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. Performance of Neural Operator Baselines on 'The Well' Dataset

    Oct 25, 2026Yash Pincha, Andy Dimnaku, Andrew Chiang +3Neural OperatorsNeural Surrogate Modeling

  2. Beyond Affine Reconstruction: Multi-Resolution Transformer DeepONets for the Radiative Transfer Equation

    Oct 24, 2026Tanguy Azéma, Marc Bocquet, Fatiha Nmira +3PDE Surrogate ModelingDeep Operator Networks

    CEREA, ENPC, EDF R&D, Institut Polytechnique de Paris, Île-de-France, France · EDF R&D, Chatou, France · Research Division, FM, 1165 Boston-Providence Turnpike, Norwood, MA 02062, USA +1

  3. FG-ConvNO: A Geometry-Aware Neural Operator for Propeller CFD Prediction

    Oct 24, 2026Yichen Di, Valentin Duruisseaux, Di Zhou +4Neural OperatorsComputational Fluid Dynamics

    Tsinghua University · California Institute of Technology · University of Tennessee +1

  4. CoPiT: A conditional Position-induced Transformer for aerodynamic field prediction on unstructured meshes

    Oct 23, 2026Junfeng Chen, Yongchen Fan, Zhonghua Qiao +1Transformer Neural OperatorNeural Operators

    Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China · Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China · Department of Mathematics and Shenzhen International Center for Mathematics, Southern University of Science and Technology, Shenzhen 518055, China

  5. RheOPT: Few-Shot Non-Newtonian Flow Prediction via Newtonian Pretraining of RheOFormer

    Oct 22, 2026Maedeh Saberi, Amir Barati Farimani, Safa JamaliNeural OperatorsComputational Fluid Dynamics

    Department of Mechanical and Industrial Engineering, Northeastern University, Boston, Massachusetts 02115, USA · Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA

  6. Planning under Noise with Neural Operators

    Oct 20, 2026Michael Chen, Hong Chul Nam, Xi Deng +1Motion PlanningStochastic Optimal Control

    Computing and Mathematical Sciences, California Institute of Technology · Center for Data Science, New York University

  7. Neural Operator Splitting for Fluid Dynamics in Complex Geometry

    Oct 20, 2026Jianxiang Li, Xi Deng, Hong Chul Nam +1PDE Operator LearningNeural Operators

    New York University

  8. CIS-Transolver: A Cross-Layer Incremental-State Neural Operator for Fine-Scale Automotive Aerodynamic Flow Prediction

    Oct 19, 2026Jianglong Liu, Zhicheng Zhu, Jia Hao +1Neural OperatorsTransformer Neural Operator

    School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China

  9. Spherical Physics-informed Neural Operator with Multi-scale Coupling for Meteorological Downscaling

    Oct 17, 2026Yiqiang Ye, Yichi Wang, Haodi Zhang +5Climate DownscalingPhysics-Informed Neural Operators

    College of Computer and Software Engineering, Shenzhen University, Shenzhen, China · School of Computer Science, Wuhan University, Wuhan, China

  10. Spatons: Spatiotonally Localized Building Blocks for Efficient XR Predistortion

    Oct 17, 2026Mohammadjavad Maheronnaghsh, Sushant Kondguli, Steve Mann +1Neural OperatorsComputational Imaging

    Department of Electrical and Computer Engineering, University of Toronto · Meta Reality Labs · Vector Institute

  11. Constructive Universal Approximation by Infinite-Dimensional Neural Networks via Gaussian-Weighted Ridgelet Transform

    Oct 16, 2026Sho Sonoda, Luca Galimberti, Yuanchao Xu +2Neural Network Approximation TheoryNeural Operators

    RIKEN Center for Advanced Intelligence Project (AIP), Nihonbashi 1-chome Mitsui Building, 1-4-1 Nihonbashi, Chuo-ku, Tokyo 103-0027, Japan · AI tech studio, CyberAgent, Inc., Shibuya Scramble Square, 2-24-12 Shibuya, Shibuya-ku, Tokyo 150-6121, Japan · Department of Mathematics, King’s College London, Strand Building, London, WC2R 2LS, UK +2

  12. Distributed Performance Boosting through Neural Control for Plug-and-Play Networks

    Oct 16, 2026Danilo Saccani, Leonardo Massai, Giancarlo Ferrari-TrecateNeural Network ControlDistributed Control

    Ecole polytechnique federale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland.

  13. Learnable Splines for Unstructured Neural Operators

    Oct 15, 2026Vignesh Gopakumar, Zhuoyuan Wang, Ander Gray +12PDE Operator LearningNeural Operators

    Centre for Artificial Intelligence, University College London · Computing + Mathematical Sciences, Caltech · LIX, École Polytechnique, CNRS, Institut Polytechnique de Paris +2

  14. HRTF Upsampling and Personalization via Neural Operators

    Oct 14, 2026Meenakshi Krishnan, You Zhang, Ramani Duraiswami +1Spatial AudioNeural Operators

    University of Maryland, College Park · Dolby Laboratories, Inc.

