CGCNN—A Graph Representation of Materials for Property Prediction and

Materials Design

Tian Xie, Jeffrey GrossmanDepartment of Materials Science and Engineering,

Massachusetts Institute of Technology11/29/2018

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Deep learning for different data types

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Images

Grid-like

Language

Time series

Graph

Relational

CNNTranslation invariance

RNNTime

invariance

GCNNode

invarianceBattaglia, et al., arXiv preprint arXiv:1806.01261 (2018).

Invariances are built into the neural networks to prevent overfitting

Representation of solid materials

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Molecule graphs• Node invariance à atom

indistinguishability • Graph construction is straightforward• All information encoded

Gasteiger, et al. Angew. Chem. Int. Ed. Engl. 32.4 (1993): 503-527.Duvenaud, et al. Adv Neural Inf Process Syst. 2015.Kearnes, et al. J. Comput. Aided Mol. Des. 30.8 (2016): 595-608.Gilmer, et al. arXiv preprint arXiv:1704.01212 (2017).Crystal (solid material) graphs

• 3D structure of materials are important

• Many materials are periodic• Bond determination can be

ambiguous• Rare elements

Innovation needed for graph construction and network design

N

N N

N

O

O

Design of CGCNN

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Tian Xie, and Jeffrey C. Grossman. Phys. Rev. Lett. 120.14 (2018): 145301.

Crystal Graph Convolutional Neural Networks (CGCNN)

¡ 3D structure: use distances as edge attributes

¡ Periodicity: multigraphs instead of normal graphs

¡ Rare elements: element encoding based on elemental properties

¡ Bond ambiguity: ”gated architecture” in GCN

3D molecules:Schütt, et al. Nat. Commun. 8 (2017): 13890.Schütt, et al. J. Chem. Phys. 148.24 (2018): 241722.

Na1 Na1Cl1

Periodic image

Prediction performance

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¡ Materials project: 87 elements, 216 space groups, up to 7 different elements and 200 atoms in unit cell.

¡ Achieve DFT accuracy on test sets for 7 properties with 10# data points.

Tian Xie, and Jeffrey C. Grossman. Phys. Rev. Lett. 120.14 (2018): 145301.

Application: solid state electrolytes

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Zeeshan Ahmad, Tian Xie, et al. ACS Cent. Sci. 4.8 (2018): 996-1006.

¡ Lithium metal batteries¡ Dendrite growth at the interface

between Lithium metal and electrolytes is a big problem

¡ Causes short circuit and capacity loss¡ Design new electrolytes to suppress

dendrite growth

¡ Kinetic model for the stability of the interface¡ Inputs: shear/bulk modulus, molar

volumes¡ Output: Stability parameter !

(negative means stable)

Ahmad, et al. Phys. Rev. Lett. 119.5 (2017): 056003.In collaboration with Zeeshan & Prof. Viswanathan from CMU

Application: solid state electrolytes

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In collaboration with Zeeshan & Prof. Viswanathan from CMU

¡ Screening Li-containing solids¡ Data: ~3400 training data from Materials

Project¡ Predicted stability parameter ! for

12,950 solid materials¡ Identified several candidates

¡ Uncertainty estimation¡ CGCNN ensembles for uncertainty

estimation¡ Extrapolation can cause higher

uncertainties

Zeeshan Ahmad, Tian Xie, et al. ACS Cent. Sci. 4.8 (2018): 996-1006.

Hierarchical visualization of CGCNN

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E0

En

E

¡ Elemental representation¡ Only the information of

elements

¡ Local representation¡ Surrounding elements¡ Local configuration

Tian Xie, and Jeffrey C. Grossman. J. Chem. Phys. 149.17 (2018): 174111.

¡ Local energy¡ Energy of the atom in

local environments

Perovskites: different compositions

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¡ Perovskites¡ A crystal structure

type ABC3

¡ Site A, B: metals¡ Site C: O, F, S, N

Tian Xie, and Jeffrey C. Grossman. J. Chem. Phys. 149.17 (2018): 174111.

Less data needed for element representations

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Tian Xie, and Jeffrey C. Grossman. J. Chem. Phys. 149.17 (2018): 174111.

234 training data (1/64)

937 training data (1/16)

3,750 training data (1/4)

15,000 training data

Boron: different configurations

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Tian Xie, and Jeffrey C. Grossman. J. Chem. Phys. 149.17 (2018): 174111.

Energy of different coordination environments

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Tian Xie, and Jeffrey C. Grossman. J. Chem. Phys. 149.17 (2018): 174111.

Tm-H solid solutions

Special stability due to Al-O, Si-O, P-O, S-O covalent bond

¡ Local energy of all 734,077 distinct coordination environments in Materials Project

¡ General trends¡ Diagonal lines: zero

local energy¡ Most stable: high

valence metals + high electronegativity non-metals à strong ionic bondseV/atom

Summary

¡ CGCNN provides a general framework to learn structure-property relations for solid materials.

¡ Uncertainty estimation is important when applying ML to real material systems.

¡ Visualization of neural networks can provide additional insights for materials design.

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References and codes

¡ References:¡ Xie, Tian, and Jeffrey C. Grossman. "Crystal Graph Convolutional Neural

Networks for an Accurate and Interpretable Prediction of Material Properties." Physical review letters 120.14 (2018): 145301.

¡ Ahmad, Zeeshan, et al. "Machine Learning Enabled Computational Screening of Inorganic Solid Electrolytes for Suppression of Dendrite Formation in Lithium Metal Anodes." ACS central science 4.8 (2018): 996-1006.

¡ Xie, Tian, and Jeffrey C. Grossman. "Hierarchical visualization of materials space with graph convolutional neural networks." The Journal of chemical physics 149.17 (2018): 174111.

¡ Codes:¡ CGCNN: https://github.com/txie-93/cgcnn

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Thank you!