Structural Embedding\nMethods for Machine Learning\nModels Accelerate Research on Stacked 2D Materials

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