Geometric Prediction: Moving Beyond Scalars

TL;DR

This paper demonstrates that equivariant neural networks can directly predict real-world geometric tensors, such as force fields and biomolecular structures, improving data efficiency and generalization in geometric prediction tasks.

Contribution

The work introduces the use of equivariant networks for direct geometric tensor prediction, surpassing scalar approximation methods and applying to complex real-world problems.

Findings

Equivariant networks successfully predict force fields and biomolecular structures.

The method generalizes well to unseen systems with limited training data.

Achieves state-of-the-art results in biomolecular structure refinement.

Abstract

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.