  Neural network force field (NNFF) is a method for performing regression on
atomic structure-force relationships, bypassing expensive quantum mechanics
calculation which prevents the execution of long ab-initio quality molecular
dynamics simulations. However, most NNFF methods for complex multi-element
atomic systems indirectly predict atomic force vectors by exploiting just
atomic structure rotation-invariant features and the network-feature spatial
derivatives which are computationally expensive. We develop a staggered NNFF
architecture exploiting both rotation-invariant and covariant features
separately to directly predict atomic force vectors without using spatial
derivatives, thereby reducing expensive structural feature calculation by
~180-480x. This acceleration enables us to develop NNFF which directly predicts
atomic forces in complex ternary and quaternary-element extended systems
comprised of long polymer chains, amorphous oxide, and surface chemical
reactions. The staggered rotation-invariant-covariant architecture described
here can also directly predict complex covariant vector outputs from local
physical structures in domains beyond computational material science.
