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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An adaptive framework for the axisymmetric pulsar magnetosphere using physics-informed Kolmogorov-Arnold networks
Jun 9, 2026Spyros Rigas, Ioannis Contopoulos, Georgios Alexandridis +1Neural PDE Solvers Physics-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
Architecture Shapes Transfer Specificity in Implicit Neural Representations
Jun 5, 2026D Yang EngNeural PDE Solvers Implicit Neural Representations
Curvature-aware dynamic precision approach for physics-informed neural networks
Jun 3, 2026Yingjie Shao, Ioannis N. Athanasiadis, George van Voorn +1Neural PDE Solvers Neural Network Optimization
Mathematical & Statistical Methods Group (Biometris), Wageningen University & Research, Wageningen, 6700AA, The Netherlands · Artificial Intelligence Group, Wageningen University & Research, Wageningen, 6700AA, The Netherlands
MeshTok: Efficient Multi-Scale Tokenization for Scalable PDE Transformers
Jun 3, 2026Yanshun Zhao, Xiaoyu Peng, Jiamin Jiang +2Neural PDE Solvers PDE 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.
Neural Galerkin Normalizing Flows for Bayesian Inference of Diffusions with Inaccessible Boundaries
Jun 3, 2026Riccardo Saporiti, Fabio NobileNormalizing Flows Neural PDE Solvers
CSQI École Polytechnique Fédérale de Lausanne Lausanne, Switzerland 1015
A Per-Component Diagnostic Protocol for Neural HJB-PIDE Solvers under Control-Dependent Lévy Jumps
May 31, 2026R. DrissiNeural PDE Solvers Stochastic Optimal Control
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 Solvers PDE 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
Oscillatory State-Space Models as Inductive Biases for Physics-Informed Neural PDE Solvers
May 29, 2026Abhishek Chandra, Taniya KapoorNeural PDE Solvers Physics-Informed ML
KTH Royal Institute of Technology Stockholm, Sweden · Wageningen University & Research Wageningen, The Netherlands
Multi-Scale Separable Fourier Neural Networks for Solving High-Frequency PDEs
May 29, 2026Qihong Yang, Qiaolin HeNeural PDE Solvers PDE Solving
School of Mathematics, Sichuan University, city=Chengdu, postcode=610065, country=China
Physics-Informed Coarsening for Multigrid Graph Neural Surrogates
May 29, 2026Amir Bazzi, David Cardinaux, Ramy Nemer +3Graph Neural Networks Neural PDE Solvers
1CEMEF, Mines Paris – PSL, Sophia Antipolis, France · 2Aubert et Duval, France · 3Transvalor, Mougins, France.
LFNO: Bridging Laplace and Fourier via Transient-Steady Decomposition
May 29, 2026Jeongun Ha, Sanga Yoon, Donghun LeeDynamical Systems Neural PDE Solvers
Department of Mathematics, Korea University, 145 Anam-ro Seongbuk-gu Seoul, Republic of Korea.
PINNs Failure Modes are Overfitting
May 29, 2026Nigel T. Andersen, Takashi MatsubaraNeural Network Generalization Neural PDE Solvers
Graduate School of Information Science and Technology Hokkaido University Sapporo, Japan · RIKEN Center for Advanced Intelligence Project (AIP) Tokyo, Japan
Striding Across Reynolds Numbers: Representation Geometry in Neural PDE Generalisation
May 28, 2026Jianing ShiNeural PDE Solvers Neural Representation Geometry
London School of Economics and Political Science.
A Novel Tensor Product-Based Neural Network for Solving Partial Differential Equations
May 28, 2026Qihong Yang, Yangtao Deng, Qiaolin He +1Neural PDE Solvers PDE Solving
School of Mathematics, Sichuan University, Chengdu, 610065, China
Small Models, Strong Priors: Architectural Inductive Bias for Parameter-Efficient Neural PDE Solvers
May 25, 2026Shyam Sankaran, Hanwen Wang, Paris PerdikarisNeural PDE Solvers PDE Operator Learning
Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania · Graduate Program in Applied Mathematics and Computational Science, University of Pennsylvania
NPSolver: Neural Poisson Solver with Iterative Physics Supervision
May 25, 2026Bocheng Zeng, Rui Zhang, Runze Mao +5Neural PDE Solvers PDE Solving
Gaoling School of Artificial Intelligence Renmin University of China Beijing, China · School of Engineering Science University of Chinese Academy of Sciences Beijing, China
Random Neural Network Expressivity for Non-Linear Partial Differential Equations
May 24, 2026Muhammed Ali Mehmood, Lukas GononNeural PDE Solvers PDE Solving
Department of Mathematics Imperial College London UK · School of Computer Science University of St. Gallen Switzerland
Mitigating Gradient Pathology in PINNs through Aligned Constraint
May 24, 2026Yichen Luo, Peiyu Zhu, Dongxiao Hu +5Neural PDE Solvers Gradient 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
