Physics-Constrained Symbolic Regression of Collision Integrals for Dilute-Gas Viscosity

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Abstract Dilute-gas viscosity is a fundamental transport property governed by binary molecular collisions and is widely used as a reference term in dense-fluid viscosity models. In this work, a physics-constrained symbolic regression framework is developed for predicting dilute-gas viscosity through the conventional Chapman–Enskog framework and a new reduced Boyle-scaled collision integral. Instead of correlating viscosity directly, the viscosity data are transformed into a dimensionless collision integral using the Boyle temperature and Boyle length derived from the second virial coefficient. A comprehensive database containing 87 fluids and 11,263 dilute-gas viscosity data points was constructed by combining high-accuracy ab initio data with carefully screened and zero-density-extrapolated experimental data. The collision-integral model was formulated as a decomposed correlation consisting of a spherical reference term, a nonpolar correction term, and a polar correction term, with additional empirical extensions for quantum and associating fluids. Symbolic regression was used to identify the analytical expression of each term considering accuracy, numerical stability, and physical consistency. The resulting model gives an overall AARD of 2.00 % for the complete database and maintains good accuracy across different fluid classes. Analysis of the final expressions shows that the dominant temperature dependence is captured by the spherical reference term, while molecular nonsphericity mainly acts through a coupled acentric factor-temperature effect. The polar correction provides a coarse but systematic empirical adjustment for polar fluids. To facilitate reproducible use, a Python implementation of the final correlation is provided in the Supporting Information.

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