Neural Partial Differential Equation Solvers

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12 papers in the last four weeks, up 71% on the four weeks before. 0.1% of all new papers.

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  1. Singular parameters and missing limits in neural PDE solvers

    Oct 5, 2026Daniel FernándezNeural Partial Differential Equation SolversNeural Ordinary Differential Equations

    Chair for Dynamics, Control, Machine Learning, and Numerics (Alexander von Humboldt Professorship), Department of Mathematics, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany.

  2. Geometry Meets Physics: Data-Efficient Pre-Training for Unstructured Neural PDE Solvers

    Oct 2, 2026Luis Medrano-Navarro, Giacomo Baldan, Qiang Liu +4Neural Partial Differential Equation SolversLarge-Scale 3D Editing Dataset

    Technical University of Munich · University of Stuttgart

  3. Warm-starting PDE solvers with any-dimensional machine learning

    Sep 30, 2026Wilson G. Gregory, George A. Kevrekidis, Ben Blum-Smith +1Neural Partial Differential Equation SolversPartial Differential Equations

    Department of Statistics and Irving Institute for Cancer Dynamics, Columbia University · Division of Applied Mathematics, Brown University · Department of Applied Mathematics and Statistics, Johns Hopkins University

  4. Transolver-σσ: Joint Spectral-Physical Subspace Modeling for Neural PDE Solving

    Sep 29, 2026Haonan Shangguan, Hang Zhou, Haixu Wu +3Neural Partial Differential Equation SolversSubspace

    School of Software, BNRist, Tsinghua University · MIT CSAIL

  5. SCOPE: Observation-Conditioned Full-Target Prediction for Sparse PDE Inference

    Sep 29, 2026Ruichen Xu, Siyao Wang, Fang Wan +8Neural Partial Differential Equation SolversPartial Differential Equations

    Stony Brook University · University of California, Davis · Independent Research +3

  6. Neural networks for spectral optimization

    Sep 28, 2026Alexis de Villeroché, Beniamin Bogosel, Stéphane Breuils +2Spectral Representation MethodNeural Partial Differential Equation Solvers

  7. When Known Physics Helps Neural PDE Models: Residual Constraints Out-Regularize Generic Priors for Nonlinear Dynamics

    Sep 27, 2026Zahra Farazpay, Aniruddha BoraNeural Partial Differential Equation SolversHeat Diffusion

    Department of Physics Louisiana Tech University Ruston, LA, USA · Department of Computer Science Texas State University San Marcos, TX, USA

  8. Theory Guided and Interpretable Neural Operator Design for Partial Differential Equation Learning

    Sep 27, 2026Zeyuan Song, Zheyu JiangNeural Partial Differential Equation SolversNeural Operators

    Oklahoma State University Stillwater, OK 74078

  9. MENO: Memory-Efficient Neural Operator

    Sep 23, 2026Shengyang Xu, Weijun Zhang, Jun Hu +1Neural Partial Differential Equation SolversNeural Operators

    School of Mathematical Sciences, Peking University, Beijing 100871, China · Chongqing Research Institute of Big Data, Peking University, Chongqing 401329, China · National Engineering Laboratory for Big Data Analysis and Applications, Peking University, Beijing 100871, China

  10. Beyond PINNs: A Unified Gauss--Newton and Petrov--Galerkin Framework for Neural and Hybrid PDE Solvers

    Sep 17, 2026Nilo Schwencke, Roland MaierVariational FormulationNeural Partial Differential Equation Solvers

  11. Stable by Construction: Variational Latent Markov Operators for Long-Horizon PDE Prediction

    Sep 15, 2026Junyi Liao, Johann Guilleminot, Vahid TarokhLong-Horizon ForecastingNeural Partial Differential Equation Solvers

    †Department of Electrical and Computer Engineering, Duke University · ‡Department of Mechanical Engineering and Materials Science, Duke University

