Quantification of gradient energy coefficients using physics-informed neural networks

Ferroelectrics are a class of multifunctional materials widely used in actuators, sensors, and information storage because of their unique electromechanical properties. To understand and utilize these properties, it is necessary to investigate ferroelectric microstructure evolution, a dynamic, nonlinear, and multi-physics coupling phenomenon. Phase-field simulations are often adopted to mimic this phenomenon. One core of phase-field models is the free energy, where the gradient energy is a primary part. However, the quantification of the associated gradient energy coefficients is a long-standing challenge in computational materials. In light of the ease of physics-informed neural networks (PINNs) to incorporate both mathematical models and data, we present a promising method to address this challenge by solving an inverse problem with PINNs. Our investigation with labeled data from simulations demonstrates the excellent performance of this method. Our further investigation with labeled data from atomic-scale high-resolution measurements also shows encouraging results, thus charting a clear path to pragmatically overcome the aforementioned challenge.