  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.
