Deep Operator Networks

Also known as DeepONet

Ask about this topic

Overview

Deep Operator Networks (DeepONets) learn operators that map an input function, such as a PDE coefficient or forcing term, to a solution function, typically using a branch network for input measurements and a trunk network for output coordinates. They are used to make repeated simulations faster in settings including fluid flow, materials, waves, and control, with approaches ranging from physics-informed training to spectral embeddings, attention, and localized expert models. Theory provides universal approximation results, while practical evaluations commonly use PDE benchmarks and compare accuracy, inference cost, and generalization across unseen inputs or geometries. A central challenge is that strong performance on familiar data may not transfer to high-frequency inputs, sharp transitions, or new geometries, and accuracy must be balanced against data needs, computational cost, and uncertainty estimates.

Latest papers

CardsList

51 papers4 papers in the last four weeks, level with the four weeks before. 0.0% of all new papers.

  1. HorizON: A Multi-Horizon Deep Operator Network for Property Prediction of Organic Battery Stacks

    Oct 27, 2026Subhash V. S. Ganti, Lukas Woelfel, Arla Diengdoh +4Materials Property PredictionDeep Operator Networks

    University of Bayreuth, Faculty of Engineering Science, Universitätsstraße 30, 95447 Bayreuth, Germany · University of Bayreuth, Bavarian Center for Battery Technology (BayBatt), Universitätsstraße 30, 95447 Bayreuth, Germany · Digital R&D, Covestro Deutschland AG, Kaiser-Wilhelm-Allee 60, 51373 Leverkusen, Germany

  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. The importance of tensor handling and implementation of physics-informed DeepONets

    Oct 15, 2026Nahum Banks, Gustavo A. M. de Almeida, Sergio MaldonadoPhysics-Informed Neural OperatorsPDE Operator Learning

    Faculty of Engineering and Physical Sciences, University of Southampton, Southampton, UK

  4. 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

  5. Spectral Super-Resolution using Spatial-Spectral Residual Operator Networks

    Sep 28, 2026Seokhyun ChinHyperspectral Image Super-ResolutionHyperspectral Imaging

    California Institute of Technology 1200 E California Boulevard, Pasadena, CA, USA

  6. Deep-Learning Solvers and Surrogates for Infinity and p-Laplace Problems

    Sep 25, 2026Tak Shing Au Yeung, Ka Chun Cheung, Hannah Potgieter +2Neural PDE SolversPDE Solving

    NVIDIA AI Technology Center, NVIDIA, Hong Kong, China · Department of Mathematics, Simon Fraser University, Burnaby, British Columbia, Canada · NVIDIA AI Technology Center, NVIDIA, Singapore, Singapore

  7. Disentangling Attention in Deep Operator Learning: A Controlled Study of Data-Driven and Physics-Informed Architectures

    Sep 3, 2026Amar Alem Koric, Qibang Liu, Seid KoricPDE Operator LearningDeep Operator Networks

    Department of Mechanical Engineering, Stanford University, Stanford, CA, 94305, USA · National Center for Supercomputing Applications, University of Illinois at Urbana-Champaign, 1205 W. Clark St., Urbana, IL, 61801, USA · The Grainger College of Engineering, Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, 1206 W. Green St., Urbana, IL, 61801, USA

  8. GenONet: A Generative operator Network for High-Resolution Precipitation Nowcasting

    Sep 1, 2026Mohammad Kian Golkar, Luciano Alves de Oliveira, Mohammad KhanjaniPrecipitation ForecastingSpatiotemporal Forecasting

    University of Illinois Urbana-Champaign · Sharif University of Technology

  9. Reconstruction of 4D Mitral Regurgitation Hemodynamics from Sparse Planar Data using Deep Operator Networks with Test-Time Adaptation

    Aug 31, 2026Jakob Marcel Hoffmann, Yosuke Hasegawa, Alexander Stroh4D ReconstructionSparse-View 3D Reconstruction

    Institute of Fluid Mechanics, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany · Center for Research on Innovative Simulation Software, Institute of Industrial Science, The University of Tokyo, Japan

  10. Spectral-Embedded Operator Learning for Three-Phase Interfacial Flow: A Ternary Cahn-Hilliard-Navier-Stokes Benchmark

    Aug 29, 2026Muhammad Abid, Arth Sojitra, Omer SanPDE Operator LearningDeep Operator Networks

    Department of Mechanical and Aerospace Engineering, University of Tennessee, Knoxville Knoxville, TN 37996, USA.

  11. Quantum SEDONet: Spectrally-Embedded Quantum Deep Operator Networks for Partial Differential Equations

    Aug 27, 2026Muhammad Abid, Arth Sojitra, Bipin Tiwari +1PDE Operator LearningDeep Operator Networks

    Department of Mechanical and Aerospace Engineering University of Tennessee, Knoxville Knoxville, TN 37996, USA

  12. Wrong-Physics Backdoors in Neural PDE Operators

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

  13. Rationally Enriched Chebyshev Trunk Bases for DeepONet Surrogates of High Péclet Entrance Transport

    Aug 20, 2026Mingeun Choi, Satish KumarPDE Surrogate ModelingDeep Operator Networks

    George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, 30332, GA, USA

  14. FAST-DeepONet: Factor-Augmented Branch Representations for High-Dimensional PDE Inputs in the Small-Sample Regime

    Aug 15, 2026Jiyong Kwon, Bongseok Kim, Guang LinPDE Operator LearningDeep Operator Networks

    School of Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, 47907, IN, USA · Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, 47907, IN, USA

