E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials

By Simon L. Batzner, Albert Musaelian, Lixin Sun, Mario Geiger, Jonathan P. Mailoa, Mordechai Kornbluth, Nicola Molinari, Tess E. Smidt, Boris Kozinsky. 2021

2,192 citations recorded by the source corpus.

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. An E(3)-equivariant deep learning interatomic potential is introduced for accelerating molecular dynamics simulations. The method obtains state-of-the-art accuracy, can faithfully describe dynamics of complex systems with remarkable sample efficiency.

Subfields: Artificial Intelligence, Materials Chemistry, Molecular Biology

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Citations in the corpus

EquiBind: Geometric Deep Learning for Drug Binding Structure Prediction (2022, methodology): “…Euclidean symmetries into GNNs. Injecting Euclidean 3D transformations into geometric DL models has become possible using equivariant message passing layers (Cohen & Welling, 2016; Thomas et al., 2018; Fuchs et al., 2020; Satorras et al., 2021; Brandstetter et al., 2021; Batzner et al., 2021).”
GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation (2022, background): “The 3D structures determine the biological and physical properties of molecules and hence play a key role in many applications such as computational drug and material de-sign (Thomas et al., 2018; Gebauer et al., 2021; Jing et al., 2021; Batzner et al., 2021).”
Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problem (2022, neutral): “[3] Simon Batzner, Albert Musaelian, Lixin Sun, Mario Geiger, Jonathan P Mailoa, Mordechai Kornbluth, Nicola Molinari, Tess E Smidt, and Boris Kozinsky.”
Scaling deep learning for materials discovery (2023, methodology): “We train a NequIP potential 30 , implemented in JAX using the e3nn-jax library 66 , with five layers, hidden features of 128 ℓ = 0 scalars, 64 ℓ = 1 vectors and 32 ℓ = 2 tensors (all even irreducible representations only, 128 x 0 e + 64 x 1 x + 32 x 2 e ), as well as an edge-irreducible…”
MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields (2022, methodology): “On the left panel of Figure 2, we replicate the experiments of [5] by training a series of invariant MACE models with increasing correlation order ν on the aspirin molecule from the rMD17 dataset.”
Geometric and Physical Quantities improve E(3) Equivariant Message Passing (2021, background): “Finally, the recently proposed LieConv (Finzi et al., 2020) and NequIP (Batzner et al., 2021) also fall in the convolutional message passing class.”
e3nn: Euclidean Neural Networks (2022, methodology): “of order l = 2 display a better learning curve than models only containing l ≤ 1 internal representations [2, 12].”
The design space of E(3)-equivariant atom-centred interatomic potentials (2022, neutral): “We denote the set of neighbors of an atom i , i.e., atoms with the cutoﬀ distance, by N ( i ).”
Towards universal neural network potential for material discovery applicable to arbitrary combination of 45 elements (2021, methodology): “1 [8] E(3) Invariant MLP X SchNet [10] E(3) Invariant GNN X DimeNet++ [11, 12] E(3) Invariant GNN X PhysNet [13] E(3) Invariant GNN X Cormorant [14] SE(3) Equivariant GNN X X SE(3)-Transformer [15] SE(3) Equivariant GNN X X NequIP [16] SE(3) Equivariant GNN X X SpookyNet [17] SE(3) Equivariant GNN X”
Generating Molecular Conformer Fields (2023, background): “…Generation is a fundamental problem in computational drug discovery and chemo-informatics, where understanding the intricate interactions between molecular and protein structures in 3D space is critical, affecting aspects such as charge distribution, potential energy, etc. (Batzner et al., 2022).”
Equivariant Graph Neural Networks for 3D Macromolecular Structure (2021, positive): “These networks have shown promising results on small molecule datasets (Thomas et al., 2018; Kondor, 2018; Anderson et al., 2019; Fuchs et al., 2020; Batzner et al., 2021) and recently also in the context of learning from macromolecular structure (Eismann et al., 2020a;b; Townshend et al., 2020).”