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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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  1. PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs

    Jul 22, 2026Amirhossein Sadr, Nima Soltani, Vahideh Moghtadaiee +3Neural PDE SolversKolmogorov-Arnold Networks

    School of Computer Science, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran · Department of Computer Science and Engineering, Shahid Beheshti University, Tehran, Iran · Cyberspace Research Institute, Shahid Beheshti University, Tehran, Iran +1

  2. Guarantees by Construction for Learned Finite Volume Schemes on Steady Supersonic Flow

    Jul 22, 2026Denis GueyffierNeural PDE SolversComputational Fluid Dynamics

    ONERA -- Institut Polytechnique de Paris · Direction Scientifique G´en´erale, ONERA · Institut Polytechnique de Paris, Palaiseau, France

  3. Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise

    Jul 21, 2026Arthur Bizzi, Olga FinkDynamical SystemsStochastic Differential Equations

    EPFL, Imperial College · EPFL

  4. Image Editing Models are Numerical Solvers

    Jul 21, 2026Ulysse MizrahiNeural PDE SolversPDE Solving

    Tel Aviv University

  5. 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.

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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.

  14. 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

  15. 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

  16. 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.

  17. 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

  18. 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

  19. 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

  20. 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

  21. 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

  22. 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

  23. 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

  24. 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

  25. 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

  26. 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

  27. 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.

  28. 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

  29. 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.

  30. 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