PINN-PBE Model for Describing Gibbsite Crystallization Dynamics

The industrial testing of the optimal control system for the gibbsite precipitation area revealed the cases where the optimizer finds and exploits vulnerabilities in the predictive data-driven model, recommending erroneous control actions. The present paper considers a more robust alternative, i.e., training of neural network models using a first-principle model, known as physics-informed neural network (PINN). To address the problem, the system of population balance equations (PBE) describing the bulk crystallization process was transformed into a linearized form, and a PINN-PBE model was generated, which represents a set of interconnected neural networks approximating the solution of the equation system under the batch conditions.