A Novel Framework for Droplet/Particle Size Distribution in Suspension Polymerization Using Physics-Informed Neural Network (PINN)

Abstract

A Machine Learning (ML) based neural network can capture the complex evolution of polymer chain distributions, accounting for factors such as initiation, propagation, and termination steps in a suspension polymerization process, by integrating stagewise molar balance model (MBM) and population balance model (PBM) with Physics-Informed Neural Network (PINN). The integrated PINN framework is proposed to efficiently solve these equations, incorporating known physical laws as constraints and minimizing errors in both the distribution and dynamics of the polymer chains. By optimizing the neural network parameters such as weight matrices and bias vector, the model reproduces the moments of the polymer molecular weight distribution in close alignment with numerical solutions, and it generates population balance solutions that exhibit excellent agreement with their analytical counterparts. Sensitivity analyses for the depth of the neural network architecture to quantify how structural choices affect model fidelity has been performed. The resulting MBM-PINN and PBM-PINN integrated framework demonstrates robustness and versatility in accurately capturing (96-97%) droplet/particle dynamics. The proposed methodology has the capability to provide a powerful tool for faster and scalable simulations of polymerization reactions, enabling better prediction of product properties which could be used for optimizing reaction conditions in industrial applications.