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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. Physics-Informed Neural Plasticity: PDE Solvers That Reshape Themselves

    Oct 7, 2026Chun-Wun Cheng, Bingcheng Hu, Angelica I. Aviles-RiveroNeural PDE SolversPDE Solving

    Shanghai Normal University · YMSC, Tsinghua University

  2. An extended deep energy method for thermo-mechanical crack propagation

    Oct 7, 2026Han Zhang, Mehrisadat Makki Alamdari, Babak Shahbodagh +4Neural PDE SolversMaterials Science

    University of New South Wales, Sydney, NSW, Australia · Central Queensland University, Melbourne, VIC, Australia · Bauhaus-Universität Weimar, Weimar, Germany

  3. FOSLS-deRhaNN: native de Rham neural classes for H(div) and H(curl) with applications to first-order system least-squares neural network methods for partial differential equations

    Oct 6, 2026Shun ZhangNeural PDE SolversNeural Network Approximation Theory

    Department of Mathematics, City University of Hong Kong, Kowloon Tong, Hong Kong, China

  4. A Neural JKO Scheme for Hellinger-Kantorovich Gradient Flows via Monge-Growth Pairs

    Oct 6, 2026Geuntaek Seo, Cheolhyeong Kim, Hwijae Son +1Neural PDE SolversPDE Solving

    Department of Mathematics, Pohang University of Science and Technology · Samsung Electronics · Department of Mathematics, Konkuk University

  5. Singular parameters and missing limits in neural PDE solvers

    Oct 5, 2026Daniel FernándezNeural PDE SolversNeural Network Optimization

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

  6. IGA-KAN: Isogeometric Analysis with Physics-Informed Closed-Form Kolmogorov-Arnold Networks for Forward and Inverse PDEs

    Oct 5, 2026Sima Naraghi, Kourosh Parand, Amirhossein Sadr +1Neural PDE SolversKolmogorov-Arnold Networks

    Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran · Department of Computer and Data Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran · Department of Cognitive Modeling, Institute for Cognitive and Brain Sciences, Shahid Beheshti University, Tehran, Iran +1

  7. Component-Level Evaluation of Adaptive PINN Training for CFD-Oriented Crystal Growth Simulation

    Oct 4, 2026Niruta Chapagain, Rohit Raj, Bertwin Kurisinkal Shine +1Neural PDE SolversPDE Surrogate Modeling

    University of Europe for Applied Sciences Potsdam, Germany · Vienna, Austria · Technische Universität Chemnitz Chemnitz, Germany +1

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

    Oct 2, 2026Luis Medrano-Navarro, Giacomo Baldan, Qiang Liu +4Synthetic Data PretrainingNeural PDE Solvers

    Technical University of Munich · University of Stuttgart

  9. Kolmogorov-Arnold Networks for Free-Boundary Partial Differential Equations

    Oct 1, 2026Tan Phuong Dong LeNeural PDE SolversPDE Solving

    Department of Applied Mathematics, University of Waterloo, Canada · Department of Statistics and Actuarial Science, University of Waterloo, Canada

  10. Physics-Informed Method of Group Data Handling: Adaptive Construction of Functional Representations with an Application to the Navier-Stokes Equations

    Sep 30, 2026Mykhailo MininNeural PDE SolversPhysics-Informed ML

    JSC KIEP, Kyiv, Ukraine

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

    Sep 30, 2026Wilson G. Gregory, George A. Kevrekidis, Ben Blum-Smith +1Neural PDE SolversPDE Surrogate Modeling

    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

  12. PE-EK-PINN: Physics Embedding with Evolving Kernel for Scalable Physics-Informed Neural Networks

    Sep 29, 2026Huiwen Zhang, Feng Ye, Chu MaNeural PDE SolversPhysics-Informed ML

    Department of Electrical & Computer Engineering Madison, WI, 53706, USA

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

    Sep 29, 2026Haonan Shangguan, Hang Zhou, Haixu Wu +3Fourier Neural OperatorNeural PDE Solvers

    School of Software, BNRist, Tsinghua University · MIT CSAIL

  14. Neural Harmonic Measure Operator

    Sep 28, 2026Jinjin He, Sinan Wang, Yuchen Sun +1Neural PDE SolversPDE Solving

    Georgia Institute of Technology

  15. GAC-PINN: Geometry-Adaptive and Constraint-Enhanced Physics-Informed Neural Networks

    Sep 28, 2026Yanxin Zhang, Yong Zhang, Houbiao LiNeural PDE SolversPhysics-Informed ML

