A General Method to Determine Universal Formula for Given Database

Bo Da^1,2*, Hideki Yoshikawa¹, Shigeo Tanuma¹,

¹Research and Services Division of Materials Data and Integrated System, National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan

²Research Center for Advanced Measurement and Characterization, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan

 ABSTRACT: The robust TPP-2M formula is the most popular empirical formula for the prediction of electron inelastic mean free paths from simple material parameters. However, the TPP-2M formula poorly describes several materials because it adopts traditional least-squares analysis. Herein, we propose a new framework based on machine learning. This framework allows a selection from an enormous number of combined terms (descriptors) to build a new formula. The number of terms in the new formula can be automatically adjusted according to the importance of the terms in the particular application scenario. The obtained framework not only provides higher average accuracy and stability but also reveals the physical meanings of several newly found descriptors, and by the principle descriptors found, a complete physical picture of IMFP is summarized. Our findings suggest that machine learning is powerful and efficient and has great potential in building a regression framework for data-driven problems.