Crystal Graph Convolutional Neural Network (CGCNN)

Represents a crystal as a multigraph where nodes are atoms and edges encode interatomic bonds across periodic boundaries. Unlike molecular graphs, CGCNN connects each atom to its nearest neighbors in both the original unit cell and its periodic images, capturing the infinite, repeating nature of crystalline solids. The graph is constructed by finding the k-nearest neighbors within a cutoff radius, with edge features initialized as a Gaussian expansion of interatomic distances.

Performs iterative message passing where atom feature vectors are updated by aggregating information from neighboring atoms. The update function concatenates the source atom vector, neighbor atom vector, and their distance-based edge features, then passes this through a learnable neural network layer followed by a soft-attention gate. This gating mechanism allows the model to selectively weight the importance of different neighboring interactions.

Explicitly accounts for translational symmetry by constructing edges that cross unit cell boundaries. When an atom's nearest neighbor lies in an adjacent periodic image, the edge is created with the correct periodic distance vector, ensuring the graph faithfully represents the infinite crystal lattice. This allows CGCNN to learn properties that depend on long-range periodic order, such as band gaps and bulk moduli.

After convolutional layers, atom-level feature vectors are aggregated into a crystal-level representation using normalized summation pooling—summing all atom vectors and dividing by the number of atoms. This permutation-invariant pooling ensures the prediction is independent of atom indexing order. The pooled vector is then passed through fully connected layers to predict target properties like formation energy, band gap, or shear modulus.

Originally trained on the Materials Project database containing DFT-calculated properties for tens of thousands of inorganic crystals. The model learns to map directly from Crystallographic Information Files (CIF) to target properties, bypassing expensive first-principles calculations. Key training targets include:

• Formation energy (eV/atom)
• Band gap (eV)
• Bulk and shear moduli (GPa)
• Poisson's ratio

Demonstrates strong transfer learning capabilities by pre-training on large DFT datasets and fine-tuning on smaller experimental datasets. The convolutional layers learn universal representations of local atomic environments that transfer across different material chemistries and properties. This enables accurate predictions even when only hundreds of training examples are available, critical for properties that are expensive to measure experimentally.