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

arXiv: https://arxiv.org/abs/1902.09742 · HTML: https://mlsanity.com/paper/1902.09742/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Feb 2019.

## Built on by (most cited first, 18 of 18)

- [Generative Modeling of Regular and Irregular Time Series Data via Koopman VAEs](https://mlsanity.com/paper/2310.02619/) (2023)
- [Noisy Recurrent Neural Networks](https://mlsanity.com/paper/2102.04877/) (2021)
- [Koopman Neural Forecaster for Time Series with Temporal Distribution Shifts](https://mlsanity.com/paper/2210.03675/) (2022)
- [Learning continuous models for continuous physics](https://mlsanity.com/paper/2202.08494/) (2022)
- [Koopman Q-learning: Offline Reinforcement Learning via Symmetries of Dynamics](https://mlsanity.com/paper/2111.01365/) (2021)
- [CKNet: A Convolutional Neural Network Based on Koopman Operator for Modeling Latent Dynamics from Pixels](https://mlsanity.com/paper/2102.10205/) (2021)
- [Stochastic Adversarial Koopman Model for Dynamical Systems](https://mlsanity.com/paper/2109.05095/) (2021)
- [A Differential Geometry Perspective on Orthogonal Recurrent Models](https://mlsanity.com/paper/2102.09589/) (2021)
- [Self-Supervised Decomposition, Disentanglement and Prediction of Video Sequences while Interpreting Dynamics: A Koopman Perspective](https://mlsanity.com/paper/2110.00547/) (2021)
- [Physics-Informed Koopman Network](https://mlsanity.com/paper/2211.09419/) (2022)
- [LaPlaSS: Latent Space Planning for Stochastic Systems](https://mlsanity.com/paper/2404.07063/) (2024)
- [Multi-Step Embed to Control: A Novel Deep Learning-based Approach for Surrogate Modelling in Reservoir Simulation](https://mlsanity.com/paper/2409.09920/) (2024)
- [Automated Global Analysis of Experimental Dynamics through Low-Dimensional Linear Embeddings](https://mlsanity.com/paper/2411.00989/) (2024)
- [Learning Predictive Control with Deep Koopman Operators for Autonomous Vehicle Motion Planning](https://mlsanity.com/paper/2606.08136/) (2026)
- [Paradigm Shift Through the Integration of Physical Methodology and Data Science](https://mlsanity.com/paper/2110.01408/) (2021)
- [Reduced-Order Surrogates for Forced Flexible Mesh Coastal-Ocean Models](https://mlsanity.com/paper/2602.05416/) (2026)
- [Making Latent Evolution Explicit: Operator-Structured Transitions for World Action Models](https://mlsanity.com/paper/2608.27259/) (2026)
- [GPU-Accelerated Astrodynamics World Models for Spacecraft Rendezvous and Proximity Operations](https://mlsanity.com/paper/2609.03067/) (2026)

## Abstract (arXiv)

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.