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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. 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

  2. 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

  3. 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.

  4. 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

  5. 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.

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

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

    AGH University of Krakow

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

  14. 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

  15. 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

  16. 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

  17. 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

  18. 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

  19. 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

  20. 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

  21. 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

  22. 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

  23. 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

  24. 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

  25. 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

  26. 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

  27. 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

  28. 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

  29. 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

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

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

    EPFL, Imperial College · EPFL