PDE Operator Learning

PDE: Partial Differential Equation

Follow this topic Ask about this topic

Momentum

24 papers in the last four weeks, up 140% on the four weeks before. 0.2% of all new papers.

Jul 13Week of Sep 28

Latest papers 148

All topics

Joint Spatiotemporal Spectral Neural Operators for Learning PDEs on Irregular Domains
Aug 30, 2026Abdolmehdi Behroozi, Chaopeng ShenPDE Surrogate Modeling PDE Operator Learning
Department of Civil and Environmental Engineering, Penn State University, University Park, PA 16802, USA
The Frame Kernel Method for Multiscale Operator Learning
Aug 25, 2026Branden Frieden, Ryan Whitehead, M. Keith Ballard +2PDE Surrogate Modeling Kernel Methods
Kahlert School of Computing, University of Utah, Salt Lake City, UT 84112, USA. · U.S. Air Force Research Laboratory, Wright-Patterson AFB, OH 45433, USA.
StationPDE: Station-Oriented Surface PDE Learning for Multi-Station Multivariate Weather Forecasting
Aug 20, 2026Xiao Wang, Changjian Chen, Rongwen Li +3Multivariate Time Series Forecasting PDE Operator Learning
Hunan University.
Kernel Methods for Learning Operators with Multiple Inputs and Outputs
Aug 12, 2026Adrien Weihs, Chunyang Liao, Jingmin Sun +1Kernel Methods PDE Operator Learning
Department of Mathematics, University of California Los Angeles, Los Angeles, CA 90095, USA. · Department of Mathematical Sciences, University of Arkansas, Fayetteville, AR, 72701, USA. · Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD 21218, USA.
FLARE++: Low-rank attention with dynamic attention routing
Aug 12, 2026Vedant Puri, Yongjie Jessica Zhang, Levent Burak KaraLow-Rank Attention PDE Surrogate Modeling
Department of Mechanical Engineering Carnegie Mellon University Pittsburgh, Pennsylvania, USA
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 +1PDE Operator Learning Data-Efficient Learning
Peking University
The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics
Aug 10, 2026Petr Badolia, Leonid Obukhov, Dmitry Bylinkin +1Dynamical Systems PDE Operator Learning
Basic Research of Artificial Intelligence Laboratory (BRAIn Lab) · Innopolis University
MoNo: Multiscale Optimal Transport Neural Operator for Solving PDEs on General Geometries
Aug 10, 2026Zijiang Yang, Xiaomeng Wu, Dongmei FuNeural PDE Solvers PDE Operator Learning
School of Automation and Electrical Engineering, University of Science and Technology Beijing · 2Beijing Engineering Research Center of Industrial Spectrum Imaging
ADEx-FNO: A Unified Ambient-Domain Framework for Fourier Neural Operators on Varying Geometries
Aug 9, 2026Roberto Nuca, Giovanni Testa, Luca Galimberti +1Fourier Neural Operator PDE Surrogate Modeling
Computer, Electrical and Mathematical Sciences and Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia · Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano, Milan, Italy · Physical Science and Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia
Unsupervised Adaptation of PDE Foundation Models
Aug 7, 2026Ziye Song, Zhao Wei, Xin Yu +2Unsupervised Domain Adaptation Low-Rank Adaptation
Nanyang Technological University · CFAR, A*STAR · Adelaide University
From Points to Edges: Edge-Conditioned Spectral Operators for Physics-Sensitive PDE Learning
Aug 7, 2026Zhentao Tan, Ruijie Quan, Yi YangPDE Surrogate Modeling PDE Operator Learning
Collaborative Innovation Center of Artificial Intelligence (CCAI), Zhejiang University, China
Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces
Aug 5, 2026Khemraj Shukla, George Em KarniadakisPDE Operator Learning Neural Network Approximation Theory
Division of Applied Mathematics, Brown University Providence, Rhode Island 02912, USA
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 Solvers PDE 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
tFUSOperator: Operator Learning for Transcranial Focused Ultrasound Digital Twins
Aug 3, 2026Minjee Seo, Haris Ghafoor, Minju Seol +2PDE Operator Learning Digital Twins
School of Mathematics and Computing (Computational Science and Engineering), Yonsei University, Seoul, Republic of Korea · Innovative & Intelligent Computational Science Institute (IN2CSI), Seoul, Republic of Korea
Modeling Unknown Nonlocal PDE Systems via Flow Map Learning
Aug 1, 2026Zhongshu Xu, Ying Li, Yanzhi Zhang +1PDE Surrogate Modeling Flow Map Learning
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.
HERO: History-Enriched Rollout Training for Long-Horizon Autoregressive Neural Operators
Jul 31, 2026Jiaquan Zhang, Shuxu Chen, Haifan Meng +6Neural Surrogate Modeling PDE Operator Learning
School of Computer Science and Engineering, UESTC · Electronics and Information Convergence Engineering, KHU · Department of Mathematical Sciences, UOL +3
Geometry-aware Incremental Neural Operator for Long-Horizon PDE prediction
Jul 31, 2026Jiaquan Zhang, Shuxu Chen, Haifan Meng +6PDE Surrogate Modeling PDE Operator Learning
School of Information and Software Engineering, UESTC · Electronics and Information Convergence Engineering, KHU · School of Computer Science and Engineering, UESTC +4
Feature Interaction Modeling for Neural Operators
Jul 30, 2026Quan Gu, Xiaoduo Li, Hongxia LiuFeature Interaction Modeling PDE Surrogate Modeling
Independent Researcher · Taiyuan University of Technology
SpectONet: A Physics-Guided Spectral Deep Operator Network for Euler-Bernoulli Beam Dynamics
Jul 28, 2026Shivani Saini, Ramesh Kumar Vats, Arup Kumar SahooStructural Mechanics PDE Operator Learning
Department of Mathematics and Scientific Computing, National Institute of Technology Hamirpur, 177005, Himachal Pradesh, India · The Hatter Department of Marine Technologies, Leon H. Charney School of Marine Sciences, University of Haifa, 3498838, Haifa, Israel
Physics Transformer: Tailoring Transformer for General PDE Prediction
Jul 27, 2026Guoze Sun, Rui Zhang, Jiankai Tang +4Transformer PDE Surrogate Modeling
Gaoling School of Artificial Intelligence, Renmin University of China, Beijing, China · School of Mechanics and Engineering Science, Peking University, Beijing, China
Extending Fourier Neural Operators for Modeling Parameterized and Coupled PDEs
Jul 26, 2026Cheng Jing, Uvini Balasuriya Mudiyanselage, Abhishek Verma +3Fourier Neural Operator PDE Solving
Arizona State University · Applied Materials Inc.
Latent PDE mapping for efficient physics-informed learning across geometries with limited data
Jul 24, 2026Ingvild Askim Adde, Mary M. Maleckar, Gabriel BalabanPDE Operator Learning Physics-Informed ML
Faculty of Health and Technology, Kristiania University of Applied Sciences, Oslo, Norway · Department of Computational Physiology, Simula Research Laboratory, Oslo, Norway
Generalized Neural Operator for Parametric and Boundary-Value Problems
Jul 24, 2026Ruoyan Li, Yizhou Sun, Wei WangEfficient Neural Network Inference PDE Solving
University of California, Los Angeles
Adaptive Mamba Neural Operators
Jul 20, 2026Zeyuan Song, Zheyu JiangPDE Solving PDE Operator Learning
School of Chemical Engineering Oklahoma State University Stillwater, OK 74078, USA
Deep Learning-based Surrogate Modelling of the LOD Method for Multiscale Problems
Jul 14, 2026Marc Haltmayer, Jaemin Seo, Yuseung Lee +3PDE Solving PDE Surrogate Modeling
Department of Artificial Intelligence, Chung-Ang University, 84 Heukseok-ro, Dongjak-gu, Seoul, 06974, Republic of Korea · Computational Science and Engineering Team, Samsung Electronics, 41 Samsung-ro, Giheung-gu, Yongin-si, 17113, Republic of Korea
An Agentic AI Scientific Community for Automated Neural Operator Discovery
Jul 13, 2026Luis Loo, Ulisses Braga-NetoAI Agents for Scientific Discovery LLM Agent Orchestration
Department of Electrical & Computer Engineering Texas A&M University, College Station, TX
PGD-NO: A Neural Operator with Precomputed Geometry Decomposition for 3D Million-scale Physics Simulations
Jul 9, 2026Weiheng Zhong, Jing Bi, Victor Oancea +1PDE Surrogate Modeling PDE Operator Learning
Department of Civil and Environmental Engineering, Grainger College of Engineering, University of Illinois Urbana-Champaign, Urbana, IL, US · Dassault Systemes Americas, Johnston, RI, US · Siebel School of Computing and Data Science, Grainger College of Engineering, University of Illinois Urbana-Champaign, Urbana, IL, US
Reliable mechanistic operator recovery with biologically-informed neural networks: principles for architecture and optimisation design
Jul 8, 2026Rebecca M. Crossley, Yuan Yin, Sarah L. Waters +1Neural Network Optimization Mechanistic Interpretability
Mathematical Institute, University of Oxford, Oxford, United Kingdom, OX2 6GG
Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension
Jul 7, 2026Rüdiger KempfKernel Methods PDE Operator Learning
Applied and Numerical Analysis University of Bayreuth 95440 Bayreuth, Germany
PDEFlow: Autonomous Agentic PDE Pipelines for Neural Operator Learning and Solver-Free Inference
Jul 6, 2026Akshat Jani, Prathamesh Gadekar, Sakhinana Sagar Srinivas +1PDE Solving PDE Surrogate Modeling
Tata Research Development and Design Center, Pune, India 411057

