Operator Learning

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Overview

Operator learning models mappings between functions, such as PDE solution maps, dynamical-system evolution, and inverse or control operators. DeepONets, Fourier neural operators, encoder–decoder networks, kernels, and transformers learn these mappings from examples, often aiming to work across different grids, geometries, or input conditions. Current methods increasingly combine multiscale or low-rank representations with physical constraints, uncertainty estimates, and specialized structure for tasks such as fluid prediction and sparse-field reconstruction. A central challenge is making resolution transfer and out-of-distribution predictions reliable: approximation theory and statistical guarantees are advancing, but success depends on the data, regularity, and structure of each problem.

Latest papers

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99 papers19 papers in the last four weeks, up 90% on the four weeks before. 0.1% of all new papers.

  1. A Probabilistic, Rotation-Preserving Kernel Operator Surrogate for Continuum-Robot Design Spaces

    Oct 19, 2026Branden Frieden, Alan Kuntz, Varun ShankarNeural Surrogate ModelingContinuum Robot Design

    The Kahlert School of Computing at the University of Utah, Salt Lake City, UT 84112, USA. · The Departments of Computer Science and Electrical and Computer Engineering at Vanderbilt University, Nashville, TN, 37203, USA.

  2. Toward Online Robust Zero-Sum Markov Games with Function Approximation

    Oct 19, 2026Chenhao Zhou, Jiyu WeiRobust RLZero-Sum Games

    College of Computer Science and Technology, Zhejiang University

  3. Digital Self-Interference Cancellation for In-Band Full-Duplex Systems Based on Transformer Neural Operators

    Oct 14, 2026Zhijie Su, Shiquan Zhang, Qiaolin HeTransformer Neural OperatorWireless Communications

    Department of Mathematics, Sichuan University, Chengdu 610065, China

  4. 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

  5. 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

  6. Learning Operators for Symmetry Discovery: From Lie Groups to Local Symmetry Geometry

    Oct 12, 2026Pavan Karjol, Scindhiya Laxmi, Prathosh APSymmetry DiscoveryOperator Learning

    Department of Electrical Communication Engineering, Indian Institute of Science, Bangalore, India · Department of Mathematics and Computing, IIT (ISM) Dhanbad, India

  7. Physics-informed random neural architectures on compact boundaryless multiply connected manifolds for random-operator models in machine learning and uncertainty quantification

    Oct 10, 2026Christian SoizePhysics-Informed MLUncertainty Quantification

    Université Gustave Eiffel, MSME UMR 8208, 5 bd Descartes, 77454 Marne-la-Vallée, France

  8. Transformer-based In-Context Score Operator Learning for Diffusion Models

    Oct 9, 2026Wuzhe Xu, Zhaiming Shen, Yulong Lu +2Diffusion ModelsIn-Context Learning

    South Dakota State University · Georgia Institute of Technology · University of Minnesota +1

  9. Low-Rank Kolmogorov-Arnold Generator Flows for Interpretable Operator Learning

    Oct 9, 2026Minjong CheonOperator LearningPDE Operator Learning

    Department of Computer Science, Korea National Open University, Seoul, South Korea.

  10. Localized Operator Learning with Adaptive Partition-of-Unity Mixture-of-Expert Networks

    Oct 3, 2026Madison Cooley, Ramansh Sharma, Shandian Zhe +2PDE Operator LearningOperator Learning

    Scientific Computing Institute, University of Utah, Salt Lake City, UT · Kahlert School of Computing, University of Utah, Salt Lake City, UT

  11. Physics is the Best Teacher: Consistency Learning for Time-Invariant Operators of Chaotic Dynamics

    Oct 2, 2026Lufang Chiang, Jiachen Yao, Thomas Y. L. Lin +1Chaotic Time-Series PredictionChaotic Dynamical Systems

    National Taiwan University · California Institute of Technology · University of Washington

  12. Langevin-Informed Transfer Learning: Replacing Target Samples by Black-Box Feedback

    Oct 1, 2026Vladimir R. Kostic, Karim Lounici, Hélène Halconruy +3Latent Dynamics ModelingTransfer Learning

    CSML, Istituto Italiano di Tecnologia · University of Novi Sad · CMAP-Ecole Polytechnique +5

  13. SupraTITO: Transferable Generative Molecular Dynamics for Supramolecular Systems

    Oct 1, 2026Weilong Chen, Nuno Costa, Julija ZavadlavOperator LearningMolecular Dynamics Simulation

    MFM Lab, TUM, Germany · AMC, TUM, Germany

  14. Attention Kernels for Learning Maps Between Heavy-Tailed Measures

    Sep 30, 2026Kailen Hargenrader, Edoardo Calvello, Bohan ChenSoftmax AttentionAttention Mechanisms

    Computing and Mathematical Sciences California Institute of Technology · Lawrence Berkeley National Laboratory University of California, Berkeley ICSI

  15. Fractional Laplace Neural Operators: Exact Architectures, an Expressivity Frontier at Criticality, and Certified Stability for Memory-Driven Network Dynamics