  12. Single-condition neural solvers encode transferable response spaces for parametric differential equations

    Sep 14, 2026Wenbo Cao, Weiwei ZhangNeural Partial Differential Equation SolversNeural Solvers

    Institute of AI for Industries, Chinese Academy of Sciences, Nanjing 211135, China · Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100190, China · School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China +2

  13. A Systematic Analysis of Automatic Differentiation versus Discretization-based Constraints for Physics-Informed PDE Solvers

    Sep 7, 2026Xing Guo, Hongwei Tang, Zewei Meng +3Neural Partial Differential Equation SolversDiscretization

    School of Systems Science and Engineering, Sun Yat-sen University, Guangzhou, China

  14. Equation Recast for Canonical Operator Learning Across Parametric PDEs

    Sep 2, 2026Qiyun Cheng, Valentin Duruisseaux, Cesar F. Clauser +7Probabilistic Operator LearningNeural Partial Differential Equation Solvers

    1Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA, USA · 2Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA, USA · Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY, USA +1

  15. DiffPDE: Masked Diffusion Language Models as PDE Solver

    Aug 31, 2026Wenxuan Guo, Yuyang Hong, Lubin Fan +4Neural Partial Differential Equation SolversPartial Differential Equations

    School of Artificial Intelligence, University of Chinese Academy of Sciences · MAIS, Institute of Automation, Chinese Academy of Sciences · Independent Researcher

  16. Learning PDE Time-Stepping with Neural Cellular Automata

    Aug 31, 2026Esha Saha, Hao WangNeural Partial Differential Equation SolversPartial Differential Equations

    1Interdisciplinary Lab for Mathematical Ecology and Epidemiology (ILMEE) & The Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton (AB), T6G 2J5, Canada

  17. Sensitivity-Constrained Neural Operators for Data-Efficient Forward and Inverse Modeling of Partial Differential Equation Systems

    Aug 30, 2026Abdolmehdi Behroozi, Chaopeng Shen, Daniel Kifer +1Neural OperatorsNeural Partial Differential Equation Solvers

    Department of Civil and Environmental Engineering, Penn State University, University Park, PA 16802, USA · School of Electrical Engineering and Computer Science, Penn State University, University Park, PA 16802, USA

  18. Reference-free logged energy-oracle recovery for neural approximations of symmetric coercive variational problems: conforming Riesz reconstruction and archive-level selection

    Aug 17, 2026Karim Bounja, Lahcen Laayouni, Boujemaa Achchab +1Reconstruction ErrorNeural Approximations

    Laboratory for Analysis and Modeling of Systems and Decision Support (LAMSAD), Hassan 1st University of Settat, Settat 26000, Morocco. · Department of Computer Science, School of Science and Engineering, Al Akhawayn University in Ifrane, Ifrane 53000, Morocco.

  19. RECAST: A Machine-Learning Framework for Correction and Super-Resolution of Coarse-Grid PDE Solvers

    Aug 12, 2026Maryam Reza, Farbod FarajiNeural Partial Differential Equation SolversPartial Differential Equations

    Independent Researcher · Department of Computing, Huxley Building, Imperial College London, London SW7 2RH, United Kingdom

  20. MoNo: Multiscale Optimal Transport Neural Operator for Solving PDEs on General Geometries

    Aug 10, 2026Zijiang Yang, Xiaomeng Wu, Dongmei FuNeural OperatorsNeural Partial Differential Equation Solvers

    School of Automation and Electrical Engineering, University of Science and Technology Beijing · 2Beijing Engineering Research Center of Industrial Spectrum Imaging

  21. Kastor: An efficient fine-tuning strategy for generative emulation of PDE simulations

    Aug 6, 2026Guillaume Couairon, Alexis Jacq, Yu-Han Wu +4EmulatorsNeural Partial Differential Equation Solvers

    Google DeepMind

  22. Improving Auto-Design of Neural PDE Solvers with a Domain-Specific Language

    Aug 5, 2026Shengxin Kong, Liwen Xu, Jingwen FuNeural Partial Differential Equation SolversEvolutionary Search

