Machine learning-enabled multivariate optimization and model-inferred process associations in the co-precipitation...

The co-precipitation synthesis of yttrium oxide (Y₂O₃) nanoparticles involves coupled precursor, acidity, dispersant, and thermal variables. We developed a machine-learning workflow to model average particle size from 30 MaxMin-sampled experiments in a six-dimensional process space. Nine regression algorithms were compared using leave-one-out prediction vectors with Bayesian hyperparameter optimization. The selected support vector regression model gave R² = 0.83, RMSE = 20.82 nm, MAE = 16.63 nm, and MedAE = 15.38 nm. SHAP and LIME identified model-level associations among synthesis variables, while follow-up DLS, zeta-potential, conductivity, FTIR, and TG measurements were consistent with a tentative SDBS/PEG6000 precursor-state regulation hypothesis. Physically constrained virtual screening generated six experimentally tested G2 routes. Their measured particle sizes ranged from 35.4 to 63.2 nm, and one G2-S05 batch yielded phase-pure, quasi-spherical Y₂O₃ nanoparticles with a TEM-derived particle-level size distribution of 35.4 ± 8.3 nm and a BET surface area of 32.79 m²·g^-1. These results establish a proof-of-concept workflow for hypothesis generation and process selection in data-limited oxide synthesis.