Deep Learning for Dynamical Systems

Research in machine learning is rapidly branching into the physical sciences, with a particular focus on dynamical systems and control. There are a number of pressing challenges in modern dynamical systems that stand to benefit from these efforts. First, many systems of interest do not have known dynamics, and dynamical systems models must be discovered from data; even systems where we have governing equations, such as turbulence, are too complex to analyze and control, motivating reduced-order models. Second, it is important to discover new coordinate systems where the dynamics are simplified. Third, physical systems often have symmetries and conservation laws that may be enforced in the learning process. In this talk, we will discuss several deep learning approaches to simultaneously discover coordinate transformations and parsimonious models of the dynamics. We will put a premium on models that are generalizable and interpretable, and will demonstrate how to bake in partially known physics. These ideas will be motivated on examples in fluid dynamics.