A Cartesian Encoding Graph Neural Network for Crystal Structures Property Prediction: Application to Thermal Ellipsoid Estimation

TL;DR

This paper presents CartNet, a graph neural network that efficiently predicts crystal properties, especially thermal ellipsoids, by encoding atomic geometry and temperature, significantly reducing computational costs and improving accuracy.

Contribution

The paper introduces CartNet, a novel GNN with a neighbor equalization technique and a Cholesky head, along with rotational data augmentation, for accurate and efficient crystal property prediction.

Findings

CartNet outperforms existing methods in ADP prediction by 10.87%.

Achieves a 34.77% improvement over theoretical approaches.

Demonstrates strong performance on multiple crystal property datasets.

Abstract

In diffraction-based crystal structure analysis, thermal ellipsoids, quantified via Anisotropic Displacement Parameters (ADPs), are critical yet challenging to determine. ADPs capture atomic vibrations, reflecting thermal and structural properties, but traditional computation is often expensive. This paper introduces CartNet, a novel graph neural network (GNN) for efficiently predicting crystal properties by encoding atomic geometry into Cartesian coordinates alongside the crystal temperature. CartNet integrates a neighbour equalization technique to emphasize covalent and contact interactions, and a Cholesky-based head to ensure valid ADP predictions. We also propose a rotational SO(3) data augmentation strategy during training to handle unseen orientations. An ADP dataset with over 200,000 experimental crystal structures from the Cambridge Structural Database (CSD) was curated to validate the approach. CartNet significantly reduces computational costs and outperforms existing methods in ADP prediction by 10.87%, while delivering a 34.77% improvement over theoretical approaches. We further evaluated CartNet on other datasets covering formation energy, band gap, total energy, energy above the convex hull, bulk moduli, and shear moduli, achieving 7.71% better results on the Jarvis Dataset and 13.16% on the Materials Project Dataset. These gains establish CartNet as a state-of-the-art solution for diverse crystal property predictions. Project website and online demo: https://www.ee.ub.edu/cartnet