DL-RSM: Deep learning-integrated response surface methodology for positive and negative-ideal environmental conditions estimation for crop yield

Understanding the most suitable and unsuitable environmental scenarios for crop production is critical to ensuring food security and sustainability. In this direction, the presented work proposes a novel approach, DL-RSM, to identify the optimized levels of environmental factors for wheat yield by integrating the Deep Learning technique with Response Surface Methodology (RSM). The uniqueness of this approach lies in its utilization of a 1-Dimensional Convolutional Neural Network model for response surface modelling. Additionally, the study has investigated the combination of numerical methods-based partial derivative calculation with a deep learning model. Specifically, our approach incorporates a symmetric difference quotient-based method for calculating partial derivatives, ultimately leading to the determination of optimal parameter values. Besides, multiple positive and negative ideal solutions are obtained from the modelled response surface using a modified gradient-based method. The effectiveness of our approach is illustrated through a case study on finding the optimized parameter values for the district-wise wheat yields of the Indo-Gangetic plains of India. The study results demonstrate the combinations of monthly rainfall levels and min. and max. temperature variations correspond to maximising and minimising wheat yield in the target region. The presented results provide significant insights into the relationship between wheat yields and the considered environmental factors that have not been sufficiently covered in the existing literature. The proposed methodology can benefit agricultural scientists, policymakers and farmers by offering an innovative approach to maximize crop yield and minimize resource utilization. Moreover, the study findings provide novel insights into the development of similar optimization strategies for other crops and systems.