Operator learning for complex nonlinear systems is increasingly common in modeling multi-physics and multi-scale systems. However, training such high-dimensional operators requires a large amount of expensive, high-fidelity data, either from experiments or simulations. In this work, we present a composite Deep Operator Network (DeepONet) for learning using two datasets with different levels of fidelity to accurately learn complex operators when sufficient high-fidelity data is not available. Additionally, we demonstrate that the presence of low-fidelity data can improve the predictions of physics-informed learning with DeepONets. We demonstrate the new multi-fidelity training in diverse examples, including modeling of the ice-sheet dynamics of the Humboldt glacier, Greenland, using two different fidelity models and also using the same physical model at two different resolutions.
@article{arxiv.2204.09157,
title = {Multifidelity Deep Operator Networks For Data-Driven and Physics-Informed Problems},
author = {Amanda A. Howard and Mauro Perego and George E. Karniadakis and Panos Stinis},
journal= {arXiv preprint arXiv:2204.09157},
year = {2023}
}