# Discovery of Algebraic Reynolds-Stress Models Using Sparse Symbolic Regression

## TL;DR

This paper introduces SpaRTA, a sparse symbolic regression method that discovers algebraic Reynolds-stress models directly from high-fidelity turbulence data, improving RANS model predictions for complex flows.

## Contribution

The paper presents a novel deterministic symbolic regression approach, SpaRTA, for data-driven turbulence modeling that promotes model sparsity and relaxes traditional assumptions.

## Key findings

- Discovered models outperform standard RANS models in predicting complex flows.
- SpaRTA effectively infers tensor polynomial models from LES/DNS data.
- Models show significant improvement in flow prediction at high Reynolds numbers.

## Abstract

** This article is published (open-access). ** A novel deterministic symbolic regression method SpaRTA (Sparse Regression of Turbulent Stress Anisotropy) 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 $k$-$\omega$ 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.