Spatial Attention Kinetic Networks with E(n)-Equivariance

by   Yuanqing Wang, et al.
John Chodera

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.


A simple algorithm for uniform sampling on the surface of a hypersphere

We propose a simple method for uniform sampling of points on the surface...

E(n) Equivariant Graph Neural Networks

This paper introduces a new model to learn graph neural networks equivar...

Roto-translated Local Coordinate Frames For Interacting Dynamical Systems

Modelling interactions is critical in learning complex dynamical systems...

Spherical Channels for Modeling Atomic Interactions

Modeling the energy and forces of atomic systems is a fundamental proble...

Critical Sampling for Robust Evolution Operator Learning of Unknown Dynamical Systems

Given an unknown dynamical system, what is the minimum number of samples...

Equivariant Neural Simulators for Stochastic Spatiotemporal Dynamics

Neural networks are emerging as a tool for scalable data-driven simulati...

Factorised Neural Relational Inference for Multi-Interaction Systems

Many complex natural and cultural phenomena are well modelled by systems...

Please sign up or login with your details

Forgot password? Click here to reset