Continuous crystallization process control with deep Galerkin method

The aim of the continuous crystallization process control is to produce final product with desirable crystal size distribution (CSD). The evolution of CSD during the process can be obtained by solving the so-called population balance equation (PBE) which governs the dynamic behavior of crystallization processes. As a model, PBE is essentially a nonlinear partial integro-differential equation. The numerical solution of such PBE is a remarkably complicated. With the advances of deep learning, a new type of neural networks called physics informed neural network (PINN), are trained for supervised learning tasks while respecting physics described by general nonlinear partial differential equations has been introduced. In this paper, we use a specific PINN called deep Galerkin method (DGM) to train the neural networks to approximate the solution of the PBE for continuous crystallization process. With the PBE solved by the DGM, we are able to optimize the temperature profile of the process to produce products matching the desired CSD. Simulation experiments are used to prove the feasibility of the proposed method.