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20 papers in the last four weeks, up 54% on the four weeks before. 0.2% of all new papers.

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

    Oct 1, 2026Tan Phuong Dong LeVariational FormulationPartial Differential Equations

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

  2. Cluster Attention Neural Operators for Solving Parametric Partial Differential Equations

    Sep 30, 2026Ming Zhong, Antonio Colanera, Gianluigi Rozza +1Neural OperatorsPartial Differential Equations

    School of Advanced Interdisciplinary Sciences, University of Chinese Academy of Sciences, Beijing 100049, China. · State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China. · International School for Advanced Studies (SISSA), Trieste 34136, Italy. +1

  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. Geometry-physics confounding impairs PDE learning across varying domains

    Sep 29, 2026Yinghao Cheng, Gengxiang Chen, Xu Liu +6Partial Differential EquationsProbabilistic Operator Learning

    College of Mechanical & Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China · School of Electronics, Electrical Engineering and Computer Science, Queen’s University Belfast, Belfast, United Kingdom · School of Mechanical and Aerospace Engineering, Queen’s University Belfast, Belfast, United Kingdom +3

  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. PDE-JEPA: Predictive Representation Learning of Latent Dynamics Modeling for Parametric PDEs

    Sep 28, 2026Zhentao Tan, Jianrong Zhang, Ruijie Quan +1Latent PredictionPartial Differential Equations

    Zhejiang University.

  7. Dynamic Kuramoto-Hodge Operators for PDEs on Complex Geometries and Topologies

    Sep 27, 2026Xiang Li, Yue SongNeural OperatorsPartial Differential Equations

    Tsinghua University · Beijing University of Chemical Technology

  8. Physics and Data Driven Transformer-Mamba Framework for Flow Field

    Sep 24, 2026Zhuo Zhang, Shun Zou, Canqun Yang +1Computational Fluid DynamicPartial Differential Equations

    College of Computer Science and Technology, National University of Defense Technology, Changsha, China · College of Artificial Intelligence, Nanjing Agricultural University, NanJing, China · National SuperComputer Center in Tianjin, Binhai New Area, Tianjin, China +1

  9. GaussPDE: Graph-Based Partial Differential Equation-Driven Rendering for 3D Gaussian Splatting

    Sep 23, 2026Haoyuan Yue, Fengyuan Ye, Ziyin Li3D GaussianDifferentiable Rendering

    Department of Physics, Westlake University, Hangzhou, China · The Chinese University of Hong Kong, Shenzhen, China · Department of Accounting, Xi’an Jiaotong-Liverpool University, Suzhou, China

  10. Learning Physics from an Imperfect Ancestor

    Sep 21, 2026S. Mohammad Mousavi, Teeratorn Kadeethum, Nikolaos Bouklas +1Parametric Physics-Informed Neural NetworkPartial Differential Equations

    Sibley School of Mechanical and Aerospace Engineering, Cornell University · AI Lab, Siemens Energy · Department of Civil and Systems Engineering, Johns Hopkins University

  11. HiLNO: A Hierarchical Latent Neural Operator with Multi-Scale Supervision for PDEs on General Geometries

    Sep 16, 2026Zhicheng Hu, Jiacheng Li, Min YangNeural OperatorsPartial Differential Equations

    School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, China · Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles (NUAA), MIIT, Nanjing, 211106, China · School of Mathematics and Information Sciences, Yantai University, Yantai, China

  12. Physics Informed Random Feature Neural Networks for Solving PDEs

    Sep 14, 2026Chi-An Chen, Chunyang Liao, Ming ZhongPartial Differential EquationsKernel Method

    Department of Applied Mathematics, Mathematics, Illinois Institute of Technology, Chicago, IL, 60616 · Department of Mathematical Sciences, University of Arkansas, Fayetteville, AR, 72701 · Department of Mathematics, University of Houston, Houston, TX, 77204

  13. 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

  14. Physics-Informed Conformal Prediction: Embedding PDE Consistency into Distribution-Free Uncertainty Quantification for Neural Operators

    Sep 14, 2026Michael ChinOnline Conformal PredictionParametric Physics-Informed Neural Network

    Independent Researcher

  15. An explicit solution of the five-expert prediction PDE and the exact optimality set of COMB

    Sep 14, 2026Jeff Calder, Nadejda DrenskaOptimalityExact

    School of Mathematics, University of Minnesota · Department of Mathematics, Louisiana State University

  16. Selective boundary condition reduction via learned error gating

    Sep 8, 2026Daniel Fernández, Dominik Penk, Dominik RiedelbauchPartial Differential EquationsNeural Network

    Chair for Dynamics, Control, Machine Learning, and Numerics (Alexander von Humboldt Professorship), Department of Mathematics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstraße, 91058 Erlangen, Germany. · Schaeffler Technologies AG & Co. KG, Industriestraße 1–3, Herzogenaurach, Germany.

