Multi-head neural networks for simulating particle breakage dynamics

Abstract

The breakage of brittle particulate materials into smaller particles under compressive or impact loads can be modelled as an instantiation of the population balance integro-differential equation. In this paper, the emerging computational science paradigm of physics-informed neural networks is studied for the first time for solving both linear and nonlinear variants of the governing dynamics. Unlike conventional methods, the proposed neural network provides rapid simulations of arbitrarily high resolution in particle size, predicting values on arbitrarily fine grids without the need for model retraining. The network is assigned a simple multi-head architecture tailored to uphold monotonicity of the modelled cumulative distribution function over particle sizes. The method is theoretically analyzed and validated against analytical results before being applied to real-world data of a batch grinding mill. The agreement between laboratory data and numerical simulation encourages the use of physics-informed neural nets for optimal planning and control of industrial comminution processes.

Keywords

• Particle breakage dynamics
• Population balance equation
• Physics-informed neural networks