COVARIANT NEURAL NETWORK ARCHITECTURE FOR DETERMINING ATOMIC POTENTIALS

摘要

Methods and systems for computationally simulating an N-body physical system are disclosed. A compound object X having N elementary parts E may be decomposed into J subsystems, each including one or more of the elementary parts and having a position vector rj and state vector ψj. A mural network having J nodes each corresponding to one of the subsystems may be constructed, the nodes including leaf nodes, a non-leaf root node, and intermediate non-leaf nodes, each being configured to compute an activation corresponding to the state of a respective subsystem. Upon receiving input data for the parts E, each node may compute ψj from rj and ψj of its child nodes using a covariant aggregation rule representing ψj as a tensor that is covariant to rotations of the rotation group SO(3). A Clebsch-Gordan transform may be applied to reduce tensor products to irreducible covariant vectors, and ψj of the root node may be computed as output of the ANN.