mlsanityData to 7 Oct 2026

Bi-fidelity Modeling of Uncertain and Partially Unknown Systems using DeepONets

arXiv 2204.00997 ↗First posted 3 Apr 2022stat.ML cs.LGcited by 27

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Abstract (arXiv)

Recent advances in modeling large-scale complex physical systems have shifted research focuses towards data-driven techniques. However, generating datasets by simulating complex systems can require significant computational resources. Similarly, acquiring experimental datasets can prove difficult as well. For these systems, often computationally inexpensive, but in general inaccurate, models, known as the low-fidelity models, are available. In this paper, we propose a bi-fidelity modeling approach for complex physical systems, where we model the discrepancy between the true system's response and low-fidelity response in the presence of a small training dataset from the true system's response using a deep operator network (DeepONet), a neural network architecture suitable for approximating nonlinear operators. We apply the approach to model systems that have parametric uncertainty and are partially unknown. Three numerical examples are used to show the efficacy of the proposed approach to model uncertain and partially unknown complex physical systems.

Key facts. Cited by 27 papers in the map (data through 7 Oct 2026). Builds on 30 of its 73 references that are in the map. First posted on arXiv 3 Apr 2022.

Builds on

30 of 73 references.

References · 30

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  3. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  4. 2015Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)cited by 1,061
  5. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 722
  6. 2016Error bounds for approximations with deep ReLU networkscited by 567
  7. 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 537
  8. 2021Physics-Informed Neural Operator for Learning Partial Differential Equationscited by 516
  9. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 470
  10. 2021Neural Operator: Learning Maps Between Function Spacescited by 413
  11. 2020Multipole Graph Neural Operator for Parametric Partial Differential Equationscited by 343
  12. 2020B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Datacited by 329
18 more
  1. 2019Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Datacited by 261
  2. 2018Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problemscited by 144
  3. 2018Physics-Informed Generative Adversarial Networks for Stochastic Differential Equationscited by 133
  4. 2019Modeling the Dynamics of PDE Systems with Physics-Constrained Deep Auto-Regressive Networkscited by 127
  5. 2018Adversarial Uncertainty Quantification in Physics-Informed Neural Networkscited by 120
  6. 2021A physics-informed variational DeepONet for predicting the crack path in brittle materialscited by 98
  7. 2021Long-time integration of parametric evolution equations with physics-informed DeepONetscited by 87
  8. 2018Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantificationcited by 81
  9. 2021Exponential Convergence of Deep Operator Networks for Elliptic Partial Differential Equationscited by 44
  10. 2021One-shot learning for solution operators of partial differential equationscited by 27
  11. 2020On transfer learning of neural networks using bi-fidelity data for uncertainty propagationcited by 26
  12. 2016Machine Learning-augmented Predictive Modeling of Turbulent Separated Flows over Airfoilscited by 20
  13. 2021Deep neural network enabled corrective source term approach to hybrid analysis and modelingcited by 16
  14. 2021Neural Network Training Using ℓ1-Regularization and Bi-fidelity Datacited by 16
  15. 2021Generalized Joint Probability Density Function Formulation inTurbulent Combustion using DeepONetcited by 8
  16. 2019Topology Optimization under Uncertainty using a Stochastic Gradient-based Approachcited by 6
  17. 2019Bi-fidelity Stochastic Gradient Descent for Structural Optimization under Uncertaintycited by 5
  18. 2020Uncertainty Quantification of Locally Nonlinear Dynamical Systems using Neural Networkscited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 7; 2023: 10; 2024: 5; 2025: 4; 2026: 1.

27 papers.

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  1. 2022Physics-Informed Deep Neural Operator Networkscited by 110
  2. 2022Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transportcited by 92
  3. 2022Learning two-phase microstructure evolution using neural operators and autoencoder architecturescited by 72
  4. 2022Reliable extrapolation of deep neural operators informed by physics or sparse observationscited by 62
  5. 2022Multifidelity Deep Operator Networks For Data-Driven and Physics-Informed Problemscited by 57
  6. 2022SVD Perspectives for Augmenting DeepONet Flexibility and Interpretabilitycited by 35
  7. 2023Stacked networks improve physics-informed training: applications to neural networks and deep operator networkscited by 21
  8. 2023Deep neural operators can serve as accurate surrogates for shape optimization: A case study for airfoilscited by 19
  9. 2023Learning in latent spaces improves the predictive accuracy of deep neural operatorscited by 19
  10. 2024Synergistic Learning with Multi-Task DeepONet for Efficient PDE Problem Solvingcited by 17
  11. 2022Multi-fidelity wavelet neural operator with application to uncertainty quantificationcited by 12
  12. 2023A Multifidelity deep operator network approach to closure for multiscale systemscited by 11
15 more
  1. 2024Multifidelity Kolmogorov-Arnold Networkscited by 9
  2. 2023Feature-adjacent multi-fidelity physics-informed machine learning for partial differential equationscited by 8
  3. 2023PINN surrogate of Li-ion battery models for parameter inference. Part I: Implementation and multi-fidelity hierarchies for the single-particle modelcited by 6
  4. 2023PINN surrogate of Li-ion battery models for parameter inference. Part II: Regularization and application of the pseudo-2D modelcited by 5
  5. 2025Data-Efficient Deep Operator Network for Unsteady Flow: A Multi-Fidelity Approach with Physics-Guided Subsamplingcited by 5
  6. 2023A Physics-Guided Bi-Fidelity Fourier-Featured Operator Learning Framework for Predicting Time Evolution of Drag and Lift Coefficientscited by 4
  7. 2024Multifidelity domain decomposition-based physics-informed neural networks and operators for time-dependent problemscited by 4
  8. 2024Alpha-VI DeepONet: A prior-robust variational Bayesian approach for enhancing DeepONets with uncertainty quantificationcited by 4
  9. 2024Multifidelity linear regression for scientific machine learning from scarce datacited by 3
  10. 2023DON-LSTM: Multi-Resolution Learning with DeepONets and Long Short-Term Memory Neural Networkscited by 1
  11. 2025Bridging quantum and classical computing for partial differential equations through multifidelity machine learningcited by 1
  12. 2026Physics-Informed Laplace Neural Operator for Solving Partial Differential Equationscited by 1
  13. 2023A Bi-fidelity DeepONet Approach for Modeling Uncertain and Degrading Hysteretic Systemscited by 0
  14. 2025Stochastic Subspace Descent Accelerated via Bi-fidelity Line Searchcited by 0
  15. 2025Discretization-independent operator learning for partial differential equationscited by 0