  15. Fractional is Better: Learnable Derivative Orders in Neural Operator Learning

    Oct 14, 2026Fares B. Mehouachi, Saif Eddin JabariPDE Operator LearningNeural Operators

    1New York University Abu Dhabi, Abu Dhabi, UAE · 2New York University, New York, NY, USA

  16. A Bregman Proximal Viewpoint on Neural Operators

    Oct 14, 2026Abdel-Rahim Mezidi, Jordan Patracone, Saverio Salzo +4Neural OperatorsFourier Neural Operator

    Université Jean Monnet Saint-Etienne, CNRS, Institut d’Optique Graduate School, Inria, Laboratoire Hubert Curien UMR 5516, F-42023, SAINT-ETIENNE, France · DIAG, Sapienza University of Rome, 00185 Rome, Italy · Computational Statistics and Machine Learning, IIT, Genova, Italy +1

  17. Wong--Zakai Convergence and FNO Learning for Stochastic Volterra Equations

    Oct 13, 2026Wonjae Lee, Jiuk Jang, Hyungbin ParkNeural OperatorsFourier Neural Operator

    InnoCore AI Meta-Scientist Research Group, KAIST, Daejeon 34141, South Korea. · Department of Mathematical Sciences, Seoul National University, Seoul 08826, South Korea. · Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, 1, Gwanak-ro, Gwanak-gu, Seoul 08826, South Korea.

  18. Operator Surrogates

    Oct 13, 2026Christoph Schwab, Josephine Westermann, Jakob ZechSurrogate ModelingOperator Learning

    SAM, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland · IWR, Uni Heidelberg, INF 205, 69120 Heidelberg, Germany

  19. High-fidelity Three-Dimensional Flow Field Reconstruction Driven by Turbulent Fluid Dynamics

    Oct 13, 2026Hanlin Kong, Jianan Wei, Yuntian Chen +2Computational Fluid DynamicsPhysics-Informed ML

    State Key Lab of Brain-Machine Intelligence, Zhejiang University, Hangzhou, Zhejiang, China · Shanghai Innovation Institute, Shanghai, China · Zhejiang Key Laboratory of Industrial Intelligence and Digital Twin, Eastern Institute of Technology, Ningbo, Zhejiang, China +1

  20. Measure Neural Mappings

    Oct 12, 2026Ricardo Baptista, Edoardo Calvello, Bohan Chen +2Operator LearningNeural Operators

    University of Toronto · Lawrence Berkeley National Laboratory · California Institute of Technology +1

  21. SPLICE: Sparse Physics Library Identification and Compositional Expansion

    Oct 12, 2026Lucas Thil, Jesse Read, Guillaume Doquet +1PDE Operator LearningNeural Operators

    LIX, ´Ecole Polytechnique · IRT SystemX · Safran Tech

  22. A physics-coupled graph neural operator for mid-plane six-component stress tensor field prediction in concrete penetration

    Oct 12, 2026Wenpu Du, Peng Zhou, Yunlong Xia +5Graph Neural OperatorsNeural Operators

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

  23. Sampling from Neural Operator Priors to Solve Partial Differential Equations

    Oct 12, 2026Andrew Millard, Joshua Murphy, Zheng ZhaoPDE SolvingPartial Differential Equations

    Department of Computer and Information Science, Linköping University, Sweden. · Department of Political Science, Trinity College Dublin, Ireland.

  24. CLNO: Conservative Local Neural Operator for Compressible Flow Prediction

    Oct 12, 2026Buxuan Wang, Rongzu Li, Qingsong ZouPDE Operator LearningNeural Operators

    School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou, China

  25. Prior or Feedback? What an LLM Uses When Adapting Neural Operators

    Oct 8, 2026Julian Chan, Javier Mora JimenezPartial Differential EquationsLLM Decision-Making

    Compare the Market

  26. F3^3NO: Frequency-Decomposed Finite-Time Flow-map Neural Operators with Cross-Scale Conditioning

    Oct 7, 2026Fan Wu, Cheng Jing, Kookjin LeePDE Operator LearningNeural Operators

    Arizona State University Tempe, AZ

  27. NEMORA: Neural Equivariant Multipole Operators for Long-Range Atomistic Learning

    Oct 7, 2026Jay L. Kaplan, Samuel Varner, Rebecca Willett +1Machine Learning Interatomic PotentialsEquivariant GNNs

    Courant Institute School of Mathematics, Computing, and Data Science, New York University, New York, NY 10012, USA · Department of Chemical and Biomolecular Engineering, Tandon School of Engineering, New York University, Brooklyn, NY 11201, USA · Department of Statistics, The University of Chicago, Chicago, IL 60637, USA +3

  28. Exact SO(3)-Equivariant Isotropic Kernels for Rotation-Robust Neural Dynamics

    Oct 7, 2026Ridham PatelPDE Surrogate ModelingPDE Operator Learning

    Indian Institute of Technology Gandhinagar, Gandhinagar, India

  29. Targeted search shows that random-device testing underestimates worst-case error in a simulated wave-based neural operator

    Oct 5, 2026Samrendra Roy, Jason Yoo, Souvik Chakraborty +1Fourier Neural OperatorUncertainty Quantification

    Department of Nuclear, Plasma, and Radiological Engineering, University of Illinois Urbana-Champaign, Urbana, IL 61801, USA · Department of Applied Mechanics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India · Yardi School of Artificial Intelligence (ScAI), Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India +1

  30. Poisson-GENERIC Neural Operators: Exact Metriplectic Structure in Function Space via Casimir Entropies

    Oct 4, 2026Jason Sulskis, Sathya RaviDynamical SystemsPDE Operator Learning

    Department of Computer Science, University of Illinois at Chicago, Chicago, IL 60607, USA · Also with the Georgia Tech Research Institute, Atlanta, GA, USA.