Prediction of sodium binding energy on 2D VS₂via machine learning: a robust accompanying method to ab initio random structure searching

In this work, we employed the back-propagation neural network (BPNN) for predicting the energetics of different sodium adsorption phases on the VS₂ monolayer generated via ab initio random structure searching (AIRSS). Two key adsorption features were identified as inputs: the average Na-Na distance and a defined adsorption feature marker that indicates the number of nearest-neighbor pairs within a sodium cluster. Using the stoichiometric structure Na_0.5VS₂ as the test system, we first generated 50 random sensible structures via AIRSS and optimized them via density functional theory (DFT) calculations to obtain the sodium binding energy per atom. From these, 30 were utilized to train 3000 BPNNs with varying numbers of neurons and types of activation functions. The remaining 20 were employed to verify the generalization of the best identified BPNN model for the considered Na_0.5VS₂ system. The calculated mean absolute error for the predicted sodium binding energy per atom is smaller than 0.1 eV. This suggests that the identified BPNN model was able to predict the sodium binding energy per atom on VS₂ with outstanding accuracy. Our results demonstrated that with the assistance of BPNN, it is possible to perform AIRSS with hundreds of random sensible structures without relying solely on DFT calculations. The uniqueness of this method lies on the utilization of a very large number of BPNN models to be trained by a relatively small number of structures. This is particularly very useful for large systems wherein the data come from DFT calculations, which is computationally expensive. Moreover, with the assistance of machine learning, the theoretical estimation of important metal-ion battery metrics such as specific energy capacity and open circuit voltage via AIRSS could be made more accurate and reliable.