Droplet coalescence in microchannels is a complex phenomenon influenced by various parameters such as droplet size, velocity, liquid surface tension, and droplet-droplet spacing. In this study, we thoroughly investigate the impact of these control parameters on droplet coalescence dynamics within a sudden expansion microchannel using two distinct numerical methods. Initially, we employ the boundary element method to solve the Brinkman integral equation, providing detailed insights into the underlying physics of droplet coalescence. Furthermore, we integrate Response Surface Methodology (RSM) to effectively optimize droplet coalescence dynamics, harnessing the power of machine learning algorithms. Our results showcase the efficacy of these computational techniques in enhancing experimental efficiency. Through rigorous evaluation utilizing Regression Coefficient and Mean Absolute Error metrics, we ascertain the accuracy of our estimations. Our findings highlight the significant influence of key parameters, specifically the non-dimensional initial distance of the droplets (D), viscosity ratio (