Machine-learning for turbulence and heat-flux model development: A review of challenges associated with distinct physical phenomena and progress to date

This review paper surveys some of the progress made to date in the use of machine learning (ML) for turbulence and heat transfer modeling. We start by identifying the challenges that various flow phenomena pose to closure modeling. These range from the misalignment between the turbulence stress tensor with the strain rates, that cannot be captured by linear stress-strain relationships, to non-constant turbulence Prandtl numbers, the coupling of multiple closures and deterministic unsteadiness, to name a few. We then introduce several machine learning concepts and frameworks for turbulence stress and heat-flux closure modeling, with a focus on model consistency. Various examples are then provided where applications of ML methods have to some degree succeeded at addressing the identified modeling challenges. We close by outlining some of the remaining challenges, in particular around the generalizability of ML-based models. Overall, further advances in ML techniques and availability of high-quality data sets will see this exciting research direction thrive and promises to lead to improved models with a wider range of applicability.