Koopman-based Deep Learning for Nonlinear System Estimation

TL;DR

This paper introduces a novel data-driven linear estimator using Koopman operator theory combined with deep reinforcement learning to predict and adaptively estimate complex nonlinear systems efficiently.

Contribution

It presents a new Koopman-based deep learning framework that improves nonlinear system estimation and prediction, adaptable to transformations without re-learning.

Findings

Effective in modeling complex nonlinear dynamics

Adaptive to system transformations without re-training

Combines Koopman theory with deep reinforcement learning

Abstract

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.