Geometric Prediction: Moving Beyond Scalars

By Raphael J. L. Townshend, Brent Townshend, Stephan Eismann, Ron O. Dror. 2020

14 citations recorded by the source corpus.

Many quantities we are interested in predicting are geometric tensors; we refer to this class of problems as geometric prediction. Attempts to perform geometric prediction in real-world scenarios have been limited to approximating them through scalar predictions, leading to losses in data efficiency. In this work, we demonstrate that equivariant networks have the capability to predict real-world geometric tensors without the need for such approximations. We show the applicability of this method to the prediction of force fields and then propose a novel formulation of an important task, biomolecular structure refinement, as a geometric prediction problem, improving state-of-the-art structural candidates. In both settings, we find that our equivariant network is able to generalize to unseen systems, despite having been trained on small sets of examples. This novel and data-efficient ability to predict real-world geometric tensors opens the door to addressing many problems through the lens of geometric prediction, in areas such as 3D vision, robotics, and molecular and structural biology.

Subfields: Artificial Intelligence, Materials Chemistry, Molecular Biology

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Citations in the corpus

Relevance of Rotationally Equivariant Convolutions for Predicting Molecular Properties (2020, background): “…which depend only on the atomic distance graph, are commonly predicted by kernel methods or Gaussian process regression [14, 15, 16, 17] or graph neural networks [18, 19], where ENNs are usually employed for predicting physical properties, which depend on atomic displacement vectors [20, 21].”
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.”
E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials (2021, methodology): “Townshend et al. [19] use the framework of Tensor-Field Networks [20] to directly predict atomic force vectors.”