Towards an Adaptive Dynamic Mode Decomposition

TL;DR

This paper introduces Adaptive Dynamic Mode Decomposition (ADMD), a novel data-driven modeling approach that employs time delay coordinates, projection, and filtering techniques to improve modeling of complex datasets.

Contribution

The paper presents ADMD, integrating filters like Fourier transform and augmented Lagrangian to enhance DMD's adaptability and effectiveness across diverse data types.

Findings

ADMD effectively reduces data rank and complexity.

It outperforms traditional DMD on various datasets.

Promising results demonstrate its potential for complex data modeling.

Abstract

Dynamic Mode Decomposition (DMD) is a data based modeling tool that identifies a matrix to map a quantity at some time instant to the same quantity in future. We design a new version which we call Adaptive Dynamic Mode Decomposition (ADMD) that utilizes time delay coordinates, projection methods and filters as per the nature of the data to create a model for the available problem. Filters are very effective in reducing the rank of high-dimensional dataset. We have incorporated 'discrete Fourier transform' and 'augmented lagrangian multiplier' as filters in our method. The proposed ADMD is tested on several datasets of varying complexities and its performance appears to be promising.