Machine learning symbolic equations for diffusion with physics-based descriptions

This work incorporates symbolic regression to propose simple and accurate expressions that fit to material datasets. The incorporation of symbolic regression in physical sciences opens the way to replace “black-box” machine learning techniques with representations that carry the physical meaning and can reveal the underlying mechanism in a purely data-driven approach. The application here is the extraction of analytical equations for the self-diffusion coefficient of the Lennard-Jones fluid by exploiting widely incorporating data from the literature. We propose symbolic formulas of low complexity and error that achieve better or comparable results to well-known microscopic and empirical expressions. Results refer to the material state space both as a whole and in distinct gas, liquid, and supercritical regions.