Structural Embedding Methods for Machine Learning Models Accelerate Research on Stacked 2D Materials

The properties of two-dimensional materials can be controlled with a high degree of freedom through stacking, so it is crucial to explore the relationship between the structures and properties of stacked two-dimensional (2D) materials. However, the large material space caused by the high degree of freedom and the large system caused by the moiré effect make density functional theory (DFT) calculations very expensive. Here, to accelerate research on stacked 2D materials, we develop a structural embedding method for machine learning models that treats intralayer bonding interactions and interlayer nonbonding interactions equally. This method performs significantly better than other traditional edge embedding methods. Permutation importance analysis revealed that electrons significantly influence the properties of stacked 2D materials. Owing to the improved accuracy of the structural embedding method, we used the structure-embedded PAINN (SE-PAINN) to predict the binding energy and band gap of twisted stacked 2D materials, which basically reproduced the DFT calculation results, while the computational cost was reduced by several orders of magnitude. The structural embedding method makes it possible to study the torsional properties of stacked 2D materials. SE-PAINN also shows promising application prospects in potential energy surface prediction. This work proposes a structural embedding method to reliably predict the properties of layered stacked 2D materials, which will open an important avenue for studying twisted stacked 2D materials.