“…Finally, machine-learning wall models have recently emerged following the development of machine-learning technologies in image classification, speech recognition, natural language processing as well as turbulence simulation and modeling (LeCun et al, 2015; Duraisamy et al, 2019; Brunton et al, 2020). Data-driven wall-stress models were developed and assessed for various incompressible flow configurations, including fully developed wall turbulence and separated turbulent flows (Huang et al, 2019; Yang et al, 2019; Lozano-Durán and Bae, 2020, 2022; Bhaskaran et al, 2021; Radhakrishnan et al, 2021; Zangeneh, 2021; Zhou et al, 2021; Bae and Koumoutsakos, 2022; Dupuy et al, 2023a). For complex configurations, Dupuy et al (2023b) introduced a machine-learning wall model that can directly operate on the unstructured grid of a LES, based on a graph neural network (GNN) architecture (Battaglia et al, 2018; Pfaff et al, 2020; Zhou et al, 2020).…”