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 166

All topics
CardsList

  1. Image Editing Models are Numerical Solvers

    Jul 21, 2026Ulysse MizrahiNeural PDE SolversPDE Solving

    Tel Aviv University

  2. Physics Closure Matters for Machine Olfaction: A Maxwell-Stefan Graph Solver for Identifiable Dynamic Gas Unmixing

    Jul 20, 2026Yue Shi, Liangxiu Han, Xin Zhang +1Graph Neural NetworksNeural PDE Solvers

    Department of Computing and Mathematics, Faculty of Science and Engineering, Manchester Metropolitan University, Manchester M1 5GD, U.K.

  3. 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

  4. Non-Asymptotic Variational Learning for Monotone Nonlinear Multiscale Elliptic Equations: Scale-Robust Primal-Dual Bounds and Strong-Form Statistical Ill-Conditioning

    Jul 17, 2026Ronald KatendePrimal-Dual OptimizationNeural PDE Solvers

    Department of Mathematics Kabale University Kikungiri Hill, Katuna Road, Kabale, Uganda

  5. Evolutionary Algorithm-Guided LLMs for Physics-Informed Neural Network Design

    Jul 17, 2026Xu Yang, Mingyang Yu, Jing Xu +1Neural PDE SolversEvolutionary Optimization

    Shanghai Institute of Intelligent Education, East China Normal University, Shanghai 200062, China · College of Artificial Intelligence, Nankai University, Tianjin 300350, China

  6. LIGO-PINN: Learned Initialization via Gated Optimization to Alleviate Convergence Failures in Physics Informed Neural Networks

    Jul 15, 2026Nilay Anurag, Shital Adhikari, Taniya Kapoor +1Neural PDE SolversNeural Network Optimization

    Department of Computer Science, Stevens Institute of Technology · Artificial Intelligence Group, Wageningen University & Research

  7. Multi-dimensional training-priority weighting based on physical information propagation paths: a unified residual-weighting framework for physics-informed neural networks

    Jul 13, 2026Zhangyi Lian, Xinda Dong, Wenxuan Huo +3Neural PDE SolversAdaptive Loss Weighting

    College of Mechanical and Vehicle Engineering Chongqing University Chongqing 400030, China · State Key Laboratory of Tribology in Advanced Equipment Department of Mechanical Engineering Tsinghua University Beijing 100084, China

  8. Learning to Discretize: Diffusion-Based Adaptive Mesh with Spectral Guidance

    Jul 13, 2026Zixuan Shen, Bingchuan Wang, Zhi Wang +1Neural PDE SolversPDE Surrogate Modeling

    Central South University · Central South University, Changsha, Hunan 410083, China · Nanjing University +1

  9. The Differential Neural Tangent Kernel and Its Positivity

    Jul 11, 2026Bangti Jin, Longjun WuNeural PDE SolversPhysics-Informed ML

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

  10. SplineNet: An Isogeometric Deep Learning Method for Complex Shells

    Jul 7, 2026Shizhou Luo, Xiaodong WeiNeural PDE Solvers

    Global College, Shanghai Jiao Tong University, Shanghai, 200240, China.

  11. LRX-PINN: A Layer-Resolving XNet Physics-Informed Neural Network with Integrated Cauchy Activations for Convection-Dominated Problems

    Jul 4, 2026Zihao Guo, Xin Li, Zhihong XiaNeural PDE SolversPDE Solving

    Institute for Advanced Research, Great Bay University, Dongguan, China · College of Computer Science and Technology, Dongguan University of Technology, Dongguan, China · Department of Mathematics, Northwestern University, Evanston, USA

  12. A Multi-Resolution Finite-Volume Inspired Deep Learning Framework for Spatiotemporal Dynamics Prediction

    Jul 1, 2026Xin-Yang Liu, Xiantao Fan, Jian-Xun WangNeural PDE SolversPDE Surrogate Modeling

    Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN, USA · Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY, USA

  13. Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains

    Jun 30, 2026Haixin Wang, Haoning Dang, Fei Wang +1Neural PDE SolversPDE Solving

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

  14. McMg: A Learned Phase-Space Multi-channel Multigrid Preconditioner for Helmholtz Equation

    Jun 29, 2026Jiwei Jia, Xinliang Liu, Juntao Wang +1Neural PDE SolversPDE Solving

    School of Mathematics, Jilin University, Changchun 130012, China · Shenzhen Loop Area Institute, Shenzhen 518038, China · Ocean University of China, Qingdao 266100, China +1

