Bi-fidelity Modeling of Uncertain and Partially Unknown Systems using DeepONets
This addresses computational and data acquisition challenges in physics and engineering, but it is incremental as it builds on existing DeepONet methods.
The paper tackles the problem of modeling complex physical systems with limited high-fidelity data by proposing a bi-fidelity approach that uses DeepONets to correct low-fidelity models, demonstrating efficacy through three numerical examples.
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.