# Koopman-based Deep Learning for Nonlinear System Estimation

arXiv: https://arxiv.org/abs/2405.00627 · HTML: https://mlsanity.com/paper/2405.00627/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 18 references that are in the map.
- First posted on arXiv 1 May 2024.

## Builds on (most cited first, 7 of 7)

- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systems](https://mlsanity.com/paper/1708.06850/) (2017)
- [On Convergence of Extended Dynamic Mode Decomposition to the Koopman Operator](https://mlsanity.com/paper/1703.04680/) (2017)
- [Diffeomorphically Learning Stable Koopman Operators](https://mlsanity.com/paper/2112.04085/) (2021)
- [Learning the Koopman Eigendecomposition: A Diffeomorphic Approach](https://mlsanity.com/paper/2110.07786/) (2021)
- [Reinforcement learning-based estimation for partial differential equations](https://mlsanity.com/paper/2302.01189/) (2023)
- [Emulation Learning for Neuromimetic Systems](https://mlsanity.com/paper/2305.03196/) (2023)

## Abstract (arXiv)

Nonlinear differential equations are encountered as models of fluid flow, spiking neurons, and many other systems of interest in the real world. Common features of these systems are that their behaviors are difficult to describe exactly and invariably unmodeled dynamics present challenges in making precise predictions. In this paper, we present a novel data-driven linear estimator based on Koopman operator theory to extract meaningful finite-dimensional representations of complex non-linear systems. The Koopman model is used together with deep reinforcement networks that learn the optimal stepwise actions to predict future states of nonlinear systems. Our estimator is also adaptive to a diffeomorphic transformation of the estimated nonlinear system, which enables it to compute optimal state estimates without re-learning.