Cormorant: Covariant Molecular Neural Networks

TL;DR

Cormorant is a novel neural network architecture that is rotationally covariant, enabling accurate learning of molecular potential energy surfaces and properties, outperforming existing methods in key benchmarks.

Contribution

The paper introduces Cormorant, a rotationally covariant neural network for molecular systems, utilizing tensor products and Clebsch-Gordan decomposition for improved physical property learning.

Findings

Outperforms competing algorithms on MD-17 dataset

Competitive with other methods on GDB-9 dataset

Operates entirely in Fourier space for efficiency

Abstract

We propose Cormorant, a rotationally covariant neural network architecture for learning the behavior and properties of complex many-body physical systems. We apply these networks to molecular systems with two goals: learning atomic potential energy surfaces for use in Molecular Dynamics simulations, and learning ground state properties of molecules calculated by Density Functional Theory. Some of the key features of our network are that (a) each neuron explicitly corresponds to a subset of atoms; (b) the activation of each neuron is covariant to rotations, ensuring that overall the network is fully rotationally invariant. Furthermore, the non-linearity in our network is based upon tensor products and the Clebsch-Gordan decomposition, allowing the network to operate entirely in Fourier space. Cormorant significantly outperforms competing algorithms in learning molecular Potential Energy Surfaces from conformational geometries in the MD-17 dataset, and is competitive with other methods at learning geometric, energetic, electronic, and thermodynamic properties of molecules on the GDB-9 dataset.