SE(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials

Abstract

This work presents Neural Equivariant Interatomic Potentials (NequIP), a SE(3)-equivariant neural network approach for learning interatomic potentials from ab-initio calculations for molecular dynamics simulations. While most contemporary symmetry-aware models use invariant convolutions and only act on scalars, NequIP employs SE(3)-equivariant convolutions for interactions of geometric tensors, resulting in a more information-rich and faithful representation of atomic environments. The method achieves state-of-the-art accuracy on a challenging set of diverse molecules and materials while exhibiting remarkable data efficiency. NequIP outperforms existing models with up to three orders of magnitude fewer training data, challenging the widely held belief that deep neural networks require massive training sets. The high data efficiency of the method allows for the construction of accurate potentials using high-order quantum chemical level of theory as reference and enables high-fidelity molecular dynamics simulations over long time scales.

Machine Learning for Fluid Mechanics

“…LSTMs have recently been used to predict aeroelastic responses across a range of Mach numbers [70]. More generally, equivariant networks seek to encode various symmetries by construction, which should improve accuracy and reduce data requirements for physical systems [71][72][73][74]. Autoencoder networks enforce the physical notion that there should be low-dimensional structure, even for high-dimensional data, by imposing an information bottleneck, given by a constriction of the number of nodes in one or more layers of the network.…”

Machine learning potentials for extended systems: a perspective

“…First implementations used only interatomic distances, but more recently the full many-body description is utilized e.g. in "equivariant message passing networks" [40]. For high-dimensional systems, a cutoff radius for the information exchange is introduced making the methods feasible for larger systems, and for each message passing step (typically between two and six are employed) the effective range of the description of the atomic environments is increased.…”

Euclidean Symmetry and Equivariance in Machine Learning

“…To predict quantities that are fundamentally generated from equivariant interactions you must either 1) include these equivariant interactions in the scalar featurization used for an invariant model (which requires knowing to include those interactions) or 2) use an equivariant model, which may make more accurate or efficient predictions because it has more expressive operations [4,5].…”

“…molecular dynamics forces) from atomic geometries and initial atomic features (e.g. atom types) [5]. You can use them to manipulate atomic geometries and hierarchical features [14].…”