Neural PDE Solvers

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 PDE Solvers via Spatio-Temporal MeanFlow

    May 9, 2026Hanru Bai, Yuncheng Zhou, Difan ZouFlow MatchingNeural PDE Solvers

    1Fudan University · 2The University of Hong Kong.

  2. Recovering Physical Dynamics from Discrete Observations via Intrinsic Differential Consistency

    May 8, 2026Yuxiang Luo, Andrew PerraultNeural PDE SolversSystem Identification

    Department of Computer Science and Engineering The Ohio State University

  3. AdamFLIP: Adaptive Momentum Feedback Linearization Optimization for Hard Constrained PINN Training

    May 8, 2026Binghang Lu, Runyu Zhang, Changhong Mou +2Neural PDE SolversConstrained Optimization

    Purdue University · Massachusetts Institute of Technology · Utah State University +1

  4. When Attention Beats Fourier: Multi-Scale Transformers for PDE Solving on Irregular Domains

    May 8, 2026Brandon Yee, Pairie Koh, Jack Rodriguez +1Neural PDE SolversPDE Solving

    Physics Lab, Yee Collins Research Group

  5. Sparse Random-Feature Neural Networks with Krylov-Based SVD for Singularly Perturbed ODE

    May 8, 2026Kevin Kurian Thomas Vaidyan, Siddharth RoutNeural PDE SolversSingular Value Decomposition

    Institute of Applied Mathematics University of British Columbia Vancouver, BC V6T 1Z4

  6. Learned Lagrangian Models of PDEs via Euler-Lagrange Residual Minimization

    May 8, 2026Lyra Zhornyak, Eric Forgoston, M. Ani HsiehNeural PDE SolversPDE Surrogate Modeling

    University of Pennsylvania · Montclair State University

  7. INEUS: Iterative Neural Solver for High-Dimensional PIDEs

    May 7, 2026Jean-Loup Dupret, Davide Gallon, Patrick CheriditoNeural PDE SolversPDE Solving

    Department of Mathematics and RiskLab, ETH Zurich, Switzerland · Applied Mathematics: Institute for Analysis and Numerics, University of Münster, Germany

  8. Hybrid Iterative Neural Low-Regularity Integrator for Nonlinear Dispersive Equations

    May 6, 2026Zhangyong Liang, Huanhuan GaoNeural PDE SolversPDE Solving

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

  9. Random test functions, H−1H^{-1} norm equivalence, and stochastic variational physics-informed neural networks

    May 5, 2026Diego MarcondesNeural PDE SolversPDE Solving

  10. Posterior-First Neural PDE Simulation: Inferring Hidden Problem State from a Single Field

    May 5, 2026Wenshuo Wang, Fan ZhangNeural PDE SolversPDE Surrogate Modeling

    School of Future Technology, South China University of Technology, China · State Key Laboratory of Ocean Sensing & Ocean College, Zhejiang University, China · Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, USA

  11. Isotropic Fourier Neural Operators

    May 4, 2026Michael F. StaddonFourier Neural OperatorNeural PDE Solvers

    Independent Researcher

  12. Mesh Based Simulations with Spatial and Temporal awareness

    May 2, 2026Paul Garnier, Vincent Lannelongue, Elie HachemGraph Neural NetworksNeural PDE Solvers

    1CEMEF - Mines Paris PSL

  13. PILIR: Physics-Informed Local Implicit Representation

    May 1, 2026Jianfeng Li, Feng Wang, Ke TangNeural PDE SolversImplicit Neural Representations

    School of Computer Science, Wuhan University · School of Computer Science and Technology, Southern University of Science and Technology

  14. A Dirac-Frenkel-Onsager principle: Instantaneous residual minimization with gauge momentum for nonlinear parametrizations of PDE solutions

    Apr 30, 2026Matteo Raviola, Benjamin PeherstorferNeural PDE SolversPDE Solving

    EPFL, Lausanne, Switzerland · Courant Institute of Mathematical Sciences, New York University, New York, NY, USA

  15. Compositional Meta-Learning for Mitigating Task Heterogeneity in Physics-Informed Neural Networks

    Apr 29, 2026Beomchul Park, Minsu Koh, Heejo Kong +1Neural PDE SolversMeta-Learning

    Department of Artificial Intelligence, Korea University, Anam-dong, Seongbuk-gu, Seoul, 02841, Republic of Korea · Department of Brain and Cognitive Engineering, Korea University, Anam-dong, Seongbuk-gu, Seoul, 02841, Republic of Korea

  16. Conflict-Aware Harmonized Rotational Gradient for Multiscale Kinetic Regimes

    Apr 27, 2026Zhangyong LiangNeural PDE SolversGradient Interference

    National Center for Applied Mathematics, Tianjin University, Tianjin, 300072, China.