    School of Sciences, North China University of Technology, Beijing, China · Beijing Zhongguancun Academy, Beijing, China

  23. Large language models for partial differential equation workflows

    Aug 4, 2026Han Wan, Rui Zhang, Hao SunNeural Partial Differential Equation SolversLarge Language Model Workflows

    Gaoling School of Artificial Intelligence, Renmin University of China, Beijing 100872, China

  24. Freeze, Then Select: Structured Field Adapters and Stability-Validated Weak Selection for PDE Discovery from Sparse Observations

    Jul 31, 2026Juncheng Zhong, Chenghuang Shen, Jianfeng Liu +5Neural Partial Differential Equation SolversFreeze

    School of Mathematical Sciences, Fudan University, Shanghai 200433, China · Shanghai Center for Mathematical Sciences, Fudan University, Shanghai 200438, China · Alibaba Group, Hangzhou, China +3

  25. Geometry-aware Incremental Neural Operator for Long-Horizon PDE prediction

    Jul 31, 2026Jiaquan Zhang, Shuxu Chen, Haifan Meng +6Neural Partial Differential Equation SolversLong-Horizon Forecasting

    School of Information and Software Engineering, UESTC · Electronics and Information Convergence Engineering, KHU · School of Computer Science and Engineering, UESTC +4

  26. Physics Transformer: Tailoring Transformer for General PDE Prediction

    Jul 27, 2026Guoze Sun, Rui Zhang, Jiankai Tang +4Neural Partial Differential Equation SolversPartial Differential Equations

    Gaoling School of Artificial Intelligence, Renmin University of China, Beijing, China · School of Mechanics and Engineering Science, Peking University, Beijing, China

  27. Perturbative-NeuSA: A Structured Spectral Framework for Time-Dependent PDEs

    Jul 27, 2026Xianli Zhu, Jia YinNeural Partial Differential Equation SolversPartial Differential Equations

    School of Mathematical Sciences, Fudan University Shanghai, China

  28. Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers

    Jul 24, 2026Zhangyong Liang, Huanhuan GaoNeural Partial Differential Equation SolversRiemannian Optimization

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

  29. Adaptive Mamba Neural Operators

    Jul 20, 2026Zeyuan Song, Zheyu JiangNeural Partial Differential Equation SolversNeural Operators

    School of Chemical Engineering Oklahoma State University Stillwater, OK 74078, USA

  30. FlashPDE: A Drop-In Fused Triton Operator Library for Neural PDE Solvers

    Jul 20, 2026Peiyu Zang, Bosen Xie, Ruoxiang Xu +1Neural Partial Differential Equation SolversPytorch

    School of Mathematical Sciences, Beijing Normal University · 2Beijing University of Posts and Telecommunications

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

    Jul 13, 2026Zixuan Shen, Bingchuan Wang, Zhi Wang +1Neural Partial Differential Equation SolversDiscretization

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

  32. Reinforcement Learning with Verifiable Physics: Post-training LLMs with Continuous Rewards

    Jul 11, 2026Pengfei Cai, Utkarsh Utkarsh, Alan Edelman +2Neural Partial Differential Equation SolversVerification Framework

    Massachusetts Institute of Technology

  33. PGD-NO: A Neural Operator with Precomputed Geometry Decomposition for 3D Million-scale Physics Simulations

    Jul 9, 2026Weiheng Zhong, Jing Bi, Victor Oancea +1Neural Partial Differential Equation SolversNeural Operators

    Department of Civil and Environmental Engineering, Grainger College of Engineering, University of Illinois Urbana-Champaign, Urbana, IL, US · Dassault Systemes Americas, Johnston, RI, US · Siebel School of Computing and Data Science, Grainger College of Engineering, University of Illinois Urbana-Champaign, Urbana, IL, US

