Neural PDE Solvers

PDE: Partial Differential Equation

Ask about this topic

Momentum

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

Jul 13Week of Sep 28
View on map

Latest papers 169

All topics
CardsList

  1. Weak Adversarial Neural Pushforward Method for the Wigner Transport Equation

    Apr 9, 2026Andrew Qing He, Wei Cai, Sihong ShaoNeural PDE Solvers

    *Department of Mathematics, Southern Methodist University, Dallas, TX, USA. · †School of Mathematical Sciences, Peking University, Beijing, China.

  2. Stochastic Dimension Implicit Functional Projections for Global Integral Conservation in High-Dimensional PINNs

    Mar 31, 2026Zhangyong Liang, Huanhuan GaoNeural PDE SolversPhysics-Informed ML

    National Center for Applied Mathematics, Tianjin University, Tianjin, 300072, China · School of Mechanical and Aerospace Engineering, Jilin University, Changchun 130025, China

  3. Stability and Bifurcation Analysis of Nonlinear PDEs via Random Projection-based PINNs: A Krylov-Arnoldi Approach

    Mar 23, 2026Gianluca Fabiani, Michail E. Kavousanakis, Constantinos Siettos +1Dynamical SystemsNeural PDE Solvers

    Hopkins Extreme Materials Institute, Johns Hopkins University, Baltimore, 21218, MD, USA · Dept. of Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, 21218, MD, USA · School of Chemical Engineering, National Technical University of Athens, 9 Iroon Polytechniou Street, Athens, 15772, Greece +2

  4. An Adaptive Machine Learning Framework for Fluid Flow in Dual-Network Porous Media

    Mar 20, 2026V. S. Maduri, K. B. NakshatralaNeural PDE SolversPhysics-Informed ML

    Department of Civil & Environmental Engineering University of Houston, Houston, Texas 77204, USA.

  5. Rigorous Error Certification for Neural PDE Solvers: From Empirical Residuals to Solution Guarantees

    Mar 19, 2026Amartya Mukherjee, Maxwell Fitzsimmons, David C. Del Rey Fernández +1Neural Network GeneralizationNeural PDE Solvers

    Department of Applied Mathematics, University of Waterloo, Waterloo, ON, Canada

  6. 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

  7. MUSA-PINN: Multi-scale Weak-form Physics-Informed Neural Networks for Fluid Flow in Complex Geometries

    Mar 9, 2026Weizheng Zhang, Xunjie Xie, Hao Pan +4Neural PDE SolversPDE Solving

    Shandong University, Qingdao, China · Tsinghua University, Beijing, China · Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing, China

  8. Jacobian-Adaptive Weighting for Stability: Enhancing Long-term Rollout of Neural Partial Differential Equation Solvers via Spatially-Adaptive Regularization

    Mar 4, 2026Fengxiang Nie, Yasuhiro SuzukiNeural PDE SolversAlgorithmic Stability

    University of Hiroshima

  9. Transolver-3: Scaling Up Transformer Solvers to Industrial-Scale Geometries

    Feb 4, 2026Hang Zhou, Haixu Wu, Haonan Shangguan +4Efficient Neural Network InferenceNeural PDE Solvers

    School of Software, BNRist, Tsinghua University, China.

  10. Deep Neural Networks as Discrete Dynamical Systems: Implications for Physics-Informed Learning

    Jan 1, 2026Abhisek Ganguly, Santosh Ansumali, Sauro SucciDynamical SystemsNeural PDE Solvers

    Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore, 560064, Karnataka, India · Italian Institute of Technology, Viale Regina Elena 291, 00161 Rome, Italy · University of Roma Tre, Italy +2

  11. PGOT: A Physics-Geometry Operator Transformer for Complex PDEs

    Dec 29, 2025Zhuo Zhang, Xi Yang, Ying Miao +5Neural PDE SolversPDE Surrogate Modeling

    National University of Defense Technology · Peking University · National University of Singapore +2

  12. Adaptive Probability Flow Residual Minimization for High-Dimensional Fokker-Planck Equations

    Dec 22, 2025Xiaolong Wu, Qifeng LiaoNeural PDE SolversPDE Solving

    School of Information Science and Technology, ShanghaiTech University, Shanghai, 201210, China

  13. Neural network-driven domain decomposition for efficient solutions to the Helmholtz equation

    Nov 19, 2025Victorita Dolean, Daria Hrebenshchykova, Stéphane Lanteri +1Neural PDE SolversPDE Solving

    Department of Mathematics and Computer Science, Eindhoven University of Technology, The Netherlands · Atlantis project-team, Inria Research Center at Université Côte d’Azur, France · MACARON project-team, Université de Strasbourg, CNRS, Inria, IRMA, France

  14. LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries

    Oct 29, 2025René P. Klausen, Ivan Timofeev, Jonas Naujoks +4Neural PDE SolversPDE Solving

    Department of Artificial Intelligence, Fraunhofer Heinrich Hertz Institute, Berlin, Germany · Department of Electrical Engineering and Computer Science, Technische Universität Berlin, Germany · BIFOLD Berlin Institute for the Foundations of Learning and Data, Berlin, Germany +1

  15. Convergence of Stochastic Gradient Methods for Wide Two-Layer Physics-Informed Neural Networks for the Poisson Equation

    Aug 29, 2025Bangti Jin, Longjun WuNeural PDE SolversPDE Solving

    Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, P.R. China

  16. Accelerating Natural Gradient Descent for PINNs with Randomized Numerical Linear Algebra

    May 16, 2025Ivan Bioli, Carlo Marcati, Giancarlo SangalliNeural PDE SolversGradient Descent

    Department of Mathematics, University of Pavia, Via A. Ferrata 5, 27100 Pavia, Italy · Department of Civil Engineering and Architecture, University of Pavia, Via A. Ferrata 3, 27100 Pavia, Italy · Istituto di Matematica Applicata e Tecnologie Informatiche “E. Magenes”, CNR, Via A. Ferrata 1, 27100 Pavia, Italy

  17. DeepSPoC: A Deep Learning Based Sequential Propagation of Chaos

    Aug 29, 2024Kai Du, Yongle Xie, Tao Zhou +1Stochastic Differential EquationsNeural PDE Solvers

    Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, 200438, China. · Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, 200433, China. · LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS, Chinese Academy of Sciences, Beijing, China.

  18. Deep learning based numerical approximation algorithms for stochastic partial differential equations

    Dec 2, 2020Christian Beck, Sebastian Becker, Patrick Cheridito +2Stochastic Differential EquationsNeural PDE Solvers

    Department of Mathematics, ETH Zurich · School of Data Science and School of Artificial Intelligence,2025 The Chinese University of Hong Kong, Shenzhen (CUHK-Shenhen) · Applied Mathematics: Institute for Analysis and Numerics, University of Münster +1

  19. Monotone Neural Policy Iteration for High-Dimensional First-Order Hamilton--Jacobi--Bellman Equations

    Date pendingMinseok Kim, Yeongjong Kim, Namkyeong Cho +1Neural PDE SolversStochastic Optimal Control

    Department of Applied Artificial Intelligence, Seoul National University of Science and Technology, Seoul, Republic of Korea. · Department of Mathematics, Pohang University of Science and Technology, Pohang, Republic of Korea. · Department of Mathematical Finance and Big Data, Gachon University, Seongnam, Republic of Korea +1