    University of Electronic Science and Technology of China, Chengdu, 611731, Sichuan, China

  16. Physics-Informed Neural Networks for Depth-Averaged Avalanche Dynamics

    Sep 28, 2026Pradyumn Singh Sikarwar, Vishal Sharma, Gaurav BhutaniNeural PDE SolversPhysics-Informed ML

    School of Mechanical and Materials Engineering, Indian Institute of Technology Mandi, India

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

    Sep 27, 2026Zeyuan Song, Zheyu JiangNeural PDE SolversNeural Network Interpretability

    Oklahoma State University Stillwater, OK 74078

  18. A Hybrid Iterative Deep Ritz Method for Elliptic Interface Problems

    Sep 23, 2026Tianhao Hu, Bangti Jin, Fengru Wang +1Neural PDE SolversPDE Solving

    Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong · Department of Mathematics & Scientific Computing Key Laboratory of Shanghai Universities, Shanghai Normal University, Shanghai 200234, China.

  19. Cost-Accuracy Trade-offs: Neural Operator vs Classical Numerical Solver

    Sep 21, 2026Daniel Zhengyu Huang, Andrew M. StuartNeural Surrogate ModelingNeural PDE Solvers

    Beijing International Center for Mathematical Research, Center for Machine Learning Research, Peking University, Beijing, China · California Institute of Technology, Pasadena, CA

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

    Sep 17, 2026Nilo Schwencke, Roland MaierGauss-Newton OptimizationNeural PDE Solvers

  21. Well-posedness of neural turbulence closures and tangent dissipation

    Sep 17, 2026Zhen Zhang, George Em KarniadakisNeural PDE SolversComputational Fluid Dynamics

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

  22. Hybrid coupling with numerics-informed neural networks and the overlapping Schwarz alternating method

    Sep 15, 2026George Chumbipuma, Irina Tezaur, Alejandro Diaz +1Neural PDE SolversPDE Solving

    Rice University · Sandia National Laboratories

  23. Physics Informed Neural Network model for the dynamical study of Abdominal Aortic Aneurysm

    Sep 14, 2026Adrián Robles Arques, Martín Ruiz Fernandez, Javier Sanchis +2Neural PDE SolversPhysics-Informed ML

    Lucentia Research; Instituto Universitario de Investigación en Informática, Universidad de Alicante, Carr. San Vicent del Raspeig, Alicante, 03690, Comunidad Valenciana, España

  24. Physics-enriched neural solvers for transient ice-flow simulation

    Sep 14, 2026Thomas Gregov, Sebastian Rosier, Brandon Finley +2Neural Surrogate ModelingNeural PDE Solvers

    Institute of Earth Surface Dynamics, Universit´e de Lausanne, Lausanne, Switzerland · Department of Geography, Universität Zürich, Zürich, Switzerland

  25. Attention Is All You Need (to Avoid Spurious Oscillations)

    Sep 11, 2026Jinyoung Jeong, Joseph B. Choi, Xinlun Cheng +3Neural PDE SolversPDE Solving

    School of Mechanical Engineering & IEDT, Kyungpook National University, Daegu, South Korea · School of Data Science, University of Virginia, Charlottesville, VA 22903, USA · Department of Mechanical Engineering, University of Iowa, Iowa City, Iowa 52242, USA +1

  26. A variational physics-informed graph neural network for heterogeneous solid mechanics

    Sep 10, 2026Aashay Rajan Yadav, Amiya Prakash Das, Ratna Kumar AnnabattulaNeural PDE SolversStructural Mechanics

    Mechanics of Materials Lab, Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, 600036, Tamil Nadu, India

  27. Solving the Elastic Wave Equation with Physics-Informed Neural Networks: A Robust and Critical Assessment

    Sep 7, 2026Davide Staub, Ben MoseleyNeural PDE SolversPhysics-Informed ML

    Department of Mathematics, ETH Zürich

  28. Latent-MoE: Domain-Aware Mixture-of-Experts for PDEs with Multi-Regime Physics

    Sep 7, 2026Hanwen Wang, Paris PerdikarisNeural PDE SolversPhysics-Informed ML

    Graduate Group of Applied Mathematics and Computational Science University of Pennsylvania Philadelphia, PA 19104 · Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania Philadelphia, PA 19104

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

    Sep 7, 2026Xing Guo, Hongwei Tang, Zewei Meng +3Automatic DifferentiationNeural PDE Solvers