  34. PDEFlow: Autonomous Agentic PDE Pipelines for Neural Operator Learning and Solver-Free Inference

    Jul 6, 2026Akshat Jani, Prathamesh Gadekar, Sakhinana Sagar Srinivas +1Neural Partial Differential Equation SolversNeural Operators

    Tata Research Development and Design Center, Pune, India 411057

  35. LLT: Local Linear Transformer for PDE Operator Learning

    Jul 4, 2026Oded Ovadia, Eli TurkelNeural OperatorsNeural Partial Differential Equation Solvers

    School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel

  36. Mosaic: A Benchmark Suite for Differentiable Physics Solvers

    Jun 26, 2026Andrin Rehmann, Heiko Zimmermann, Dion HäfnerNeural Partial Differential Equation SolversDifferentiable Physics

    Pasteur Labs, Brooklyn, NY, USA

  37. Error-Conditioned Neural Solvers

    Jun 25, 2026Haina Jiang, Liam Wang, Peng-Chen Chen +4Neural Partial Differential Equation SolversNeural Solvers

    University of Michigan · KAIST AI · Los Alamos National Laboratory

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

    Jun 20, 2026Zhangyong Liang, Huanhuan GaoNeural Partial Differential Equation SolversPartial Differential Equations

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

  39. A fast direct solver based neural network for solving PDEs

    Jun 18, 2026Jashwanth Reddy Kadaru, Vaishnavi GujjulaNeural Partial Differential Equation SolversPartial Differential Equations

    Department of Computer Science & Engineering, International Institute of Information Technology Bangalore (IIIT-B), India · Department of Data Science and Artificial Intelligence, International Institute of Information Technology Bangalore (IIIT-B), India

  40. Starter-Iterator Neural Operator: A Unified Architecture for High-Fidelity Forward and Inverse PDE Problems

    Jun 16, 2026Kuilin Qin, Lianfang Wang, Xu Sun +4Neural OperatorsNeural Partial Differential Equation Solvers

  41. Operator Boosting Produces Pareto-Efficient PDE Surrogates

    Jun 16, 2026Lennon J. ShikhmanNeural OperatorsNeural Partial Differential Equation Solvers

    Georgia Institute of Technology College of Computing Atlanta, Georgia, USA

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

    Jun 12, 2026Reza T Batley, Andrew Kichline, Sourav SahaNeural Partial Differential Equation SolversPartial Differential Equations

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

  43. How Much Memory Do We Need? Adaptive Memory Gate for Neural Operators

    Jun 11, 2026Jihyeon Hur, Yongseok Kwon, Min-Gi Jo +2Neural OperatorsNeural Partial Differential Equation Solvers

    1KAIST, Republic of Korea.

  44. AutoPDE: Reliable Agentic PDE Solving via Explicitly Represented Solver Strategies

    Jun 9, 2026Huanshuo Dong, Keyao Zhang, Hong Wang +6Neural Partial Differential Equation SolversClassical Numerical Solver

    University of Science and Technology of China · 2Zhejiang University · University of the Chinese Academy of Sciences +2

  45. Learning Where to Simulate: Generative Active Sampling for Online PDE Surrogate Training

    Jun 8, 2026Pierre Cesar, Sofya Dymchenko, Abhishek Purandare +1Surrogate ModelsMachine Learning Surrogates

    DATAMOVE · Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, LIG, Grenoble, France

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

    Jun 3, 2026Yanshun Zhao, Xiaoyu Peng, Jiamin Jiang +2Neural Partial Differential Equation SolversTransformer Architectures

    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.

