Session: 1.2 - Machine Learning, Reduced Order Modeling in CFD and Design Optimization

Paper Number: 157903

157903 - 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. `overfitted’. 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 first demonstrated on two flow classes with known analytical solutions: closure of the  the polymeric stress tensor in Oldroyd-B steady pipe flow and closure of the redistribution tensor for homogenous free shear turbulence.

Presenting Author: Sarah Beetham Oakland University

Presenting Author Biography: