Discovery of Reduced Order Models Using Complexity-Penalized Sparse Regression

Abstract

Identifying fluid mechanical reduced order models that are simple, rooted in physics and computationally tractable has been historically challenging. Although data-driven approaches have become increasingly popular, many of these methods result in models that feature impressive accuracy, but degrees of complexity that make them unlikely to represent a ‘true’ solution and increasingly likely to be ‘over-fitted’. In this work, an alternate methodology to formulate compact, algebraic fluids closures is presented. In this method, sparse regression is applied to ‘trusted data’ to determine a minimal set of basis tensors required to capture relevant physics. The coefficients for each of the tensor bases are postulated through a mathematical classifier and the ideal model is selected by minimizing a cost functional that penalizes both model error and model complexity; here, complexity is measured by a standardized computational cost of the mathematical operations in each model. The methodology is demonstrated in two contexts for closure of the non-Newtonian polymeric stress tensor in Oldroyd-B steady pipe flow: (1) a transport closure for the anisotropic conformation tensor and (2) an algebraic closure of the polymeric stress tensor.