Variable projection methods for an optimized dynamic mode decomposition

TL;DR

This paper introduces an optimized dynamic mode decomposition algorithm using variable projection, improving accuracy and noise robustness for unevenly spaced data in dynamical systems analysis.

Contribution

It presents a novel, efficient algorithm for optimized DMD leveraging variable projection, enhancing performance with uneven sampling and noise.

Findings

Less bias in noisy data compared to standard DMD

Effective for synthetic and real dynamical system data

Flexible framework for DMD-based analysis

Abstract

The dynamic mode decomposition (DMD) has become a leading tool for data-driven modeling of dynamical systems, providing a regression framework for fitting linear dynamical models to time-series measurement data. We present a simple algorithm for computing an optimized version of the DMD for data which may be collected at unevenly spaced sample times. By making use of the variable projection method for nonlinear least squares problems, the algorithm is capable of solving the underlying nonlinear optimization problem efficiently. We explore the performance of the algorithm with some numerical examples for synthetic and real data from dynamical systems and find that the resulting decomposition displays less bias in the presence of noise than standard DMD algorithms. Because of the flexibility of the algorithm, we also present some interesting new options for DMD-based analysis.