N-body Networks: a Covariant Hierarchical Neural Network Architecture for Learning Atomic Potentials

By Risi Kondor. 2018

110 citations recorded by the source corpus.

We describe N-body networks, a neural network architecture for learning the behavior and properties of complex many body physical systems. Our specific application is to learn atomic potential energy surfaces for use in molecular dynamics simulations. Our architecture is novel in that (a) it is based on a hierarchical decomposition of the many body system into subsytems, (b) the activations of the network correspond to the internal state of each subsystem, (c) the "neurons" in the network are constructed explicitly so as to guarantee that each of the activations is covariant to rotations, (d) the neurons operate entirely in Fourier space, and the nonlinearities are realized by tensor products followed by Clebsch-Gordan decompositions. As part of the description of our network, we give a characterization of what way the weights of the network may interact with the activations so as to ensure that the covariance property is maintained.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry, Molecular Biology, Neural Architecture Search & AutoML, Computational Chemistry & Drug Discovery, AI for Physical Sciences

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

In Materials Chemistry

In Molecular Biology

In Neural Architecture Search & AutoML

In Computational Chemistry & Drug Discovery

In AI for Physical Sciences

Citations in the corpus

SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks (2020, background): “[20] and Kondor [11] showed that the kernel W lies in the span of an equivariant basis {W J } J=|k−`|.”
Isometric Transformation Invariant and Equivariant Graph Convolutional Networks (2020, background): “Concerning point clouds, Thomas et al. (2018); Kondor (2018) discussed the way to provide rotation equivariance.”
Cormorant: Covariant Molecular Neural Networks (2019, methodology): “…where even the nonlinear part of the neural network’s operation is performed in Fourier space: independently of each other [Thomas et al., 2018] and [Kondor, 2018] were to ﬁrst to use the Clebsch–Gordan transform inside rotationally covariant neural networks for learning physical systems, while…”
Tensor Field Networks: Rotation- and Translation-Equivariant Neural Networks for 3D Point Clouds (2018, background): “Further discussion of related theory can be found in [20], [21], and [22].”
Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Network (2018, methodology): “The Clebsch–Gordan decomposition has recently appeared in two preprints discussing neural networks for learning physical systems [21, 22].”
On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groups (2018, background): “, 2018)), and, even more recently, since the submission of the original version of the present paper in (Thomas et al., 2018; Kondor, 2018; Weiler et al., 2018).”
A General Theory of Equivariant CNNs on Homogeneous Spaces (2018, background): “Some choices include norm nonlinearities [3] for unitary representations, tensor product nonlinearities [8], or gated nonlinearities where a scalar field is normalized by a sigmoid and then multiplied by another field [6].”
CubeNet: Equivariance to 3D Rotation and Translation (2018, methodology): “However, with the exception of Cohen and Welling [9] (projections on sphere), Kondor [28] (point clouds), and Thomas et al.”
Intertwiners between Induced Representations (with Applications to the Theory of Equivariant Neural Networks) (2018, methodology): “SE(3)-equivariant networks were ﬁrst described and implemented by Kondor [2018], Thomas et al. [2018].”
On Learning Sets of Symmetric Elements (2020, unknown): “…rotations (Dieleman et al., 2016; Cohen & Welling, 2016a;b; Worrall et al., 2017), spherical symmetries (Cohen et al., 2018; 2019b; Esteves et al., 2017), or 3D symmetries (Weiler et al., 2018; Winkels & Cohen, 2018; Worrall & Brostow, 2018; Kondor, 2018; Thomas et al., 2018; Weiler et al., 2018).”
Geometric Prediction: Moving Beyond Scalars (2020, background): “Recently, neural networks have emerged that do encode constraints such as rotations and translations [3], [4], [5].”
End-to-End Learning on 3D Protein Structure for Interface Prediction (2018, background): “Equivariant networks represent another recent and exciting line of work extending these symmetry functions [11], [12], [13].”
Scale-Equivariant Steerable Networks (2019, background): “Kondor & Trivedi (2018) prove that a feed-forward neural network is equivariant to transformations from G if and only if it is constructed from G-equivariant convolutional layers.”
The design space of E(3)-equivariant atom-centred interatomic potentials (2022, unknown): “We denote the set of neighbors of an atom i , i.e., atoms with the cutoﬀ distance, by N ( i ).”
Deep learning of vortex-induced vibrations (2018, background): “[33], as well as the contemporary works of Kondor [34, 35], Hirn [36], and Mallat [37].”