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

  30. Residual neural networks overcome the curse of dimensionality for semilinear heat equations

    Sep 3, 2026Ilkhom Mukhammadiev, Diyora SalimovaNeural PDE SolversPDE Solving

    Department of Applied Mathematics, University of Freiburg, Germany

  31. Computing stable configurations of confined smectic liquid crystals with a deep variational framework

    Sep 3, 2026Yuchen Xie, Baoming Shi, Yucen Han +1Neural PDE SolversMaterials Science

    School of Mathematical Sciences, Peking University, Beijing 100871, China · Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027, USA · Center for Applied Mathematics, Renmin University of China, Beijing 100872, China +1

  32. Geometry-aware Latent Autoregressive Generative Model for PDEs in Complex Domains

    Aug 31, 2026Zi Wang, Minghui Xu, Tapan MukerjiGraph Neural NetworksNeural PDE Solvers

    Department of Energy Science and Engineering Stanford University Stanford, CA 94305

  33. 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 +1Neural PDE Solvers

    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.

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

    Aug 12, 2026Maryam Reza, Farbod FarajiNeural PDE SolversPDE Solving

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

  35. Forward Trajectory Steering for Hamilton-Jacobi Reachability Analysis

    Aug 11, 2026Sungje Park, Stephen TuReachability AnalysisNeural PDE Solvers

    with the Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA, USA.

  36. Derivative Computation in PINNs: Automatic Differentiation, Finite Differences and Beyond

    Aug 11, 2026Maciej J. Mikulski, Tadeusz UhlAutomatic DifferentiationNeural PDE Solvers

    AGH University of Krakow

  37. Efficient Weak-Entropy PINN for Solving Hyperbolic Conservation Laws

    Aug 11, 2026Qi Gao, Kuang Huang, Xuan DiNeural PDE SolversPDE Solving

    Department of Civil Engineering and Engineering Mechanics, Columbia University · Department of Mathematics, The Chinese University of Hong Kong · Center for Smart Cities, Data Science Institute, Columbia University

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

    Aug 10, 2026Zijiang Yang, Xiaomeng Wu, Dongmei FuNeural PDE SolversPDE Operator Learning

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

  39. Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing

    Aug 10, 2026Konrad Kleinberg, Thomas KruseNeural PDE SolversPDE Solving

    Department of Mathematics & Informatics, University of Wuppertal, Germany

  40. Hierarchical rank-evolving representation for physics-informed neural networks

    Aug 10, 2026Ruoyang Su, Xi-Le Zhao, Kun Li +1Tensor NetworksNeural PDE Solvers

    University of Electronic Science and Technology of China, No.2006, Xiyuan Ave, West Hi-Tech Zone, Chengdu, 611731, Sichuan, P.R.China · Southwestern University of Finance and Economics, 555, Liutai Avenue, Wenjiang District, Chengdu, 611130, Sichuan, P.R.China

  41. Eikonal Regularisation in Physics-Informed Neural Networks for Three-Dimensional Level-Set Advection: Transferability of Two-Dimensional Design Principles

    Aug 8, 2026Muhammad Akbar KhanNeural PDE SolversPhysics-Informed ML

    Department of Mathematics, NED University of Engineering and Technology, Karachi 75270, Pakistan

  42. Finite basis physics-informed neural networks with hard constraints for viscous fluid flow in highly perforated domains

    Aug 8, 2026Jeeeun Lee, Denis Korolev, Miro Duhovic +1Neural PDE SolversPhysics-Informed ML

    Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Yuseong-gu, Daejeon, 34141, Republic of Korea · Weierstrass-Institute for Applied Analysis and Stochastics, Anton-Wilhelm-Amo-Str. 39, Berlin, 10117, Germany · Leibniz-Institut für Verbundwerkstoffe GmbH, Erwin-Schrödinger-Str. 58, Kaiserslautern, 67663, Germany

  43. Weak Adversarial Neural Pushforward Method for Boltzmann Equation

    Aug 7, 2026Jenia Fardousi Koly, Andrew Qing He, Wei CaiNeural PDE Solvers

    Department of Mathematics, Southern Methodist University, Dallas, Texas, USA

  44. Optimal Neural Network Approximation via Empirical Least Squares with Deterministic Samples

    Aug 7, 2026Xinliang Liu, Tong Mao, Jinchao XuNeural PDE SolversReLU Neural Networks

    School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China · Shenzhen Loop Area Institute, Shenzhen 518000, P. R. China

