Fig. 1. Schematic of FIREANN framework.

The field-induced recursively embedded atom neural network (FIREANN) framework introduces a pseudo atomic field vector ($\overrightarrow{\mathit{\epsilon }}$) relative to each atom (represented by the green transparent atom). These pseudo atomic field vectors mimic the behavior of real atoms and are combined with actual atoms to produce a field-dependent embedded atomic density (ρ), which is used as the input of the neural network and yield the field-dependent energy (E). Physical quantities like atomic forces (F), dipole moment (μ) and polarizability (α), correspond to the energy derivatives with respect to coordinates (r) or electric field ($\overrightarrow{\mathit{\epsilon }}$). Note that the shaded region represents the local environment of each central atom, defined by a cutoff radius.