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

2025-01-30

AI Summary

To address the computational inefficiency and difficulty in balancing physical plausibility with accuracy in conventional anisotropic displacement parameter (ADP) estimation for crystals, this work introduces CartNet—the first graph neural network integrating Cartesian geometric encoding with temperature information. Key contributions include: (1) novel joint modeling of atomic Cartesian coordinates and temperature; (2) a neighborhood-balanced aggregation mechanism explicitly distinguishing covalent bonds from van der Waals contacts; (3) a Cholesky decomposition-based output head ensuring strict positive definiteness of predicted ADP matrices; and (4) SO(3)-equivariant data augmentation to enhance rotational robustness. Evaluated on a self-constructed dataset of >200,000 crystal structures from the Cambridge Structural Database (CSD), CartNet reduces ADP prediction error by 10.87% over state-of-the-art methods and by 34.77% over first-principles calculations. Downstream crystal property prediction accuracy improves by 7.71% on the Jarvis dataset and 13.16% on the Materials Project dataset.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models
• Computer Vision: Adversarial Attacks & Robustness

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Ad search and search for Web retail
• Systems and Infrastructure for Web, Mobile and WoT: Sustainability and carbon-aware systems for Web, mobile, and WoT

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

Problem

• Anisotropic Displacement Parameters
• Crystal Properties
• Computational Methods

Innovation

• CartNet
• crystal property prediction
• anisotropic displacement parameters