Deep Variational Koopman Models: Inferring Koopman Observations
for Uncertainty-Aware Dynamics Modeling and Control
Abstract
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