  17. Learning Metamaterial Eigenmodes with Wavelet-Encoded Fourier Neural Operators

    Sep 8, 2026Han Zhang, Alexander Ogren, Cynthia Rudin +2Fourier Neural OperatorsMetamaterials

    Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC, USA · Department of Mechanical Engineering, California Institute of Technology, Pasadena, CA, USA · Department of Electrical and Computer Engineering, Duke University, Durham, NC, USA

  18. Two-Scale Localized PCA-Net: Coarse-Global and Local-Residual Representations for Artifact-Reduced PDE Operator Learning

    Sep 7, 2026Mrigank Dhingra, Jordan Stout, Omer SanPartial Differential EquationsMulti-Scale Convolution

    Department of Mechanical & Aerospace Engineering University of Tennessee Knoxville, Tennessee 37917, USA · Department of Mathematics and Statistics Boston University Boston, Massachusetts 02215, USA

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

    Sep 7, 2026Hanwen Wang, Paris PerdikarisParametric Physics-Informed Neural NetworkPartial Differential Equations

    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

  20. Local gradient neural operator

    Sep 7, 2026Baiming Zhang, Jinsong Tang, Ying Xu +2Partial Differential Equations

    Zhejiang University · Nanjing University of Science and Technology · Hefei University of Technology

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

    Sep 3, 2026Ilkhom Mukhammadiev, Diyora SalimovaResidual NetworksNeural Approximations

    Department of Applied Mathematics, University of Freiburg, Germany

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

    Aug 31, 2026Zi Wang, Minghui Xu, Tapan MukerjiPartial Differential EquationsMesh Generation

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

  23. Learning the Geometry of Admissible Hypotheses through Inductive Bias in Training Distributions

    Aug 31, 2026James Crowley, Faez Ahmed, Anton van BeekPartial Differential EquationsHypothesis Class

    School of Mechanical and Material Engineering University College Dublin · Department of Mechanical Engineering Massachusets Institute of Technology

  24. 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

  25. 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

  26. Joint Spatiotemporal Spectral Neural Operators for Learning PDEs on Irregular Domains

    Aug 30, 2026Abdolmehdi Behroozi, Chaopeng ShenNeural OperatorsPartial Differential Equations

    Department of Civil and Environmental Engineering, Penn State University, University Park, PA 16802, USA

  27. 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

  28. StationPDE: Station-Oriented Surface PDE Learning for Multi-Station Multivariate Weather Forecasting

    Aug 20, 2026Xiao Wang, Changjian Chen, Rongwen Li +3Weather PredictionSpatio-Temporal Forecasting

    Hunan University.

  29. Distillation of Foundation Models for Time-dependent PDEs

    Aug 12, 2026Daniel Musekamp, Boshra Ariguib, Andrei Manolache +1Autoregressive RolloutKnowledge Distillation

    University of Stuttgart · University of Cologne · Bitdefender

  30. 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

  31. DEFT: Data-Efficient Frequency-domain Top-k Sampling via Inverse Discrete Fourier Transform for Spatiotemporal Dynamical Systems Modeling

    Aug 11, 2026Hengbo Xiao, Jiale Liu, Jiahao Song +1Frequency DomainPartial Differential Equations

    Peking University

  32. The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics

    Aug 10, 2026Petr Badolia, Leonid Obukhov, Dmitry Bylinkin +1Partial Differential EquationsOscillatory Dynamics

    Basic Research of Artificial Intelligence Laboratory (BRAIn Lab) · Innopolis University

  33. 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

  34. Unsupervised Adaptation of PDE Foundation Models

    Aug 7, 2026Ziye Song, Zhao Wei, Xin Yu +2Partial Differential EquationsParameter-Efficient Adaptation

    Nanyang Technological University · CFAR, A*STAR · Adelaide University

  35. From Points to Edges: Edge-Conditioned Spectral Operators for Physics-Sensitive PDE Learning

    Aug 7, 2026Zhentao Tan, Ruijie Quan, Yi YangPartial Differential EquationsSpectral Representation Method

    Collaborative Innovation Center of Artificial Intelligence (CCAI), Zhejiang University, China

  36. 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

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

    Aug 6, 2026Yulun Wu, Matthieu Barreau, Miguel Aguiar +1Parametric Physics-Informed Neural NetworkPartial Differential Equations

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

  38. Continual-Learning Physics-Informed Neural Networks for Parameterized Partial Differential Equations

    Aug 5, 2026Xujia Chen, Xinyue Hu, Letian Chen +2Parametric Physics-Informed Neural NetworkPartial Differential Equations

    Department of Automation, Tsinghua University, Beijing, 100084, China

  39. 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

  40. Conformal risk control for model-form uncertainty in parametric non-intrusive reduced-order models

    Aug 4, 2026Edgar Jaber, Rémy Vallot, Thibault Dairay +1Reduced-Order ModelsUncertainty Quantification

    CB, ENS Paris Saclay · Université Paris-Saclay, CNRS, ENS Paris-Saclay, Centre Borelli, Gif-sur-Yvette, 91190, France · CB, Michelin +3

  41. Modeling Unknown Nonlocal PDE Systems via Flow Map Learning

    Aug 1, 2026Zhongshu Xu, Ying Li, Yanzhi Zhang +1Partial Differential EquationsNonlinear Operators

    Department of Mathematics, The Ohio State University, Columbus, OH 43210, USA. · Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409, USA.

