Learning theory for dynamical systems
Speaker: Suddhasattwa Das, Texas Tech University
Date: February 2, 2023
Abstract: The task of modeling and forecasting a dynamical system is one of the oldest problems, and it remains challenging. Broadly, this task has two subtasks: Extracting the full dynamical information from a partial observation, and then explicitly learning the dynamics from this information. These two subtasks can be combined into a single mathematical framework using the language of spaces, maps, and commutations. The framework also unifies two of the most common learning paradigms- delay coordinates and reservoir computing. This framework provides a platform for two other investigations of the reconstructed system- its dynamical stability and the growth of error under iterations. We show that these questions are deeply tied to more fundamental properties of the underlying system related to the behavior of matrix cocycles over the base dynamics, its non-uniform hyperbolic behavior, and the operator-theoretic properties of the dynamics.