Formation Energy Prediction Of Defective Two-dimensional Materials Based On Multi-layer Descriptorvia Deep Learning

Two-dimensional materials,represented by graphene,have received a lot of attention and research from the scientific community for their many excellent physicochemical properties and high potential applications.Compared with conventional bulk materials,the surface structure of 2D materials with large specific surfaces usually contains a large number and different types of defects,which often have significant effects on the intrinsic properties of the materials.In order to study the microscopic mechanisms of material defects,first-principles computational simulation methods represented by density functional theory（DFT）are usually used.However,for two-dimensional systems with a large number of atoms and complex defect types and distributions,direct simulation using DFT often requires huge computational resources.With the development of artificial intelligence in recent years,new techniques based on machine learning have provided new solutions for dealing with large-area 2D defect systems.However,there are still many challenges to achieve fast and accurate prediction of 2D defect systems:on the one hand,due to the lack of material defect data and the high cost of obtaining large amounts of data,it is important to find a method that can obtain training samples for large-area 2D defect systems at low cost;on the other hand,the development of descriptors that can accurately describe large-area 2D defect systems plays a key role in the framework of machine learning.These descriptors should be able to distinguish between different defect types,different defect concentrations,and different defect distributions.However,the dimensionality of most descriptors increases with the number of atoms,which tends to lead to dimensional catastrophes,so the development of methods that can reduce the dimensionality of descriptors without losing information is urgently needed.Based on a deep learning framework,this thesis presents a systematic study of the defect system of two-dimensional materials represented by graphene and molybdenum disulfide,using multilayer structural descriptors as the main descriptive means,with the following two main aspects:（1）Deep learning-based formation energy prediction of large-area graphene defect system.We propose a multi-step workflow that can rapidly predict the energy of large-scale defect system.We obtain the formation energy of different defects in small cells by DFT calculation,and consider the effect of the interaction between different defects on the energy,and randomly stitch the small cells under the restriction to obtain the structure and formation energy of the larger system,so as to obtain a large amount of data for training machine learning models at low cost.Based on a deep learning network framework,we develop a convolutional neural network（CNN）to predict the formation energy of the graphene defect system at large scales,and construct a multilayer structural descriptor suitable for deep learning.By encoding the chemical bonding parameters in a two-dimensional material,the defect system structure can be completely described.We found that the CNN model trained with the multilayer descriptors can accurately predict the formation energy of graphene systems over 300 nm² with a mean absolute error（MAE）of 47 me V per 1000 atoms.The generalization ability to unknown defects was also fully tested.The effect of defect type,concentration and distribution on the formation energy of the whole system was further investigated.（2）Deep learning-based formation energy prediction of large-area molybdenum disulfide defect systems.Based on the above work,we wish to extend the multistep workflow and multilayer descriptors to the more general case of binary-component transition metal-sulfide compound systems.Molybdenum disulfide（Mo S₂）was selected as the test system,and a descriptor matrix that can describe its structure was constructed by encoding bond positions,bond lengths and bond angles.Using CNN for training,the MAE of predicted formation energy for defective Mo S₂ systems over 650 nm² is 53 me V per 1000 atoms,successfully demonstrating that our deep learning method can be extended to more complex 2D defective systems and providing a new approach for the study of large scale 2D material defective systems.In addition,we have developed an auto-encoder suitable for the structure of transition metal-sulfide compounds,which can generate the encoding of multilayer structure matrices since by extracting the atomic position coordinates and geometric calculations,which is more efficient compared to manual.