Neural PDE Solvers

PDE: Partial Differential Equation

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Overview

Neural PDE solvers approximate fields, time evolution, or mappings from equation inputs to solutions, with potential benefits for repeated simulations, inverse problems, and high-dimensional settings. Physics-informed neural networks (PINNs) train on equation residuals, while weak-form and variational methods use integral or energy principles; neural operators learn mappings across families of PDE instances. Other approaches use randomized or separable features, and hybridize learned models with finite-element, finite-volume, or multigrid solvers. The central tension is achieving reliable accuracy, conservation, and long-term stability while reducing total computational cost; generalization beyond training conditions and rigorous error guarantees remain important challenges.

Latest papers

CardsList

272 papers47 papers in the last four weeks, up 74% on the four weeks before. 0.3% of all new papers.

  1. A Hybrid Physics-informed holomorphic neural networks Method

    Oct 28, 2026Zhijie Su, Qiaolin He, Zhiping Mao +1PDE SolvingNeural PDE Solvers

    Department of Mathematics, Sichuan University, No. 24, Section 1, South Yihuan Road, Chengdu, 610065, China · Eastern Institute of Technology, Ningbo, No. 2911, Haijiang Avenue, Zhenhai District, Ningbo, 315200, China

  2. QD-PINN:A Physics-Informed Neural Network Approach to Bayesian Quickest Detection in High-Dimensional Diffusions

    Oct 27, 2026Hang Ye, Yi Liu, Haipeng XingOptimal StoppingNeural PDE Solvers

    Department of Applied Mathematics and Statistics, Stony Brook University

  3. CFL-aware edge design for graph neural solvers of hyperbolic transport

    Oct 24, 2026Jinyoung Jeong, Joseph B. Choi, Xinlun Cheng +3Neural PDE SolversPartial Differential Equations

    School of Mechanical Engineering & Research Institute of Engineering Design & Technology, 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

  4. Latent dynamics for reconstructing fine-scale PDE trajectories from coarse observations

    Oct 24, 2026Chenhao Si, Zishan Qian, Shing-Tung Yau +2Latent Dynamics ModelingPDE Surrogate Modeling

    School of Data Science, The Chinese University of Hong Kong, Shenzhen, Shenzhen, China. · Institute of Statistics and Big Data, Renmin University, Beijing, China. · Beijing Key Laboratory of Topological Statistics and Applications for Complex Systems, Beijing Institute of Mathematical Sciences and Applications, Beijing, China. +1

  5. Solving and Learning Navier-Stokes Dynamics with the Neural Basis Method

    Oct 23, 2026Yuhe Wang, Zhu Wang, Min WangNeural PDE SolversComputational Fluid Dynamics

    Institute for Scientific Computation, Texas A&M University, College Station, TX 77843, USA · Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA · Department of Mathematics, University of Houston, TX 77204, USA

  6. Cautious Conflict-Free Inverse Gradient Methods

    Oct 22, 2026Damian Hattler, Qiang Liu, Nils ThuereyGradient InterferenceNeural PDE Solvers

    School of Computation, Information and Technology, Technical University of Munich, Garching, DE 85748

  7. Convex Equilibrium Potentials for Monge--Ampère: Curvature Bounds and A Posteriori Evaluation

    Oct 22, 2026Edison Vázquez, Yingdong Lu, Tomasz NowickiNeural PDE SolversPartial Differential Equations

    Departamento de Matemáticas, CINVESTAV, México · IBM Research, Thomas J. Watson Research Center, Yorktown Heights, New York, USA

  8. DuoPIC: Uncertainty-Aware Voxel-Level Digital Twins of Cerebral Perfusion with Transport PDEs in Acute Stroke

    Oct 20, 2026Anh Duong Tran, Quang-Anh N. D., Toan Sy Pham +4Digital TwinsMedical Image Analysis

    Vietnam National University · London Digital Twin Research Centre, Middlesex University · University of Alberta +4

  9. PaPi: Parallel Picard-Duhamel Integration for Fast Neuro-Spectral Architectures

    Oct 20, 2026Arthur Bizzi, Márcio Marques, Kleyton Da Costa +4Neural PDE SolversNumerical Integration

    Imperial College London London, United Kingdom · Instituto de Matemática Pura e Aplicada Rio de Janeiro, RJ, Brazil · Computer Science University College London London, United Kingdom +3

  10. Soliton Profiles in 1D: Enhanced Neural-Network Solvers and Constrained Deep Ritz Methods

    Oct 20, 2026Chandler Haight, Alex D Rodriguez, Svetlana RoudenkoNeural PDE SolversPDE Solving