  17. Shared-kernel Wavelet Neural Networks for Poisson Image Reconstruction

    Apr 27, 2026Yuanhao Gong, Tan Tang, Qianyan LiuNeural PDE SolversImage Reconstruction

  18. Adaptive-Distribution Randomized Neural Networks for PDEs: A Low-Dimensional Distribution-Learning Framework

    Apr 27, 2026You Yang, Fei WangNeural PDE SolversPDE Operator Learning

    School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China. · School of Mathematics and Statistics & State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China.

  19. Collocation-based Robust Physics Informed Neural Networks for time-dependent simulations of pollution propagation under thermal inversion conditions on Spitsbergen

    Apr 24, 2026Leszek Siwik, Maciej Sikora, Natalia Leszczyńska +7Neural PDE SolversAir Quality Prediction

    AGH University of Krakow, Faculty of Computer Science, Al. Mickiewicza 30, Kraków, 30-059, Poland · Medical University of Silesia-Katowice, Faculty of Medical Sciences, ul. Poniatowskiego 15, Katowice, 40-055, Poland · The University Centre in Svalbard, Longyearbyen, Box 156 N-9171, Longyearbyen, Norway +4

  20. A Green-Integral-Constrained Neural Solver with Stochastic Physics-Informed Regularization

    Apr 23, 2026Mohammad Mahdi Abedi, David Pardo, Tariq AlkhalifahNeural PDE SolversPDE Solving

    University of the Basque Country (UPV/EHU), Department of Mathematics, Spain · Basque Center for Applied Mathematics (BCAM), Bilbao, Spain · Ikerbasque, Basque Foundation for Science, Bilbao, Spain +1

  21. CO2_2 sequestration hybrid solver using isogeometric alternating-directions and collocation-based robust variational physics informed neural networks (IGA-ADS-CRVPINN)

    Apr 22, 2026Askold Vilkha, Tomasz Służalec, Marcin Łoś +1Neural PDE SolversPDE Solving

    AGH University of Krakow, Faculty of Computer Science, Al. Mickiewicza 2026 30, Kraków, 30-059, Poland

  22. Virtual boundary integral neural network for three-dimensional exterior acoustic problems

    Apr 19, 2026Jiahao Li, Qiang Xi, Ilia Marchevskiy +1Neural PDE SolversPDE Solving

    College of Mechanics and Engineering Science, Hohai University, Nanjing 211100, China · Department of Applied Mathematics, Bauman Moscow State Technical University, Moscow 105005, Russia

  23. FlowRefiner: Flow Matching-Based Iterative Refinement for 3D Turbulent Flow Simulation

    Apr 18, 2026Yilong Dai, Yiming Sun, Yiheng Chen +3Flow MatchingNeural PDE Solvers

    University of Alabama · University of Pittsburgh

  24. PINNACLE: An Open-Source Computational Framework for Classical and Quantum PINNs

    Apr 17, 2026Shimon Pisnoy, Hemanth Chandravamsi, Ziv Chen +4Neural PDE SolversPDE Surrogate Modeling

    †Faculty of Mechanical Engineering, Technion Israel Institute of Technology, Haifa, Israel. · ‡Corresponding author. · §The Andrew and Erna Viterbi Faculty of Electrical & Computer Engineering, Technion Israel Institute of Technology, Haifa, Israel. +2

  25. A Structure-Preserving Graph Neural Solver for Parametric Hyperbolic Conservation Laws

    Apr 17, 2026Jiamin Jiang, Shanglin Lv, Jingrun ChenGraph Neural NetworksNeural PDE Solvers

    School of Artificial Intelligence and Data Science and Suzhou Institute for Advanced Research, University of Science and Technology of China, and Suzhou Big Data & AI Research and Engineering Center, China · School of Mathematical Sciences, University of Science and Technology of China, China · School of Mathematical Sciences and Suzhou Institute for Advanced Research, University of Science and Technology of China, and Suzhou Big Data & AI Research and Engineering Center, China

  26. G-PARC: Graph-Physics Aware Recurrent Convolutional Neural Networks for Spatiotemporal Dynamics on Unstructured Meshes

    Apr 16, 2026Jack T. Beerman, Tyler J. Abele, Mehdi Taghizadeh +6Neural PDE SolversPDE Surrogate Modeling

    School of Data Science, University of Virginia, Charlottesville, VA 22903, United States · Department of Engineering Systems and Environment, University of Virginia, Charlottesville, VA 22903, United States · Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, VA 22903, United States +1

  27. Stochastic-Dimension Frozen Sampled Neural Network for High-Dimensional Gross-Pitaevskii Equations on Unbounded Domains

    Apr 10, 2026Zhangyong Liang, Huanhuan GaoNeural PDE SolversPDE Solving

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

  28. 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.

  29. 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

  30. 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

  31. 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.

  32. 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

  33. 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

  34. 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

  35. 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

  36. 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.

  37. 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

  38. 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

  39. 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

  40. 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

  41. 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

  42. 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

  43. 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

  44. 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.

  45. 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

  46. 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