用实验数据训练机器学习模型，让喷雾模拟更真实地反映液滴碰撞的随机性。
Data-driven Learning of Probabilistic Model of Binary Droplet Collision for Spray Simulation
- 基于3.35万组实验数据，用LightGBM学习液滴碰撞的非线性规律。
- 模型在8种碰撞模式下准确率达99.2%，过渡区仍保持敏感性。
- 转换为概率形式后可直接用于仿真，适合做喷雾建模的研究者。
液滴二元碰撞在高密度喷雾中普遍存在。传统确定性模型难以刻画碰撞过程中的过渡与随机行为。为此，我们采用机器学习方法——轻量梯度提升机（LightGBM），基于包含33,540个实验案例的综合性数据集进行训练，覆盖了韦伯数、奥内佐格数、撞击参数、尺寸比和环境压力等广泛范围内的八类碰撞模式。所提机器学习分类器在99.2%的准确率下捕捉到高度非线性的区域边界，并在过渡区域保持敏感性。为便于在喷雾模拟中应用，该模型被转化为概率形式的多项式逻辑回归，仍保留93.2%的准确率，并能映射连续的跨区域过渡。进一步引入偏骰子采样机制，将概率结果转化为确定但具有随机性的实际碰撞结果。本工作首次基于实验数据构建了高维、概率化的液滴碰撞模型，提供了一种物理一致、全面且易用的喷雾模拟解决方案。
原文摘要 · Abstract (English)
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.
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