Neuroevolving monotonic PINNs for particle breakage analysis

Artificial intelligence has the potential to positively impact various facets of today’s minerals industry. This paper is a first showcase of physics-informed neural networks (PINNs) for simulating the breakage of large particles into smaller fragments in a grinding mill, which is undeniably one of the most energy-intensive phases in the processing of mineral ores. The breakage is governed by a population balance integro-differential equation, whose accurate solution is crucial to support precise planning and control of processes to meet product specifications and sustainability goals. However, solutions derived using existing PINN algorithms, while computationally efficient, are found to violate a basic mathematical property of monotonicity of the modelled cumulative distribution function over particle sizes. This renders the solution of little practical use. Guided by the implicit function theorem, we discover that a synergy of existing techniques with neuroevolutionary algorithms can lead to the desired creation of monotonic PINNs. Real-world data of a batch grinding mill is used to validate our method, establishing PINNs as a powerful tool for simulating particle breakage dynamics.