Equivariant message passing for the prediction of tensorial properties and molecular spectra

By Kristof T. Schütt, Oliver T. Unke, Michael Gastegger. International Conference on Machine Learning, 2021

803 citations recorded by the source corpus.

Message passing neural networks have become a method of choice for learning on graphs, in particular the prediction of chemical properties and the acceleration of molecular dynamics studies. While they readily scale to large training data sets, previous approaches have proven to be less data efficient than kernel methods. We identify limitations of invariant representations as a major reason and extend the message passing formulation to rotationally equivariant representations. On this basis, we propose the polarizable atom interaction neural network (PaiNN) and improve on common molecule benchmarks over previous networks, while reducing model size and inference time. We leverage the equivariant atomwise representations obtained by PaiNN for the prediction of tensorial properties. Finally, we apply this to the simulation of molecular spectra, achieving speedups of 4-5 orders of magnitude compared to the electronic structure reference.

Subfields: Computational Theory and Mathematics, Materials Chemistry, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/00f39c314542902cd1b03842069e5d3ed441a5c3

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Citations in the corpus

Learning local equivariant representations for large-scale atomistic dynamics (2022, methodology): “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”
GeoMol: Torsional Geometric Generation of Molecular 3D Conformer Ensembles (2021, background): “…chemical, and physical properties [Guimaraes et al., 2012, Schütt et al., 2018, Klicpera et al., 2019, Axelrod and Gomez-Bombarelli, 2020b, Schütt et al., 2021] such as charge distribution, potential energy, docking poses [McGann, 2011], shape similarity [Kumar and Zhang, 2018],…”
Efficient and Accurate Physics-aware Multiplex Graph Neural Networks for 3D Small Molecules and Macromolecule Complexes (2022, methodology): “Another approach for predicting geometric vectors is to use equivariant networks with components that are all carefully designed to implement the equivariance of geometric vectors [7, 28, 35].”
Geometric deep learning on molecular representations (2021, methodology): “When applied to quantum chemistry tasks, GNNs can use 3D information by including radial and angular information in the edge features of the graph28,36,37, which has proved beneficial for estimating quantum chemical energies and other properties of equilibrium and non-equilibrium molecular conformat”
SpookyNet: Learning force fields with electronic degrees of freedom and nonlocal effects (2021, methodology): “The SchNet and PaiNN models for the QM7-X experiments use F = 128 features, as well as T = 6 and T = 3 interactions, respectively.”
MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields (2022, methodology): “Equivariant message-passing schemes [5, 43, 8] lift the degeneracy of most structures by containing directional information in the messages.”
e3nn: Euclidean Neural Networks (2022, neutral): “There also exist restricted equivariant methods, that use only scalar or vector operations on scalar and vector representations; these are a strict subset of the operations allowed with an equivariant network [23, 26].”
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 ).”
EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representations (2023, neutral): “These operations include tensor products and equivariant linear operations, equivariant layer normalization [52] and gate activation [12, 34].”
Geometric and Physical Quantities improve E(3) Equivariant Message Passing (2021, background): “A different but also fully message passing based approach can be found in Geometric Vector Perceptrons (GVP) (Jing et al., 2020), Vector Neurons (Deng et al., 2021), and PaiNN (Sch¨utt 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.”