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. Equation Recast for Canonical Operator Learning Across Parametric PDEs

    Sep 2, 2026Qiyun Cheng, Valentin Duruisseaux, Cesar F. Clauser +7PDE Operator LearningOperator Learning

    1Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA, USA · 2Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA, USA · Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY, USA +1

  2. Learning the Constitutive Behavior of Materials via Neural Operators and Causal Attention: Case Studies in Plasticity and Damage

    Sep 2, 2026Rishabh Arora, Lisa Scheunemann, Tim Brepols +1Causal AttentionNeural Operators

    Institute of Applied Mechanics, RWTH Aachen University, Mies-van-der-Rohe-Str. 1, D-52074 Aachen, Germany · ACCESS e.V., Intzestr. 5, D-52072 Aachen, Germany

  3. Learning with Volterra Neural Networks: A System Theoretic Perspective

    Sep 1, 2026Haoyu Yun, Hamid Krim, Yufang BaoKernel MethodsNeural Operators

    Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, NC, USA · Department of Mathematics and Computer Science, Fayetteville State University, Fayetteville, NC, USA

  4. VATO: A Vortex-Force-Aware Transformer Operator for Unsteady Separated Aerofoil Flows

    Sep 1, 2026Xingxin Yang, Zhan Zhang, Yichen Li +1Transformer Neural OperatorPDE Operator Learning

    aDepartment of Engineering, King’s College London, London, WC2R 2LS, UK

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

    Aug 30, 2026Abdolmehdi Behroozi, Chaopeng ShenPDE Surrogate ModelingPDE Operator Learning

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

  6. Sensitivity-Constrained Neural Operators for Data-Efficient Forward and Inverse Modeling of Partial Differential Equation Systems

    Aug 30, 2026Abdolmehdi Behroozi, Chaopeng Shen, Daniel Kifer +1PDE Surrogate ModelingJacobian Regularization

    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

  7. Conformal Uncertainty Quantification Guarantees for Neural Operators

    Aug 28, 2026Tom Stent, Nicolas BoulléFair Conformal PredictionUncertainty Quantification

    Department of Mathematics Imperial College London London, SW7 2AZ, UK

  8. Euclidean Fourier Neural Operators

    Aug 28, 2026Nathanael Bosch, Niklas Frederik Schmitz, Michael F. HerbstFourier Neural OperatorNeural Operators

    Mathematics for Materials Modelling (MatMat), Institute of Mathematics & Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland

  9. Enforcing Dirichlet Boundary Conditions in Operator Learning

    Aug 27, 2026Andrew M. Stuart, Margaret TrautnerPDE Operator LearningNeural Operators

    Caltech · ETH Zürich Department of Mathematics

  10. Continually learning neural-operator surrogate for three-dimensional airborne electromagnetic Bayesian inversion

    Aug 26, 2026Jaehong Chung, Andrew Lockwood, Jef CaersPDE Surrogate ModelingBayesian Inverse Problems

    Mineral-X, Department of Earth and Planetary Sciences, Stanford University, USA · Xcalibur Smart Mapping, Perth, Australia

  11. A Constitutive Markov Physics-Informed Neural Operator (MPNO) for Autoregressive Stability in Transient Dynamics

    Aug 26, 2026Wenpu Du, Peng Zhou, Yunlong Xia +5PDE Operator LearningPhysics-Informed Neural Operators

    School of Environment and Safety Engineering, North University of China, Taiyuan, 030051, China

  12. Low-Latency Activation-Regularized Sparse Neural Operators with Distillation Assistance Towards Real-Time Neuromorphic Virtual Sensing

    Aug 25, 2026William Howes, Farid Ahmed, Syed Bahauddin AlamActivation SparsityNeuromorphic Computing

    Grainger College of Engineering, Nuclear, Plasma & Radiological Engineering Department, University of Illinois Urbana-Champaign, Urbana, IL, USA · National Center for Supercomputing Applications, Urbana, IL, USA

  13. Inertial Manifold Neural Operator for Dissipative Time-Dependent Partial Differential Equations

    Aug 24, 2026Xiaoyang Xie, Clarence W. RowleyPDE SolvingPDE Operator Learning

    Program in Applied and Computational Mathematics (PACM), Princeton University, Princeton, 08540, New Jersey, United States. · Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, 08540, New Jersey, United States.

