Unveiling the principle descriptor for predicting the electron inelastic mean free path based on a machine learning framework

The TPP-2M formula is the most popular empirical formula for the estimation of the electron inelastic mean free paths (IMFPs) in solids from several simple material parameters. The TPP-2M formula, however, poorly describes several materials because it relies heavily on the traditional least-squares analysis. Herein, we propose a new framework based on machine learning to overcome the weakness. This framework allows a selection from an enormous number of combined terms (descriptors) to build a new formula that describes the electron IMFPs. The resulting framework not only provides higher average accuracy and stability but also reveals the physics meanings of several newly found descriptors. Using the identified principle descriptors, a complete physics picture of electron IMFPs is obtained, including both single and collective electron behaviors of inelastic scattering. Our findings suggest that machine learning is robust and efficient to predict the IMFP and has great potential in building a regression framework for data-driven problems. Furthermore, this method could be applicable to find empirical formula for given experimental data using a series of parameters given a priori, holds potential to find a deeper connection between experimental data and a priori parameters.