A method for obtaining the exfoliation energy of two-dimensional nanomaterials using machine learning

Abstract

The invention discloses a method for obtaining the stripping energy of two-dimensional nanomaterials by machine learning, and belongs to the field of machine learning. The invention aims to solve the problems of imperfect feature generation process, insufficient consideration of feature range and low model prediction accuracy in existing machine learning models. M kinds of AB-type 2D nanomaterials and corresponding m stripping energies are collected from a database to form a data set, and multiple prediction models are trained using the data set to obtain multiple trained prediction models, and candidate prediction models are further pre-screened; features are screened using the mutual information method and the variance inflation factor method to obtain a feature set that makes the candidate prediction model have good performance, and the candidate prediction model is trained using the screened feature set and stripping energy to obtain a trained candidate prediction model, from which the optimal prediction model is selected; the AB-type 2D nanomaterial to be tested is input into the trained optimal prediction model to predict the corresponding stripping energy. The invention is used to obtain the stripping energy of two-dimensional nanomaterials.

Description

Technical Field

[0001] The invention relates to a method for predicting the stripping energy of two-dimensional nanomaterials, and belongs to the field of machine learning. Background Art

[0002] In 2004, Geim and Novoselov successfully prepared graphene from graphite by mechanical exfoliation and won the Nobel Prize in Physics in 2010. Since then, two-dimensional (2D) nanomaterials have attracted widespread attention from scholars and gradually become a star in the field of materials science.

[0003] 2D nanomaterials are usually defined as crystalline materials with a thickness as low as a single layer or a few layers of atoms, in which the atoms in the plane are bound by strong covalent bonds, while the adjacent layers are bound by van der Waals interactions. Compared with three-dimensional (3D) crystalline materials, 2D nanomaterials exhibit many excellent electronic, mechanical, optical and chemical properties due to their special structure. In 2D nanomaterials, the existence of quantum confinement effects causes electrons to move freely only in a two-dimensional plane. This unique electron confinement effect makes it have great application prospects in new condensed materials, electronic devices and optoelectronic devices. Y. Qiao et al. and P. Snapp et al. used graphene to prepare electronic skin and photoelectric sensors for human health detection, respectively. In addition, 2D nanomaterials also have extremely excellent mechanical strength, flexibility and high transmittance. For example, graphene is the material with the highest known stiffness, with a Young's modulus of 1TPa and a transmittance of 97.7%. On the other hand, 2D nanomaterials can provide more active sites due to their unique structure, that is, extremely thin thickness and ultra-high specific surface area, so that they can show excellent performance in the fields of batteries, supercapacitors, catalysis and molecular sieves. Cui et al. prepared a hybrid electrode composed of graphene and a small amount of phosphorene nanosheets and applied it to sodium ion batteries. The electrode showed a specific capacity of 2440mA·h / g at a current density of 0.05A / g. In addition, compared with 3D crystalline materials, 2D nanomaterials can be used as an ideal platform for methods such as surface chemical modification, functionalization, element doping or molecular adsorption to improve their performance and design their functions at the atomic scale. With these excellent properties, 2D nanomaterials have been widely used in many fields, such as solar cells, field effect transistors, light-emitting devices, photodetectors, displays, sensors, lasers and photocatalysis. Obviously, the development of new multifunctional 2D nanomaterials has become a research hotspot in the field of materials science.

[0004] Since the synthesis of graphene, research on new 2D nanomaterials has exploded, with thousands of research papers on 2D nanomaterials published every year. Density functional theory (DFT) studies by Mounet et al. show that 1,825 2D nanomaterials may be exfoliated from their bulk layered materials. In addition, single-layer 2D nanomaterials can be generated into multilayer van der Waals heterostructures by stacking, which further increases the potential number of 2D nanomaterials. On the basis of proposing many potential new 2D nanomaterials, scholars have also developed numerous 2D nanomaterial databases, such as 2D Materials Encyclopedia (2DmatPedia), Computational 2D Materials Database (C2DB), MaterialsCloud Two-Dimensional Crystals Database, MaterialsWeb, and high-throughput databases including spin splitting and magnetic properties. However, only hundreds of 2D nanomaterials have been experimentally prepared. So far, the main methods for preparing 2D nanomaterials that have been developed experimentally include chemical vapor deposition (CVD), molecular beam epitaxy (MBE), liquid phase exfoliation, and photolithography. Among them, mechanical exfoliation has become an important means of preparing pure phase 2D nanomaterials due to its advantages such as simple preparation process, low preparation cost and high sample quality. In addition, because the prepared two-dimensional nanomaterials have the highest crystal quality, mechanical exfoliation is also the most ideal preparation method for studying the intrinsic properties of two-dimensional nanomaterials. After successfully synthesizing graphene, Novoselov et al. also used mechanical exfoliation to prepare h-BN, MoS2, NbSe2 and Bi2Sr2CaCu2O xTheir work inspired the preparation of many other types of 2D nanomaterials, such as other 2D transition metal sulfides TMDs (TiS2, TaS2, WS2, WSe2, TaSe2, etc.), metal oxides, black phosphorus (BP) and metal-organic frameworks (MOFs). It can be seen that mechanical exfoliation is of great significance in the preparation of two-dimensional nanomaterials. The exfoliation energy is a key parameter to measure whether a two-dimensional nanomaterial can be obtained by mechanical exfoliation. In previous studies, the exfoliation energy was defined as the energy required to peel off a single atomic layer from the surface of a layered bulk material. This is directly related to the actual mechanical exfoliation process. According to the definition of exfoliation energy, the exfoliation energy is equal to the difference between the total energy of the layered bulk material composed of N atomic layers and the total energy of the isolated atomic layer plus the remaining N-1 layers of the bulk material. In order to obtain a convergent exfoliation energy result, a larger N value is required in the calculation, which leads to a significant increase in the computational cost. Therefore, scholars also use the interlayer binding energy with relatively small computational complexity to approximate the exfoliation energy. However, both theoretical and experimental studies have shown that what is directly related to the stripping energy is not the interlayer binding energy, but the interlayer binding force; only the interlayer binding force can more accurately reflect the ease of stripping of two-dimensional materials. Therefore, there are still differences in the academic community's understanding of stripping energy, and it is still a great challenge to explore and reveal the internal mechanism that affects the stripping energy.

