Topological Data Analysis in Materials Science: The Case of High-Temperature Cuprate Superconductors
I. Yu. Torshin, К. В. Рудаков
Abstract
Abstract— Adequate formalization of problems is the most important task that has to be solved in order to apply the modern methods of so-called “machine learning” to real problems. The effective application of the metric, logical, regression, and other algorithms of machine learning becomes possible only when feature generation procedures and classes of objects are adequately defined. In this study, the theory of topological analysis of poorly formalized problems and the theory of analysis of labeled graphs were applied to the problem of predicting numerical characteristics of crystalline materials. The methods developed were tested on the problem of predicting the critical temperature of superconducting transition (Tc) of high-temperature cuprate superconductors (1450 structures). As a result, in a tenfold 6 : 1 cross-validation, the best model with a linear recognition operator yielded quite high average value of the correlation coefficient (r = 0.77) between the predicted and experimentally determined values of Tc.