A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systems

• URL: http://arxiv.org/abs/2312.07511v2
• Date: Wed, 13 Mar 2024 17:38:27 GMT
• Title: A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systems
• Authors: Alexandre Duval, Simon V. Mathis, Chaitanya K. Joshi, Victor Schmidt, Santiago Miret, Fragkiskos D. Malliaros, Taco Cohen, Pietro Li\`o, Yoshua Bengio and Michael Bronstein
• Abstract summary: Recent advances in computational modelling of atomic systems represent them as geometric graphs with atoms embedded as nodes in 3D Euclidean space. Geometric Graph Neural Networks have emerged as the preferred machine learning architecture powering applications ranging from protein structure prediction to molecular simulations and material generation. This paper provides a comprehensive and self-contained overview of the field of Geometric GNNs for 3D atomic systems.
• Score: 87.30652640973317
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Recent advances in computational modelling of atomic systems, spanning molecules, proteins, and materials, represent them as geometric graphs with atoms embedded as nodes in 3D Euclidean space. In these graphs, the geometric attributes transform according to the inherent physical symmetries of 3D atomic systems, including rotations and translations in Euclidean space, as well as node permutations. In recent years, Geometric Graph Neural Networks have emerged as the preferred machine learning architecture powering applications ranging from protein structure prediction to molecular simulations and material generation. Their specificity lies in the inductive biases they leverage - such as physical symmetries and chemical properties - to learn informative representations of these geometric graphs. In this opinionated paper, we provide a comprehensive and self-contained overview of the field of Geometric GNNs for 3D atomic systems. We cover fundamental background material and introduce a pedagogical taxonomy of Geometric GNN architectures: (1) invariant networks, (2) equivariant networks in Cartesian basis, (3) equivariant networks in spherical basis, and (4) unconstrained networks. Additionally, we outline key datasets and application areas and suggest future research directions. The objective of this work is to present a structured perspective on the field, making it accessible to newcomers and aiding practitioners in gaining an intuition for its mathematical abstractions.

Related papers

• Geometry Informed Tokenization of Molecules for Language Model Generation [85.80491667588923]
  We consider molecule generation in 3D space using language models (LMs) Although tokenization of molecular graphs exists, that for 3D geometries is largely unexplored. We propose the Geo2Seq, which converts molecular geometries into $SE(3)$-invariant 1D discrete sequences.
  arXiv  Detail & Related papers  (2024-08-19T16:09:59Z)
• A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applications [67.33002207179923]
  This paper presents a survey of data structures, models, and applications related to geometric GNNs. We provide a unified view of existing models from the geometric message passing perspective. We also summarize the applications as well as the related datasets to facilitate later research for methodology development and experimental evaluation.
  arXiv  Detail & Related papers  (2024-03-01T12:13:04Z)
• On the Completeness of Invariant Geometric Deep Learning Models [22.43250261702209]
  Invariant models are capable of generating meaningful geometric representations by leveraging informative geometric features in point clouds. We show that GeoNGNN, the geometric counterpart of one of the simplest subgraph graph neural networks (subgraph GNNs), can effectively break these corner cases' symmetry. By leveraging GeoNGNN as a theoretical tool, we further prove that: 1) most subgraph GNNs developed in traditional graph learning can be seamlessly extended to geometric scenarios with E(3)-completeness.
  arXiv  Detail & Related papers  (2024-02-07T13:32:53Z)
• A quatum inspired neural network for geometric modeling [14.214656118952178]
  We introduce an innovative equivariant Matrix Product State (MPS)-based message-passing strategy. Our method effectively models complex many-body relationships, suppressing mean-field approximations. It seamlessly replaces the standard message-passing and layer-aggregation modules intrinsic to geometric GNNs.
  arXiv  Detail & Related papers  (2024-01-03T15:59:35Z)
• Symmetry-Informed Geometric Representation for Molecules, Proteins, and Crystalline Materials [66.14337835284628]
  We propose a platform, coined Geom3D, which enables benchmarking the effectiveness of geometric strategies. Geom3D contains 16 advanced symmetry-informed geometric representation models and 14 geometric pretraining methods over 46 diverse datasets.
  arXiv  Detail & Related papers  (2023-06-15T05:37:25Z)
• 3D Molecular Geometry Analysis with 2D Graphs [79.47097907673877]
  Ground-state 3D geometries of molecules are essential for many molecular analysis tasks. Modern quantum mechanical methods can compute accurate 3D geometries but are computationally prohibitive. We propose a novel deep learning framework to predict 3D geometries from molecular graphs.
  arXiv  Detail & Related papers  (2023-05-01T19:00:46Z)
• A new perspective on building efficient and expressive 3D equivariant graph neural networks [39.0445472718248]
  We propose a hierarchy of 3D isomorphism to evaluate the expressive power of equivariant GNNs. Our work leads to two crucial modules for designing expressive and efficient geometric GNNs. To demonstrate the applicability of our theory, we propose LEFTNet which effectively implements these modules.
  arXiv  Detail & Related papers  (2023-04-07T18:08:27Z)
• GeoMol: Torsional Geometric Generation of Molecular 3D Conformer Ensembles [60.12186997181117]
  Prediction of a molecule's 3D conformer ensemble from the molecular graph holds a key role in areas of cheminformatics and drug discovery. Existing generative models have several drawbacks including lack of modeling important molecular geometry elements. We propose GeoMol, an end-to-end, non-autoregressive and SE(3)-invariant machine learning approach to generate 3D conformers.
  arXiv  Detail & Related papers  (2021-06-08T14:17:59Z)
• Learning Geometry-Dependent and Physics-Based Inverse Image Reconstruction [9.565653662306806]
  We present a new approach to learn inverse imaging that exploit the underlying geometry and physics. We first introduce a non-Euclidean encoding-decoding network that allows us to describe the unknown and measurement variables. We then learn the geometry-dependent physics in between the two domains by explicitly modeling it via a bipartite graph.
  arXiv  Detail & Related papers  (2020-07-18T21:53:27Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.