Integrating plant growth-promoting rhizobacteria and machine learning for drought tolerance assessment in green bean (Phaseolus vulgaris L.)

Drought stress is one of the most critical constraints limiting crop productivity worldwide, particularly under increasing water scarcity driven by climate change. In this study, the effects of plant growth-promoting rhizobacteria (PGPR) on green bean (Phaseolus vulgaris L.) under varying irrigation regimes were evaluated, and their responses were further analyzed using machine learning (ML) approaches. A greenhouse experiment was conducted using four irrigation levels (I100, I80, I60, and I40) and three bacterial treatments, including Stenotrophomonas rhizophila EU.2B33 (R2), Bacillus marisflavi EU.18 (R1), and their combination (R3). Severe water deficit (I40) reduced shoot and root biomass by approximately 40% compared to full irrigation. However, PGPR applications significantly mitigated these effects, with S. rhizophila EU.2B33 (R2) producing the highest shoot fresh weight (68.03 g), representing an increase of approximately 20% compared to the control. Chlorophyll content declined markedly under drought stress, whereas PGPR treatments increased total chlorophyll levels by more than 80% under moderate stress conditions (I60). The most pronounced PGPR-mediated improvements were observed under moderate water deficit (I60–I80), while effects under severe stress (I40) were present but comparatively limited. In addition, PGPR applications reduced oxidative stress indicators, including hydrogen peroxide (H₂O₂) and malondialdehyde (MDA), and decreased membrane damage. To better capture nonlinear relationships among treatments and plant responses, multilayer perceptron neural network (MLPNN) and generalized regression neural network (GRNN) models were developed. GRNN demonstrated superior predictive performance for stress-related traits, achieving up to R 2 = 0.87 for catalase activity, whereas MLPNN performed better for more stable traits such as carotenoids (R 2 = 0.89).The integration of PGPR-based treatments and machine learning provides a robust framework for improving drought tolerance assessment and optimizing sustainable crop management under water-limited conditions.