mlsanityData to 7 Oct 2026

Multifidelity Deep Operator Networks For Data-Driven and Physics-Informed Problems

arXiv 2204.09157 ↗First posted 19 Apr 2022math.NA cs.LG cs.NAcited by 57

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Abstract (arXiv)

Operator learning for complex nonlinear systems is increasingly common in modeling multi-physics and multi-scale systems. However, training such high-dimensional operators requires a large amount of expensive, high-fidelity data, either from experiments or simulations. In this work, we present a composite Deep Operator Network (DeepONet) for learning using two datasets with different levels of fidelity to accurately learn complex operators when sufficient high-fidelity data is not available. Additionally, we demonstrate that the presence of low-fidelity data can improve the predictions of physics-informed learning with DeepONets. We demonstrate the new multi-fidelity training in diverse examples, including modeling of the ice-sheet dynamics of the Humboldt glacier, Greenland, using two different fidelity models and also using the same physical model at two different resolutions.

Key facts. Cited by 57 papers in the map (data through 7 Oct 2026). Builds on 17 of its 55 references that are in the map. First posted on arXiv 19 Apr 2022.

Builds on

17 of 55 references.

References · 17

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  2. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  3. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 722
  4. 2017DGM: A deep learning algorithm for solving partial differential equationscited by 674
  5. 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 537
  6. 2020Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanismcited by 231
  7. 2022Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transportcited by 92
  8. 2021Long-time integration of parametric evolution equations with physics-informed DeepONetscited by 87
  9. 2021Improved architectures and training algorithms for deep operator networkscited by 85
  10. 2020Transfer learning based multi-fidelity physics informed deep neural networkcited by 68
  11. 2022Nonlocal Kernel Network (NKN): a Stable and Resolution-Independent Deep Neural Networkcited by 45
  12. 2022Bi-fidelity Modeling of Uncertain and Partially Unknown Systems using DeepONetscited by 27
5 more
  1. 2021Multifidelity Modeling for Physics-Informed Neural Networks (PINNs)cited by 25
  2. 2013A computational framework for infinite-dimensional Bayesian inverse problems: Part II. Stochastic Newton MCMC with application to ice sheet flow inverse problemscited by 19
  3. 2021Transfer Learning on Multi-Fidelity Datacited by 17
  4. 2021Neural Network Training Using ℓ1-Regularization and Bi-fidelity Datacited by 16
  5. 2021Generalized Joint Probability Density Function Formulation inTurbulent Combustion using DeepONetcited by 8

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 5; 2023: 14; 2024: 8; 2025: 15; 2026: 15.

57 papers.

