Hierarchical cross-scale machine learning for enhanced interpretation and prediction of phosphorus removal by metal...

Phosphorus pollution necessitates advanced water remediation technologies. Metal-oxide materials show significant promise but face complexity arising from interdependent multiscale factors-spanning molecular speciation, material nanostructure, and operational conditions. Conventional machine learning (ML) approaches may suffer from interpretability bias, where macroscopic features disproportionately dominate predictions, obscuring critical nano/molecular-scale mechanisms. To overcome this limitation, we introduce a cross-scale hierarchical ML framework that integrates a mechanism-aware descriptor-the Phosphorus Selectivity Index (PSI)-to explicitly bridge molecular/nanoscale information with operational-scale kinetics. PSI quantitatively captures structure-reactivity relationships between phosphorus species and metal oxide active sites and correlates with DFT adsorption energies (Pearson R = 0.72). Embedding PSI corrects biased interpretation from our basic multi-scale model and improves prediction of phosphorus removal kinetics (log(k)). The cross-scale hierarchical model (CSO model) significantly outperformed the basic multi-scale model (MSO), achieving superior test-set accuracy (R² = 0.77 vs. 0.69 for log(k)), elevating the mechanistic relevance of pore nanostructure, phosphorus functional groups, and quantum descriptors (i.e., E_gap). Independent validations on challenging phosphonates/organophosphate esters showed lower prediction errors with the CSO model than the MSO model. This work establishes a promising cross-scale hierarchical and mechanism-aware ML framework for predictive design of phosphorus-removal materials and accurate rate forecasting, advancing the translation from microscopic insight to engineering practice for water treatment functional materials.