Learning polarization using equivariant neural networks

Polarization is key to the understanding of dielectrics and ferroelectrics, and recent advances, such as the modern theory of polarization [1] and electric enthalpy functionals [2], have opened the path to computational studies of polarization in crystals. However, the high computational cost associated with these simulation techniques remains a challenging problem of electronic structure calculations. Here, we introduce an equivariant neural network approach to efficiently learn and predict the polarization for each atomic configuration, building on and extending state-of-the-art machine learning force field architectures. This allows for the study of the polarization autocorrelation function over a molecular dynamics simulation at first-principles accuracy, thereby enabling the simulation of infrared spectrum, frequency-dependent dielectric constant, and Raman cross section from first principles. Our scheme is implemented within the E(3)-equivariant NequIP/Allegro framework [3], and is interfaced with the LAMMPS code.

[1] R. Resta, Macroscopic polarization in crystalline dielectrics: the geometric phase approach, Rev. Mod. Phys. 66, 899 (1994).

[2] P. Umari and A. Pasquarello, Ab initio molecular dynamics in a finite homogeneous electric field, Phys. Rev. Lett. 89, 157602 (2002).

[3] A. Musaelian, S. Batzner, A. Johansson, L. Sun, C. Owen, M. Kornbluth, and B. Kozinsky, Learning local equivariant representations for large-scale atomistic dynamics, Nat. Commun. 14, 579 (2023).