Aug 30, 2026, cs.LGJ/K move · Enter open · S save

Joint Spatiotemporal Spectral Neural Operators for Learning PDEs on Irregular Domains

Abdolmehdi Behroozi, Chaopeng Shen

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

PDE Surrogate Modeling PDE Operator Learning Spectral Methods Neural Operators

Open paper AskPDF arXiv

Learning solution operators for partial differential equations (PDEs) on irregular and geometry-dependent domains remains a central challenge in scientific machine learning. While spectral methods provide strong inductive biases for modeling global interactions, they are typically limited to regular domains, and existing neural approaches often require domain warping, interpolation, or costly geometric embeddings. We introduce the \textbf{Graph Spectral Neural Operator (GSNO)}, a neural operator that combines spatial graph spectral decompositions with temporal Fourier transforms through a unified space--time spectral kernel. This formulation enables globally coherent operator learning on non-Cartesian discretizations without domain warping or autoregressive rollouts. By replacing learned geometric embeddings with a graph Laplacian spectral basis, GSNO provides geometry-aware spectral learning with low parameter complexity. Across steady and unsteady PDE benchmarks on irregular and geometry-dependent domains, GSNO achieves strong accuracy with reduced runtime and parameter counts, while demonstrating robust zero-shot generalization across mesh resolutions and geometry families.

Momentum

Related topics

Latest papers 148