Spatial Attention Kinetic Networks with E(n)-Equivariance
This work addresses the problem of high computational cost in geometric deep learning for researchers and practitioners in fields like molecular dynamics and physics simulation, offering an incremental improvement over existing methods.
The paper tackled the computational expense of current E(n)-equivariant neural networks for physical modeling by proposing a simpler functional form using neurally parametrized linear combinations of edge vectors, resulting in competitive performance in many-body system modeling tasks with significantly faster speed.
Neural networks that are equivariant to rotations, translations, reflections, and permutations on n-dimensional geometric space have shown promise in physical modeling for tasks such as accurately but inexpensively modeling complex potential energy surfaces to guiding the sampling of complex dynamical systems or forecasting their time evolution. 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.