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interpretability of the IGNN model classification process is enhanced through the t-distributed stochastic neighbor
embedding (t-SNE) visualization method. Additionally, the IGNN model exhibited excellent performance in
predicting the density of multicomponent complex intermetallic compounds, indicating its robustness and
generalizability. This study presents a graph neural network (GNN) method suitable for multi-crystal structure data
modeling, providing a novel computational framework for density prediction in intermetallic compounds. This
advancement represents a significant contribution to this field, paving the way for more targeted material selection
and application in lightweight technologies.

Keywords: Intermetallic compounds, density, machine learning, graph neural network

INTRODUCTION
Owing to their unique physical and chemical properties, intermetallic compounds are recognized for
considerable application potential in modern industry, particularly in aerospace, energy, electronics, and
automotive industries . These compounds are usually composed of two or more metallic elements in
[1-3]
defined ratios, demonstrating excellent mechanical properties, corrosion resistance, thermal stability, and
magnetic properties through their specific crystal structures. Such attributes render intermetallic
compounds a vital option for creating high-performance and durable materials, meeting the demands of
[4-6]
modern technology for materials withstanding extreme conditions . Density, a critical parameter of
intermetallic compounds, is essential for their material properties and applications, and it directly influences
[7-9]
the lightweight design capabilities required in many industrial applications . For example, lightweight
materials are required in the aerospace and automotive fields to maintain low density without sacrificing
strength under extreme conditions, such as high temperatures and pressures, to reduce structural load and
improve fuel efficiency while reducing greenhouse gas emissions [10,11] .

Although density is crucial for the applications of intermetallic compounds, their experimental
measurement is challenging, particularly when involving multiple metallic elements and complex crystal
structures. Certain intermetallic compounds may not be reliably synthesized in the laboratory due to
preparation difficulties or compound instability, increasing the difficulty and cost of experimental density
measurement [12,13] . The efficiency of direct experimental density measurement is considered low, especially
when large-scale compound data needs to be studied. Consequently, developing effective methods for
density prediction holds practical significance. Density prediction via theoretical models or data-driven
methods can reduce experimental costs and time, while also offering a reliable foundation for high-
throughput material screening and early design. However, accurate prediction of intermetallic compound
density faces some challenges. Conventional physical models such as density functional theory (DFT) are
known to yield accurate results on smaller datasets but are inefficient for large-scale density predictions [14,15] .
Additionally, physical models struggle to accurately address isomers, where compounds of the same
chemical composition exhibit significant density differences due to varying crystal structures. Such factors,
relatively common in intermetallic compounds, further complicate and increase the difficulty of prediction.

To address these challenges, data-driven machine learning methods have been gradually introduced into the
field of intermetallic compounds in recent years [16-18] . Researchers have employed machine learning
algorithms to predict the physical properties of intermetallic compounds. Although these traditional
machine learning methods have demonstrated some effectiveness in improving prediction efficiency, they
also encounter limitations in handling complex crystal structures, particularly in capturing structural
differences between isomers. Traditional machine learning models are generally reliant on Vegard’s law,
which calculates the average feature representations by summing the elemental features to the properties of
the entire compounds. However, these methods are limited, as they fail to sufficiently incorporate the