Authors

John Graff, Matthew J. Ringuette, Tarunraj Singh and Francis D. Lagor,

Source

AIAA Journal, 58 (9).

Abstract

Dynamic mode decomposition (DMD) yields a linear, approximate model of a system’s dynamics that is built from data. This paper seeks to reduce the order of this model by identifying a reduced set of modes that best fit the output. A model selection algorithm from statistics and machine learning known as least angle regression (LARS) is adopted. LARS is modified to be complex-valued, and LARS is used to select DMD modes. The resulting algorithm is referred to 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. LARS4DMD has the advantage that the sparsity parameter required for DMDSP is not needed. Numerical results from a Poiseuille flow test problem show that LARS4DMD yields reduced-order models that have comparable performance to DMDSP. Use of the LARS4DMD algorithm on particle image velocimetry data of a rotating fin confirms this conclusion on experimental data. Results further suggest that LARS4DMD may be slightly more robust to noise in the experimental data.

@article{Graff_20_AIAAJ,
author = {J. Graff, M. Ringuette, T. Singh and F. Lagor},
title = {Reduced-Order Modeling for Dynamic Mode Decomposition Without an Arbitrary Sparsity Parameter},
journal = {AIAA Journal},
volume = {58},
number = {9},
year = {2020},
doi = {doi: 10.2514/1.J059207},
eprint = {https://arc.aiaa.org/doi/10.2514/1.J059207}
}