Deep Learning of PDF Turbulence Closure

A new data-driven method is presented for learning the PDF turbulence closure using deep learning. The method is based on a recently developed physics-informed deep learning model and relies on the physics as expressed by partial differential equations. We solve the single-point PDF equation in homogeneous turbulence using deep neural networks to describe the classical binary scalar mixing problem. In this setting, the neural network learns the conditional expected statistics via observing the PDF data. The performance of this data-driven strategy is appraised against the exact solution where the PDF is given by the amplitude mapping closure (AMC) of Kriachnan.