Deep Variational Koopman Models: Inferring Koopman Observations for Uncertainty-Aware Dynamics Modeling and Control
This addresses the challenge of uncertainty-aware dynamics modeling and control for researchers in dynamical systems and machine learning, representing an incremental advancement by combining variational inference with Koopman theory.
The paper tackles the problem of inferring unknown observable functions in Koopman theory for nonlinear dynamical systems, introducing the Deep Variational Koopman (DVK) model to infer distributions over observations for linear propagation, and demonstrates effectiveness in long-term prediction and improved control by accounting for uncertainty.
Koopman theory asserts that a nonlinear dynamical system can be mapped to a linear system, where the Koopman operator advances observations of the state forward in time. However, the observable functions that map states to observations are generally unknown. We introduce the Deep Variational Koopman (DVK) model, a method for inferring distributions over observations that can be propagated linearly in time. By sampling from the inferred distributions, we obtain a distribution over dynamical models, which in turn provides a distribution over possible outcomes as a modeled system advances in time. Experiments show that the DVK model is effective at long-term prediction for a variety of dynamical systems. Furthermore, we describe how to incorporate the learned models into a control framework, and demonstrate that accounting for the uncertainty present in the distribution over dynamical models enables more effective control.