  15. Learning Unsteady Aneurysm Hemodynamics with Physics-Informed DeepONets

    Aug 13, 2026Oscar L. Cruz-Gonzalez, Valérie Deplano, Badih GhattasDeep Operator NetworksPhysics-Informed Neural Operators

    Aix Marseille Univ, CNRS, AMSE UMR 7316, Marseille, France · Aix Marseille Univ, CNRS, Centrale Marseille, IRPHE UMR 7342, Marseille, France

  16. Two-Step MV-DeepONet: Probabilistic Operator Learning for Uncertainty Propagation Driven by Random Input Fields

    Aug 10, 2026Yupei Nie, Lei Wang, Jiasen LiuUncertainty QuantificationPDE Surrogate Modeling

    School of Mathematics and Physics, North China Electric Power University, Beijing 102206, P.R. China · School of Energy Power and Mechanical Engineering, North China Electric Power University, Beijing 102206, P.R. China

  17. Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces

    Aug 5, 2026Khemraj Shukla, George Em KarniadakisPDE Operator LearningNeural Network Approximation Theory

    Division of Applied Mathematics, Brown University Providence, Rhode Island 02912, USA

  18. Feature Interaction Modeling for Neural Operators

    Jul 30, 2026Quan Gu, Xiaoduo Li, Hongxia LiuFeature Interaction ModelingPDE Surrogate Modeling

    Independent Researcher · Taiyuan University of Technology

  19. Inverse Learning of Latent Risk-Neutral Densities from Irregular Option Quotes

    Jul 29, 2026Lennon J. Shikhman, Michael Galarnyk, Aadi Dash +1Quantitative FinanceDeep Operator Networks

    College of Computing, Georgia Institute of Technology, USA · College of Engineering, Georgia Institute of Technology, USA · Department of Mathematics and Systems Engineering, Florida Institute of Technology, USA

  20. SpectONet: A Physics-Guided Spectral Deep Operator Network for Euler-Bernoulli Beam Dynamics

    Jul 28, 2026Shivani Saini, Ramesh Kumar Vats, Arup Kumar SahooStructural MechanicsPDE 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

  21. Learning Physics-Informed Surrogate Model of Linear Elastic Displacement Fields from Geometry

    Jul 10, 2026Rodolphe Barlogis, Ferhat Tamssaouet, Quentin Falcoz +1Structural MechanicsPDE Surrogate Modeling

    PROMES-CNRS, Universit´e Perpignan Via Domitia (UPVD), Perpignan, France · LAAS-CNRS, Universit´e de Toulouse (UT), Toulouse, France

  22. Hybrid Least Squares/Gradient Descent Methods for MIONets

    Jul 8, 2026Jun Choi, Chang-Ock Lee, Minam MoonGradient DescentNeural Network Optimization

    Department of Mathematical Sciences, KAIST, Daejeon 34141, KOREA · Department of Mathematics, Korea Military Academy, Seoul 01805, KOREA

  23. Adaptive Distance-Aware Trunk Deep Operator Learning for Long-Span Roadway Bridges

    Jun 18, 2026Bilal Ahmed, Diab W. Abueidda, Waleed El-Sekelly +2Deep Operator Networks

    Civil and Urban Engineering Department, New York University Abu Dhabi, United Arab Emirates · New York University Abu Dhabi, United Arab Emirates · Department of Structural Engineering, Mansoura University, Mansoura, Egypt

  24. 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

  25. Smooth Piecewise Cutting for Neural Operator to Handle Discontinuities and Sharp Transitions

    May 19, 2026Ha Dang, Sebastian Schmidt, Juergen HesserPDE Operator LearningDeep Operator Networks

    Mannheim Institute for Intelligent Systems in Medicine, Heidelberg University · Interdisciplinary Center for Scientific Computing (IWR), Heidelberg University · Heidelberg Institute for Theoretical Studies (HITS), Heidelberg University +2

  26. Neural Operators for Design-Space Surrogate Modeling of Tendon-Actuated Continuum Robots

    May 18, 2026Branden Frieden, James M. Ferguson, Alan Kuntz +1Tendon-Driven ActuationFourier Neural Operator

    The Robotics Center and 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.

  27. Diffusion-Based Stochastic Operator Networks for Uncertainty Quantification in Stochastic Partial Differential Equations

    May 16, 2026Phuoc-Toan Huynh, Richard Archibald, Feng BaoUncertainty QuantificationStochastic PDEs

    Department of Mathematics, Florida State University, Tallahassee, FL, USA · Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA

  28. fPINN-DeepONet: A Physics-Informed Operator Learning Framework for Multi-term Time-fractional Mixed Diffusion-wave Equations

    May 15, 2026Binghang Lu, Zhaopeng Hao, Christian Moya +1PDE SolvingDeep Operator Networks

    Department of Mathematics, Purdue University West Lafayette, IN 47907, USA · School of Mechanical Engineering, Purdue University West Lafayette, IN 47907, USA

  29. A numerical study into neural network surrogate model performance for uncertainty propagation

    May 15, 2026Noah Wade, Kirubel TeferraNeural Surrogate ModelingUncertainty Quantification

    ASEE Postdoctoral Associate, U.S. Naval Research Laboratory, Washington, DC, 20375, USA · U.S. Naval Research Laboratory, Washington, 20375, DC, USA

  30. Frequency Bias and OOD Generalization in Neural Operators under a Variable-Coefficient Wave Equation

    May 13, 2026Runlong Xie, An LuoFourier Neural OperatorPDE Solving

    Independent Researcher · School of Statistics, University of Minnesota, MN, USA.