Smart machine learning or discovering meaningful physical and chemical contributions through dimensional stacking

Despite remarkable advances in characterization techniques of functional materials yielding an ever growing amount of data, the interplay between the physical and chemical phenomena underpinning materials' functionalities is still often poorly understood. Dimensional reduction techniques have been used to tackle the challenge of understanding materials' behavior, leveraging the very large amount of data available. Here, we present a method for applying physical and chemical constraints to dimensional reduction analysis, through dimensional stacking. Compared to traditional, uncorrelated techniques, this approach enables a direct and simultaneous assessment of behaviors across all measurement parameters, through stacking of data along specific dimensions as required by physical or chemical correlations. The proposed method is applied to the nanoscale electromechanical relaxation response in (1 − x)PMN-xPT solid solutions, enabling a direct comparison of electric field- and chemical composition-dependent contributors. A poling-like, and a relaxation-like behavior with a domain glass state are identified, and their evolution is tracked across the phase diagram. The proposed dimensional stacking technique, guided by the knowledge of the underlying physics of correlated systems, is valid for the analysis of any multidimensional dataset, opening a spectrum of possibilities for multidisciplinary use.