Neural Operators

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Overview

Neural operators learn maps from input fields, parameters, or geometries to output fields, often approximating the solution map of a partial differential equation. DeepONet uses branch and trunk networks, Fourier Neural Operators learn interactions in spectral space, and graph and transformer operators handle irregular meshes and complex geometries; physics-informed losses and structure-preserving designs add physical constraints. These models can make repeated simulation, forecasting, and inverse design much faster than running a numerical solver for every case. A central challenge is making predictions reliable across new resolutions, geometries, and physical regimes while preserving stability over long rollouts and matching classical solvers when high accuracy is required.

Latest papers

CardsList

313 papers52 papers in the last four weeks, up 24% on the four weeks before. 0.3% of all new papers.

  1. Spectrally Safe Neural Operator Warm-Starts for Large-Scale Newton Solvers

    Jun 20, 2026Jaemin Oh, Youngkyu Lee, Jerome Darbon +1Spectral RegularizationPDE Solving

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

  2. TF-SNO: Time-Frequency Gated Spectral Neural Operators for Learning Non-Stationary Partial Differential Equations

    Jun 19, 2026Yitian Zhou, Chaoning Zhang, Zhenzhen Huang +8PDE SolvingPDE Operator Learning

    University of Electronic Science and Technology of China Chengdu, China · Institute of Software, Chinese Academy of Sciences Beijing, China · Harbin Institute of Technology Shenzhen, China

  3. ELADO: Elliptic PDE Assessment Datasets for Operator Learning

    Jun 18, 2026Frank Ehebrecht, Toni Scharle, Martin AtzmuellerSynthetic Benchmark GenerationPDE Operator Learning

    Osnabrück University, Semantic Information Systems Group, Osnabrück, Germany · ROSEN Technology and Research Center GmbH, Lingen, Germany · German Research Center for Artificial Intelligence (DFKI), Osnabrück, Germany

  4. Comparative Study of Neural Surrogate Architectures for Autoregressive Prediction of Internal Battery States

    Jun 18, 2026Gihyun Lee, Thorben Menne, Simon Olma +2Neural Surrogate ModelingPDE Surrogate Modeling

    Technische Universität Berlin, Berlin, Germany · IAV GmbH, Berlin, Germany

  5. A fast direct solver based neural network for solving PDEs

    Jun 18, 2026Jashwanth Reddy Kadaru, Vaishnavi GujjulaPDE SolvingPDE Operator Learning

    Department of Computer Science & Engineering, International Institute of Information Technology Bangalore (IIIT-B), India · Department of Data Science and Artificial Intelligence, International Institute of Information Technology Bangalore (IIIT-B), India

  6. ITNet: A Learnable Integral Transform That Subsumes Convolution, Attention, and Recurrence

    Jun 17, 2026Ashim Dhor, Rasel Mondal, Pin-Yu ChenTransformer AttentionConvolutional Neural Networks

    Indian Institute of Science Education and Research Bhopal · IBM Research

  7. Starter-Iterator Neural Operator: A Unified Architecture for High-Fidelity Forward and Inverse PDE Problems

    Jun 16, 2026Kuilin Qin, Lianfang Wang, Xu Sun +4PDE Surrogate ModelingPDE Operator Learning

  8. Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning

    Jun 16, 2026Oriol Vendrell-Gallart, Nima Negarandeh, Ramin BostanabadUncertainty QuantificationPDE Surrogate Modeling

    Department of Mechanical and Aerospace Engineering University of California, Irvine Irvine, CA 92617

  9. Operator Boosting Produces Pareto-Efficient PDE Surrogates

    Jun 16, 2026Lennon J. ShikhmanPDE Surrogate ModelingDeep Operator Networks

    Georgia Institute of Technology College of Computing Atlanta, Georgia, USA

  10. Generalization Guarantees for Multi-Input Neural Operator Learning in Sobolev Spaces

    Jun 16, 2026Yahong Yang, Zecheng Zhang, Wei Zhu +2Neural Network Approximation TheoryOperator Learning

    School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, GA 30332-0160, USA. · Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN 46556, USA. · Department of Mathematics, Hong Kong Baptist University, FSC1202, Fong Shu Chuen Building, Hong Kong Baptist University, Kowloon Tong, Hong Kong.

