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Physics-Guided Deep Learning for Dynamics Forecasting

Abstract

Modeling complex dynamics is a fundamental task in science, such as turbulence modeling and weather forecasting. Physics-based models, which rely on mathematical principles, can accurately predict dynamics but can be computationally intensive and not fully known. Deep Learning provides efficient alternatives to simulating dynamics but it lacks physical consistency and struggles with generalization. Thus, there is a growing need for integrating prior physics knowledge with deep learning to take the best of both types of approaches to better solve scientific problems. Thus, the study of physics-guided DL emerged and has gained great progress.

In this thesis, we described the physics-guide DL for dynamics forecasting and presented several approaches to improving the physical consistency, accuracy, and generalization of DL models for dynamics forecasting. The approaches include incorporating prior physical knowledge into the design of model architecture and loss functions for improved physical consistency and accuracy, leveraging model-based meta-learning for improved generalization across heterogeneous domains, simplifying nonlinear dynamics with Koopman theory for improved generalization over temporal distributional shifts, and incorporating symmetries into deep dynamics models for improved generalization across relevant symmetry groups and consistency with conservation laws. In the end, we also summarize the challenges in this field and discuss the emerging opportunities for future research.

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