Deep Koopman Learning using Noisy Data

TL;DR

This paper introduces a robust deep Koopman learning framework that effectively approximates system dynamics from noisy data by accounting for measurement noise and updating observable functions, demonstrated on standard benchmarks.

Contribution

It presents a novel deep Koopman approach that handles bounded measurement noise by modifying observable functions, improving robustness and ease of implementation.

Findings

Effective noise mitigation in Koopman learning

Improved accuracy over existing methods

Validated on standard benchmarks

Abstract

This paper proposes a data-driven framework to learn a finite-dimensional approximation of a Koopman operator for approximating the state evolution of a dynamical system under noisy observations. To this end, our proposed solution has two main advantages. First, the proposed method only requires the measurement noise to be bounded. Second, the proposed method modifies the existing deep Koopman operator formulations by characterizing the effect of the measurement noise on the Koopman operator learning and then mitigating it by updating the tunable parameter of the observable functions of the Koopman operator, making it easy to implement. The performance of the proposed method is demonstrated on several standard benchmarks. We then compare the presented method with similar methods proposed in the latest literature on Koopman learning.