Multifidelity Deep Operator Networks For Data-Driven and Physics-Informed Problems ...

• Main Authors: Howard, Amanda A., Perego, Mauro, Karniadakis, George E., Stinis, Panos
• Format: Text
• Language: unknown
• Published: arXiv 2022
• Subjects: Numerical Analysis math.NA; Machine Learning cs.LG; FOS Mathematics; FOS Computer and information sciences; glacier; Greenland; Humboldt Glacier; Ice Sheet
• Online Access: https://dx.doi.org/10.48550/arxiv.2204.09157; https://arxiv.org/abs/2204.09157

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. ...