Virtual Node Graph Neural Network for Full Phonon Prediction
The structure-property relationship plays a central role in materials
science. Understanding the structure-property relationship in solid-state
materials is crucial for structure design with optimized properties. The past
few years witnessed remarkable progress in correlating structures with
properties in crystalline materials, such as machine learning methods and
particularly graph neural networks as a natural representation of crystal
structures. However, significant challenges remain, including predicting
properties with complex unit cells input and material-dependent,
variable-length output. Here we present the virtual node graph neural network
to address the challenges. By developing three types of virtual node approaches
- the vector, matrix, and momentum-dependent matrix virtual nodes, we achieve
direct prediction of $\Gamma$-phonon spectra and full dispersion only using
atomic coordinates as input. We validate the phonon bandstructures on various
alloy systems, and further build a $\Gamma$-phonon database containing over
146,000 materials in the Materials Project. Our work provides an avenue for
rapid and high-quality prediction of phonon spectra and bandstructures in
complex materials, and enables materials design with superior phonon properties
for energy applications. The virtual node augmentation of graph neural networks
also sheds light on designing other functional properties with a new level of
flexibility.
Ryotaro Okabe, Abhijatmedhi Chotrattanapituk, Artittaya Boonkird, Nina Andrejevic, Xiang Fu, Tommi S. Jaakkola, Qichen Song, Thanh Nguyen, Nathan Drucker, Sai Mu, Bolin Liao, Yongqiang Cheng, Mingda Li
# Virtual Node Graph Neural Network for Full Phonon Prediction

###### Abstract

The structure-property relationship plays a central role in materials science. Understanding the structure-property relationship in solid-state materials is crucial for structure design with optimized properties. The past few years witnessed remarkable progress in correlating structures with properties in crystalline materials, such as machine learning methods and particularly graph neural networks as a natural representation of crystal structures. However, significant challenges remain, including predicting properties with complex unit cells input and material-dependent, variable-length output. Here we present the virtual node graph neural network to address the challenges. By developing three types of virtual node approaches - the vector, matrix, and momentum-dependent matrix virtual nodes, we achieve direct prediction of \(\Gamma\)-phonon spectra and full dispersion only using atomic coordinates as input. We validate the phonon bandstructures on various alloy systems, and further build a \(\Gamma\)-phonon database containing over 146,000 materials in the Materials Project. Our work provides an avenue for rapid and high-quality prediction of phonon spectra and bandstructures in complex materials, and enables materials design with superior phonon properties for energy applications. The virtual node augmentation of graph neural networks also sheds light on designing other functional properties with a new level of flexibility.

## Introduction

The structure-property relationship defines one of the most fundamental questions in materials science [16, 21]. The ubiquitous presence of structure-property relationships profoundly influences almost all branches of materials sciences, such as structural materials [3], energy harvesting and conversion and energy storage materials [17, 5, 19], catalysts [37] and polymers [13], and quantum materials [15]. However, despite its central importance to materials design, building an informative structure-property relationship can be nontrivial. On the one hand, the number of stable structures grows exponentially with unit cell size [22], and the structure design efforts have been largely limited to crystalline solids with relatively small unit cells. On the other hand, certain material properties are challenging to acquire due to experimental or computational complexities.

In the past few years, data-driven and machine-learning methods play an increasingly important role in materials science and significantly boost the research on building structure-property relationships [24, 6, 38]. Complex structures such as porous materials [1, 27], nanoalloys [10, 36], and grain boundaries [34] are becoming more feasible to handle, and properties ranging from mechanical strength to quantum ordering can be learned with increased confidence [9, 29]. One particular powerful approach is the graph neural networks (GNNs) [7]. By representing atoms as graph nodes and interatomic bonds as graph edges, GNNs