High Dimensional and Low Sample Size Case Statistics for the Screening on Crystal Information of the Solid-State Electrolytes

Battery is one of the most important device to achieve carbon neutrality. We anticipated that all Li-ion solid-state batteries would be safer than conventional batteries. The key issue of the all solid state battery is the high ion resistance of the solid state electrolyte. In recent years, researchers have adopted materials informatics methods to explore innovative solid electrolytes with high ionic conductivity. High-throughput simulations in recent years have made it possible to search for large numbers of candidate electrolyte materials, but the cost of accurate property calculations is too high to be thoroughly investigated.<br/>We use the X-ray diffraction (XRD) pattern and radial distribution function (RDF) calculated from the crystal information file (CIF) as the features. The screening model is trained by the XRD and RDF dataset labeled by using the simulated migration energy. This dataset contains the low sample size positive labeled data as compared to its dimension. This is the so-called high-dimensional low-sample-size (HDLSS). The HDLSS situation results in overfitting to the data and obstruct the accurate prediction of the ion conductivity.<br/>In this research, we screen the copper oxide solid state electrolyte by using the HDLSS statistics. We consider a regularized principal component analysis (RPCA) and a high-dimensional quadratic discriminant analysis (HD-QDA) by using HDLSS asymptotics. We demonstrate the RPCA method to specify the indicator from high dimensional XRD and RDF data. The quadratic discriminant analysis for HDLSS situation trained by using less than 10 positive samples can extract a few desirable samples from a hundreds of ordinary samples. The proposed approach can be utilized for the other challenge of the crystal structure screening.