Stochastic Physics-Informed Neural Networks on Lie Groups for Learning Underwater Vehicle Dynamics

Accurate models of underwater vehicle motion are needed for autonomous execution of marine tasks like infrastructure inspection and scientific sampling. However, such motion is challenging to characterize using traditional physics-based methods. This paper presents a novel data-driven framework for learning stochastic underwater vehicle dynamics. Using Euler-Poincaré dynamics and the geometry of Lie groups, we develop a stochastic physics-informed neural network architecture that respects the physical and geometric constraints of underwater vehicles. Our approach leverages structure-preserving stochastic integration and builds upon moment matching and finite dimensional matching to ensure geometrically-consistent training. We evaluate our approach in simulation and on an underwater vehicle navigating dock pylons in a harbor environment. The results demonstrate that our method learns accurate and robust dynamics models, enabling safe model-based control in challenging marine environments.