IV-Net: A neural network for elliptic PDEs with random and highly varying coefficients
May 24, 2026Shan Zhong, George BirosNeural PDE Solvers PDE 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
Hermite-NGP: Gradient-Augmented Hash Encoding for Learning PDEs
May 23, 2026Jinjin He, Zhiqi Li, Sinan Wang +1Neural PDE Solvers PDE Solving
Georgia Institute of Technology, Atlanta, GA, USA.
WINO: A Weak-Form Physics Informed Neural Operator for Hyperelasticity on Variable Domains
May 23, 2026Bokai Zhu, Qinghui Zhang, Timon RabczukNeural PDE Solvers PDE 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.
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 Solvers Spectral Bias
1Dartmouth College · 2CUHK Shenzhen · 3Lawrence Berkeley National Lab
Fast Reconstruction of Exact Maxwell Dynamics from Sparse Data
May 19, 2026Dan DeGenaro, Xin Li, Obed Amo +4Neural PDE Solvers Neural Network Approximation Theory
Department of Computer Science, Georgetown University · Department of Mathematics, Georgetown University · Department of Mathematics and Statistics, Old Dominion University +2
Breakeven complexity: A new perspective on neural partial differential equation solvers
May 14, 2026Yijing Zhang, Nicholas Roberts, Tanya Marwah +1Neural PDE Solvers Benchmark Design
University of Wisconsin–Madison · Google DeepMind
Unbiased and Second-Order-Free Training for High-Dimensional PDEs
May 14, 2026Jaemin Seo, Surin Lee, Jae Yong LeeStochastic Differential Equations Neural PDE Solvers
Department of Artificial Intelligence, Chung-Ang University, Seoul, Republic of Korea.
Di-BiLPS: Denoising induced Bidirectional Latent-PDE-Solver under Sparse Observations
May 13, 2026Zhonghao Li, Chaoyu Liu, Qian ZhangNeural PDE Solvers Latent Diffusion Models
School of Science, Harbin Institute of Technology, Shenzhen, China · Department of Theoretical Physics and Applied Mathematics, University of Cambridge, Cambridge, United Kingdom
MetaColloc: Optimization-Free PDE Solving via Meta-Learned Basis Functions
May 12, 2026Zichuan YangNeural PDE Solvers Meta-Learning
School of Mathematical Sciences Tongji University Shanghai, P.R. China
Neural-Schwarz Tiling for Geometry-Universal PDE Solving at Scale
May 12, 2026Paolo Secchi, Daniel S. Balint, Marco MauriziNeural PDE Solvers PDE Solving
Imperial College London · Italian Institute of Artificial Intelligence
Chebyshev Center-Based Direction Selection for Multi-Objective Optimization and Training PINNs
May 11, 2026Hoyeol Yoon, Seoungbin Bae, Nam Ho-Nguyen +1Neural PDE Solvers Neural Network Optimization
Department of Industrial & Systems Engineering, KAIST · Discipline of Business Analytics, The University of Sydney · Department of Mathematical Sciences, Seoul National University
MC $^2$ : Monte Carlo Correction for Fast Elliptic PDE Solving
May 10, 2026Ethan Hsu, Hong Meng Yam, Ivan GeNeural PDE Solvers PDE Solving
Stanford University

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

Spyros Rigas, Ioannis Contopoulos, Georgios Alexandridis, Antonios Nathanail

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

Neural PDE Solvers Physics-Informed ML

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The pulsar magnetosphere has only recently been addressed using Physics-Informed Neural Networks (PINNs), by deploying a domain-decomposition approach and treating the separatrix and equatorial current sheet as infinitesimally thin discontinuities. However, this baseline requires extensive manual hyperparameter tuning, achieves limited final accuracy and demands several hours of training. We refine this framework by introducing domain-specific neural architectures based on Kolmogorov-Arnold networks, an automated adaptive training pipeline and a physics-based convergence criterion that eliminate the need for manual calibration. The proposed methodology delivers self-consistent axisymmetric magnetosphere solutions with mean squared errors of the PDE residuals at O(1e-6) in double precision - an improvement of two orders of magnitude over the baseline - while achieving convergence in under 20 minutes in single precision. Importantly, the method reliably resolves stellar radii reduced by up to 80% compared to the baseline, overcoming the severe spatial scale disparities that also challenge traditional solvers. Furthermore, by varying the flux that opens to infinity, we provide a correction to the equation that connects it to the equatorial T-point's position. The complete framework is released as the open-source library PulsarX.

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