[0005] In previous studies, DFT based on first principles has become the main tool for studying the electronic structure properties of solid materials and determining the stripping energy of 2D nanomaterials. However, DFT cannot accurately describe the van der Waals interaction, which poses a challenge to accurately calculate the stripping energy of 2D nanomaterials. To solve this problem, scholars have developed methods such as non-empirical van der Waals functionals, dispersion-corrected atomic center potentials (DCACPs), and Grimme empirical dispersion corrections to correct van der Waals interactions. However, these methods usually rely on some form of parameterization, and in some cases cannot accurately describe the van der Waals interactions of 2D nanomaterials, resulting in inaccurate calculation accuracy and thus calculation failure. In addition, these theoretical calculations not only consume a lot of time and computational costs, but also require researchers to have deep professional knowledge, which is not easy for researchers engaged in experimental research, which poses a huge challenge to the preparation of new multifunctional 2D nanomaterials. Therefore, in order to accelerate the research and development of 2D nanomaterials, new and more efficient methods for calculating the stripping energy of 2D nanomaterials need to be developed.

[0006] In recent years, machine learning (ML) has become an effective tool for studying 2D nanomaterials; it can learn and summarize the laws of development from available data when the underlying physical mechanism is unknown. Machine learning algorithms have the ability to process large-scale data and can effectively process multidimensional data including experiments, calculations and simulations, such as crystal structure, material composition, performance parameters, etc. By mining potential laws and patterns from large amounts of data, machine learning models can extract useful information from complex data and discover the correlations among them. For example, by analyzing the relationship between the crystal structure and performance of materials, machine learning models can discover the structure-performance correlation laws hidden behind the data, which helps researchers explain the properties and behaviors of materials. Lu et al. constructed a thermodynamic stability dataset, a magnetic ground state dataset, and a band gap dataset using 2569 2D materials, and combined the crystal graph and elemental properties in the form of multiple feature layers to develop a "crystal graph multilayer descriptor (CGMD)". On this basis, three gradient boosting classification (GBC) algorithms were trained and trained on a small-scale dataset. The resulting machine learning model successfully screened out about 90 intrinsic FM materials with ideal band gaps and excellent thermodynamic stability. Acosta et al. used 1845 2D magnetic materials as a data set to train a machine learning model to predict magnetic order (ferromagnetic or antiferromagnetic) and identify new 2D magnetic compounds. The results showed that the random forest model had an accuracy of 86% in predicting magnetism, and the material map obtained using the sure independence screening (SIS) method and the sparse method had an accuracy of about 90% in predicting magnetic order. In addition, they used the Shapley additive interpretation method to clarify that atomic spin-orbit coupling (SOC) is the decisive feature for identifying ferromagnetic and antiferromagnetic ordered separation modes.

[0007] In addition, scholars have also made some progress in using machine learning technology to study the stripping energy of 2D nanomaterials. For example, Wan et al. used 4401 2D materials as a data set, defined 12 descriptors, and established four machine learning models: regression tree model (RT), support vector machine (SVM), multiple linear regression (MLR) and ensemble trees (ET) to predict the stripping energy of 2D materials. The results show that the ET model exhibits the highest stripping energy prediction accuracy (about 89%) and the strongest generalization ability. Tohidi et al. developed an automated process that combines geometric structure screening with a random forest classifier (with a recall rate of up to 98%) to accurately and quickly predict three-dimensional crystalline materials that can be stripped into two-dimensional materials. Although scholars have made some progress in predicting the stripping energy of materials using machine learning; however, this research work did not predict the stripping energy of these materials. It can be seen that there is currently little research work on applying machine learning to the prediction of material stripping energy, and the proposed stripping energy prediction model still has problems such as imperfect feature generation process, insufficient consideration of feature range and low model prediction accuracy. Summary of the invention

[0008] The purpose of the present invention is to solve the problems of existing machine learning models, such as imperfect feature generation process, insufficient consideration of feature range and low model prediction accuracy, and proposes a method for obtaining the exfoliation energy of two-dimensional nanomaterials using machine learning.

[0009] A method for obtaining the peeling energy of two-dimensional nanomaterials by using machine learning, the method comprising the following contents:

[0010] Step 1, collecting m AB-type 2D nanomaterials and corresponding m stripping energies from a two-dimensional material database to form a data set, wherein the m 2D nanomaterials all include the same characteristic types, all contain n characteristics, and m and n are both positive integers greater than 0;

[0011] The n characteristics of each AB-type 2D nanomaterial in the data set and the exfoliation of the AB-type 2D nanomaterial can form a sample;

[0012] Step 2, model pre-screening: using the data set to train multiple prediction models and perform grid search hyperparameter optimization to obtain multiple trained prediction models, and pre-screen multiple candidate prediction models from the prediction models;

[0013] Step 3: Perform the first round of screening and update features:

[0014] Calculate the mutual information value between each feature in the data set and the stripping energy; obtain the variance inflation factor value of each feature based on the complex correlation coefficient between each feature and all other features, sort the obtained variance inflation factor values ​​from large to small, remove a feature with the minimum mutual information value from the top six in the variance inflation factor ranking, and use the remaining features as the features obtained after the first round of screening;

[0015] Step 4, using the features obtained after the first round of screening and each candidate prediction model, calculate the root mean square error of the ten-fold cross validation of each candidate prediction model corresponding to the features after the first round of screening; using n kinds of features and each candidate prediction model, calculate the root mean square error of the ten-fold cross validation of each candidate prediction model corresponding to the n kinds of features, and judge whether the root mean square error of the ten-fold cross validation of the candidate prediction model corresponding to the n-1 features after the first round of screening under the same candidate prediction model is less than or equal to the root mean square error of the ten-fold cross validation of the candidate prediction model corresponding to the n kinds of features. If yes, execute step 5; if not, train multiple candidate prediction models using n kinds of features and stripping energy and perform random search hyperparameter optimization to obtain multiple trained candidate prediction models; select the optimal trained prediction model from multiple trained candidate prediction models;

