Reduced-order modeling using Dynamic Mode Decomposition and Least Angle Regression
This is an incremental improvement for researchers in reduced-order modeling and fluid dynamics, as it offers a parameter-free alternative to an existing method.
The paper tackled the problem of reducing the order of models from Dynamic Mode Decomposition by using Least Angle Regression to select modes, resulting in LARS4DMD, which achieved comparable performance to an existing benchmark method on a Poiseuille flow test problem.
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.