Figure4

Figure 4. GNNs applied in CSP. (A) Prediction pipeline; (B) Examples of structures stored in database. Reproduced from Ref.^[144]. CC BY 4.0; (C) MPNN predicts the quantum properties of an organic molecule. Reproduced from Ref.^[128]. CC BY-NC 4.0; (D) Illustration of the CGCNN, including construction of the crystal graph and then building the structure of the convolutional neural network on top of the crystal graph. Reproduced with permission^[107]. Copyright 2018, American Physical Society; (E) Overview of MEGNet. The initial graph is represented by the set of atomic attributes $$ V = \{v_i\}_{i=1}^{N_v} $$, bond attributes $$ E = \{(e_k, r_k, s_k)\}_{k=1}^{N_e} $$, and global state attributes $$ u $$. Reproduced with permission^[126]. Copyright 2019, American Chemical Society; (F) ALIGNN convolution layer alternates between message passing on the bond graph and its line graph. Reproduced from Ref.^[133]. CC BY 4.0. GNNs: Graph neural networks; CSP: crystal structure prediction; MPNN: message passing neural network; CGCNN: crystal graph convolutional neural network; MEGNet: materials graph network; ALIGNN: atomistic line graph neural network.