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.

该研究介绍了 Deep Variational Koopman 模型的方法，可以推断随时间线性传播的观测分布，从而获得动力模型的分布并提供模型系统随时间推进的可能结果分布，同时也将学习的模型应用到控制框架中并表明考虑到分布中存在的不确定性能更好地控制。