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

## TL;DR

The paper introduces Deep Variational Koopman models that infer distributions over observations for nonlinear systems, enabling uncertainty-aware long-term prediction and control.

## Contribution

It proposes a novel deep variational approach to infer distributions over Koopman observations, enhancing long-term prediction and control under uncertainty.

## Key findings

- Effective long-term prediction across various systems.
- Uncertainty modeling improves control performance.
- Distribution over models captures system variability.

## 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.