Machine learning and mathematical modeling for comparative analysis of green-synthesized ZnO nanoparticles as seed nano-priming agents for linseed

L.) is a multipurpose crop valued for its oil, fiber, and nutraceutical properties, but micronutrient deficiencies and low nutrient-use efficiency often limit its productivity. Zinc is essential for plant physiological processes, yet conventional fertilization frequently suffers from poor bioavailability. Nanotechnology-based seed priming offers a promising approach to improve nutrient delivery and crop performance. This study evaluated green-synthesized zinc oxide nanoparticles (ZnO NPs) as seed priming agents in linseed, comparing their effects with those of chemically synthesized ZnO NPs and bulk ZnO. We hypothesized that biogenic ZnO nanoparticles would induce superior agronomic responses compared to chemical and bulk forms, exhibiting dose- and time-dependent (hormetic) effects that can be effectively captured using statistical and machine learning models. Seeds of cultivar 'Yılmaz' were primed with ZnO formulations at 25, 50, and 75 ppm for 1, 2, and 4 h. Experiments under field conditions assessed morphological and yield-related traits. ANOVA and response surface methodology (RSM) were used to analyze treatment effects, while machine learning models, including K-Nearest Neighbors (KNN), Random Forest (RF), Extra Trees, Support Vector Regression (SVR), Extreme Gradient Boosting (XGBoost), Categorical Boosting (CatBoost), and Multi-Layer Perceptron (MLP), modeled nonlinear relationships between nanoparticle treatments and plant traits. Biogenic ZnO nanoparticles significantly enhanced agronomic traits compared with chemical nanoparticles and bulk ZnO. Optimal responses were observed at moderate concentrations (25 ppm) and specific exposure durations, showing a hormetic effect. RSM indicated significant interactions among nanoparticle type, concentration, and priming duration. KNN achieved the highest predictive accuracy (R² = 0.84), and feature analysis identified nanoparticle concentration and exposure time as key factors. These results demonstrate that biogenic ZnO nanoparticle seed priming is a sustainable strategy to improve linseed productivity, highlighting the value of integrating experimental and data-driven approaches in crop research.