[0016] Step 5: Perform the jth round of screening and updating features. The initial value of j is 2:

[0017] Calculate the mutual information value between each feature obtained after the j-1th round of screening and the stripping energy, obtain the variance inflation factor value of each feature according to the complex correlation coefficient between each feature and all other features, sort the obtained variance inflation factor values ​​from large to small, remove a feature with the minimum mutual information value from the top six in the variance inflation factor ranking, and the remaining features are used as the features obtained after the jth round of screening;

[0018] Step 6: Determine whether the root mean square error of the ten-fold cross validation of the candidate prediction model corresponding to the feature after the j-th round of screening under the same candidate prediction model is less than or equal to the root mean square error of the ten-fold cross validation of the candidate prediction model corresponding to the feature after the j-1-th round of screening. If yes, set j=j+1 and execute step 5. If not, use the features obtained after the j-1-th round of screening and the stripping energy to train multiple candidate prediction models and perform random search hyperparameter optimization to obtain multiple trained candidate prediction models, and select the trained optimal prediction model from the multiple trained candidate prediction models.

[0019] Step 7: Input the AB-type 2D nanomaterial to be tested into the trained optimal prediction model to predict the corresponding stripping energy.

[0020] Preferably, in step 1, the stripping energy is expressed as:

[0021] E exf =E 2D -E bulk Formula 1,

[0022] In the formula, E exf is the peeling energy, E 2D is the energy of each atom in the 2D nanomaterial, E bulk is the energy of each atom in the layered bulk material.

[0023] Preferably, the mutual information value I(X i ; Y), expressed as:

[0024]

[0025] In the formula, x i Represents feature X i The value of y represents the value of the peeling energy Y, p(x i ,y) is X i The joint probability distribution of and Y, p(x i ) and p(y) are respectively X i and the marginal probability distribution of Y.

[0026] Preferably, the variance inflation factor value of each feature is expressed as:

[0027]

[0028] Where VIF i is the variance inflation factor value of the i-th feature, R i is the multiple correlation coefficient between the ith feature and all other features.

[0029] Preferably, in step 2, multiple prediction models are trained using the data set and grid search hyperparameter optimization is performed to obtain multiple trained prediction models, and multiple candidate prediction models are pre-screened from the prediction models. The specific process is:

[0030] The data set is divided into 10 parts equally, and each part is used as a validation set, and the remaining 9 parts are used as training sets, forming a total of 10 validation and training sets;

[0031] Use 10 training sets from the 10 validation training sets to train each prediction model in turn and perform grid search hyperparameter optimization to obtain each trained model;

[0032] The AB-type 2D nanomaterials in 10 validation training sets were input into each training completed model in turn, and the root mean square error of each training completed model was calculated. A total of 10 root mean square errors were obtained for each training completed model. The 10 root mean square errors obtained for each training completed model were averaged, and the average was used as the ten-fold cross-validation error of the corresponding training completed model. The ten-fold cross-validation error of each training completed model was compared with the preset error, and the training completed model corresponding to the closest preset error was selected as the candidate prediction model.

[0033] Preferably, in steps 4 and 5, the optimal prediction model is selected from multiple trained candidate prediction models, and the specific process is:

[0034] The n features and stripping energies or the features and stripping energies obtained after the j-1th round of screening are divided into a training set and a test set;

[0035] Using the training set to train multiple candidate prediction models and perform random search hyperparameter optimization to obtain each trained candidate prediction model;

[0036] The AB-type 2D nanomaterials in the test set are input into each trained candidate prediction model, and each trained candidate prediction model outputs a prediction value; based on the prediction value of each trained candidate prediction model and the stripping energy in the test set, multiple performance evaluation indicators of each trained candidate prediction model are calculated, and the trained candidate prediction model whose multiple performance evaluation indicators all meet the preset performance evaluation indicators is selected as the optimal prediction model.

[0037] Preferably, the multiple evaluation indicators are determination coefficient, root mean square error, mean square error and mean absolute error.

[0038] Preferably, the coefficient of determination is expressed as:

[0039]

[0040] In the formula, m is the total number of data, is the machine learning prediction value of sample i, is the DFT calculated value of sample i, is the average value of the DFT calculated value;

[0041] The root mean square error is expressed as:

[0042]

[0043] The mean square error is expressed as:

[0044]

[0045] The mean absolute error is expressed as:

[0046]

[0047] Preferably, the contribution value of each characteristic of the AB-type 2D nanomaterial to the stripping energy in the optimal prediction model is It is expressed as:

[0048]

[0049] Where n represents the number of features, S is the subset of all features that does not include feature x, and p(S∪x) represents the predicted value of the selected machine learning prediction model when feature x is taken into account, while p(S) is the predicted value when feature x is not taken into account.

[0050] The beneficial effects of the present invention are:

[0051] The present invention proposes a simple machine learning model to quickly and efficiently predict the stripping energy of 2D nanomaterials, so as to accelerate the discovery of new multifunctional 2D nanomaterials with lower stripping energy, and provide theoretical support for the experimental synthesis of 2D nanomaterials by mechanical stripping. The present invention is first based on a training set consisting of m types of AB-type 2D nanomaterials, uses the training set to train multiple prediction models, and finally selects several candidate prediction models from the multiple prediction models. The mutual information method and the variance inflation factor method are used to gradually screen features from the m types of features, and irrelevant and redundant features are eliminated according to the changes in the performance of the candidate models. A set of representative optimal feature subsets are screened from the initial feature set, with the aim of effectively reducing the dimension of the data, improving the efficiency of model training, reducing model complexity, and helping to prevent model overfitting, making the model results easier to interpret. The candidate prediction model is trained using the screened feature set, and multiple performance evaluation indicators of each trained candidate prediction model are calculated. The candidate prediction model with the best performance is selected as the optimal prediction model, and the trained optimal prediction model is used to predict the AB-type 2D nanomaterial to be tested to obtain the corresponding stripping energy. Therefore, the method of selecting features in the present invention is simple, and the selected features are not only representative but also more comprehensive, so that the stripping energy predicted by the model is more accurate.

