Spatial Attention Kinetic Network with E(n)-Equivariance

Neural networks that are equivariant to rotations, translations, reflections, and permutations on $n$-dimensional geometric space have shown promise in physical modeling---from modeling potential energy surfaces to forecasting the time evolution of dynamical systems. Current state-of-the-art methods employ spherical harmonics to encode higher-order interactions among particles, which are computationally expensive. In this paper, we propose a simple alternative functional form that uses neurally parametrized linear combinations of edge vectors to achieve equivariance while still universally approximating node environments. Incorporating this insight, we design spatial attention kinetic networks with E(n)-equivariance, or SAKE, which are competitive in many-body system modeling tasks while being significantly faster.