Probabilistic Symbolic-Distillation Model of Droplet Collision for Spray Simulation at High Ambient Pressures
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.
Related
- Conditional Error Exponents of Probabilistic Quantum Resource Distillation
- Simulation of quantum entangled states by classical probabilistic models
- Gate-Based Quantum Simulation of Finite-Temperature Open-System Dynamics: A Post-Processing Reconstruction Approach for Collision Models
- Efficient fidelity simulation of high-rate magic distillation circuits
- Probabilistic Simulation of Gas-Liquid Interfaces with Coupled Flow Matching on Spherical Harmonics
BibTeX
@misc{xu2026probabilistic,
title = {{Probabilistic Symbolic-Distillation Model of Droplet Collision for Spray Simulation at High Ambient Pressures}},
author = {Weiming Xu and Tao Yang and Peng Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37202},
eprint = {2609.37202},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37202},
}
RIS
TY - UNPB
TI - Probabilistic Symbolic-Distillation Model of Droplet Collision for Spray Simulation at High Ambient Pressures
AU - Weiming Xu
AU - Tao Yang
AU - Peng Zhang
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37202
UR - https://arxiv.org/abs/2609.37202
AB - 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.
ER -