  11. Factorized Neural Operators Decompose Dynamic and Persistent Responses

    Jun 15, 2026Hao Tang, Yuechen Duan, Jiongyu Zhu +3Mechanistic InterpretabilityPDE Operator Learning

    School of Medicine, University of Dundee, United Kingdom. · School of Data Science, Fudan University, China. · School of Mathematical Sciences, Fudan University, China. +3

  12. PhysGuard: Fisher-Guided Gradient Projection for Sim-to-Real Neural PDE Surrogates

    Jun 15, 2026Changjian Zhou, Junfeng Fang, Negin Yousefpour +3Synthetic-to-Real Domain AdaptationPDE Surrogate Modeling

    Faculty of Engineering and IT, University of Melbourne · School of Computing, National University of Singapore · Artificial Intelligence Research Institute, IFLYTEK Co., Ltd.

  13. Towards Data-Efficient Cross-Device Generalization of Grad-Shafranov Equilibria via Transfer Learning Neural Operator

    Jun 13, 2026Jay Phil Yoo, William Howes, Yashika Ghai +3Transfer LearningPDE Operator Learning

    Grainger College of Engineering, Nuclear, Plasma & Radiological Engineering Department, University of Illinois Urbana-Champaign, Urbana, IL, USA · Fusion Energy Division, Oak Ridge National Lab, Oak Ridge, TN, USA · National Center for Supercomputing Applications, Urbana, IL, USA +2

  14. Zero-shot generalization of transformer neural operators to larger domains

    Jun 12, 2026Armand de Villeroché, Sibo Cheng, Vincent Le Guen +5Transformer Neural OperatorLocal Attention

    CEREA, ENPC, EDF R&D, Institut Polytechnique de Paris, Île-de-France, France · SINCLAIR AI Laboratory, Saclay, Île-de-France, France · EDF R&D, Île-de-France, France +1

  15. A Fixed-Point Neural Operator for Size- and Functional-Transferable Hamiltonian Prediction

    Jun 12, 2026Yunhong Lou, Xihang Yue, Xinran Wei +2Quantum ChemistryMolecular Property Prediction

    1Zhejiang University, Hangzhou, China. · 2Zhongguancun Academy, Beijing, China. · 3Zhongguancun Institute of Artificial Intelligence, Beijing, China.

  16. How Much Memory Do We Need? Adaptive Memory Gate for Neural Operators

    Jun 11, 2026Jihyeon Hur, Yongseok Kwon, Min-Gi Jo +2Memory-Augmented Neural NetworksFourier Neural Operator

    1KAIST, Republic of Korea.

  17. Harness In-Context Operator Learning with Chain of Operators

    Jun 10, 2026Minghui Yang, Ling Guo, Liu YangOOD GeneralizationPDE Operator Learning

    Department of Mathematics, Shanghai Normal University, Shanghai, China · Department of Mathematics, National University of Singapore, Singapore

  18. HAMNO: A Hierarchical Adaptive Multi-scale Neural Operator with Physics-Informed Learning for Dynamical Systems

    Jun 10, 2026Mostafa Bamdad, Mohammad Sadegh Eshaghi, Timon RabczukNeural PDE SolversPhysics-Informed Neural Operators

    Chair of Computational Mechanics, Institute of Structural Mechanics, Bauhaus-Universität Weimar, 99423 Weimar, Germany · Chair of Computational Science and Simulation Technology, Institute of Photonics, Department of Mathematics and Physics, Leibniz University Hannover, 30167 Hannover, Germany

  19. Topological Neural Operators

    Jun 8, 2026Lennart Bastian, Samuel Leventhal, Mustafa Hajij +1PDE Operator LearningNeural Operators