[0052] Finally, the present invention uses the Shapley Additive Interpretation (SHAP) method to interpret the model, and deeply reveals the key factors affecting the prediction of 2D nanomaterial exfoliation energy from two aspects: the overall composition structure of the material and the properties of the constituent atoms. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 Flow chart of the method for obtaining the exfoliation energy of two-dimensional nanomaterials using machine learning;

[0054] Figure 2is the frequency histogram of the stripping energy distribution in the initial data set;

[0055] Figure 3 Comparison of RMSE performance of six machine learning models in ten-fold cross validation after grid search hyperparameter optimization;

[0056] Figure 4 Flow chart for screening n features;

[0057] Figure 5 This is a comparison chart of the RMSE performance of candidate models in the feature selection process; Figure 6 It is a visualization diagram of the initial feature set and the updated feature set reduced to three-dimensional and two-dimensional dimensions, where Figure 6 (a) is the 3D visualization of the initial feature set. Figure 6 (b) is the 3D visualization of the updated feature set. Figure 6 (c) is a two-dimensional visualization of the initial feature set. Figure 6 (d) is a two-dimensional visualization of the updated feature set;

[0058] Figure 7 This is a 5-fold cross validation graph of the CatBoost model using RMSE as the performance evaluation indicator;

[0059] Figure 8 Scatter plots of the stripping energies predicted by different models and fitted with the stripping energies calculated by DFT and individual SHAP plots predicted for three different materials, where: Figure 8 (a) is a scatter plot of the stripping energy predicted by the CatBoost model and the stripping energy calculated by DFT. Figure 8 (b) is a scatter plot of the stripping energy predicted by the XGBoost model and the stripping energy calculated by DFT. Figure 8 (c) is the individual SHAP graph predicted for AgCl2 material. Figure 8 (d) is the predicted individual SHAP graph for PtSe2 material. Figure 8 (e) A separate SHAP diagram for WC3 material prediction, showing the SHAP positive (red) and negative (blue) feature weights of the three materials. The bar size represents the SHAP value, the base value is the mean of the stripping energy on the training data, and the output value f(x) represents the predicted stripping energy of the three materials.

[0060] Fig. 9 This is a ranking chart of the importance of the first 20 features of the optimized CatBoost model. DETAILED DESCRIPTION

[0061] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0062] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other. The present invention is further described below in conjunction with the drawings and specific embodiments, but is not intended to be a limitation of the present invention.

[0063] Example:

[0064] A method for obtaining the peeling energy of two-dimensional nanomaterials by using machine learning, the method comprising the following contents:

[0065] Step 1, collecting m AB-type 2D nanomaterials and corresponding m stripping energies from a two-dimensional material database to form a data set, wherein the m 2D nanomaterials all include the same characteristic types, all contain n characteristics, and m and n are both positive integers greater than 0;

[0066] The n characteristics of each AB-type 2D nanomaterial in the data set and the exfoliation of the AB-type 2D nanomaterial can form a sample;

[0067] Step 2, model pre-screening: using the data set to train multiple prediction models and perform grid search hyperparameter optimization to obtain multiple trained prediction models, and pre-screen multiple candidate prediction models from the prediction models;

[0068] Step 3: Perform the first round of screening and update features:

[0069] Calculate the mutual information value between each feature in the data set and the stripping energy; obtain the variance inflation factor value of each feature based on the complex correlation coefficient between each feature and all other features, sort the obtained variance inflation factor values ​​from large to small, remove a feature with the minimum mutual information value from the top six in the variance inflation factor ranking, and use the remaining features as the features obtained after the first round of screening;

[0070] Step 4: Calculate the root mean square error of the ten-fold cross validation of each candidate prediction model corresponding to the features after the first round of screening by using the features and each candidate prediction model obtained after the first round of screening; Calculate the root mean square error of the ten-fold cross validation of each candidate prediction model corresponding to the n features by using n features and each candidate prediction model, and determine whether the root mean square error of the ten-fold cross validation of the candidate prediction model corresponding to n-1 features after the first round of screening under the same candidate prediction model is less than or equal to the root mean square error of the ten-fold cross validation of the candidate prediction model corresponding to the n features. If yes, execute step 5; if not, train multiple candidate prediction models using n features and stripping energy and perform random search hyperparameter optimization to obtain multiple trained candidate prediction models, and select the optimal trained prediction model from the multiple trained candidate prediction models;

[0071] Step 5: Perform the jth round of screening and updating features. The initial value of j is 2:

[0072] Calculate the mutual information value between each feature obtained after the j-1th round of screening and the stripping energy, obtain the variance inflation factor value of each feature according to the complex correlation coefficient between each feature and all other features, sort the obtained variance inflation factor values ​​from large to small, remove a feature with the minimum mutual information value from the top six in the variance inflation factor ranking, and the remaining features are used as the features obtained after the jth round of screening;

[0073] Step 6: Determine whether the root mean square error of the ten-fold cross validation of the candidate prediction model corresponding to the feature after the j-th round of screening under the same candidate prediction model is less than or equal to the root mean square error of the ten-fold cross validation of the candidate prediction model corresponding to the feature after the j-1-th round of screening. If yes, set j=j+1 and execute step 5. If not, use the features obtained after the j-1-th round of screening and the stripping energy to train multiple candidate prediction models and perform random search hyperparameter optimization to obtain multiple trained candidate prediction models, and select the trained optimal prediction model from the multiple trained candidate prediction models.

[0074] Step 7: Input the AB-type 2D nanomaterial to be tested into the trained optimal prediction model to predict the corresponding stripping energy.

