Using machine learning and analytical modelling to predict pharmaceutical breakthrough in biochar columns

Predicting the breakthrough of pharmaceuticals in biochar adsorption systems remains challenging, as adsorption behaviour strongly depends on both biochar characteristics and pharmaceutical properties. In this study, a comprehensive pharmaceutical breakthrough dataset was evaluated using analytical models (modified and unmodified) alongside Machine Learning (ML) approaches. The modified Dose Response, Yoon-Nelson, and Clark models described the breakthrough behaviour of most pharmaceuticals more accurately than their unmodified forms. The prediction performance does, however, remain sensitive to breakthrough complexity and data quality, which could lead to substantial over- or underestimation. ML models, particularly Random Forest and CatBoost, were able to reconstruct compound-specific breakthrough curves. During pointwise selection, models achieved high predictive accuracy. A more rigorous evaluation withheld an entire compound from training (leave-one-compound-out, LOCO), testing the models' ability to extrapolate to an unseen compound. This was supported by the incorporation of pharmaceutical physicochemical properties alongside breakthrough data, allowing the model to capture compound-specific breakthrough behaviour. Overall, ML provides a powerful tool for predicting pharmaceutical breakthrough in biochar systems and, when combined with analytical models, offers strong potential for data-driven prediction of previously uncharacterised compounds. This approach can improve understanding of adsorption processes and reduce the need for extensive experimental testing of biochar columns.