    Sep 30, 2026Mauricio Herrera-MarínOperator LearningNeural Operators

    Facultad de Ingenier´ıa, Universidad del Desarrollo, Santiago, Chile

  16. Super-Resolving Unseen Hyperspectral Sensors at Any Scale via Spatial Operators

    Sep 30, 2026Ji-Xuan He, Guohang Zhuang, Bo Junge +6Hyperspectral Image Super-ResolutionOperator Learning

    Xi’an Jiaotong University · Hefei University of Technology · National University of Singapore +1

  17. Into the danger zone: stable extrapolation in high-dimensional function and operator learning

    Sep 29, 2026Ben Adcock, Simone Brugiapaglia, Xuemeng WangOOD GeneralizationGeneralization Bounds

    Simon Fraser University · Concordia University

  18. Learning Conditional Expectation Operators via Functional Newton Updates

    Sep 28, 2026Thiago Ramos, Alek Fröhlich, Daniel Perazzo +1Density Ratio EstimationLow-Rank Approximation

    Federal University of São Carlos · CSML, Istituto Italiano di Tecnologia and University of Genoa · CSML, Istituto Italiano di Tecnologia and University College London

  19. Universal Approximation of Measure-to-Measure Operators by Pushforwards

    Sep 28, 2026Takashi Furuya, Nicholas H. Nelsen, Frank ColeTransformerUniversal Approximation

    Doshisha University, RIKEN AIP · UT Austin · UCLA

  20. Adapting neural operators for mechanics decisions under changing operating conditions

    Sep 27, 2026Prashant K. Jha, Koffi Enakoutsa, Ian Galloway +1Neural Surrogate ModelingSurrogate-Assisted Optimization

    Department of Mechanical Engineering, South Dakota School of Mines and Technology, Rapid City, SD 57701, USA · Department of Mathematics, University of California, Los Angeles, Los Angeles, CA 90095, USA

  21. Neural Scaling Laws of Transformer Operator Network

    Sep 27, 2026Haoran Yan, Zhongjie Shi, Yuanzhe Xi +2Neural Network GeneralizationNeural Network Approximation Theory

    School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA · Department of Mathematics, Emory University, Atlanta, GA 30322, USA · School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA

  22. Learning in the Transverse Subspace: A Minimal Representation for Divergence-Free Operator Learning

    Sep 27, 2026Yifei SunPDE Operator LearningOperator Learning

  23. Why Directly Learning Periodic Trajectories Can Fail

    Sep 26, 2026Kaixin Zheng, Anita LaytonOperator LearningTrajectory Representation Learning

    University of Waterloo Waterloo, ON, Canada

  24. MENO: Memory-Efficient Neural Operator

    Sep 23, 2026Shengyang Xu, Weijun Zhang, Jun Hu +1PDE Surrogate ModelingPDE Operator Learning

    School of Mathematical Sciences, Peking University, Beijing 100871, China · Chongqing Research Institute of Big Data, Peking University, Chongqing 401329, China · National Engineering Laboratory for Big Data Analysis and Applications, Peking University, Beijing 100871, China

  25. SDC-GON: Singular Decomposition and Consistency-Regularized Green's Operator Networks for Solving Partial Differential Equations

    Sep 19, 2026Yingchao Huang, Xin Wang, Shanshan Yao +2PDE Operator LearningOperator Learning

    Faculty of Digital Innovation, Arts & Sciences, Saskatchewan Polytechnic, Regina SK S4S 5X1, Canada · Civil and Environmental Engineering, University of Alberta, Edmonton AB T6G 2H5, Canada · Energy Systems Engineering, Faculty of Engineering and Applied Science, University of Regina, SK S4S 0A2, Canada +1

  26. Demystifying Linear Operator Learning for Control Systems

    Sep 16, 2026Max Beier, Nicolas Hoischen, Sandra Hirche +1System IdentificationOperator Learning

    Chair of Information-Oriented Control, School of Computation, Information and Technology, Technical University of Munich, 80333 Munich, Germany

  27. Resolution-Independent Analysis of Encoder--Decoder Operator Learning via Limiting Kernels

    Sep 12, 2026Lei Shi, Jia-Qi Yang, Ding-Xuan ZhouOperator LearningKernel Methods

    School of Mathematical Sciences and Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai 200433, China. · School of Mathematics and Statistics, the University of Sydney, Sydney, New South Wales 2006, Australia.

  28. Deep operator learning for efficient sampling from invariant measures of stochastic differential equations

    Sep 10, 2026Ling Guo, Lei Li, Jingtong ZhangStochastic Differential EquationsDiffusion Sampling

    Department of Mathematics, Shanghai Normal University, Shanghai, China · School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, China · Institute of Natural Sciences, MOE-LSC, Shanghai Jiao Tong University, Shanghai, China

  29. 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

  30. The Frame Kernel Method for Multiscale Operator Learning

    Aug 25, 2026Branden Frieden, Ryan Whitehead, M. Keith Ballard +2PDE Surrogate ModelingKernel 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.