Geometric and Physical Quantities Improve E(3) Equivariant Message Passing

Abstract

Including covariant information, such as position, force, velocity or spin is important in many tasks in computational physics and chemistry. We introduce Steerable E(3) Equivariant Graph Neural Networks (SEGNNs) that generalise equivariant graph networks, such that node and edge attributes are not restricted to invariant scalars, but can contain covariant information, such as vectors or tensors. This model, composed of steerable MLPs, is able to incorporate geometric and physical information in both the message and update functions. Through the definition of steerable node attributes, the MLPs provide a new class of activation functions for general use with steerable feature fields. We discuss ours and related work through the lens of equivariant non-linear convolutions, which further allows us to pin-point the successful components of SEGNNs: non-linear message aggregation improves upon classic linear (steerable) point convolutions; steerable messages improve upon recent equivariant graph networks that send invariant messages. We demonstrate the effectiveness of our method on several tasks in computational physics and chemistry and provide extensive ablation studies.

Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics

“…Building on these concepts, equivariant architectures have been explored for developing interatomic potential models. Notably, the NequIP model [15], followed by several other equivariant implementations [26,27,33,34,40], demonstrated unprecedentedly low error on a large range of molecular and materials systems, accurately describes structural and kinetic properties of complex materials, and exhibits remarkable sample efficiency. In both the present work and in NequIP, the representation D X [g] of an operation g ∈ O(3) on an internal feature space X takes the form of a direct sum of irreducible representations (commonly referred to as irreps) of O(3).…”

“…In this work, we present Allegro, an equivariant deep learning approach that retains the high accuracy of the recently proposed class of equivariant MPNNs [15,26,27,[32][33][34] while combining it with strict locality and thus the ability to scale to large systems. We demonstrate that Allegro not only obtains state-of-the-art accuracy on a series of different benchmarks but can also be parallelized across devices to access hundreds of millions of atoms.…”

EquiBind: Geometric Deep Learning for Drug Binding Structure Prediction

“…Incorporating 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). Our method follows Ganea et al (2021a) to incorporate SE(3) pairwise equivariance into message passing neural networks for the drug binding problem.…”

Message Passing Neural PDE Solvers

“…Solution differences u i − u j make sense by thinking of the message passing as a local difference operator, like a numerical derivative operator. Parameters θ PDE are inserted into the message passing similar to Brandstetter et al (2021) Decoder After message passing, we use a shallow 1D convolutional network with shared weights across spatial locations to output the K next timestep predictions at grid point x i . For each node i, the processor outputs a vector f M i .…”