Interpretable Machine Learning for the Design of (K, Na)NbO ₃ -Based Piezoceramics Using Combinatorial and Knowledge-Embedded Descriptors

The piezoelectric properties of potassium sodium niobate (KNN)-based ceramics can be effectively enhanced via chemical modification. However, the wide variety of dopants and the lack of efficient, rational screening methods have hindered the search for KNN materials with expected performance. In this study, we develop an interpretable framework to investigate the critical features that drive machine learning (ML)-based predictions of the piezoelectric constant <i>d</i>₃₃ in KNN-based ceramics. Using Shapley Additive exPlanations, we quantitatively analyze the nonlinear and interactive effects of these features on <i>d</i>₃₃ inference. The identified tipping points, which distinguish between the positive and negative influential ranges of features (e.g., 1105 °C for the sintering temperature), contribute to guiding the pursuit of enhanced piezoelectricity. Furthermore, we employ the Sure Independence Screening and Sparsifying Operator to combine these features with various mathematical operators, resulting in combinatorial descriptors that exhibit approximate linearity with <i>d</i>₃₃. Transparent linear expressions composed of two such combinatorial descriptors exhibit comparable performance to the "black-box" models trained with individual features. Moreover, these combinatorial descriptors are found to enhance the performance of ML models, with excellent performance metrics of MAE < 30 pC/N and <i>R</i>² > 0.9 reached. This study highlights the importance of rationally designing material features to ensure the interpretability and performance of ML. Our findings provide valuable insights into the complex mechanisms underlying <i>d</i>₃₃ enhancement in KNN-based ceramics from a feature-centric perspective.