(477j) Adaptive Spectral Graph Convolutional Neural Network in Crystal Property Prediction

Machine Learning (ML) has been more and more widely used in accelerating the design of new materials due to its close accuracy and less computational cost in predicting material properties comparing to simulation methods. However, existing ML methods for designing of crystalline materials are usually not flexible to handle different crystal types or hard to interpret because of the arbitrary size. Although there are more generalized models such as Crystal Graph Convolutional Neural Networks (CGCNN) which utilized graph CNN to encode the structure of a crystal, they are over-localized and impossible to learn beyond the bond connectivity. Here we show a stronger and more adaptive framework, based on spectral convolutional neural network, which is not only capable for arbitrary crystal structure but also learns a unique graph representation based on both global and local topology of each crystal.

First a crystal graph is produced base on the cif file of the crystal similar to CGCNN, and each node is encoded with its atomic properties such as electronegativity, covalent radius, etc. The connectivity is determined based on the distance between each atom. The graph Laplacian L is then obtained by performing graph Fourier transformation on the crystal graph. The transformation process can be decomposed by a complete set of eigenvectors U and the eigenvalue matrix LAMBDA(λ), which represents the topology of the graph. The spectral filter g_θ(λ) generates a customized convolution kernel on the graph in space which can be formulated by

g_θ(λ)=(sum from k=0 to k=k-1)∑θ_kλ^k

Where k can be interpreted as the number of convolutions in space.

However, this graph convolution cannot exploit the topological property of the graph. It is possible that the disconnected nodes have larger correlation than those connected nodes. To achieve the capability to learn from the geometric structure, we adapted a new spectral filter from Li et.al¹ which takes a non Euclean metric so that it learns a residual graph apart from the intrinsic crystal graph which makes a correction on the original graph Laplacian L:

L(with hat) = L + αL_res

The overall intrinsic plus residue graph is trained with the spectral graph convoluted neural network to predict chemical properties of crystal and results are compared with various existing models.

[1] Li, R., Wang, S., Zhu, F. and Huang, J., 2018, April. Adaptive graph convolutional neural networks. In Thirty-second AAAI conference on artificial intelligence.