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A Bi-fidelity DeepONet Approach for Modeling Uncertain and Degrading Hysteretic Systems

arXiv 2304.12609 ↗First posted 25 Apr 2023stat.ML cs.LGcited by 0

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Abstract (arXiv)

Nonlinear systems, such as with degrading hysteretic behavior, are often encountered in engineering applications. In addition, due to the ubiquitous presence of uncertainty and the modeling of such systems becomes increasingly difficult. On the other hand, datasets from pristine models developed without knowing the nature of the degrading effects can be easily obtained. In this paper, we use datasets from pristine models without considering the degrading effects of hysteretic systems as low-fidelity representations that capture many of the important characteristics of the true system's behavior to train a deep operator network (DeepONet). Three numerical examples are used to show that the proposed use of the DeepONets to model the discrepancies between the low-fidelity model and the true system's response leads to significant improvements in the prediction error in the presence of uncertainty in the model parameters for degrading hysteretic systems.

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References · 31

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  3. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
  4. 2015Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)cited by 1,070
  5. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 734
  6. 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 540
  7. 2021Physics-Informed Neural Operator for Learning Partial Differential Equationscited by 527
  8. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 473
  9. 2021Neural Operator: Learning Maps Between Function Spacescited by 414
  10. 2020Multipole Graph Neural Operator for Parametric Partial Differential Equationscited by 349
  11. 2020B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Datacited by 335
  12. 2019Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Datacited by 262
19 more
  1. 2018Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problemscited by 147
  2. 2018Physics-Informed Generative Adversarial Networks for Stochastic Differential Equationscited by 135
  3. 2019Modeling the Dynamics of PDE Systems with Physics-Constrained Deep Auto-Regressive Networkscited by 129
  4. 2018Adversarial Uncertainty Quantification in Physics-Informed Neural Networkscited by 120
  5. 2021A physics-informed variational DeepONet for predicting the crack path in brittle materialscited by 98
  6. 2022Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transportcited by 92
  7. 2021Long-time integration of parametric evolution equations with physics-informed DeepONetscited by 89
  8. 2018Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantificationcited by 81
  9. 2022Wavelet neural operator: a neural operator for parametric partial differential equationscited by 78
  10. 2022Multifidelity Deep Operator Networks For Data-Driven and Physics-Informed Problemscited by 58
  11. 2021Exponential Convergence of Deep Operator Networks for Elliptic Partial Differential Equationscited by 44
  12. 2021One-shot learning for solution operators of partial differential equationscited by 30
  13. 2022Bi-fidelity Modeling of Uncertain and Partially Unknown Systems using DeepONetscited by 27
  14. 2020On transfer learning of neural networks using bi-fidelity data for uncertainty propagationcited by 26
  15. 2021Deep neural network enabled corrective source term approach to hybrid analysis and modelingcited by 16
  16. 2022Multi-fidelity wavelet neural operator with application to uncertainty quantificationcited by 12
  17. 2023A Multifidelity deep operator network approach to closure for multiscale systemscited by 11
  18. 2019Topology Optimization under Uncertainty using a Stochastic Gradient-based Approachcited by 6
  19. 2020Uncertainty Quantification of Locally Nonlinear Dynamical Systems using Neural Networkscited by 3

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