Regularity and Neural Approximation

    Jul 30, 2026Jae-Hwan Choi, Hyojae Lim, Jinsol Seo +2Neural PDE SolversPDE Solving

  9. Physics-Informed Broad Learning System: An Efficient Backpropagation-Free Framework for Solving Partial Differential Equations

    Jul 28, 2026Pinki Khatun, M. Sajid, Abhinav Jha +1Neural PDE SolversPDE Solving

    Department of Industrial Engineering, Università degli Studi di Firenze, Viale Morgagni 40/44, 50134 Firenze, Italy · Department of Mathematics, Indian Institute of Technology Indore, Indore 453552, India · Department of Mathematics, Indian Institute of Technology Gandhinagar, Palaj, Gandhinagar, 382055, Gujarat, India

  10. Score-Based Stabilization for Time-Dependent Problems

    Jul 27, 2026Eshed Gal, Eldad Haber, Uri AscherNeural PDE SolversPDE Solving

    University of British Columbia Vancouver, British Columbia, Canada

  11. Global Convergence of DGM and PINN Algorithms for Solving Nonlinear PDEs

    Jul 27, 2026Justin Sirignano, Konstantinos Spiliopoulos, Samuel CohenNeural PDE SolversOptimization Convergence Analysis

    Mathematical Institute, University of Oxford · Department of Mathematics and Statistics, Boston University

  12. Perturbative-NeuSA: A Structured Spectral Framework for Time-Dependent PDEs

    Jul 27, 2026Xianli Zhu, Jia YinNeural Surrogate ModelingNeural PDE Solvers

    School of Mathematical Sciences, Fudan University Shanghai, China

  13. Variational Boosting for Physics-Informed Neural Networks

    Jul 27, 2026Kaylee Vo, Pavlos ProtopapasEnsemble LearningPDE Solving

    Harvard University

  14. Extending Fourier Neural Operators for Modeling Parameterized and Coupled PDEs

    Jul 26, 2026Cheng Jing, Uvini Balasuriya Mudiyanselage, Abhishek Verma +3Fourier Neural OperatorPDE Solving

    Arizona State University · Applied Materials Inc.

  15. Generalized Neural Operator for Parametric and Boundary-Value Problems

    Jul 24, 2026Ruoyan Li, Yizhou Sun, Wei WangEfficient Neural Network InferencePDE Solving

    University of California, Los Angeles

  16. Label-Free Finite-Volume-Residual Training of Attention Graph Neural Networks for Coupled Thermo-Fluid Fields

    Jul 22, 2026Tianyu Li, Zhiwei Cao, Qingang Zhang +3Neural Surrogate ModelingGraph Neural Networks

    Interdisciplinary Graduate Programme, Nanyang Technological University, Singapore, Singapore. · School of Future Technology, Fuzhou University, Fuzhou, China. · College of Computing and Data Science, Nanyang Technological University, Singapore, Singapore. +2

  17. A Structure-Adaptive Random Feature Method for High-Dimensional Elliptic PDEs

    Jul 22, 2026Jiale Linghu, Hao Dong, Yangshuai WangPDE SolvingRandom Feature Methods

    School of Mathematics and Statistics, Xidian University, Xi’an 710071, China. · Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, 119076, Singapore

  18. Boundary-Adapted PINNs for Elliptic Dirichlet Problems: H2(Ω)H^2(Ω) A Priori Error Bounds with Application to Mean Escape Time Computation

    Jul 21, 2026Nathanael Tepakbong, Jun Fan, Xiang Zhou +1PDE SolvingNeural Network Approximation Theory

    Department of Data Science, City University of Hong Kong · Department of Mathematics, Hong Kong Baptist University · Department of Mathematics, City University of Hong Kong +1

  19. Image Editing Models are Numerical Solvers

    Jul 21, 2026Ulysse MizrahiNeural PDE SolversPDE Solving

    Tel Aviv University

  20. Adaptive Mamba Neural Operators

    Jul 20, 2026Zeyuan Song, Zheyu JiangPDE SolvingPDE Operator Learning

    School of Chemical Engineering Oklahoma State University Stillwater, OK 74078, USA

