First-principles based data-driven strain engineering for ferroelectrics via active machine learning: A nonlinear piezoelectric constitutive equation

Strain engineering is a crucial approach in the engineering field to optimize various physical properties of materials by applying mechanical strain loading. However, it is extremely challenging to find out the best conditions of strain with unprecedented physical properties in the vast strain space consisting of six components. Here, we developed a technical framework that enables efficient exploration of physical properties in the vast strain space based on machine learning (i.e., artificial neural networks), active learning, and high-throughput first-principles calculation. We demonstrated the active learning technique to successfully and efficiently construct an accurate machine learning model for ferroelectric PbTiO3 with minimal first-principles datasets (only 3.7% of the vast strain-space). Our machine learning model can accurately predict the nonlinear mechanical deformation and electromechanical response in the three components of normal strain loading. We also carried out strain optimization of piezoelectric response using the machine learning model and found that a large piezoelectric response is five times larger than without strain loading. We showed that the physical property explorer framework constructed in this study makes it possible to optimize strain for various material properties in a vast strain space by calculating only a small number of data points. These results suggest paving the way for constructing nonlinear piezoelectric constitutive equations for novel piezoelectric devices via strain engineering.