Fig. 1. Overview of the descriptor (a), grid (b), graph (c), and the "global + local" (d) representations of the chemical structure used for ML, where CNN and MPNN denote convolution neural network and message passing neural network [38], respectively. The white, red, blue and gray squares illustrate the feature vectors corresponding to the different representations.

Fig. 2. Symmetry elements contained in SV (a), DV (b) and HV (c) defects with different N contents, where Cn, i, σ and E represent n-fold rotation axis, symmetry center, vertical mirror, and identity element, respectively. Numbers in parentheses distinguish structures containing different symmetry elements. TM atom protrudes from the plane in SV, while in DV and HV, it is in the same plane as other atoms owing to the large defect space in DV and HV.

Fig. 3. Workflow of the double-input single-output GLCNN framework based on the "global + local" strategy, where the gray and blue spheres represent C and Pd atoms, respectively. First, the original chemical structure is expanded and gridded, and multiple channels are added. Subsequently, all channels are cropped, flipped, and resized to generate the input of the CNN module. In contrast, the 1D descriptor related to the adsorption site is fed as the second input and concatenated with the output from the CNN module to form a new input, which is finally transmitted to the fully connected (FC) module to obtain the predicted adsorption energy.

Fig. 4. Structure of original sample (a) and a collection of (b) cropped and flipped data (c) derived from it, taking the channel of atomic number as example. Electronegativity channels of catalysts with (d) cis and (e) trans configurations. The original grid with a size of 128×128 is reduced to 32×32 after the processing of a 64×64 sliding window and Gaussian reconstruction. Gray and blue spheres represent C and Pd atoms, respectively. All augmented data represents the same chemical structure. The dark blue background and fluorescent green/blue highlights represent the vacuum area and atoms respectively.

Fig. 5. Architecture of the CNN model. Grids and descriptors are the two inputs of GLCNN, where 6×(32×32) represents grids with the size of 32×32 containing 6 channels, and 15×1 denotes 15 features. Conv2d represents a 2D convolution layer, where 6×(5×5) represents 6 kernels with the size of 5×5. MaxPool2d is the maximum pooling layer with the size of the pooling window set at (2×2). FC is the fully connected layer, where 101×2000 represents the shape of the input and output of the FC layer. The blue and red boxes belong to “global” and “local” sections, respectively. Layers in the green box integrate the outputs of the "global" and "local" sections and produce the final prediction.

Fig. 6. (a) Learning curve of the GLCNN in predicting OH adsorption energies, in which MAE*s are estimated by the five-fold cross-validation approach. Comparison between DFT-calculated and model-predicted values of OH adsorption energies using GLCNN (b), linear regression13 (c) and CGCNN35 (d), where a histogram of data distribution is displayed on the top of (b). Insets show the comparison between DFT-calculated and model-predicted values of data with cis/trans (red/green) configurations in the test set. Points of the same shape denote paired cis/trans configurations with the same cell expansion coefficient, defect type, and N content.

Fig. 7. (a) PFI analysis of the GLCNN model. The black vertical dashed line represents the MAE* of the model without permutation (0.099 eV). Distribution of the difference of OH adsorption energies for DV (b) and HV (c) defects with cis/trans configurations. Energy subtraction occurs between cis and trans configurations with the same cell expansion coefficient, defect type, and N content (i.e., Fig. S1(a) and Fig. S1(b), or Fig. S1(c) and Fig. S1(d)). A difference greater than 0.6 eV is rare and not shown.

Fig. 8. Intermediate output of the first convolution (a) and activation (b) layer and the second convolution (c) and activation layer (d). The red circle enclosed the obvious feature extraction. Thermal diagrams obtained from Grad-CAM analysis of the first (e) and second (f) convolution layer.

Fig. 9. t-SNE analysis using the adsorption energy of OH (a,d,g), group number of TM (b,e,h), defect type (c,f,i) as fitting or classification criteria of the first (a?c), second (d?f), and third (g?i) FC layers, respectively. The numbers 3-12 in (b) represent the group of the TMs in the periodic table from left to right, which is consistent with the element attribute setting in the pymatgen python package (Fig. S3).