Causal inference in statistics insights into stress-induced ferroelectric states in SrTiO 3: disentangling piezoelectric and flexoelectric effects from birefringence images

In materials science, experimental conditions are precisely controlled to ensure high reproducibility. This property is well suited for causal inference in statistics, yet its potential remains unrealized. In this study, we integrate causal inference with structural equation modeling (SEM) to analyze birefringence images of the stress-induced ferroelectric SrTiO[Formula: see text]. Random forest analysis identified retardance at 14.1 K, [Formula: see text], as a key predictor of the ferroelectric phase transition temperature, [Formula: see text]. SEM revealed strong correlations between [Formula: see text] and [Formula: see text]s, although multicollinearity in [Formula: see text]s necessitated sparse principal component analysis to transform [Formula: see text] and [Formula: see text] into two independent components, [Formula: see text] and [Formula: see text], for subsequent causal analysis. Directed acyclic graphs (DAGs) based on SEM helped infer causal relationships, revealing [Formula: see text]‘s predominant influence on [Formula: see text] in stress/strain-concentrated regions (cluster E12) and [Formula: see text]‘s influence in uniform stress/strain regions (cluster E34). Two-model learner (T-Learner) analysis revealed the factors behind the higher [Formula: see text] in E12 than in E34. Specifically, the difference in magnitude of the piezoelectric effect, which occurs uniformly throughout the substrate, causes [Formula: see text] to increase by 0.36 K [0.18 K, 0.54 K], while the flexoelectric effect, which occurs only in E12, causes it to increase by an additional 1.49 K [1.23 K, 1.75 K]. These findings demonstrate the utility of causal inference in disentangling piezoelectric and flexoelectric effects in the stress-induced ferroelectric SrTiO[Formula: see text].