542 mechanics to build a physics-informed screening framework that accelerates the discovery of selective mineral-processing reagents. 2. OBJECTIVES AND SCOPE This study aims to demonstrate an implementable, industry-relevant workflow for accelerated reagent discovery in mineral processing, using phosphate beneficiation as the primary case study. The objectives are to: (1) develop a physics-informed computational screening framework that integrates AI with quantum-mechanical descriptors to rapidly evaluate and rank candidate reagent molecules for selectivity and performance; (2) target the key separation bottleneck in phosphate processing - improving selectivity against carbonate minerals to enable more efficient flotation and reduce phosphate losses to tailings; (3) incorporate uncertainty-aware modeling using probabilistic machine learning to support risk-informed decisions and to guide where additional simulations or experiments most improve confidence; and (4) translate results into practical outputs for reagent selection, along with a scalable workflow that can be extended to other criticalmineral systems. The framework prioritizes environmentally compatible reagents validated through established flotation development pathways, targeting improvements in reagent efficiency and safety, water consumption, and phosphate product quality. 3. METHODOLOGY OR APPROACH For this study, we constructed a density functional theory (DFT)-derived demonstration dataset of 22 chemically diverse flotation-reagent molecules spanning carboxylic and hydroxamic acids, amines/amides, phosphates, sulfates/sulfonates, (dithio)carbamates, and related chemotypes (neutral and ionic forms, varied chain lengths). For each molecule, we computed key quantum-mechanical descriptors including dipole moment (μ), HOMO–LUMO gap (gap), LUMO energy (lumo), and polarizability (α), and paired these with DFT-calculated adsorption energies (kJ/mol) on two mineral surfaces relevant to phosphate beneficiation: fluorapatite (001) and dolomite (104). Because DFT is expensive, the dataset intentionally represents a realistic low-data regime while remaining sufficiently varied to demonstrate a physics-informed Gaussian Process Regression (GPR) workflow for predicting reagent–mineral interactions. We treat adsorption on fluorapatite (y₁) and dolomite (y₂) as coupled response variables that exhibit a correlation (Figure 1); rather than requiring data-intensive co-kriging (Goovaerts, 1997) (which needs semi-variograms of N!, of N# and their cross-variogram), we use PCA to transform N! and N# into uncorrelated principal components (v₁, v₂), fit GPR models independently in the PC space, and then back-transform predictions (¡¶! and ¡¶#) to obtain ŷ₁ and ŷ₂. Figure 1 summarizes the original response trade-off and the PCA scores, where PC1 captures the dominant trade-off (70% variance) and PC2 captures the remaining orthogonal variation (30%), enabling uncertainty-aware prediction and screening under practical data constraints. Figure 1: Scatterplot between calculated adsorption energies (N!, N#), and removal of linear correlation using PCA.
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