[0075] Specifically, in step 1, the data of the training set for predicting the stripping energy model of AB-type 2D nanomaterials comes from the 2DmatPedia database. 2DmatPedia is an open database that integrates the structure, energy and electronic properties of more than 6,000 2D materials. The data in the database are all calculated based on first-principles DFT in the Vienna Ab initio Simulation Package (VASP) software, the Perdew-Burke-Ernzerhof (PBE) approximation is used for exchange-correlation functionals, and the frozen-core all-electron projection augmented wave (PAW) method is used for electron-ion interactions. The cutoff energy of the plane wave expansion of the electronic wave function is set to 520 eV. Among them, the stripping energy E in the database exf By E exf =E 2D -E bulk Get, E 2D is the energy of each atom in the 2D material, E bulk is the energy of each atom in the layered bulk material. In the calculation of the stripping energy, the dispersion-corrected vdW–optB88 exchange-correlation functional is used to consider the interlayer dispersion interaction in the layered material.

[0076] When collecting data sets, 2745 AB-type 2D nanomaterials can be selected as the initial data set. The stripping energy distribution range of the entire data set is from -1.2187eV / atom to 3.0565eV / atom, which conforms to the normal distribution as a whole ( Figure 2 ), the average value of the stripping energy is about 0.166eV. The highest frequency of the stripping energy is in the range of 0-0.5eV. In addition, all the raw indicator data have been standardized.

[0077] In step 1, the selection of n features:

[0078] Designing a set of descriptors (features) for the stripping energy prediction of AB-type 2D nanomaterials is equivalent to creating a set of quantitative expressions. These expressions can not only uniquely define each material in the data set, but also are related to the physical and chemical properties that affect the target variable (stripping energy). In order to obtain features that contain material prior knowledge but are not too complex, this embodiment searches for features based on structure and material components. This is because the physical and chemical properties of the constituent atoms determine the properties of the corresponding materials to a large extent. These properties directly affect the macroscopic properties of molecules and crystal structures. As shown in Table 1, 28 descriptors were selected, including various features reflecting atomic size, geometric properties, physical properties, and thermal properties, to construct the initial feature set.

[0079] Table 1 28 feature descriptors and corresponding symbols of the initial dataset of AB-type 2D nanomaterials

[0080]

[0081] In step 3, in the feature engineering stage, feature selection is a crucial link, and its main goal is to maximize the correlation between features and stripping energy and minimize the redundancy between features. By eliminating irrelevant and redundant features, a set of representative optimal feature subsets are screened out from the initial feature set. This can effectively reduce the dimension of the data, improve the efficiency of model training, reduce model complexity, and help prevent model overfitting, making the model results easier to interpret. This embodiment performs feature selection from two aspects:

[0082] The first is the correlation between the features and the stripping energy. Features with strong correlation contribute more to the model's prediction of the stripping energy and should be retained first. This study uses the mutual information method to evaluate the correlation between each feature and the stripping energy. This method can take into account any type of correlation (including linear and nonlinear); the second is the correlation between features. Too high correlation between features may lead to multicollinearity problems, affecting the stability of the model and the accuracy of the prediction results. This study uses the variance inflation factor (VIF) to measure the degree of linear correlation between features. VIF takes into account the relationship between a feature and all other features, and can more comprehensively evaluate whether a feature has multicollinearity problems. Based on these two methods, we designed a feature selection process, such as Figure 4 In the initial feature set, the six features with the highest VIF are first calculated and sorted, and the feature with the lowest correlation with the stripping energy is eliminated, as shown in Figure 5 As shown in the figure, cross-validation is then performed to evaluate the model performance. If the performance improves, the VIF value and mutual information value are recalculated and feature selection is performed again. This cycle is repeated until the model performance no longer improves (that is, the RMSE value no longer decreases). After the feature selection process, we screened out 24 representative optimal feature subsets (see Table 2 for details).

[0083] In order to observe the data distribution after data processing and feature engineering, the t-Distributed Stochastic Neighbor Embedding (t-SNE) algorithm was used to successfully reduce the feature dimension to three dimensions ( Figure 6 (a) and Figure 6 (b)) and two-dimensional ( Figure 6 (c) and Figure 6 (d)) and visualize the spatial distribution of the input variables after dimensionality reduction. Compared with the initial data ( Figure 6 (a) and Figure 6 (b)), the data set after data processing and feature engineering shows obvious clustering phenomenon ( Figure 6 (c) and Figure 6 (d)). In addition, Figure 6More sample points are shown in (b). This result shows that the concentration and regularity of the data are improved by effectively removing noise and redundant information. Therefore, the distribution of sample points is more compact, indicating that the dataset after data processing and feature engineering is more orderly and structured. This helps the model to better learn the essential characteristics of the data and improve the prediction accuracy and generalization ability of the model. In order to optimize the XGBoost model and the CatBoost model, the random search method is used for hyperparameter optimization. The selection of hyperparameters is mainly focused on six key parameters (see Table 3 and Table 4 for details). In order to ensure effective exploration of the hyperparameter space, the number of iterations is set to 5000 so that the optimal hyperparameters can be found within a reasonable time frame (Table 3 and Table 4).

[0084] Table 2 24 descriptors and their corresponding symbols of AB-type 2D nanomaterials after feature engineering and data processing; A and B represent the first and second elements in the formula, respectively

[0085]

[0086]

[0087] Table 3 Hyperparameters, hyperparameter space and optimal hyperparameters in the process of hyperparameter optimization of CatBoost model using random search method

[0088]

[0089] Table 4 Hyperparameters, hyperparameter space and optimal hyperparameters in the process of XGBoost model hyperparameter optimization using random search method

[0090]

[0091] Table 5 RMSE, MAE, MSE and R of the CatBoost model and XGBoost model after hyperparameter optimization on the training set and test set 2 value

[0092]

[0093] After determining the optimal hyperparameters, the model was trained again and the test set was used for model evaluation. The results showed that the CatBoost model performed optimally on the test set and achieved the expected performance, with an RMSE of 0.070 and an R 2 is 0.909 (see Figure 7 and Table 5). The prediction performance is better than the ET model proposed by Wan et al. (RMSE is 0.071, R 20.890). In addition, in order to verify the stability and generalization ability of the CatBoost model, this study used RMSE as the performance evaluation indicator and performed a 5-fold cross validation. The validation results confirmed the good stability and generalization ability of the CatBoost model on different data subsets (see Figure 6 ). Therefore, the CatBoost model is able to establish an effective nonlinear mapping between input features and stripping energies, and thus accurately predict the stripping energies of unexplored new datasets.

