Probabilistic Symbolic-Distillation Model of Droplet Collision for Spray Simulation at High Ambient Pressures
Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Xu, Weiming, Yang, Tao, Zhang, Peng
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Awards: G3694180948, G4623843887, G58323548
OpenAlex ID: W7214890240