Multivariate temperature-series analysis of stress-induced ferroelectricity in SrTiO3: a machine learning approach with K-shape clustering and hierarchical Bayesian estimation

ABSTRACTA new machine learning approach that transforms time-series analysis into temperature-series analysis is introduced to analyze stress-induced ferroelectricity in SrTiO3 at 231 MPa using birefringence images observed at successive temperatures. The spatial distribution of the temperature-series data for each of the 42,280 pixels was clustered using the multivariate [Formula: see text]-shape clustering method based on the shape similarity of the temperature dependence. In addition, to obtain the structural and ferroelectric phase transition temperatures, [Formula: see text] and [Formula: see text], hierarchical Bayesian temperature-series estimation was performed at each pixel (as a lower level) constrained over the entire cluster (as a higher level) considering the measurement error. Consequently, the K-shape clustering method revealed four clusters corresponding to elongated ferroelectric domains, explained by slight differences in retardance and fast-axis direction. Statistical analysis of the Bayesian posterior probability distribution showed a uniform distribution of [Formula: see text] over the sample, but an inhomogeneous distribution of [Formula: see text]. The higher [Formula: see text] regions exhibited a concentration of stress and/or strain. The Pearson correlation coefficient calculations suggested a strong to moderate relationship between the distribution of TF and the ferroelectric state, while the correlation between Tc and the ferroelectric state was weak or nonexistent. The combination of machine learning and statistics provides a more reliable and less arbitrary approach to analyzing temperature-series data. These multilevel analyses are particularly useful in studying critical phenomena near phase transition temperatures in condensed matter physics.