[0094] The following is a detailed description of the process of selecting candidate prediction models described in step 2:

[0095] In step 2, multiple prediction models are trained using the data set and grid search hyperparameter optimization is performed to obtain multiple trained prediction models, and multiple candidate prediction models are pre-screened from the prediction models. The specific process is as follows:

[0096] The data set is divided into 10 parts equally, one of which is used as a validation set and the other 9 as training sets, forming a total of 10 validation and training sets;

[0097] Each prediction model is trained in turn using 10 sets of training sets in the 10 validation training sets, and grid search hyperparameter optimization is performed to obtain each trained prediction model.

[0098] The AB-type 2D nanomaterials of the 10 validation sets in the 10 validation training sets were input into each trained model in turn, and the root mean square error of each trained model was calculated, and a total of 10 root mean square errors were obtained for each trained model; the 10 root mean square errors obtained for each trained model were averaged, and the average was used as the ten-fold cross-validation error of the corresponding trained model; the ten-fold cross-validation error of each trained model was compared with the preset error, and the trained model corresponding to the closest preset error was selected as the candidate prediction model.

[0099] A ten-fold cross-validation method is used to select candidate prediction models from multiple prediction models. The specific steps are as follows: first, the data set is divided into 10 parts, numbered from 0 to 9, and the data corresponding to one of the numbers is selected each time as the validation set, and the data corresponding to the remaining numbers are used as the training set; the remaining 9 training sets are used to train one prediction model, and the root mean square error of the model on the validation set is calculated. The process is repeated 10 times, each time using a validation set with a different number, and a total of 10 root mean square error values ​​are obtained; the 10 root mean square error values ​​are averaged to obtain the ten-fold cross-validation error of the corresponding model; by comparing the ten-fold cross-validation error of each prediction model with the preset error, the prediction model that meets the requirements is selected as the candidate prediction model.

[0100] This example uses six machine learning models, Elastic Net Regression (EN), Bayesian Ridge Regression (BR), Support Vector Regression (SVR), Random Forest Regression (RFR), Extreme Gradient Boosting (XGBoost) and Category Boosting (CatBoost). Each model has its unique advantages to cope with different types of data challenges, which can ensure the integrity of the analysis of this study and the reliability of the results.

[0101] EN is a linear regression model that uses two regularization methods, L1 (Lasso regression) and L2 (ridge regression). L1 regularization makes the model sparse, while L2 regularization prevents the model from overfitting and improves the stability of the model. Therefore, EN has a good performance in dealing with multicollinearity problems. BR introduces prior distribution and maximizes posterior probability for parameter estimation, which is very suitable for dealing with multicollinearity problems and provides parameter probability distribution to estimate uncertainty. SVR is a regression model with high robustness and excellent generalization ability. SVR aims to find a smooth function so that the error between the predicted value and the true value is less than the preset threshold, so as to achieve a good balance between maintaining model complexity and processing noisy data. In addition, SVR allows the error between the predicted value and the actual value of some sample points to exceed the set threshold, so that the noise of the data can be better processed. At the same time, SVR minimizes the complexity of the function and tries to keep the function smooth to prevent overfitting. These characteristics make SVR show excellent performance in many practical applications, especially in dealing with high-dimensional feature data. RFR is a highly robust ensemble learning model that prevents overfitting by building multiple decision trees and averaging the prediction results, and has excellent interpretability. It is suitable for processing regression prediction and feature selection problems of large-scale high-dimensional data. XGBoost is an efficient and flexible optimization distributed gradient boosting algorithm that prevents overfitting by fitting the current model residual and regularization. It is efficient and robust in processing large-scale high-dimensional data, supports custom loss functions and evaluation indicators, and has strong adaptability. CatBoost is a machine learning algorithm based on gradient boosting decision trees. Its uniqueness lies in the use of Ordered Boosting and target encoding technology. These two technologies enable CatBoost to effectively process classification features and prevent model overfitting, thereby significantly improving the performance of the model in complex data distribution prediction tasks.

[0102] Figure 3 The RMSE values ​​of the six machine learning models after grid search hyperparameter optimization in the ten-fold cross validation are given. It can be seen that the prediction performance of the linear models EN and BR is weak, which shows that the relationship between the 28 descriptors and the stripping energy is nonlinear, and the linear model cannot fully capture its data characteristics. In addition, although the prediction performance of the SVR model and the RFR model is improved compared with EN and BR, their prediction accuracy has not reached the ideal level, which reflects that the nonlinear relationship between the descriptors and the stripping energy is quite complex. Compared with these four models, the XGBoost model and the CatBoost model based on the gradient boosting algorithm perform best in the prediction of stripping energy. These two models are good at processing complex data and nonlinear relationships, and can improve the fit of the data and the accuracy of prediction. They can effectively handle the complex nonlinear relationship between features and improve the model performance through ensemble learning strategies. In addition, both models have mechanisms to prevent overfitting, such as regularization and pruning. These mechanisms can control the complexity of the model by adjusting parameters, avoid overfitting on the training set, and thus improve the generalization ability of the model. Therefore, the XGBoost model and the CatBoost model are selected for further research on the prediction of stripping energy.

