Data-driven Learning of Probabilistic Model of Binary Droplet Collision for Spray Simulation

Binary droplet collisions are ubiquitous in dense sprays. Traditional deterministic models cannot adequately represent transitional and stochastic behaviors of binary droplet collision. To bridge this gap, we developed a probabilistic model by using a machine learning approach, the Light Gradient-Boosting Machine (LightGBM). The model was trained on a comprehensive dataset of 33,540 experimental cases covering eight collision regimes across broad ranges of Weber number, Ohnesorge number, impact parameter, size ratio, and ambient pressure. The resulting machine learning classifier captures highly nonlinear regime boundaries with 99.2% accuracy and retains sensitivity in transitional regions. To facilitate its implementation in spray simulation, the model was translated into a probabilistic form, a multinomial logistic regression, which preserves 93.2% accuracy and maps continuous inter-regime transitions. A biased-dice sampling mechanism then converts these probabilities into definite yet stochastic outcomes. This work presents the first probabilistic, high-dimensional droplet collision model derived from experimental data, offering a physically consistent, comprehensive, and user-friendly solution for spray simulation.