Sparse Statistical Modeling in Condensed Matter Physics

Abstract

In this work we explore the possibility of using sparse statistical modeling in condensed matter physics. The procedure is employed to two well known problems: elemental superconductors and heavy fermions, and was shown that in most cases performs better than other AI methods, such as machine or deep learning. More importantly, sparse modeling has two major advantages over other methods: the ability to deal with small data sets and in particular its interpretabilty. Namely, sparse modeling can provide insight into the calculation process and allow the users to give physical interpretation of their results. We argue that many other problems in condensed matter physics would benefit from these properties of sparse statistical modeling.

Figures (4)

• Figure 1: Confusion chart of classification with SLDA. The four classes refer to Table \ref{['tab:groups']}. The sparse model achieved 82$\%$ prediction accuracy.
• Figure 2: (a) Most important predictors of superconductivity in elements at atmospheric pressure. (b) Most important predictors of superconductivity at high pressures. The symbols refer to predictors from Table \ref{['tab:properties']}. Note that vertical axes does not have any physical meaning; only the relative values among different predictors are important.
• Figure 3: Predicted critical temperature versus actual critical temperature T$_c$ for elemental superconductors. The plot includes predictions from BCS bcs, McMillan mcmillan68 and SISSO formulas sisso discussed in the text, as well as the predictions from the sparse model.
• Figure 4: Statistical coefficient R$^2$ for a sparse model designed to predict the effective mass of heavy fermions. Singular value decomposition is shown to dramatically increase the value of R$^2$.