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  1. 2022Physics-Informed Deep Neural Operator Networkscited by 110
  2. 2022Physics-Informed Machine Learning: A Survey on Problems, Methods and Applicationscited by 88
  3. 2022Reliable extrapolation of deep neural operators informed by physics or sparse observationscited by 62
  4. 2024Towards a Foundation Model for Partial Differential Equations: Multi-Operator Learning and Extrapolationcited by 45
  5. 2023Deep Operator Network Approximation Rates for Lipschitz Operatorscited by 24
  6. 2023Stacked networks improve physics-informed training: applications to neural networks and deep operator networkscited by 21
  7. 2024Self-adaptive weights based on balanced residual decay rate for physics-informed neural networks and deep operator networkscited by 20
  8. 2023Deep neural operators can serve as accurate surrogates for shape optimization: A case study for airfoilscited by 19
  9. 2022Multi-fidelity surrogate modeling using long short-term memory networkscited by 18
  10. 2023A DeepONet multi-fidelity approach for residual learning in reduced order modelingcited by 14
  11. 2024Separable DeepONet: Breaking the Curse of Dimensionality in Physics-Informed Machine Learningcited by 14
  12. 2023A multifidelity approach to continual learning for physical systemscited by 13
38 more
  1. 2022Multi-fidelity wavelet neural operator with application to uncertainty quantificationcited by 12
  2. 2023Sound propagation in realistic interactive 3D scenes with parameterized sources using deep neural operatorscited by 12
  3. 2023A Multifidelity deep operator network approach to closure for multiscale systemscited by 11
  4. 2024Multifidelity Kolmogorov-Arnold Networkscited by 9
  5. 2023Efficient kernel surrogates for neural network-based regressioncited by 7
  6. 2023Residual Multi-Fidelity Neural Network Computingcited by 5
  7. 2024Conformalized Prediction of Post-Fault Voltage Trajectories Using Pre-trained and Finetuned Attention-Driven Neural Operatorscited by 5
  8. 2025Data-Efficient Deep Operator Network for Unsteady Flow: A Multi-Fidelity Approach with Physics-Guided Subsamplingcited by 5
  9. 2025Physics-Informed Time-Integrated DeepONet: Temporal Tangent Space Operator Learning for High-Accuracy Inferencecited by 5
  10. 2025Spectral Embedding via Chebyshev Bases for Robust DeepONet Approximationcited by 5
  11. 2023A Physics-Guided Bi-Fidelity Fourier-Featured Operator Learning Framework for Predicting Time Evolution of Drag and Lift Coefficientscited by 4
  12. 2024Multifidelity domain decomposition-based physics-informed neural networks and operators for time-dependent problemscited by 4
  13. 2023Branched Latent Neural Mapscited by 3
  14. 2024Liquid Fourier Latent Dynamics Networks for fast GPU-based numerical simulations in computational cardiologycited by 3
  15. 2025Physics-Informed DeepONet Coupled with FEM for Convective Transport in Porous Media with Sharp Gaussian Sourcescited by 3
  16. 2023Mechanical Characterization and Inverse Design of Stochastic Architected Metamaterials Using Neural Operatorscited by 2
  17. 2025Active Learning with Bayesian Multi-Fidelity Laplace Neural Operators for Oscillatory Parametric PDEscited by 2
  18. 2025Single vs. Multiple Branches in DeepONet and S-DeepONet: Network Architecture Follows Coupling in Multiphysics Systemscited by 2
  19. 2025Assessing the performance of correlation-based multi-fidelity neural emulatorscited by 2
  20. 2026Surrogates for Physics-based and Data-driven Modelling of Parametric Systems: Review and New Perspectivescited by 2
  21. 2023DON-LSTM: Multi-Resolution Learning with DeepONets and Long Short-Term Memory Neural Networkscited by 1
  22. 2024Inpainting Computational Fluid Dynamics with Deep Learningcited by 1
  23. 2025Model-Agnostic Knowledge Guided Correction for Improved Neural Surrogate Rolloutcited by 1
  24. 2025Causal Multi-fidelity Surrogate Forward and Inverse Models for ICF Implosionscited by 1
  25. 2025Bridging quantum and classical computing for partial differential equations through multifidelity machine learningcited by 1
  26. 2026Multi-Fidelity SINDy: Sparse Discovery of Nonlinear Dynamical Systems with Fidelity-Weighted Measurementscited by 1
  27. 2023A Bi-fidelity DeepONet Approach for Modeling Uncertain and Degrading Hysteretic Systemscited by 0
  28. 2025An optimal Petrov-Galerkin framework for operator networkscited by 0
  29. 2025Virtual domain extension for imposing boundary conditions in flow simulation using pre-trained local neural operatorcited by 0
  30. 2025Discretization-independent operator learning for partial differential equationscited by 0
  31. 2025Multimodal Neural Operators for Real-Time Biomechanical Modelling of Traumatic Brain Injurycited by 0
  32. 2025Bifidelity Karhunen-Lo`eve Expansion Surrogate with Active Learning for Random Fieldscited by 0
  33. 2026Multi-fidelity graph-based neural networks architectures to learn Navier-Stokes solutions on non-parametrized 2D domainscited by 0
  34. 2026FilDeep: Learning Large Deformations of Elastic-Plastic Solids with Multi-Fidelity Datacited by 0
  35. 2026The Error of Deep Operator Networks Is the Sum of Its Parts: Branch-Trunk and Mode Error Decompositionscited by 0
  36. 2026Improving the accuracy of physics-informed neural networks via last-layer retrainingcited by 0
  37. 2026pADAM: A Plug-and-Play All-in-One Diffusion Architecture for Multi-Physics Learningcited by 0
  38. 2026Optimization-Embedded Active Multi-Fidelity Surrogate Learning for Multi-Condition Airfoil Shape Optimizationcited by 0

50 most cited of 57 All 57 (JSON)