    Imperial College London, UK · University of San Francisco, USA

  20. Geometry-Aware Anisotropic Boundary Correction for Aerodynamic Simulation

    Jun 8, 2026Xin Zhang, Yipeng Huang, Shu Jiang +2Neural OperatorsComputational Fluid Dynamics

    School of Informatics, Xiamen University, Xiamen, China · Institute of Artificial Intelligence, Xiamen University, Xiamen, China

  21. From inverse problems to neural operators: prediction, mechanism, and generalization of data-driven models

    Jun 8, 2026Conor RowanScientific DiscoveryScientific ML

    Aerospace Engineering2026 University of Colorado Boulder 3775 Discovery DriveJun 9 Boulder, CO 80309

  22. Conformal Prediction for Neural Operators: Distribution-Free Uncertainty Quantification in Physics Simulation

    Jun 7, 2026Michael ChinUncertainty QuantificationPDE Surrogate Modeling

    Independent Researcher

  23. GENERIC-FNO: Embedding Energy Conservation and Entropy Production into Fourier Neural Operators

    Jun 6, 2026Jason Sulskis, Sathya RaviFourier Neural OperatorPhysics-Informed Neural Operators

    Department of Computer Science, University of Illinois at Chicago · Applied Systems Laboratory, Systems Integration Division, Georgia Tech Research Institute

  24. Correcting Neural Operator Spectral Bias via Diffusion Posterior Sampling with Sparse Observations

    Jun 2, 2026Niccolò Perrone, Fanny Lehmann, Stefania Fresca +1PDE Surrogate ModelingSpectral Bias

    Université Paris-Saclay, CentraleSupélec, CNRS, ENS Paris-Saclay · Laboratoire de Mécanique Paris-Saclay UMR 9026 · 8-10 rue Joliot Curie, 91190 Gif-sur-Yvette, France +5

  25. Let There Be Light: Reflection, Refraction and Scattering for Neural Operators

    Jun 2, 2026Keke Wu, Yixuan Zhang, Jingrun ChenPDE Operator LearningNeural Operators

    Suzhou Institute for Advanced Research, University of Science and Technology of China, Suzhou 215123, China · School of Artificial Intelligence and Data Science, University of Science and Technology of China, Hefei 230026, China · Suzhou Big Data & AI Research and Engineering Center, Suzhou 215123, China +2

  26. EqGINO: Equivariant Geometry-Informed Fourier Neural Operators for 3D PDEs

    Jun 2, 2026Sungwon Kim, Juho Song, Seungmin Shin +3Fourier Neural OperatorPDE Surrogate Modeling

    Graduate School of Data Science, KAIST, Daejeon, Republic of Korea · Mathematical Sciences, KAIST, Daejeon, Republic of Korea · LG Electronics, Pyeong-taek, Republic of Korea +1

  27. Will Accurate Fields Mislead Photonic Design? FromGlobal Accuracy to Port Readout

    Jun 2, 2026Yitian Zhang, Yonghong chen, Youming Chen +6Neural Surrogate ModelingPhysics-Based Simulation

    Sun Yat-sen University · The Hong Kong University of Science and Technology (Guangzhou)

  28. Spectral Audit of In-Context Operator Networks

    Jun 1, 2026Zhiwei Gao, Liu Yang, George Em KarniadakisPDE Operator LearningOperator Learning

    Division of Applied Mathematics, Brown University, Providence, RI, USA · Department of Mathematics, National University of Singapore, Singapore

  29. Variation Spaces for Encoder--Decoder Neural Operators: Approximation and Generalization

    May 31, 2026Jia-Qi Yang, Lei ShiNeural Network Approximation TheoryOperator Learning

    School of Mathematical Sciences and Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai 200433, China.

  30. Revisiting Neural Processes via Fourier Transform and Volterra Series

    May 31, 2026Peiman Mohseni, Nick Duffield, Raymond K. W. WongNeural ProcessesFrequency-Domain Feature Learning

    Texas A&M University, College Station, Texas, USA.