  14. Read, Write, Relax: Why Neural PDE Surrogates Need Both Global and Local Processing

    Aug 21, 2026Anuj Kumar, Heiko Zimmermann, Josiah Bjorgaard +4PDE Surrogate ModelingNeural PDE Solvers

    Pasteur Labs, Brooklyn, NY, USA · Cornell University, Ithaca, NY, USA · Institute for Simulation Intelligence, New York, NY, USA

  15. STCO: Conditional Neural Operators for Time-Dependent PDEs

    Aug 20, 2026Xingxin Yang, Zhan Zhang, Juan LiPDE Operator LearningNeural Operators

    Department of Engineering, King’s College London, London, United Kingdom

  16. Shared Physics Responses Recover Hidden Rankings in Neural Operator Libraries

    Aug 20, 2026Hanbing Liang, Fujun LiuModel SelectionNeural Operators

    Nanophotonics and Biophotonics Key Laboratory of Jilin Province, School of Physics, Changchun University of Science and Technology, Changchun 130022, P.R. China

  17. Wrong-Physics Backdoors in Neural PDE Operators

    Aug 20, 2026Hanbing Liang, Fujun LiuBackdoor AttacksData Poisoning Attacks

  18. Multi-stage neural operator learning with application for convolutions

    Aug 19, 2026Zhiping Mao, Zhenye Wen, Yong Zhang +1Operator LearningNeural Operators

    School of Mathematical Sciences, Eastern Institute of Technology, Ningbo, 315200 Ningbo, China · School of Mathematics and Statistics, Wuhan University, 430072 Wuhan, China · Center for Applied Mathematics and KL-AAGDM, Tianjin University, 300072 Tianjin, China +2

  19. GCNO: Gramian Chebyshev Neural Operator for Physics-Based Compression of Wireless Channels

    Aug 19, 2026Rafid Umayer Murshed, Shahab Hamidi-Rad, Elahe Soltanaghai +1Wireless CommunicationsNeural Operators

    Department of Computer Science, University of Illinois Urbana-Champaign · InterDigital AI Lab

  20. Self-supervised In-context Operator Learning for Stochastic Mean-Field Control

    Aug 18, 2026Suyi Gao, Mo Zhou, Rongjie LaiOperator LearningNeural Operators

    Department of Mathematics, Purdue University, West Lafayette, USA · Department of Mathematics, University of California, Los Angeles, USA

  21. MiNO: Cotangent-bundle propagator learning for PDEs

    Aug 15, 2026Gnankan Landry Regis N'guessan, Bum Jun KimPDE Operator LearningPartial Differential Equations

    Axiom Research Group · Department of Applied Mathematics and Computational Science, The Nelson Mandela African Institution of Science and Technology, 404 Nganana, Kikwe, Arumeru, P.O. Box 447, Arusha, 23311, Tanzania · African Institute for Mathematical Sciences, Research and Innovation Centre, KN 3 Road, Gasharu Cell, Kicukiro Sector, Kicukiro District, Kigali, Rwanda +1

  22. From Fixed Grids to Moving Particles:A Transferable Latent Operator for Fluid Dynamics

    Aug 14, 2026Meng Li, Chuqi Chen, Zhengqing Gao +4Neural OperatorsComputational Fluid Dynamics

    Shanghai Artificial Intelligence Laboratory · The Hong Kong University of Science and Technology · University of Michigan +2

  23. Flux-form spatiotemporal neural operators for coarse-grained dynamics of multiscale PDEs

    Aug 11, 2026Junfeng ChenPDE Surrogate ModelingPDE Operator Learning

    Department of Mathematics, The Hong Kong University of Science and Technology, Hong Kong, China

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

    Aug 10, 2026Petr Badolia, Leonid Obukhov, Dmitry Bylinkin +1Dynamical SystemsKuramoto Model

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

  25. 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

  26. ADEx-FNO: A Unified Ambient-Domain Framework for Fourier Neural Operators on Varying Geometries

    Aug 9, 2026Roberto Nuca, Giovanni Testa, Luca Galimberti +1Fourier Neural OperatorPDE 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

  27. Neural Operators for Immersed-Boundary Soft Swimmers Locomotion

    Aug 7, 2026Mohammad Sadegh Eshaghi, Yizheng Wang, Navid Valizadeh +2PDE Surrogate ModelingRobot Locomotion

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

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

    Aug 7, 2026Zhentao Tan, Ruijie Quan, Yi YangPDE Surrogate ModelingPDE Operator Learning

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

  29. A neural operator view on U-Nets for inverse imaging problems

    Aug 6, 2026Alexander Auras, Martin Burger, Samira Kabri +2U-NetNeural Operators

    Computer Vision Group, University of Siegen, Hölderlinstraße 3, 57076 Siegen, Germany · Helmholtz Imaging, Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, Hamburg, 22607, Germany · Fachbereich Mathematik, Universität Hamburg, Bundesstrasse 55, Hamburg, 20146, Germany

  30. 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