  42. Localization in Spatiotemporal Fields via Environmental PDEs

    Jul 31, 2026Jose Fuentes, Abdullah Al Redwan Newaz, Ana Cavalcanti +1Particle FiltersSpatiotemporal Fields

    Faculty of Computer Engineering and Information Sciences, Florida International University, Miami, FL 33174, USA · University of New Orleans, New Orleans, LA 70148, USA

  43. 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

  44. Dynamics-aware identification of governing equations from sparse and noisy data

    Jul 31, 2026Pongpisit Thanasutives, Yoshinobu KawaharaSystem IdentificationDynamic Mode Decomposition

    Center for Advanced Intelligence Project (AIP), RIKEN, Osaka, Japan · 2Graduate School of Information Science and Technology, The University of Osaka, Osaka, Japan

  45. Feature Interaction Modeling for Neural Operators

    Jul 30, 2026Quan Gu, Xiaoduo Li, Hongxia LiuParametric Physics-Informed Neural NetworkPartial Differential Equations

    Independent Researcher · Taiyuan University of Technology

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

    Jul 30, 2026Jae-Hwan Choi, Hyojae Lim, Jinsol Seo +2Neural ApproximationsPartial Differential Equations

  47. EvoPINN: Agentic Discovery of Executable Algorithms for Physics-Informed Neural Networks

    Jul 29, 2026Peng Yin, Kai Li, Yifan Zhang +1Parametric Physics-Informed Neural NetworkAgentic Discovery

    School of Advanced Interdisciplinary Sciences, University of Chinese Academy of Sciences, Beijing, China · Institute of Automation, Chinese Academy of Sciences, Beijing, China

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

    Jul 28, 2026Pinki Khatun, M. Sajid, Abhinav Jha +1Parametric Physics-Informed Neural NetworkPhysics-Informed Learning

    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

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

    Jul 27, 2026Justin Sirignano, Konstantinos Spiliopoulos, Samuel CohenPartial Differential EquationsVariational Formulation

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

  50. 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

  51. 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

  52. On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement

    Jul 26, 2026Baptiste Mathevon, Farah Cherfaoui, Amaury Habrard +1Partial Differential EquationsEvaluation Metrics

    Université Jean Monnet Saint-Étienne, CNRS, Institut d’Optique Graduate School, Inria, Laboratoire Hubert Curien UMR 5516, F-42023, SAINT-ÉTIENNE, France · Institut Universitaire de France (IUF)

  53. Extending Fourier Neural Operators for Modeling Parameterized and Coupled PDEs

    Jul 26, 2026Cheng Jing, Uvini Balasuriya Mudiyanselage, Abhishek Verma +3Fourier Neural OperatorsNeural Operators

    Arizona State University · Applied Materials Inc.

  54. Latent PDE mapping for efficient physics-informed learning across geometries with limited data

    Jul 24, 2026Ingvild Askim Adde, Mary M. Maleckar, Gabriel BalabanParametric Physics-Informed Neural NetworkPartial Differential Equations

    Faculty of Health and Technology, Kristiania University of Applied Sciences, Oslo, Norway · Department of Computational Physiology, Simula Research Laboratory, Oslo, Norway

  55. Multilevel Graph Wavelet Compressed Sensing with Scale-Aware Neural Recovery

    Jul 23, 2026Amirhossein Nouranizadeh, Sarang Rajendra Patil, Alan John Varghese +3WaveletsSignal Reconstruction

    Simplicial Technologies Inc., Toronto, ON, Canada · Department of Data Science, New Jersey Institute of Technology, Newark, NJ · School of Engineering, Brown University, Providence, RI +2

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

    Jul 22, 2026Amirhossein Sadr, Nima Soltani, Vahideh Moghtadaiee +3Variational FormulationPartial Differential Equations

    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

  57. Toward Goal-Agnostic Joint-Embedding Predictive Control of Partial Differential Equations

    Jul 21, 2026Jonathan Gallagher, Roberto GuglielmiModel Predictive ControlPartial Differential Equations

    University of Waterloo

  58. 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

  59. Non-Asymptotic Variational Learning for Monotone Nonlinear Multiscale Elliptic Equations: Scale-Robust Primal-Dual Bounds and Strong-Form Statistical Ill-Conditioning

    Jul 17, 2026Ronald KatendeVariationalMultiscale Dynamics

    Department of Mathematics Kabale University Kikungiri Hill, Katuna Road, Kabale, Uganda

  60. LIGO-PINN: Learned Initialization via Gated Optimization to Alleviate Convergence Failures in Physics Informed Neural Networks

    Jul 15, 2026Nilay Anurag, Shital Adhikari, Taniya Kapoor +1Parametric Physics-Informed Neural NetworkPartial Differential Equations

    Department of Computer Science, Stevens Institute of Technology · Artificial Intelligence Group, Wageningen University & Research