Discovery of viscoelastic constitutive models with complexity-penalized sparse regression

Identifying fluid mechanical constitutive 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. In this talk, we present an alternate methodology to formulate compact, algebraic constitutive models for viscoelastic fluids. 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 for the polymeric stress tensor: steady pipe flow and start-up Poiseuille flow of Oldroyd-B fluids. These validation cases are chosen due to their increasing level of complexity--statistically one- and two-dimensional, respectively. Finally, the methodology is applied to three-dimensional direct numerical simulations of a viscoelastic jet of a FENE-P fluid; the resulting, learned constitutive model is demonstrated in a forward solve and compared with the original training data.