  15. A Posteriori Error Analysis for Decoupled Neural Approximations of Fully Coupled FBSDEs with Control Mismatch

    Jun 28, 2026Xichuan ZhangStochastic Differential EquationsNeural PDE Solvers

    Intelligent Game and Decision Lab, Beijing 100091, China

  16. Higher-Order Fourier Neural Operator: Explicit Mode Mixer for Nonlinear PDEs

    Jun 26, 2026Alex Colagrande, Paul Caillon, Eva Feillet +1Fourier Neural OperatorNeural PDE Solvers

    Miles Team, LAMSADE, Université Paris Dauphine-PSL, Paris, France · Université Paris-Saclay, CNRS, LISN, 91400, Orsay, France · ESPCI PSL, Paris, France

  17. Error-Conditioned Neural Solvers

    Jun 25, 2026Haina Jiang, Liam Wang, Peng-Chen Chen +4Neural PDE SolversPDE Surrogate Modeling

    University of Michigan · KAIST AI · Los Alamos National Laboratory

  18. fTNN: a tensor neural network for fractional PDEs

    Jun 25, 2026Qingkui Ma, Hehu Xie, Xiaobo YinTensor NetworksNeural PDE Solvers

    School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan 430079, China · SKLMS, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, No.55, Zhongguancun Donglu, Beijing 100190, China · School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China +1

  19. Dirac-Frenkel dynamics with inertia for nonlinearly parametrized solutions of evolution problems

    Jun 23, 2026Matteo Raviola, Benjamin PeherstorferDynamical SystemsNeural PDE Solvers

    Scientific Computing and Uncertainty Quantification - CADMOS Chair, EPFL · Courant Institute of Mathematical Sciences, New York University

  20. A Zeroth-Order Deep Learning Method for Fully Nonlinear Parabolic Partial Differential Equations with Unknown Coefficients

    Jun 23, 2026Yanwei Jia, Du Ouyang, Huyên Pham +1Neural PDE SolversPDE Solving

    Department of Systems Engineering and Engineering Management The Chinese University of Hong Kong Shatin, New Territories, Hong Kong SAR · Department of Mathematical Sciences Tsinghua University Beijing, Beijing 100084, China · CMAP Ecole Polytechnique Route de Saclay, Palaiseau 91128, France +1

  21. Deep numerical schemes for systems of Ergodic BSDEs with applications to regime-switching forward utilities

    Jun 23, 2026Guillaume Broux-Quemerais, Sarah Kaakai, Anis Matoussi +1Stochastic Differential EquationsNeural PDE Solvers

    LMM · 1Laboratoire Manceau de Mathématiques & FR CNRS No 2962, Institut du Risque et de l’Assurance, Le Mans Université · LAGA +1

  22. Parameterized Representations via Implicit Stochastic Modulation for High-Dimensional and High-Order Neural PDE Solvers

    Jun 20, 2026Zhangyong Liang, Huanhuan GaoNeural PDE SolversPDE Solving

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

  23. Modularity-Free Conflict-Averse Training for Generalized PINNs

    Jun 18, 2026Heejo Kong, Beomchul Park, Sung-Jin Kim +1Neural PDE SolversGradient Interference

    Department of Brain and Cognitive Engineering, Korea University, Seoul, Republic of Korea · Department of Artificial Intelligence, Korea University, Seoul, Republic of Korea

  24. Structure-Oriented Randomized Neural Networks for Poisson-Nernst-Planck and Poisson-Nernst-Planck-Navier-Stokes Systems

    Jun 18, 2026Yunlong Li, Fei WangNeural PDE SolversComputational Fluid Dynamics

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

  25. Physics-Informed Neural Network with Squeeze-Excitation-like Attention

    Jun 18, 2026Yun-Fei Song, Long-Gang Pang, Fu-Peng Li +1Neural PDE SolversPhysics-Informed ML

    Key Laboratory of Quark and Lepton Physics (MOE) & Institute of Particle Physics, Central China Normal University, Wuhan 430079, China · Artificial Intelligence and Computational Physics Research Center, Central China Normal University, Wuhan 430079, China · Key Laboratory of Nuclear Physics and Ion-beam Application (MOE) & Institute of Modern Physics, Fudan University, Shanghai 200433, China +2

  26. Trainable Photonic Measurement for Physics-Informed PDE Learning

    Jun 17, 2026Jiale Linghu, Hao Dong, Yangshuai WangNeural PDE SolversQuantum Machine Learning

    School of Mathematics and Statistics, Xidian University, Xi’an, Shaanxi, 710071, China. · Department of Mathematics, Faculty of Science, National University of Singapore, Singapore, 119077, Singapore.

  27. INI-VPINN: A Variational Physics-Informed Neural Network with Implicit Neumann and Interface Handling for Multi-Material Domains with Geometric Singularities

    Jun 16, 2026Shayan Dodge, Alessandro Formisano, Sami BarmadaNeural PDE SolversPDE Solving

    DESTeC, University of Pisa, Pisa, Italy · DESTeC University of Pisa Pisa, Italy · Department of Engineering, University of Campania Luigi Vanvitelli, Aversa, Italy +1

  28. Petrov-Galerkin Variational Physics-Informed Neural Network Framework for Two-Dimensional Singularly Perturbed Problems

    Jun 15, 2026Vijay Kumar, Gautam SinghNeural PDE SolversPhysics-Informed ML

    Department of Mathematics, National Institute of Technology Tiruchirappalli, Tiruchirappalli, 620015, Tamil Nadu, India.

  29. Separable Neural Architectures as Physical World Models: from Mathematical Theory to Applications

    Jun 12, 2026Reza T Batley, Andrew Kichline, Sourav SahaNeural PDE SolversPDE Solving

    Kevin T. Crofton Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, 1600 Innovation Drive, Blacksburg, 24060, VA, United States

  30. HAMNO: A Hierarchical Adaptive Multi-scale Neural Operator with Physics-Informed Learning for Dynamical Systems

    Jun 10, 2026Mostafa Bamdad, Mohammad Sadegh Eshaghi, Timon RabczukNeural PDE SolversPhysics-Informed Neural Operators

    Chair of Computational Mechanics, Institute of Structural Mechanics, Bauhaus-Universität Weimar, 99423 Weimar, Germany · Chair of Computational Science and Simulation Technology, Institute of Photonics, Department of Mathematics and Physics, Leibniz University Hannover, 30167 Hannover, Germany

  31. An adaptive framework for the axisymmetric pulsar magnetosphere using physics-informed Kolmogorov-Arnold networks

    Jun 9, 2026Spyros Rigas, Ioannis Contopoulos, Georgios Alexandridis +1Neural PDE SolversPhysics-Informed ML

    Department of Digital Industry Technologies, School of Science, National and Kapodistrian University of Athens, 34400 Psachna, Greece · Research Center for Astronomy and Applied Mathematics, Academy of Athens, 11527 Athens, Greece

  32. Architecture Shapes Transfer Specificity in Implicit Neural Representations

    Jun 5, 2026D Yang EngNeural PDE SolversImplicit Neural Representations

  33. Curvature-aware dynamic precision approach for physics-informed neural networks

    Jun 3, 2026Yingjie Shao, Ioannis N. Athanasiadis, George van Voorn +1Neural PDE SolversNeural Network Optimization

    Mathematical & Statistical Methods Group (Biometris), Wageningen University & Research, Wageningen, 6700AA, The Netherlands · Artificial Intelligence Group, Wageningen University & Research, Wageningen, 6700AA, The Netherlands

  34. MeshTok: Efficient Multi-Scale Tokenization for Scalable PDE Transformers

    Jun 3, 2026Yanshun Zhao, Xiaoyu Peng, Jiamin Jiang +2Neural PDE SolversPDE Surrogate Modeling

    School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China · Suzhou Institute for Advanced Research, University of Science and Technology of China, Suzhou 215123, China.

