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

Abstract

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.

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Cited by in corpus (8)

• Review of multi-fidelity models
• A multi-fidelity deep operator network (DeepONet) for fusing simulation and monitoring data: Application to real-time settlement prediction during tunnel construction
• Separable DeepONet: Breaking the Curse of Dimensionality in Physics-Informed Machine Learning
• Self-adaptive weights based on balanced residual decay rate for physics-informed neural networks and deep operator networks
• A multifidelity approach to continual learning for physical systems
• Residual Multi-Fidelity Neural Network Computing
• Transfer Learning on Multi-Dimensional Data: A Novel Approach to Neural Network-Based Surrogate Modeling
• Physics-Informed Time-Integrated DeepONet: Temporal Tangent Space Operator Learning for High-Accuracy Inference