PDE Solving

PDE: Partial Differential Equation

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19 papers in the last four weeks, up 111% on the four weeks before. 0.2% of all new papers.

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

    Jul 6, 2026Akshat Jani, Prathamesh Gadekar, Sakhinana Sagar Srinivas +1PDE SolvingPDE Surrogate Modeling

    Tata Research Development and Design Center, Pune, India 411057

  2. 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

  3. An Optimisation Framework for the Well-Conditioned Training of Physics-Informed Neural Networks

    Jul 2, 2026Joseph Webb, Sadok Jerad, Coralia CartisGauss-Newton OptimizationPDE Solving

    Mathematical Institute, University of Oxford, Oxford, United Kingdom

  4. Frequency Shift Physics-Informed Extreme Learning Machine for Solving High-Frequency Partial Differential Equations

    Jul 2, 2026Xiong Xiong, Ruonan Zhai, Zheng Zeng +3PDE SolvingFrequency-Domain Feature Learning

    School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an, 710072, China · MIIT Key Laboratory of Dynamics and Control of Complex Systems, Northwestern Polytechnical University, Xi’an, 710072, China · College of Science, Shijiazhuang University, Shijiazhuang, 050035, China +2

  5. GAIA: Geometry-Adaptive Operator Learning for Forward and Inverse Problems

    Jul 1, 2026Meenakshi Krishnan, Pranav Pulijala, Ke Chen +2PDE SolvingImage Reconstruction

    University of Maryland, College Park · University of Delaware, Newark

  6. 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.

  7. 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

  8. Fourier Neural Operators with Least-Squares Readout Refit for Learning Random Obstacle-to-Solution Maps

    Jun 28, 2026Chenhui Zhu, Fei WangFourier Neural OperatorPDE 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.

  9. Mosaic: A Benchmark Suite for Differentiable Physics Solvers

    Jun 26, 2026Andrin Rehmann, Heiko Zimmermann, Dion HäfnerAutomatic DifferentiationPDE Solving

    Pasteur Labs, Brooklyn, NY, USA

  10. Operator Learning for Cubic Nonlinear Schrödinger Equation on Periodic Domains

    Jun 25, 2026Emmanuel E. Oguadimma, Victory C. Obieke, Xueying YuFourier Neural OperatorPDE Solving

  11. 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

  12. 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

  13. Hessian-augmented Supervised Learning for Hamilton-Jacobi-Bellman PDEs

    Jun 22, 2026Matías Gómez-Aedo, Behzad Azmi, Yuyang Huang +2Value Function EstimationPDE Solving

    Department of Mathematics, Imperial College London, South Kensington Campus, SW7 2AZ London, UK · Department of Mathematics and Statistics, University of Konstanz, Germany · RICAM and Institute of Mathematics and Scientific Computing, University of Graz, Austria

  14. Adaptive Hard-Soft Physics-Informed Neural Networks for Robust Boundary-Constrained PDE Solving

    Jun 22, 2026Duc Tien Nguyen, Trinh Minh Tuan, Nguyen Duc Manh +2PDE SolvingAdaptive Loss Weighting

    aCollege of Engineering and Computer Science, VinUniversity, Hanoi, Vietnam · bCenter for AI Research, VinUniversity, Hanoi, Vietnam · dDepartment of Mathematics and Informatics, Hanoi University of Science and Technology, Hanoi, Vietnam +1

  15. 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

  16. Spectrally Safe Neural Operator Warm-Starts for Large-Scale Newton Solvers

    Jun 20, 2026Jaemin Oh, Youngkyu Lee, Jerome Darbon +1Spectral RegularizationPDE Solving

    Division of Applied Mathematics, Brown University, Providence, RI 02912, USA

  17. TF-SNO: Time-Frequency Gated Spectral Neural Operators for Learning Non-Stationary Partial Differential Equations

    Jun 19, 2026Yitian Zhou, Chaoning Zhang, Zhenzhen Huang +8PDE SolvingPDE Operator Learning