  45. Alternating Levenberg-Marquardt Training of Physics-Informed Neural Networks with Fourier-Enhanced Features

    Aug 6, 2026Yulun Wu, Matthieu Barreau, Miguel Aguiar +1Neural PDE SolversSpectral Bias

    Division of Decision and Control Systems, School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, Stockholm, 100 44, Sweden

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

    Aug 5, 2026Shengxin Kong, Liwen Xu, Jingwen FuNeural PDE SolversLarge Language Model-Guided Optimization

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

  47. From Non-Convex Self-Concordant Regularization to Scalable Quasi-Newton Training of PINNs

    Aug 4, 2026Chenhao Si, Kang An, Shiqian Ma +1Neural PDE SolversSecond-Order Optimization

    School of Data Science, The Chinese University of Hong Kong, Shenzhen, 2001 Longxiang Road, Longgang District, Shenzhen, 518172, Guangdong, China · Department of Computational Applied Mathematics and Operations Research, Rice University, 6100 Main Street, MS 134, Houston, 77005-1827, Texas, USA · Data Science and AI Institute, and Department of Applied Mathematics and Statistics, Johns Hopkins University, 3400 N. Charles Street, Baltimore, 21218, Maryland, USA

  48. Neural Networks with Local Converging Inputs for Efficient Options Pricing Models

    Aug 3, 2026Harris Cobb, Wenbo Hao, Yingjie LiuNeural Surrogate ModelingNeural PDE Solvers

    School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332

  49. Convex Neural Energy Elements: Monolithic Finite-Element Assembly of Geometry-Parameterized Neural Operators with Stability and Error Guarantees

    Aug 3, 2026Hongyue Jiang, Jianjiang Zhan, Chenzhuo Zhang +1Neural PDE SolversPDE Operator Learning

    School of Civil and Hydraulic Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China · National Center of Technology Innovation for Digital Construction, Huazhong University of Science and Technology, Wuhan, 430074, China

  50. Physics-Informed Neural Networks for Complex Eigenfrequency Identification and Mode Structure Reconstruction of the Ground-State ITG Branch

    Aug 3, 2026Dengdi Sun, Bingbing Zhang, Xiao Wang +5Neural PDE SolversPhysics-Informed ML

    School of Artificial Intelligence, Anhui University, Hefei, China · School of Computer Science and Technology, Anhui University, Hefei, China · School of Physics and Electronic Information, Anhui Normal University, Wuhu, China +1

  51. Hybrid Lagrangian-Eulerian Model for Lagrangian Fluid Simulation

    Aug 2, 2026Ruoyan Li, Wei Wang, Yizhou SunNeural PDE SolversComputational Fluid Dynamics

    University of California, Los Angeles

  52. Fractional Parabolic Partial Differential Equations in Anisotropic Spectral Barron Spaces: Regularity and Neural Approximation

    Jul 30, 2026Jae-Hwan Choi, Hyojae Lim, Jinsol Seo +2Neural PDE SolversPDE Solving

  53. Physics-Informed Broad Learning System: An Efficient Backpropagation-Free Framework for Solving Partial Differential Equations

    Jul 28, 2026Pinki Khatun, M. Sajid, Abhinav Jha +1Neural PDE SolversPDE Solving

    Department of Industrial Engineering, Università degli Studi di Firenze, Viale Morgagni 40/44, 50134 Firenze, Italy · Department of Mathematics, Indian Institute of Technology Indore, Indore 453552, India · Department of Mathematics, Indian Institute of Technology Gandhinagar, Palaj, Gandhinagar, 382055, Gujarat, India

  54. Score-Based Stabilization for Time-Dependent Problems

    Jul 27, 2026Eshed Gal, Eldad Haber, Uri AscherNeural PDE SolversPDE Solving

    University of British Columbia Vancouver, British Columbia, Canada

  55. Global Convergence of DGM and PINN Algorithms for Solving Nonlinear PDEs

    Jul 27, 2026Justin Sirignano, Konstantinos Spiliopoulos, Samuel CohenNeural PDE SolversOptimization Convergence Analysis

    Mathematical Institute, University of Oxford · Department of Mathematics and Statistics, Boston University

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

    Jul 27, 2026Xianli Zhu, Jia YinNeural Surrogate ModelingNeural PDE Solvers

    School of Mathematical Sciences, Fudan University Shanghai, China

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

    Jul 24, 2026Zhangyong Liang, Huanhuan GaoNeural PDE SolversRiemannian Optimization

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

  58. 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

  59. 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

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

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

    EPFL, Imperial College · EPFL