Deep Operator Networks

Also known as DeepONet

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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

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

  1. NSPOD: Accelerating Krylov solvers via DeepONet-learned POD subspaces

    May 8, 2026Francesc Levrero-Florencio, Youngkyu Lee, Jay Pathak +1PDE SolvingStructural Mechanics

    Synopsys UK Ltd, UK · Division of Applied Mathematics, Brown University, Rhode Island, USA · Synopsys Inc, California, USA

  2. Learning the Helmholtz equation operator with DeepONet for non-parametric 2D geometries

    May 1, 2026Rodolphe Barlogis, Ferhat Tamssaouet, Quentin Falcoz +1PDE SolvingPDE Operator Learning

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

  3. Conformalized Quantum DeepONet Ensembles: Towards Scalable Operator Learning with Distribution-Free Guarantees

    May 1, 2026Purav Matlia, Christian Moya, Guang LinUncertainty QuantificationHybrid Quantum-Classical ML

    Department of Computer Science Purdue University · Department of Mathematics Purdue University · Department of Mathematics Department of Mechanical Engineering Purdue University

  4. Physics-Guided Dimension Reduction for Simulation-Free Operator Learning of Stiff Differential-Algebraic Systems

    Apr 21, 2026Huy Hoang Le, Haoguang Wang, Christian Moya +2Reduced-Order ModelingDeep Operator Networks

    School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907 USA · Department of Mathematics, Purdue University, West Lafayette, IN 47907 USA · Department of Electrical and Computer Engineering, New Jersey Institute of Technology, Newark, NJ 07102 USA

  5. Learning the Riccati solution operator for time-varying LQR via Deep Operator Networks

    Apr 20, 2026Jun Chen, Umberto Biccari, Junmin WangFeedback ControlDeep Operator Networks

  6. Multi-Head Residual-Gated DeepONet for Coherent Nonlinear Wave Dynamics

    Apr 13, 2026Zhiwei Fan, Yiming Pan, Daniel CocaDeep Operator NetworksNeural Operators

    School of Engineering, Newcastle University, NE1 7RU, United Kingdom · School of Physical Science and Technology, ShanghaiTech University, Shanghai 200031, China

  7. Operator Learning for Predicting Bulk Wave Parameters of Spectral Wave Models

    Apr 7, 2026Shukai Cai, Sourav Dutta, Mark Loveland +4PDE Surrogate ModelingPDE Operator Learning

    Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, 201 E 24th St, Austin, 78712, TX, USA · Information Technology Laboratory, U.S. Army Engineer Research and Development Center, MS, USA · Department of Mechanical Engineering and Technology Management, Norwegian University of Life Sciences, Ås, Norway +1

  8. CoNBONet: Conformalized Neuroscience-inspired Bayesian Operator Network for Reliability Analysis

    Mar 23, 2026Shailesh Garg, Souvik ChakrabortyUncertainty QuantificationBayesian Neural Networks

    Department of Applied Mechanics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India. · Department of Applied Mechanics, Yardi School of Artificial Intelligence (YScAI), Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India.

  9. Direct Interval Propagation Methods using Neural-Network Surrogates for Uncertainty Quantification in Physical Systems Surrogate Model

    Mar 22, 2026Ghifari Adam Faza, Jolan Wauters, Fabio Cuzzolin +2Uncertainty PropagationUncertainty Quantification

    LMSD, Department of Mechanical Engineering, KU Leuven, Heverlee, 3001, Belgium · RAM, Department of Mechanical Engineering, KU Leuven, Brugge, 8200, Belgium · Visual Artificial Intelligence Laboratory, Oxford Brookes University, Oxford, UK +1

  10. A Hybrid Conditional Diffusion-DeepONet Framework for High-Fidelity Stress Prediction in Hyperelastic Materials

    Mar 18, 2026Purna Vindhya Kota, Meer Mehran Rashid, Somdatta Goswami +1Neural Surrogate ModelingHyperelasticity

    Department of Civil and Systems Engineering, Johns Hopkins University, 3400 N. Charles Street, Baltimore, 21218, MD, USA

  11. Translation Invariance of Neural Operators for the FitzHugh-Nagumo Model

    Mar 18, 2026Luca PellegriniFourier Neural OperatorPDE Operator Learning

    Department of Mathematics, University of Pavia, Pavia, Italy · Euler Institute, Faculty of Informatics, Universit`a della Svizzera italiana, Lugano, Switzerland

  12. Topological DeepONets and a generalization of the Chen-Chen operator approximation theorem

    Mar 12, 2026Vugar IsmailovNeural Network Approximation TheoryDeep Operator Networks

  13. Tau-BNO: Brain Neural Operator for Tau Transport Model

    Mar 9, 2026Nuutti Barron, Heng Rao, Urmi Saha +6Neural Surrogate ModelingPDE Surrogate Modeling

    Department of Radiology and Biomedical Imaging, University of California San Francisco, USA · College of Computer Science and Engineering, Northeastern University, China · Department of Computer Science, Wake Forest University, USA +1

  14. Tackling multiphysics problems via finite element-guided physics-informed operator learning

    Mar 2, 2026Yusuke Yamazaki, Reza Najian Asl, Markus Apel +2Multiphysics SimulationPhysics-Informed Neural Operators

    Graduate School of Science and Technology, Keio University, Hiyoshi3-14-1,Kohoku-ku, Yokohama 223-8522, Japan · Chair of Structural Analysis, Technical University of Munich, Arcisstraße 21, 80333 Munich, Germany · ACCESS e.V., Intzestr. 5, 52072 Aachen, Germany +1

  15. Quantum AS-DeepOnet: Quantum Attentive Stacked DeepONet for Solving 2D Evolution Equations

    Feb 28, 2026Hongquan Wang, Hanshu Chen, Ilia Marchevsky +1PDE Operator LearningDeep Operator Networks

    School of Mathematics, Hohai University, Nanjing, Jiangsu 211100, China · College of Mechanics and Engineering Science, Hohai University, Nanjing, Jiangsu 211100, China · Department of Applied Mathematics, Bauman Moscow State Technical University, Moscow 105005, Russia

  16. The Error of Deep Operator Networks Is the Sum of Its Parts: Branch-Trunk and Mode Error Decompositions

    Feb 25, 2026Alexander Heinlein, Johannes TarazDeep Operator NetworksNeural Operators

    Delft Institute of Applied Mathematics, Delft University of Technology, Delft, 2628CD, The Netherlands

  17. Spectral Embedding via Chebyshev Bases for Robust DeepONet Approximation

    Dec 9, 2025Muhammad Abid, Omer SanPDE Surrogate ModelingPDE Operator Learning

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

  18. PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems

    Jul 29, 2025Tiantian Sun, Jian ZuNeural OperatorsDeep Operator Networks

    School of Mathematics and Statistics, Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun 130024, P.R. China

  19. New universal operator approximation theorem for encoder-decoder architectures

    Mar 31, 2025Janek Gödeke, Pascal FernselNeural Network Approximation TheoryDeep Operator Networks

    Center for Industrial Mathematics University of Bremen

  20. From Theory to Application: A Practical Introduction to Neural Operators in Scientific Computing

    Mar 7, 2025Prashant K. JhaNeural Surrogate ModelingFourier Neural Operator

    Department of Mechanical Engineering, South Dakota School of Mines and Technology, Rapid City, SD 57701, USA.

  21. Exponential Convergence of Deep Operator Networks for Elliptic Partial Differential Equations

    Dec 15, 2021Carlo Marcati, Christoph SchwabPDE SolvingPDE Operator Learning

    Seminar for Applied Mathematics, ETH Zurich, Switzerland