A survey of machine learning wall models for large eddy simulation

This survey investigates wall modeling in large eddy simulations (LES) using data-driven machine learning (ML) techniques. To this end, we implement three ML wall models in an open-source code and compare their performances with the equilibrium wall model in LES of half-channel flow at eleven friction Reynolds numbers between $180$ and $10^{10}$. The three models have ''seen'' flows at only a few Reynolds numbers. We test if these ML wall models can extrapolate to unseen Reynolds numbers. Among the three models, two are supervised ML models, and one is a reinforcement learning ML model. The two supervised ML models are trained against direct numerical simulation (DNS) data, whereas the reinforcement learning ML model is trained in the context of a wall-modeled LES with no access to high-fidelity data. The two supervised ML models capture the law of the wall at both seen and unseen Reynolds numbers--although one model requires re-training and predicts a smaller von K\'arm\'an constant. The reinforcement learning model captures the law of the wall reasonably well but has errors at both low ($Re_\tau<10^3$) and high Reynolds numbers ($Re_\tau>10^6$). In addition to documenting the results, we try to ''understand'' why the ML models behave the way they behave. Analysis shows that the errors of the supervised ML model is a result of the network design and the errors in the reinforcement learning model arise due to the present choice of the ''states'' and the mismatch between the neutral line and the line separating the action map. In all, we see promises in data-driven machine learning models