Discovery of Algebraic Reynolds-Stress Models Using Sparse Symbolic Regression

Abstract

A novel deterministic symbolic regression method SpaRTA is introduced to infer algebraic stress models for the closure of RANS equations directly from high-fidelity LES or DNS data. The models are written as tensor polynomials and are built from a library of candidate functions. The machine-learning method is based on elastic net regularisation which promotes sparsity of the inferred models. By being data-driven the method relaxes assumptions commonly made in the process of model development. Model-discovery and cross-validation is performed for three cases of separating flows, i.e. periodic hills (Re=10595), converging-diverging channel (Re=12600) and curved backward-facing step (Re=13700). The predictions of the discovered models are significantly improved over the k-ω SST also for a true prediction of the flow over periodic hills at Re=37000. This study shows a systematic assessment of SpaRTA for rapid machine-learning of robust corrections for standard RANS turbulence models.

Sparse identification of multiphase turbulence closures for coupled fluid–particle flows

“…In Schmelzer et al. (2020) the models are written as tensor polynomials and built from a library of candidate functions. In Beetham & Capecelatro (2020) Galilean invariance of the resulting models are guaranteed through thoughtful tailoring of the feature space.…”

“…Schmelzer, Dwight & Cinnella (2020) and Beetham & Capecelatro (2020) recently extended the sparse identification framework of Brunton et al (2016) to infer algebraic stress models for the closure of RANS equations. In Schmelzer et al (2020) the models are written as tensor polynomials and built from a library of candidate functions. In Beetham & Capecelatro (2020) Galilean invariance of the resulting models are guaranteed through thoughtful tailoring of the feature space.…”

“…In fact, traditional modelling techniques have relied nearly exclusively on this notion. Schmelzer, Dwight & Cinnella (2020) and Beetham & Capecelatro (2020) recently extended the sparse identification framework of Brunton et al (2016) to infer algebraic stress models for the closure of RANS equations. In Schmelzer et al (2020) the models are written as tensor polynomials and built from a library of candidate functions.…”

A perspective on machine learning methods in turbulence modeling

“…From the RANS modeling community, a number of publications on fitting the Reynolds stress tensor (or the discrepancy to existing models) based, for example, on a decomposition into its eigenvectors have been published [68,77,82]. Remarkable achievements have been the incorporation of field inversion techniques to reduce model‐data inconsistencies and the direct embedding of constraints like Galilean invariances into the network [34,40,56].…”

Feature engineering and symbolic regression methods for detecting hidden physics from sparse sensor observation data

“…FFX is influenced by both GP and CS to better distill physical models from data. FFX has been applied to recover hidden physical laws 21 , canonical governing equations 53 and Reynolds stress models for the RANS equations 54 . Some other potential algorithms for deterministic SR are elite bases regression (EBR) 55 and prioritized grammar enumeration (PGE) 56 .…”