Deep learning of turbulent scalar mixing

Based on recent developments in physics-informed deep learning and deep hidden physics models, we put forth a framework for discovering turbulence models from scattered and potentially noisy spatiotemporal measurements of the probability density function (PDF). The models are for the conditional expected diffusion and the conditional expected dissipation of a Fickian scalar described by its transported single-point PDF equation. The discovered models are appraised against an exact solution derived by the amplitude mapping closure (AMC)-Johnson-Edgeworth translation (JET) model of binary scalar mixing in homogeneous turbulence.