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

TL;DR

NequIP introduces an E(3)-equivariant neural interatomic potential that learns from ab-initio data to enable accurate, energy-conserving molecular dynamics with exceptional data efficiency. By representing atomic features as geometric tensors and using filters built from radial functions and spherical harmonics, NequIP captures rotationally equivariant interactions up to a configurable rank $l_{ ext{max}}$, surpassing prior invariant and equivariant approaches in both accuracy and data efficiency. Across MD-17, CCSD/CCSD(T)-level training, water/ice, surface reactions, amorphous glass formation, and superionic conduction, NequIP achieves state-of-the-art performance with orders-of-magnitude less training data in many cases, and faithfully reproduces structural and kinetic properties. The work demonstrates the practical impact of enforcing $E(3)$-equivariance in learned interatomic potentials, enabling high-fidelity simulations at high levels of theory and broad applicability to chemistry, materials science, and condensed matter physics.

Abstract

This work presents Neural Equivariant Interatomic Potentials (NequIP), an E(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 E(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 and diverse set of 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.

Figures (13)

• Figure 1: Left: a set of atoms is interpreted as an atomic graph with local neighborhoods. Middle: every atom carries a set of scalar, vector, and higher-order tensor features with it. Right: atoms exchange information via filters, that are again geometric tensors of increasing order.
• Figure 2: The NequIP network architecture. Left: atomic numbers are embedded into $l=0$ features, which are refined through a series of interaction blocks, creating scalar and higher-order tensor features. An output block then generates atomic energies, which are pooled to give the total predicted energy. Middle: the interaction block, containing the convolution. Right: the convolution combines the radial function $R(r)$ which operates only on interatomic distances with the spherical harmonic projection of the unit vector $\hat{r}_{ij}$ via a tensor product.
• Figure 3: Perspective view of atomic configurations of (a) bidentate HCOO (b) monodentate HCOO and (c) CO$_2$ and a hydrogen adatom on a Cu(110) surface. The blue, red, black, and white spheres represent Cu, O, C, and H atoms, respectively. The subset shown in each subplot is the corresponding top view along the $<110>$ orientation.
• Figure 4: Quenched glass structure of Li4P2O7. The insets show the P-O-O tetrahedral bond angle (bottom left) as well as the O-P-P bridging angle between corner-sharing phosphate tetrahedra (top right).
• Figure 5: Left: Radial Distribution Function, middle: Angular Distribution Function, tetrahedral bond angle, right: Angular Distribution Function, bridging oxygen. All are defined as probability density functions; NequIP results are averaged over 10 runs with different initial velocities.