Electric-field driven nuclear dynamics of liquids and solids from a multi-valued machine-learned dipolar model

The driving of vibrational motion by external electric fields is a topic of continued interest, due to the possibility of assessing new or metastable material phases with desirable properties. Here, we combine ab initio molecular dynamics within the electric-dipole approximation with machine-learning neural networks (NNs) to develop a general, efficient and accurate method to perform electric-field-driven nuclear dynamics for molecules, solids, and liquids. We train equivariant and autodifferentiable NNs for the interatomic potential and the dipole, modifying the model infrastructure to account for the multi-valued nature of the latter in periodic systems. We showcase the method by addressing property modifications induced by electric field interactions in a polar liquid and a polar solid from nanosecond-long molecular dynamics simulations with quantum-mechanical accuracy. For liquid water, we present a calculation of the dielectric function in the GHz to THz range and the electrofreezing transition, showing that nuclear quantum effects enhance this phenomenon. For the ferroelectric perovskite LiNbO₃, we simulate the ferroelectric to paraelectric phase transition and the non-equilibrium dynamics of driven phonon modes related to the polarization switching mechanisms, showing that a full polarization switch is not achieved in the simulations.