  11. GeoDiv KAN Solver for Time Fractional Navier Stokes Equations on Complex Domains to Realistic CFD Reconstruction

    Oct 19, 2026Yatin Kumar, Shivani Saini, Ramesh Kumar VatsNeural PDE SolversPartial Differential Equations

    Department of Mathematics and Scientific Computing, National Institute of Technology Hamirpur, Hamirpur, Himachal Pradesh, 177005, India

  12. LowNet: Looped Wavelet Neural Networks with 24 Learnable Parameters for Solving Poisson Equations

    Oct 18, 2026Yuanhao GongPDE SolvingNeural PDE Solvers

    Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences

  13. Certified neural approximations for parabolic obstacle problems

    Oct 16, 2026Davood DamircheliNeural PDE SolversPartial Differential Equations

    Department of Mathematics, Louisiana State University, Baton Rouge, 70803, LA, USA

  14. Same Target, Different Origins: Aligning Latent Rollout for Consistent PDE Emulation

    Oct 15, 2026Xinying Li, Jing Xu, Wenjun Wang +4Neural PDE SolversPDE Operator Learning

    Fudan University · Shanghai Academy of AI for Science

  15. Adaptive Randomized Neural Networks for PDEs: Structure-Aware Feature Redistribution and Residual-Driven Block Enrichment

    Oct 15, 2026You Yang, Fei WangNeural PDE SolversRandom Feature Methods

    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.

  16. The Physics Is the Network: Fast, Training-Free Neural Emulation

    Oct 14, 2026Luka Todorovic, Kaushal Gianchandani, Sai RavelaNeural PDE SolversNeural Surrogate Modeling

    Department of Mathematics and Department of Statistics, University of Michigan, Ann Arbor, MI · NASA Postdoctoral Program Fellow, NASA Goddard Institute for Space Studies, New York, NY · Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA

  17. Beyond Time Induction: Structured Conditional Neural Solvers for Parametric Stochastic-Volatility Pricing

    Oct 13, 2026Jose Miguel Lara Rangel, Mixtli Vazquez MendozaNeural PDE SolversPhysics-Informed ML

    University College London, UK · Aicraft, Mexico

  18. A Method for Exact Enforcement of Boundary Conditions on General Curved Triangular Domains: Algorithm and Application to Scientific Machine Learning

    Oct 12, 2026Suchuan Dong, Yuchuan ZhangPDE SolvingNeural PDE Solvers

    Center for Computational and Applied Mathematics Department of Mathematics Purdue University, USA

  19. Neural Network Preconditioning: A Case Study for the Solution of the Parametric Helmholtz Equation

    Oct 12, 2026Luc Giraud, Carola Kruse, Paul Mycek +2PDE SolvingNeural PDE Solvers

    Inria, Concace joint team between Airbus CR&T, Cerfacs and Inria · Cerfacs, Concace joint team between Airbus CR&T, Cerfacs and Inria · Current affiliation: Opticalp +1

  20. PDE-PFN: Prior-Data Fitted Neural PDE Solver

    Oct 9, 2026Jaehyeon Park, Mingu Kang, Dongseok Lee +5Neural PDE SolversPDE Solving

    SolverX · KAIST · Seoul National University +3

  21. Enriched Holomorphic Neural Networks for 2D and 3D Laplace Problems

    Oct 8, 2026Kalp Shah, Andrei Vlad Nicula, Mihnea Andrei Bârsan +4Neural PDE SolversPDE Solving

    University of Amsterdam · Technical University of Denmark

  22. Cova-PINN: Cross-Domain Conservation Physics-Informed Neural Network for Fluid-Solid Conjugate Heat Transfer in Complex Geometries

    Oct 8, 2026Weizheng Zhang, Xunjie Xie, Hao Pan +1Physics-Informed MLNeural PDE Solvers

    Shandong University · Tsinghua University

  23. Transferability of Learned States in Neural PDE Solvers

    Oct 7, 2026Shunye Wang, Haochen Wen, Shuo Li Liu +3Neural PDE SolversPDE Surrogate Modeling

    University of Chicago · University of Cambridge · Princeton University +2

  24. A mesh-based neural energy method for the simulation of heterogeneous composites

    Oct 7, 2026Pius J. M. Wichmann, Stefan Hildebrand, Sandra KlingeNeural PDE SolversStructural Mechanics

    Department of Structural and Computational Mechanics, Technische Universität Berlin, Straße des 17. Juni 135, Berlin, 10623, Berlin, Germany

  25. 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

  26. 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

  27. 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

  28. 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

  29. 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.

  30. 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