[0103] The following is a detailed description of the process of selecting the optimal prediction model:

[0104] In steps 4 and 5, the optimal prediction model is selected from multiple trained candidate prediction models. The specific process is as follows:

[0105] The n features and stripping energies or the features and stripping energies obtained after the j-1th round of screening are divided into a training set and a test set;

[0106] Using the training set to train multiple candidate prediction models and perform random search hyperparameter optimization to obtain each trained candidate prediction model;

[0107] The AB-type 2D nanomaterials in the test set are input into each trained candidate prediction model, and each trained candidate prediction model outputs a prediction value; based on the prediction value of each trained candidate prediction model and the stripping energy in the test set, multiple performance evaluation indicators of each trained candidate prediction model are calculated, and the trained candidate prediction model whose multiple performance evaluation indicators all meet the preset performance evaluation indicators is selected as the optimal prediction model.

[0108] Specifically, the entire dataset was randomly divided into a training set and a test set with a ratio of 9:1. The training set was used to fit the relationship between the descriptor and the peeling energy, while the test set was used to evaluate the prediction and generalization capabilities of the model. In addition, four regression indices (R 2 , RMSE, MSE and MAE) describe the prediction accuracy of the model.

[0109] The following are the preferred methods for evaluation indicators:

[0110] The various evaluation metrics are coefficient of determination, root mean square error, mean square error, and mean absolute error.

[0111] The coefficient of determination is expressed as:

[0112]

[0113] In the formula, m is the total number of data, is the machine learning prediction value of sample i, is the DFT calculated value of sample i, is the average value of the DFT calculated value;

[0114] The root mean square error is expressed as:

[0115]

[0116] The mean square error is expressed as:

[0117]

[0118] The mean absolute error is expressed as:

[0119]

[0120] Specifically, in order to comprehensively evaluate the predictive performance of the machine learning model, this study used four regression evaluation indicators: Coefficient of Determination (R 2 ), Root Mean Square Error (RMSE), Mean Absolute Error (MSE), and Mean Absolute Error (MAE). Among them, MSE measures the mean of the squared difference between the predicted value and the actual value. Its characteristic is that it gives greater weight to large errors, thereby imposing greater constraints on the model when large errors occur. RMSE, as the square root of MSE, can more intuitively reflect the scale of the prediction error, but is less sensitive to the error than MSE. MAE measures the average absolute difference between the predicted value and the actual value, and its robustness to outliers is better than MSE and RMSE. R 2 It is an indicator to measure the model's ability to explain data variance. Its value range is from 0 to 1. The closer the value is to 1, the stronger the model's ability to explain the data. The formulas for these evaluation indicators are shown in Formulas 3 to 6.

[0121] The expression of mutual information value is introduced below:

[0122]

[0123] In the formula, x i Represents feature X i The value of y represents the value of the peeling energy Y, p(x i ,y) is X i The joint probability distribution of and Y, p(x i ) and p(y) are respectively X i and the marginal probability distribution of Y.

[0124] The following is the expression for the variance inflation factor value:

[0125]

[0126] Where VIF i is the variance inflation factor value of the i-th feature, R i is the multiple correlation coefficient between the ith feature and all other features.

[0127] The following lists the contribution of each characteristic of the AB-type 2D nanomaterial to the stripping energy in the optimal prediction model. for:

[0128]

[0129] Where n represents the number of features, S is the subset of all features that does not include feature x, p(S∪x) represents the predicted value of the selected machine learning prediction model when feature x is taken into account, and p(S) is the predicted value when feature x is not taken into account.

[0130] Specifically, in order to evaluate the contribution of each feature to the target variable (stripping energy), the SHAP (contribution value) method was used to interpret the machine learning model. SHAP is a model interpretation method based on the concept of Shapley Value in game theory, which can accurately assign an importance score to each feature that represents its contribution to the prediction result. The main advantage of SHAP is its model independence and can be applied to various machine learning models. Through the SHAP method, the degree of influence of each feature on the prediction result can be intuitively revealed, and the complex relationship between the feature and the prediction result can be further revealed. For a model with n features, the SHAP value of feature x can be calculated by formula 8. Since the missing effect of a feature in the selected machine learning model depends on other features, The SHAP value of each feature quantifies its positive or negative contribution, where features with higher SHAP absolute values ​​contribute more to the prediction results.

[0131] Revealing the clear relationship between features and the output of black-box machine learning models is extremely challenging. To solve this problem, this embodiment adopts the SHAP method based on the Shapley value principle in game theory. The SHAP method can not only rank the importance of features, but also reveal the positive and negative contributions of each feature, providing global (feature importance) and local (single instance) interpretability for the optimized machine learning model. In the global model interpretation, each feature is assigned a unique weight. Fig. 9 The SHAP interpretation of the optimized CatBoost model and the top 20 most important features are given. Each sample point corresponds to a compound in the dataset, where red and blue represent higher and lower feature values, respectively. The positive or negative contribution of each feature can be represented by its SHAP value. Fig. 9 As shown in Figure 2, SN is the most important feature, with most of the higher values ​​having a significant positive impact on the model output, while a few lower values ​​have a negative impact on the model output. To further reveal how the selected features affect the stripping energy output of the compound, the CatBoost model provides SHAP plots of individual materials to explain different types of 2D nanomaterials, such as Figure 8 (c) - Figure 8 (e) is shown. The base value is the average output value of the machine learning model on the entire training set. The positive contribution and negative contribution are represented by red and blue arrows, respectively, corresponding to the influence of different features in driving the stripping energy away from and close to the baseline. The contribution of the feature increases with the length of the corresponding arrow. According to the local interpretation results, it can be seen that, as mentioned earlier, each feature plays a different role in different 2D nanomaterials. For example, for the SN feature, its effect on WC3 is positive, with a SHAP value of 187.0; while its effect on AgCl2 and PtSe2 is negative, with SHAP values ​​of 14.0 and 164.0, respectively. Therefore, once the sum of the positive contributions of all features is greater than the sum of the negative contributions, the final predicted value of the stripping energy is greater than the base value. The results show that the stripping energy is not determined by a single factor, but is the result of the synergistic effect of multiple factors. In addition, the effect of a single factor on the final stripping energy is not fixed and can show a positive or negative effect.