  35. Neural Galerkin Normalizing Flows for Bayesian Inference of Diffusions with Inaccessible Boundaries

    Jun 3, 2026Riccardo Saporiti, Fabio NobileNormalizing FlowsNeural PDE Solvers

    CSQI École Polytechnique Fédérale de Lausanne Lausanne, Switzerland 1015

  36. A Per-Component Diagnostic Protocol for Neural HJB-PIDE Solvers under Control-Dependent Lévy Jumps

    May 31, 2026R. DrissiNeural PDE SolversStochastic Optimal Control

  37. A holomorphic neural network framework for 3D boundary value problems governed by harmonic potentials

    May 29, 2026Enrico Ballini, Allan Peter Engsig-Karup, Tito AndriolloNeural PDE SolversPDE Solving

    Department of Mechanical and Production Engineering, Aarhus University, Aarhus, Denmark · Department of Applied Mathematics and Computer Science, Technical University of Denmark, Kongens Lyngby, Denmark

  38. Oscillatory State-Space Models as Inductive Biases for Physics-Informed Neural PDE Solvers

    May 29, 2026Abhishek Chandra, Taniya KapoorNeural PDE SolversPhysics-Informed ML

    KTH Royal Institute of Technology Stockholm, Sweden · Wageningen University & Research Wageningen, The Netherlands

  39. Multi-Scale Separable Fourier Neural Networks for Solving High-Frequency PDEs

    May 29, 2026Qihong Yang, Qiaolin HeNeural PDE SolversPDE Solving

    School of Mathematics, Sichuan University, city=Chengdu, postcode=610065, country=China

  40. Physics-Informed Coarsening for Multigrid Graph Neural Surrogates

    May 29, 2026Amir Bazzi, David Cardinaux, Ramy Nemer +3Graph Neural NetworksNeural PDE Solvers

    1CEMEF, Mines Paris – PSL, Sophia Antipolis, France · 2Aubert et Duval, France · 3Transvalor, Mougins, France.

  41. LFNO: Bridging Laplace and Fourier via Transient-Steady Decomposition

    May 29, 2026Jeongun Ha, Sanga Yoon, Donghun LeeDynamical SystemsNeural PDE Solvers

    Department of Mathematics, Korea University, 145 Anam-ro Seongbuk-gu Seoul, Republic of Korea.

  42. PINNs Failure Modes are Overfitting

    May 29, 2026Nigel T. Andersen, Takashi MatsubaraNeural Network GeneralizationNeural PDE Solvers

    Graduate School of Information Science and Technology Hokkaido University Sapporo, Japan · RIKEN Center for Advanced Intelligence Project (AIP) Tokyo, Japan

  43. Striding Across Reynolds Numbers: Representation Geometry in Neural PDE Generalisation

    May 28, 2026Jianing ShiNeural PDE SolversNeural Representation Geometry

    London School of Economics and Political Science.

  44. A Novel Tensor Product-Based Neural Network for Solving Partial Differential Equations

    May 28, 2026Qihong Yang, Yangtao Deng, Qiaolin He +1Neural PDE SolversPDE Solving

    School of Mathematics, Sichuan University, Chengdu, 610065, China

  45. Small Models, Strong Priors: Architectural Inductive Bias for Parameter-Efficient Neural PDE Solvers

    May 25, 2026Shyam Sankaran, Hanwen Wang, Paris PerdikarisNeural PDE SolversPDE Operator Learning

    Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania · Graduate Program in Applied Mathematics and Computational Science, University of Pennsylvania

  46. NPSolver: Neural Poisson Solver with Iterative Physics Supervision

    May 25, 2026Bocheng Zeng, Rui Zhang, Runze Mao +5Neural PDE SolversPDE Solving

    Gaoling School of Artificial Intelligence Renmin University of China Beijing, China · School of Engineering Science University of Chinese Academy of Sciences Beijing, China

  47. Random Neural Network Expressivity for Non-Linear Partial Differential Equations

    May 24, 2026Muhammed Ali Mehmood, Lukas GononNeural PDE SolversPDE Solving

    Department of Mathematics Imperial College London UK · School of Computer Science University of St. Gallen Switzerland

  48. Mitigating Gradient Pathology in PINNs through Aligned Constraint

    May 24, 2026Yichen Luo, Peiyu Zhu, Dongxiao Hu +5Neural PDE SolversGradient Interference

    Department of Information Science and Engineering, KTH Royal Institute of Technology, Stockholm, Sweden · School of Advanced Manufacturing and Robotics, Peking University, Beijing, China · School of Advanced Technology, Xi’an Jiaotong-Liverpool University, Suzhou, China +2

