Reduced-order modeling using Dynamic Mode Decomposition and Least Angle Regression
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.
Cite
@article{arxiv.1905.07027,
title = {Reduced-order modeling using Dynamic Mode Decomposition and Least Angle Regression},
author = {John Graff and Xianzhang Xu and Francis D. Lagor and Tarunraj Singh},
journal= {arXiv preprint arXiv:1905.07027},
year = {2020}
}
Comments
14 pages, 2 Figures, Submitted to AIAA Aviation Conference 2019