    University of Electronic Science and Technology of China Chengdu, China · Institute of Software, Chinese Academy of Sciences Beijing, China · Harbin Institute of Technology Shenzhen, China

  18. Agentic Symbolic Search: Characterizing PDEs Beyond Hand-crafted Expressions, Meshes, and Neural Networks

    Jun 18, 2026Zongmin Yu, Liu YangAI Agents for Scientific DiscoveryPDE Solving

    National University of Singapore

  19. Quantum-classical physics-informed Kolmogorov-Arnold networks for PDEs

    Jun 18, 2026Xiang Rao, Yuxuan ShenPDE SolvingHybrid Quantum-Classical ML

    1. School of Petroleum Engineering, Yangtze University, Wuhan 430100, China · 2. School of Computer Science, Yangtze University, Jingzhou 434023, China · 3. State Key Laboratory of Low Carbon Catalysis and Carbon Dioxide Utilization (Yangtze University), Wuhan 430100, China +2

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

    Jun 18, 2026Jashwanth Reddy Kadaru, Vaishnavi GujjulaPDE SolvingPDE Operator Learning

    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

  21. Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System

    Jun 18, 2026Zhiwen Yu, Derong Yang, Liujian Zhang +5PDE SolvingUniversal Approximation

    School of Computer Science and Engineering, South China University of Technology, Guangzhou 510006, China · Peng Cheng Laboratory, Shenzhen 518000, China · School of Future Technology, South China University of Technology, Guangzhou 510006, China +2

  22. Acceleration of an algebraic multigrid pressure solver using graph neural networks

    Jun 17, 2026Eric Chillón, Artur K. Lidtke, Nguyen Anh Khoa Doan +1Graph Neural NetworksPDE Solving

    Faculty of Mechanical Engineering, Delft University of Technology, The Netherlands · Maritime Research Institute Netherlands, The Netherlands · Department of Aeronautics, Imperial College London, United Kingdom

  23. A Convex Quasilinearization Method for Solving Nonlinear PDEs with Physics-Informed Neural Networks

    Jun 16, 2026Gbenga T. Awojinrin, Abdul-Akeem Olawoyin, Rami M. YounisPDE SolvingPhysics-Informed ML

    Texas A&M University, College Station, Texas, U.S.A.

  24. 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

  25. RepNN: Tackling spectral bias in deep neural networks for regression and PDE problems via parameter reparameterization

    Jun 15, 2026Yong Wang, Tao Zhou, Xuhui MengPDE SolvingSpectral Bias

    Institute of Interdisciplinary Research for Mathematics and Applied Science, School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China · Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

  26. 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

  27. Robin-Neumann Coupling of PINN and FEM Solvers: A Steklov-Poincaré View, with Application to Fluid-Structure Interaction with Contact

    Jun 12, 2026Mikel LandajuelaPDE SolvingPhysics-Informed ML

    Lawrence Livermore National Laboratory

  28. Physics-Informed Neural Networks and Radial Basis Functions for PDEs with Dirac Delta Sources

    Jun 10, 2026Manuel Reyna, Alexandre TartakovskyPDE SolvingPhysics-Informed ML

    Department of Civil and Environmental Engineering, University of Illinois Urbana-Champaign, 205 North Mathews Avenue, Urbana, 61801, IL, USA

  29. A Constrained Natural-Language Interface for Variational Multi-Physics Finite Element Simulations in FEniCS

    Jun 9, 2026Nilay Upadhyay, Wesley F. ReinhartPDE SolvingLLM Prompting

    Department of Engineering Science and Mechanics, The Pennsylvania State University, University Park, PA 16802, USA · Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16802, USA

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

    Jun 9, 2026Huanshuo Dong, Keyao Zhang, Hong Wang +6AI Coding AgentsPDE Solving

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