Robust Dynamic Mode Decomposition

TL;DR

This paper introduces a robust dynamic mode decomposition method that enhances statistical and numerical robustness, effectively handling outliers and heavy-tailed distributions in dynamical system data.

Contribution

The proposed RDMD method combines projection statistics and a Schweppe-type Huber estimator for improved robustness and stability in dynamic mode decomposition.

Findings

Outperforms existing methods in numerical simulations

Handles outliers and non-Gaussian noise effectively

Demonstrates better convergence and stability

Abstract

This paper develops a robust dynamic mode decomposition (RDMD) method endowed with statistical and numerical robustness. Statistical robustness ensures estimation efficiency at the Gaussian and non-Gaussian probability distributions, including heavy-tailed distributions. The proposed RDMD is statistically robust because the outliers in the data set are flagged via projection statistics and suppressed using a Schweppe-type Huber generalized maximum-likelihood estimator that minimizes a convex Huber cost function. The latter is solved using the iteratively reweighted least-squares algorithm that is known to exhibit a better convergence property and numerical stability than the Newton algorithms. Several numerical simulations using canonical models of dynamical systems demonstrate the excellent performance of the proposed RDMD method. The results reveal that it outperforms several other methods proposed in the literature.