# Reduced-order modeling using Dynamic Mode Decomposition and Least Angle Regression

## TL;DR

This paper introduces LARS4DMD, a novel method combining Dynamic Mode Decomposition with Least Angle Regression to efficiently select modes for reduced-order modeling without needing a regularization parameter.

## Contribution

The paper presents LARS4DMD, a new algorithm that integrates LARS with DMD for automatic mode selection, simplifying the process and maintaining performance.

## Key findings

- LARS4DMD achieves comparable accuracy to DMDSP.
- LARS4DMD does not require a regularization parameter.
- Numerical tests on Poiseuille flow validate the method.

## Abstract

Dynamic Mode Decomposition (DMD) yields a linear, approximate model of a system's dynamics that is built from data. We seek to reduce the order of this model by identifying a reduced set of modes that best fit the output. We adopt a model selection algorithm from statistics and machine learning known as Least Angle Regression (LARS). We modify LARS to be complex-valued and utilize LARS to select DMD modes. We refer to the resulting algorithm as Least Angle Regression for Dynamic Mode Decomposition (LARS4DMD). Sparsity-Promoting Dynamic Mode Decomposition (DMDSP), a popular mode-selection algorithm, serves as a benchmark for comparison. Numerical results from a Poiseuille flow test problem show that LARS4DMD yields reduced-order models that have comparable performance to DMDSP. LARS4DMD has the added benefit that the regularization weighting parameter required for DMDSP is not needed.