Fluid mixing optimization with reinforcement learning

Fluid mixing is crucial in various industrial processes. In this study, focusing on the characteristics that reinforcement learning (RL) is suitable for global-in-time optimization, we propose utilizing RL for fluid mixing optimization of passive scalar fields. For the two-dimensional fluid mixing problem described by the advection-diffusion equations, a trained mixer realizes an exponentially fast mixing without any prior knowledge. The stretching and folding by the trained mixer around stagnation points are essential in the optimal mixing process. Furthermore, this study introduces a physically reasonable transfer learning method of the trained mixer: reusing a mixer trained at a certain Péclet number to the mixing problem at another Péclet number. Based on the optimization results of the laminar mixing, we discuss applications of the proposed method to industrial mixing problems, including turbulent mixing.