  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.
