Machine Learning Materials Response to Electric Fields

Material response properties to external fields fundamentally dictate the performance of modern technologies involving dielectric, ferroelectric, and piezoelectric devices. However, predicting the dynamic response of realistic material systems to external stimuli with atomistic quantum accuracy remains a long-standing challenge in computational materials physics. To address this, we introduce a machine-learning framework where response properties stem from exact differential relationships between a generalized potential function and applied external fields. Focusing on electric fields, the method predicts response properties within a unified model that enforces exact physical constraints, symmetries, and conservation laws. We demonstrate that our physics-based approach accurately captures the vibrational, dielectric, and ferroelectric behaviors of materials under arbitrary electric fields, including temperature and frequency dependence. This enables us to investigate the time evolution of ferroelectric hysteresis at a large scale, revealing the intrinsic mechanisms of nucleation and growth governing ferroelectric domain switching.