Computational and machine learning models for optimising germination under cold stress conditions of common bean with titania ( TiO 2 ) nanoparticles

Common bean ( Phaseolus vulgaris ) is an important edible legume that is sensitive to cold stress, especially at the germination and the seedling stage, leading to low germination and seedling vigour. Application of external stimulants can help to alleviate cold stress in plants at early stages. Titanium dioxide (TiO 2 ) is one of the nanoparticles that can be used for this purpose. In this study, different concentrations of TiO 2 (0, 50, and 100 mg/L) were added to the Murashige and Skoog medium. Surface‐sterilised seeds were cultured on the TiO 2 ‐enriched medium and transferred to 0 and 4°C for 120 and 240 h, then transferred to the growth room, automated at 24°C. The germination data were recorded daily and analysed using the GerminaR package in R. Seven different germination variables named germination percentage (GRP), mean germination time (MGT), mean germination rate (MGR), germination speed, uncertainty (UNC), synchronisation (SYN), coefficient of variation in germination time, seedling vigour, and coefficient of velocity of germination (CVG) were analysed by Taguchi design (TD) and response surface regression analysis (RSRA). Results of the TD revealed temperature, time, and TiO 2 as the most important factors based on the largest signal‐to‐noise ratio. RSRA revealed the impact of TiO 2 , temperature, and TiO 2 × time on GRP. TiO 2 × time was found to be important for MGT and CVG. The UNC factor was also regulated by temp., time, and temp. × times. The multi‐output Random Forest model produced a mean cross‐validated R 2 of 0.718 across the germination metrics, with the highest values recorded for MGT ( R 2 = 0.872) and MGR ( R 2 = 0.755), while comparatively low R 2 scores were recorded for SYN and CVG. This study allows us to understand the germination pattern for common beans under cold stress conditions and can be used for testing other crops.