  49. IV-Net: A neural network for elliptic PDEs with random and highly varying coefficients

    May 24, 2026Shan Zhong, George BirosNeural PDE SolversPDE Solving

    Oden Institute for Computational Science and Engineering, The University of Texas at Austin, 201 E 24th St, Austin, 78712, TX, USA · Walker Department of Mechanical Engineering, The University of Texas at Austin, 3012026 E Dean Keeton St, Austin, 78712, TX, USA

  50. Hermite-NGP: Gradient-Augmented Hash Encoding for Learning PDEs

    May 23, 2026Jinjin He, Zhiqi Li, Sinan Wang +1Neural PDE SolversPDE Solving

    Georgia Institute of Technology, Atlanta, GA, USA.

  51. WINO: A Weak-Form Physics Informed Neural Operator for Hyperelasticity on Variable Domains

    May 23, 2026Bokai Zhu, Qinghui Zhang, Timon RabczukNeural PDE SolversPDE Solving

    School of Science, Harbin Institute of Technology, Shenzhen, P. R. China. · School of Science, Harbin Institute of Technology, Shenzhen, Guangdong. · Institute of Structural Mechanics, Bauhaus-Universität Weimar, Weimar, 99423, Germany.

  52. Iterative Refinement Neural Operators are Learned Fixed-Point Solvers: A Principled Approach to Spectral Bias Mitigation

    May 21, 2026Xiaotian Liu, Shuyuan Shang, Xiaopeng Wang +2Neural PDE SolversSpectral Bias

    1Dartmouth College · 2CUHK Shenzhen · 3Lawrence Berkeley National Lab

  53. Fast Reconstruction of Exact Maxwell Dynamics from Sparse Data

    May 19, 2026Dan DeGenaro, Xin Li, Obed Amo +4Neural PDE SolversNeural Network Approximation Theory

    Department of Computer Science, Georgetown University · Department of Mathematics, Georgetown University · Department of Mathematics and Statistics, Old Dominion University +2

  54. Breakeven complexity: A new perspective on neural partial differential equation solvers

    May 14, 2026Yijing Zhang, Nicholas Roberts, Tanya Marwah +1Neural PDE SolversBenchmark Design

    University of Wisconsin–Madison · Google DeepMind

  55. Unbiased and Second-Order-Free Training for High-Dimensional PDEs

    May 14, 2026Jaemin Seo, Surin Lee, Jae Yong LeeStochastic Differential EquationsNeural PDE Solvers

    Department of Artificial Intelligence, Chung-Ang University, Seoul, Republic of Korea.

  56. Di-BiLPS: Denoising induced Bidirectional Latent-PDE-Solver under Sparse Observations

    May 13, 2026Zhonghao Li, Chaoyu Liu, Qian ZhangNeural PDE SolversLatent Diffusion Models

    School of Science, Harbin Institute of Technology, Shenzhen, China · Department of Theoretical Physics and Applied Mathematics, University of Cambridge, Cambridge, United Kingdom

  57. MetaColloc: Optimization-Free PDE Solving via Meta-Learned Basis Functions

    May 12, 2026Zichuan YangNeural PDE SolversMeta-Learning

    School of Mathematical Sciences Tongji University Shanghai, P.R. China

  58. Neural-Schwarz Tiling for Geometry-Universal PDE Solving at Scale

    May 12, 2026Paolo Secchi, Daniel S. Balint, Marco MauriziNeural PDE SolversPDE Solving

    Imperial College London · Italian Institute of Artificial Intelligence

  59. Chebyshev Center-Based Direction Selection for Multi-Objective Optimization and Training PINNs

    May 11, 2026Hoyeol Yoon, Seoungbin Bae, Nam Ho-Nguyen +1Neural PDE SolversNeural Network Optimization

    Department of Industrial & Systems Engineering, KAIST · Discipline of Business Analytics, The University of Sydney · Department of Mathematical Sciences, Seoul National University

  60. MC2^2: Monte Carlo Correction for Fast Elliptic PDE Solving

    May 10, 2026Ethan Hsu, Hong Meng Yam, Ivan GeNeural PDE SolversPDE Solving

    Stanford University