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

TL;DR

This paper introduces a bi-fidelity modeling approach using DeepONets to efficiently approximate complex physical systems with uncertainty and partial knowledge, reducing computational costs and improving accuracy.

Contribution

It proposes a novel bi-fidelity DeepONet framework to model discrepancies between low- and high-fidelity data in uncertain, partially unknown systems.

Findings

Effective modeling of uncertain systems demonstrated in three numerical examples.

Significant reduction in computational resources compared to high-fidelity simulations.

Improved accuracy over low-fidelity models in representing true system responses.

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 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.