  21. FlashPDE: A Drop-In Fused Triton Operator Library for Neural PDE Solvers

    Jul 20, 2026Peiyu Zang, Bosen Xie, Ruoxiang Xu +1Automatic DifferentiationNeural PDE Solvers

    School of Mathematical Sciences, Beijing Normal University · 2Beijing University of Posts and Telecommunications

  22. Trainable Spline Representations for Physics-Informed Learning

    Jul 17, 2026Giovanni Canali, Nicola Demo, Gianluigi RozzaPDE SolvingPhysics-Informed ML

    Mathematics Area, mathLab, SISSA, via Bonomea 265, I-34136, Trieste, Italy · FAST Computing Srl, via Mazzini 20, I-34136, Trieste, Italy

  23. Subgrid-Scale Parameterization in Burgers' Equation Using Structure-Preserving Neural Networks and Entropy Variables

    Jul 16, 2026Aijaz Nazir, Ilya TimofeyevNeural Surrogate ModelingPDE Solving

    Dept. of Mathematics, University of Houston, Houston, TX 77204

  24. Operator-Informed Gaussian Processes for Complex Helmholtz Wavefields: From Synthetic Benchmarks to In Vivo Brain Elastography

    Jul 15, 2026Boyuan Deng, Kshitiz Upadhyay, Michael ShieldsPDE SolvingPhysics-Informed ML

    Department of Civil and Systems Engineering, Johns Hopkins University · Department of Aerospace Engineering and Mechanics, University of Minnesota

  25. Spectral-Informed Neural Networks Outperform Spectral Methods in High-dimensional PDEs

    Jul 15, 2026Tianchi Yu, Ivan OseledetsPDE SolvingPhysics-Informed ML

    1AXXX · 2Applied AI Institute · 3INM

  26. Deep Learning-based Surrogate Modelling of the LOD Method for Multiscale Problems

    Jul 14, 2026Marc Haltmayer, Jaemin Seo, Yuseung Lee +3PDE SolvingPDE Surrogate Modeling

    Department of Artificial Intelligence, Chung-Ang University, 84 Heukseok-ro, Dongjak-gu, Seoul, 06974, Republic of Korea · Computational Science and Engineering Team, Samsung Electronics, 41 Samsung-ro, Giheung-gu, Yongin-si, 17113, Republic of Korea

  27. SPARC-Net: A Spectral, Causality-Aware, and Hard-Constrained Physics-Informed Architecture for Stiff and Shock-Dominated Partial Differential Equations

    Jul 13, 2026Divyavardhan Singh, Dimple Sonone, Hammad Mohammad +1PDE SolvingSpectral Bias

    Dept. of Electronics Engg. SVNIT Surat, India

  28. Physics-Informed Neural Embeddings of PDE Solution Families

    Jul 7, 2026Raul Jimenez, Svitlana Mayboroda, Pavlos Protopapas +3Intrinsic DimensionalityPDE Solving

    Institute of Cosmos Sciences (ICC), University of Barcelona, Martí i Franquès 1, ES-08028, Barcelona, Spain. · Department of Mathematics, ETH Zurich, Rämistrasse 101, 8092, Zürich, Switzerland. · Institute for Applied Computational Science, Harvard University, Cambridge, MA, USA. +1

  29. Black Hole Black Boxes: Numerical Black Hole Metrics via AInstein Neural Networks

    Jul 6, 2026Tancredi Schettini Gherardini, Edward Hirst, Alexander George StapletonPDE SolvingPhysics-Informed ML

    Instituto de Matemática, Estatística e Computação Científica (IMECC) da Universidade Estadual de Campinas (UNICAMP), 13083-859, Brasil · Mathematisches Institut (MI), University of Bonn, Bonn, Germany · Max Planck Institute for Mathematics, Bonn, Germany +1

  30. MeGA-MP: Metric Graph Advection Message Passing -- A Physics-Informed Message Passing Operator for Advection-Dominated Metric Graphs

    Jul 6, 2026Janine Strotherm, Luca Hermes, André Artelt +1Graph Representation LearningPDE Solving

    Bielefeld University