Inverse design of comminution process parameters using physics-informed neural operator learning

The comminution of renewable terrestrial resources is a critical step in various industrial processes, from biofuel production to the development of sustainable materials. Traditional methods for predicting comminution outcomes often rely on empirical models that may fall short in capturing the complex dynamic process in comminution. In this talk, I will present a deep learning-assisted comminution model designed to accurately predict the particle size distribution resulting from the comminution of renewable terrestrial resources. Our approach introduces an enhanced Deep Neural Operator (DNO+) model, designed to learn how comminution outcomes are influenced by a parameter space consisting of both manufacturing parameters and material properties. DNO+ significantly extends the engineering applicability of the standard DNO model that only admits feed and outcome particle size distributions. To reduce the reliance of DNO+ on experimental data and enable effective DNO+ training on small experimental datasets, we integrate a transport equation of a population balance model (PBM) into the DNO+ framework, creating a physics-informed enhanced deep learning operator (PIDNO+) model. This integration endows the model with robust predictive capabilities across diverse conditions. By sharing the parameter network in PIDNO+ with the PBM model during optimization and employing physics-constrained symbolic regression, we demonstrate the process of new model discovery for the comminution process from limited training data using physics-informed neural operator learning. Subsequently, the feasibility and efficiency of the new discovered model are validated through testing experimental data obtained in laboratory facilities. Our results show that the PIDNO+ model achieves remarkable accuracy in calibration, establishing its potential as a surrogate model for inverse design of comminution process parameters in renewable terrestrial materials preprocessing.