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Volume 115
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Prediction of immersion mill performance and energy use via machine learning (Open Access)
Daniel Weston a b *, Li Liu b, Christopher Windows-Yule a
a School of Chemical Engineering, University of Birmingham, Birmingham, B15 2TT, UK
b Johnson Matthey Technology Centre, P.O. Box 1, Belasis Avenue, Billingham, TS23 1LB, UK
10.1016/j.partic.2026.05.023
Volume 115, August 2026, Pages 336-355
Received 30 January 2026, Revised 6 May 2026, Accepted 29 May 2026, Available online 10 June 2026, Version of Record 19 June 2026.
E-mail: dtw545@student.bham.ac.uk
Highlights

• Symbolic regression predicted immersion mill performance with a sparse dataset.

• The generated equations provided interpretable rules for process optimisation.

• This approach minimised energy use whilst achieving a target particle size.


Abstract

This study performs a comparative assessment of three Machine Learning (ML) models to determine their robustness in data-sparse industrial environments for predicting and optimising the performance and energy consumption of an immersion mill. By employing active learning strategies that target high-variance regions in process space, a limited experimental dataset (15 batches) was found sufficient to accurately predict mill performance, provided the correct model architecture is chosen. Three models were used: Random Forest Regression (RFR), Gradient Boosted Trees (GBT) and Symbolic Regression (SR). Based on performance when used on completely unseen data, as well as interpretability and usability, the SR models were found to be the most effective for this application. The simple algebraic form of the SR models allowed for direct use in exploring ‘what-if’ scenarios, and equally allowed either model to serve as a constraint for the other to minimise energy use to achieve a target particle size. An unexpected finding during this work was that the relationship between final particle size and impeller speed and grinding media content is weaker than for classic vertical stirred mill designs owing to transport and/or mixing mechanisms novel to this particular mill design. The result of this study is a set of predictive models that can be used in optimising the immersion milling process, and effectively responding to changes in feed Particle Size Distribution (PSD) whilst minimising energy use.

Graphical abstract
Keywords
Machine learning; Wet milling; Prediction; Optimisation
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