Bi-fidelity modeling of uncertain and partially unknown systems using DeepONets

Subhayan De, Matthew Reynolds, Malik Hassanaly, Ryan N. King, Alireza Doostan

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

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. 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 a low-fidelity response in the presence of a small training dataset from the true system’s response using a deep operator network, a neural network architecture suitable for approximating nonlinear operators. We apply the approach to 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 physical systems.

Original languageEnglish (US)
Pages (from-to)1251-1267
Number of pages17
JournalComputational Mechanics
Volume71
Issue number6
DOIs
StatePublished - Jun 2023
Externally publishedYes

Keywords

  • Bi-fidelity method
  • Deep operator network
  • Neural network
  • Uncertain system
  • Uncertainty quantification

ASJC Scopus subject areas

  • Computational Mechanics
  • Ocean Engineering
  • Mechanical Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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