  47. Correcting Neural Operator Spectral Bias via Diffusion Posterior Sampling with Sparse Observations

    Jun 2, 2026Niccolò Perrone, Fanny Lehmann, Stefania Fresca +1Neural OperatorsNeural Partial Differential Equation Solvers

    Université Paris-Saclay, CentraleSupélec, CNRS, ENS Paris-Saclay · Laboratoire de Mécanique Paris-Saclay UMR 9026 · 8-10 rue Joliot Curie, 91190 Gif-sur-Yvette, France +5

  48. Let There Be Light: Reflection, Refraction and Scattering for Neural Operators

    Jun 2, 2026Keke Wu, Yixuan Zhang, Jingrun ChenNeural OperatorsNeural Radiance Fields

    Suzhou Institute for Advanced Research, University of Science and Technology of China, Suzhou 215123, China · School of Artificial Intelligence and Data Science, University of Science and Technology of China, Hefei 230026, China · Suzhou Big Data & AI Research and Engineering Center, Suzhou 215123, China +2

  49. Cellular Sheaf Neural Operators for Structure-Preserving Surrogate Modeling of Constrained PDEs

    May 31, 2026Lennon J. Shikhman, Shane GilbertieNeural OperatorsNeural Partial Differential Equation Solvers

    College of Computing, Georgia Institute of Technology, Atlanta, 30332, GA, USA · Department of Aerospace, Physics and Space Sciences, Florida Institute of Technology, Melbourne, 32901, FL, USA

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

    May 29, 2026Abhishek Chandra, Taniya KapoorParametric Physics-Informed Neural NetworkNeural Partial Differential Equation Solvers

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

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

    May 29, 2026Qihong Yang, Qiaolin HeNeural Partial Differential Equation SolversPartial Differential Equations

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

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

    May 28, 2026Jianing ShiReynolds-Averaged Navier-StokesNeural Partial Differential Equation Solvers

    London School of Economics and Political Science.

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

    May 28, 2026Qihong Yang, Yangtao Deng, Qiaolin He +1Neural Partial Differential Equation SolversPartial Differential Equations

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

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

    May 25, 2026Shyam Sankaran, Hanwen Wang, Paris PerdikarisNeural Partial Differential Equation SolversDeep Learning Architectures

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

  55. Autoregression-Free Neural Operators for Time-Dependent PDEs

    May 25, 2026Jiaquan Zhang, Caiyan Qin, Haoyu Bian +7Neural OperatorsNeural Partial Differential Equation Solvers

    School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China · School of Robotics and Advanced Manufacture, Harbin Institute of Technology, Shenzhen, Guangdong 518055, China · School of Mathematical Sciences, Capital Normal University, Beijing 100048, China +3

  56. PDEInvBench: A Comprehensive Dataset and Design Space Exploration of Neural Networks for PDE Inverse Problems

    May 25, 2026Divyam Goel, Nithin Chalapathi, Sanjeev Raja +1Neural Partial Differential Equation SolversBayesian Inverse Problems

    Department of Computer Science, UC Berkeley · Departments of Computer Science and Chemical EngineeringMay UC Berkeley; LBNL

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

    May 23, 2026Jinjin He, Zhiqi Li, Sinan Wang +1Neural Partial Differential Equation SolversPartial Differential Equations

    Georgia Institute of Technology, Atlanta, GA, USA.

  58. An End-to-End PyTorch Interface for Differentiable PDE Solvers: A RANS Model-Correction Study

    May 19, 2026Luca Saverio, Michele Alessandro Bucci, Gianmarco Farro +2Neural Partial Differential Equation SolversPartial Differential Equations

    MONHADE · Digital Sciences & Technologies Department, Safran Tech, Magny-Les-Hameaux, 78114, France. · DAAA, ONERA, Institut Polytechnique de Paris, Meudon, 92190, France. +1

  59. AOT-POT: Adaptive Operator Transformation for Large-Scale PDE Pre-training

    May 15, 2026Qitan Lv, Hong Wang, Zhongkai Hao +5Neural OperatorsNeural Partial Differential Equation Solvers

    University of Science and Technology of China · 2Shanghai AI Laboratory · Department of Electronic Engineering, Tsinghua University, China

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

    May 14, 2026Yijing Zhang, Nicholas Roberts, Tanya Marwah +1Neural Partial Differential Equation SolversReynolds-Averaged Navier-Stokes

    University of Wisconsin–Madison · Google DeepMind