Reduced-Order Modeling for Dynamic Mode Decomposition Without an Arbitrary Sparsity Parameter

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.