2. Calculation details
2.1. Crystal structure and calculations method As shown in Fig. S1, a 4 × 4 × 1 graphene supercell with 32 C atoms for all calculations is presented. As described above, all surface geometry is modeled as a periodic flat plate system, with a 20 Åvacuum between the surfaces sufficient to prevent interaction between periodic images. The first principle calculation utilized the generalized gradi- ent approximation (GGA) in addition to the Perdew–Burke–Ernzerhof (PBE) [27,28]. Among the best theoretical methodologies for studying the many-body problem and computing ground state properties is density functional theory (DFT) [29–31]. To achieve this, we employed projected augmented wave pseudo-potentials with GGA parametrized PBE, as implemented in the Cambridge Sequential Total Energy Pack- age (CASTEP) [32]. Atomic spin polarization was considered for the database generation, and dispersion interactions of DFT-D (van der Waals dispersion corrections) was chosen. A plane wave function cut off energy (E   ) of 470 eV was specified [33], and the Monkhorst- Pack special K-grid point method was employed for the Brillouin zone, with an 8 × 8 × 1 K-point grid point adopted for the calculation [33].
The computational process operated with high iterative convergence accuracy (5.0 × 10−7 eV/atom), the accuracy of calculation enhances the reliability and precision of the crystal structure. The force acting on each atom is no more than 0.01 eV/Å, the maximum displacement is 5.0 × 10−4 Å, and the internal stress is no more than 0.02 GPa. 2.2. Machine learning databases and models In order to overcome the challenges for computer hardware posed by DFT calculations, we designed various machine learning algorithms to predict the results of DFT calculations of adsorption energy and ad- sorption distance between different atoms and single vacancy graphene. As shown in Fig. 1(a), the machine learning scheme for accelerated prediction of single vacancy graphene adsorption properties consists of three steps: (1) adsorption property database building, (2) machine learning model building and screening, and (3) periodic table ele- ment adsorption property prediction. The machine learning process accelerates the DFT computation through three parts: Data generation, model construction, and prediction. Cross-validation cuts the dataset into smaller subsets and loops them as validation sets, which can improve the reliability of results in small-sample machine learning. The genetic algorithm obtains the optimal connection weights by a cycle of selection, crossover, and mutation. The machine learning method shows advantages over the traditional DFT calculation in terms of time cost. Our machine learning approach aims to establish regression relationships between the adsorption properties of different atoms and single vacancy graphene based on the results of a limited number of DFT calculations. By comparing multiple machine learning algo- rithms, four machine learning models are built using the best-fitting algorithm to predict the adsorption energy and adsorption distance, respectively. The machine learning models used in this paper include BP neural network(BPNN), K-nearest neighbor(KNN), support vector machine(SVM), and decision tree(DT). Among them, the BPNN model has three network layers, which are input layer, output layer, and hide layer respectively. The model adds back propagation of the output error of artificial neurons to the standard artificial neural network to obtain a more accurate mapping relationship between input layers and output layers, as shown in Fig. 1(a). Meanwhile, as shown in Fig. 1(a), genetic algorithm can simulate the replication, crossover and mutation that occur in natural selection and heredity. Through the evolution of reproduction from generation to generation, the individual that is most adapted to the environment can be obtained. We evaluated and screened four different models using a five-fold cross-validation method, with 80% and 20% of the data used for training and validation, respectively. After selecting the best model, to ensure that the final model contains as much information as possible and to avoid the risk of overfitting, we used 85% of the data for training and 15% for validation. The genetic algorithm can optimize the connection power coefficients between artificial neurons to obtain a better performing model. 翻译成中文