发表机构
City University of Hong Kong; Shenzhen Research Institute, City University of Hong Kong（香港城市大学; 香港城市大学深圳研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对现有液滴碰撞模型边界确定性的局限，提出基于近四万实验数据的概率符号蒸馏模型，以模糊边界替代突变切换，并优于传统解析模型。
AI 中文摘要
液滴碰撞在许多化学工程过程中（如喷雾干燥、喷雾冷却、农业喷洒和燃烧）控制着液滴群体动力学。现有的解析模型在碰撞结果之间施加确定性的成对边界，而机器学习分类器则缺乏解析碰撞子模型所需的显式函数形式。在本研究中，我们利用近四万个实验事件（涵盖八个状态区间和五个无量纲参数，其中包括超过五千个环境压力高达50 atm的数据）开发了一种概率符号蒸馏模型。一个机器学习教师模型从这些数据中学习联合结果概率分布，随后符号回归将其蒸馏为八个特定类别的表达式，这些表达式共同定义了一个耦合解析模型。所得的解析场将突变的区间切换替换为有限宽度的模糊边界。该模型优于所评估的传统解析边界模型，并揭示其主要局限性在于零宽度边界无法表示渐变的概率过渡。“偏置骰子”采样方案为欧拉-拉格朗日喷雾模拟提供了一种统计上一致且实践上方便的模型实现。
英文摘要
Droplet collision governs droplet population dynamics in many chemical engineering processes, such as spray drying, spray cooling, agricultural spraying, and combustion. Existing analytical models impose deterministic, pairwise boundaries between collision outcomes, whereas machine-learning classifiers lack the explicit functional form required of analytical collision submodels. In this study, we develop a probabilistic symbolic-distillation model using nearly forty thousand experimental events spanning eight regimes and five dimensionless parameters, including over five thousand data for ambient pressure up to 50 atm. A machine-learning teacher learns the joint outcome-probability landscape from these data, and symbolic regression subsequently distils it into eight class-specific expressions that jointly define a coupled analytical model. The resulting analytical field replaces abrupt regime switching with finite-width fuzzy boundaries. It outperforms the evaluated conventional analytical boundary models and reveals that their main limitation is the inability of zero-width boundaries to represent gradual probability transitions. The "biased-dice" sampling scheme provides a statistically consistent and practically convenient model implementation for Eulerian-Lagrangian spray simulation.
Comments32 pages, 13 figures, 2 tables
