Developing an improved crystal graph convolutional neural network framework for accelerated materials discovery

The recently proposed crystal graph convolutional neural network (CGCNN) offers a highly versatile and accurate machine learning (ML) framework by learning material properties directly from graphlike representations of crystal structures (“crystal graphs”). Here, we develop an improved variant of the CGCNN model (iCGCNN) that outperforms the original by incorporating information of the Voronoi tessellated crystal structure, explicit three-body correlations of neighboring constituent atoms, and an optimized chemical representation of interatomic bonds in the crystal graphs. We demonstrate the accuracy of the improved framework in two distinct illustrations: First, when trained/validated on 180 000/20 000 density functional theory (DFT) calculated thermodynamic stability entries taken from the Open Quantum Materials Database (OQMD) and evaluated on a separate test set of 230 000 entries, iCGCNN achieves a predictive accuracy that is significantly improved, i.e., 20% higher than that of the original CGCNN. Second, when used to assist a high-throughput search for materials in the $\mathrm{ThC}{\mathrm{r}}_2\mathrm{S}{\mathrm{i}}_2$ structure-type, iCGCNN exhibited a success rate of $31\%$ which is 155 times higher than an undirected high-throughput search and 2.4 times higher than that of the original CGCNN. Using both CGCNN and iCGCNN, we screened 132 600 compounds with elemental decorations of the $\mathrm{ThC}{\mathrm{r}}_2\mathrm{S}{\mathrm{i}}_2$ prototype crystal structure and identified a total of 97 unique stable compounds by performing 757 DFT calculations, accelerating the computational time of the high-throughput search by a factor of 65. Our results suggest that the iCGCNN can be used to accelerate high-throughput discoveries of new materials by quickly and accurately identifying crystalline compounds with properties of interest.

Figure 1

Illustration of iCGCNN crystal graph. The crystal graph shown on the far right represents the local environment of atom $\mathit{A}$. Multiple edges connect $\mathit{A}$ to neighboring nodes to show the number of Voronoi neighbors. The nodes and edges are embedded with vectors that characterize the constituent atoms $({\mathit{v}}_{\mathit{i}},{\mathit{v}}_{\mathit{j}})$ and their correlations with neighboring atoms $({\mathit{u}}_{{\left(\mathit{i},\mathit{i}\right)}_{\mathit{k}}},{\mathit{u}}_{{\left(\mathit{i},\mathit{j}\right)}_{\mathit{k}}})$ respectively. Edge vectors include information about the Voronoi polyhedra such as solid angle, area, and volume.

Figure 2

Predictive accuracies of CGCNN and iCGCNN using strategy 1. Hull distances are evaluated by taking the differences between ML-predicted formation energies and DFT-calculated convex hull energies. (a), (b) DFT vs ML formation energies for (a) CGCNN and (b) iCGCNN. Red arrows indicate the common outliers in CGCNN and iCGCNN predictions. (c), (d) DFT vs ML predicted hull distances for (c) CGCNN and (d) iCGCNN. Close up on compounds with hull distances smaller than 50 meV/atom for (c) and (d) are shown in (e) and (f) respectively.

Figure 3

Predictive accuracies of CGCNN and iCGCNN using strategy 2. ML models are trained to directly predict the hull distances. (a), (b) DFT vs ML predicted hull distances for (a) CGCNN and (b) iCGCNN. Closeup on compounds with hull distances smaller than 50 meV/atom for (a) and (b) are shown in (c) and (d) respectively.

Figure 4

(a) Structure of $\mathrm{ThC}{\mathrm{r}}_2\mathrm{S}{\mathrm{i}}_2$. (b) Periodic table where colored elements were substituted into $\mathrm{ThC}{\mathrm{r}}_2\mathrm{S}{\mathrm{i}}_2$ structure to generate new compounds.

Figure 5

Periodic tables where elements are color-coded based on the number of stable occurrences on the (a) Th site, (b) Cr site, and (c) Si site.