Physics-informed learning of dynamical systems and planning of autonomous underwater vehicles

Abstract

Data-driven modeling of a dynamical system has become a fundamental task in many modern science and engineering applications, including physics emulation and robotics control. Although machine learning models provide alternatives to efficiently recognizing complex patterns from data, a main concern in applying them to modeling physical systems stems from their physics-agnostic design, leading to learning methods lacking in interpretability, robustness, generalization, and data efficiency. To mitigate this concern, this thesis studies physics-informed machine learning methods, which integrate prior physical knowledge to enhance model performance. First, we present a Gaussian process model for learning the Helmholtz-Hodge decomposition of dynamical systems, showing how combining certain differential invariants with symmetries allows us to reconstruct system dynamics while extracting interpretable physical features. Then, we develop an optimization framework for learning oceanic flow fields, demonstrating the advantage of leveraging eddy geometry and fluid incompressibility as additional constraints. Finally, we construct a Bayesian parametric model for learning the dynamics of Autonomous Underwater Vehicles (AUVs), with its prior learned from physics-based simulations and posterior updated online. These models of ocean flow fields and AUV dynamics enables us to plan safe and efficient trajectories for AUVs. These algorithms have been validated in simulated environments, illustrating the advantages of physics-informed modeling of dynamical systems for several applications.