Machine-learning-based interatomic potentials are widely employed in atomistic simulations, but they struggle to capture long-range electrostatic correlations, which are ubiquitous in polar and biomolecular systems. We present a physics-informed machine-learning interatomic potential that incorporates long-range electrostatic interactions through a polarizable framework. Our model combines two equivariant message-passing neural networks: one for short-range interactions and the other for environment-dependent atomic dipoles. The model is trained not only on energies and forces but also on Born effective-charge tensors, enabling accurate predictions of field-induced properties such as infrared absorption spectra and LO–TO phonon splittings. We validate the method on ionic solids (NaCl), liquid water, and halide perovskites (MAPbI3), demonstrating improved modeling of long-range polarization effects while maintaining competitive accuracy in energy and force predictions. Our results highlight the necessity of explicit long-range electrostatics for capturing collective phenomena in insulating and polar materials.
Li et al. (Fri,) studied this question.