Relevance of Rotationally Equivariant Convolutions for Predicting Molecular Properties

By Benjamin Kurt Miller, Mario Geiger, Tess E. Smidt, Frank No'e. 2020

85 citations recorded by the source corpus.

Equivariant neural networks (ENNs) are graph neural networks embedded in $\mathbb{R}^3$ and are well suited for predicting molecular properties. The ENN library e3nn has customizable convolutions, which can be designed to depend only on distances between points, or also on angular features, making them rotationally invariant, or equivariant, respectively. This paper studies the practical value of including angular dependencies for molecular property prediction using the QM9 data set. We find that for fixed network depth, adding angular features improves the accuracy on most targets. For most, but not all, molecular properties, distance-only e3nns (L0Nets) can compensate by increasing convolutional layer depth. Our angular-feature e3nn (L1Net) architecture beats previous state-of-the-art results on the global electronic properties dipole moment, isotropic polarizability, and electronic spatial extent.

Subfields: Computational Theory and Mathematics, Materials Chemistry, Physical and Theoretical Chemistry, Model Architectures, Computational Chemistry & Drug Discovery

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Citations in the corpus

E(n) Equivariant Graph Neural Networks (2021, background): “Anderson et al. (2019); Miller et al. (2020) include SO (3) equivariance in its intermediate layers for modelling the behavior and properties of molecular data.”
GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation (2022, background): “…is ubiquitous in machine learning for atomic systems, e.g. , the vectors of atomic dipoles or forces should rotate accordingly w.r.t. the conformation coordinates (Thomas et al., 2018; Weiler et al., 2018; Fuchs et al., 2020; Miller et al., 2020; Simm et al., 2021; Batzner et al., 2021).”
Learning Gradient Fields for Molecular Conformation Generation (2021, background): “, 3D roto-translation equivariance of molecular conformations or point clouds (Thomas et al., 2018; Weiler et al., 2018; Fuchs et al., 2020; Miller et al., 2020; Simm et al., 2021).”
Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs (2022, background): “Equivariant neural networks [72, 43, 80, 23, 50, 74, 4, 38, 65, 63, 77, 5, 71, 46, 51] operate on geometric tensors like type-L vectors to achieve equivariance.”
Learning local equivariant representations for large-scale atomistic dynamics (2022, unknown): “6 Cormorant [23] 22 21 21 20 LieConv [55] 19 19 24 22 L1Net [56] 13.”
e3nn: Euclidean Neural Networks (2022, methodology): “So far, e3nn and Euclidean neural networks have been applied to diverse applications: finding symmetry breaking order parameters [28], predicting molecular properties [18], prediction of phonon density of states [6], prediction of the interatomic potentials [2], developing deep learning for diffusio”
EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representations (2023, unknown): “2 Related Works SE(3)/E(3) -Equivariant GNNs. Equivariant neural networks [5,7,11–18 , 31– 38] use equivariant irreps features built from vector spaces of irreducible representations ( irreps Invariant GNNs. Prior works [4,8,43–51] extract invariant information from 3D atomistic graphs and operate…”
Geometric and Physical Quantities improve E(3) Equivariant Message Passing (2021, methodology): “The equivariant steerable methods (Thomas et al., 2018; Anderson et al., 2019; Miller et al., 2020; Fuchs et al., 2020) that we compare against in our experiments can all be written in convolution form where, in the latter case, the linear transformations additionally depend on an input dependent…”
An Introduction to Electrocatalyst Design using Machine Learning for Renewable Energy Storage (2020, background): “An exploration of the tradeoffs between equivariant and invariant pairwise information is provided by [124].”