Learned discretizations for passive scalar advection in a two-dimensional turbulent flow

Calculating the evolution of a passive scalar in a turbulent flow requires resolving the intricate stretching and folding of the scalar field. Traditionally, this requires that the computational mesh is much smaller than the smallest scale of the concentration field. Here we demonstrate the use of machine learning to learn discretizations of the governing equation that give accurate computations with a coarser mesh. The model learns the universal small scale structures of the concentration field stretching, allowing it to accurately interpolate with less information.