  ** 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.
