Multifidelity Deep Operator Networks For Data-Driven and Physics-Informed Problems
This addresses a bottleneck in modeling complex nonlinear systems like multi-physics systems for researchers and engineers, but it is incremental as it builds on existing DeepONet methods.
The paper tackles the problem of training high-dimensional operator learning models when expensive high-fidelity data is scarce, by introducing a composite Deep Operator Network that leverages both high- and low-fidelity datasets, resulting in improved accuracy for data-driven and physics-informed tasks, as demonstrated in examples like ice-sheet dynamics modeling.
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.