[0132] This study uses the SHAP method to rank the features. Fig. 9 ), deeply explored the internal mechanism that affects the exfoliation energy of two-dimensional nanomaterials. The space group number (SN) is the most important feature for predicting the exfoliation energy of two-dimensional nanomaterials. Fig. 9It can be seen that a larger space group number has a positive effect on the prediction of the stripping energy, while a smaller space group number has a negative effect. In crystallography, the higher the symmetry of the crystal system, the larger its space group number is usually. A crystal structure with high symmetry usually means that its atomic arrangement is more regular and uniform, making the force distribution between atoms more uniform, thereby reducing the total energy of the crystal and improving its stability. In the process of stripping two-dimensional nanomaterials from the matrix, the first thing to overcome is the interaction between the stripping layer and the rest of the body. Therefore, the space group number greatly affects the stripping energy of 2D nanomaterials.

[0133] In addition, melting point (ATM / BTM), boiling point (BTB) and heat of evaporation (AH / BH) are also important factors that affect the prediction of 2D nanomaterial exfoliation energy. The melting point is the temperature required for a substance to change from a solid to a liquid, while the boiling point is the temperature required for a substance to change from a liquid to a gas. The heat of evaporation refers to the amount of heat required for a unit mass of a substance to change from a liquid to a gas. All three processes require overcoming the interaction forces between molecules or atoms. For 3D crystalline materials with a layered structure, the interaction forces between layers are an important factor affecting their heat of evaporation, melting point and boiling point. If the interlayer interactions of the material are strong, a higher temperature is required to overcome these interactions and separate the two parts connected by the interlayers. Therefore, materials with strong interlayer interactions usually have higher heat of evaporation, melting point and boiling point. On the contrary, materials with weak interlayer interactions have lower heat of evaporation, melting point and boiling point.

[0134] Atomic radius (ARa / BRa), ionic radius (ARi / BRi) and atomic volume (BV) are also crucial features in the prediction of stripping energy. Atomic radius refers to the average distance between the nucleus and the outermost electron in the electron cloud. Ionic radius refers to the distance from the nucleus to its outermost electron cloud in an ionic crystal. Atomic volume refers to the size of the space occupied by an atom, usually defined as the volume of the lattice unit in which the atom is located divided by the number of atoms in each lattice unit. These three features reflect the distance and spatial size between atoms or ions, which can directly affect the interlayer spacing in 3D layered materials, thereby affecting the strength of interlayer interactions, and have a great impact on stripping energy.

[0135] Atomic number (AN / BN), conductivity (Aq / Bq), ionization energy (AIP / BIP) and electron affinity (BEA / AEA) of elements are closely related to the electronic structure of the elements. For 2D van der Waals heterostructures, when two different 2D nanomaterials are superimposed together, the superposition of the electron clouds between the two at the heterojunction will produce new electronic states, which in turn affect the interlayer van der Waals interaction. Therefore, changes in the electronic structure of 2D nanomaterials can change the interlayer interaction of the material, thereby affecting the stripping energy of the system.

[0136] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the present invention. It should therefore be understood that many modifications may be made to the exemplary embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in a manner different from that described in the original claims. It should also be understood that features described in conjunction with individual embodiments may be used in other described embodiments.

Claims

1. A method for obtaining the peeling energy of two-dimensional nanomaterials using machine learning, characterized in that: The method comprises the following: Step 1, collecting m AB-type 2D nanomaterials and corresponding m stripping energies from a two-dimensional material database to form a data set, wherein the m 2D nanomaterials all include the same characteristic types, all contain n characteristics, and m and n are both positive integers greater than 0; The n characteristics of each AB-type 2D nanomaterial in the data set and the exfoliation of the AB-type 2D nanomaterial can form a sample; Step 2, model pre-screening: using the data set to train multiple prediction models and perform grid search hyperparameter optimization to obtain multiple trained prediction models, and pre-screen multiple candidate prediction models from the prediction models; Step 3: Perform the first round of screening and update features: Calculate the mutual information value between each feature in the data set and the stripping energy; obtain the variance inflation factor value of each feature based on the complex correlation coefficient between each feature and all other features, sort the obtained variance inflation factor values ​​from large to small, remove a feature with the minimum mutual information value from the top six in the variance inflation factor ranking, and use the remaining features as the features obtained after the first round of screening; Step 4: Calculate the root mean square error of the ten-fold cross validation of each candidate prediction model corresponding to the features after the first round of screening by using the features and each candidate prediction model; Calculate the root mean square error of the ten-fold cross validation of each candidate prediction model corresponding to the n features by using n features and each candidate prediction model, and determine whether the root mean square error of the ten-fold cross validation of the candidate prediction model corresponding to n-1 features after the first round of screening under the same candidate prediction model is less than or equal to the root mean square error of the ten-fold cross validation of the candidate prediction model corresponding to the n features. If yes, execute step 5; if not, train multiple candidate prediction models using n features and stripping energy and perform random search hyperparameter optimization to obtain multiple trained candidate prediction models; select the optimal prediction model from multiple trained candidate prediction models; Step 5: Perform the jth round of feature screening and update according to the feature update method in step 3, and the initial value of j is 2; Step 6: Determine whether the root mean square error of the ten-fold cross validation of the candidate prediction model corresponding to the feature after the j-th round of screening under the same candidate prediction model is less than or equal to the root mean square error of the ten-fold cross validation of the candidate prediction model corresponding to the feature after the j-1-th round of screening. If yes, set j=j+1 and execute step 5. If not, use the features obtained after the j-1-th round of screening and the stripping energy to train multiple candidate prediction models and perform random search hyperparameter optimization to obtain multiple trained candidate prediction models, and select the trained optimal prediction model from the multiple trained candidate prediction models. Step 7, inputting the AB-type 2D nanomaterial to be tested into the trained optimal prediction model to predict the corresponding stripping energy; The variance inflation factor value for each feature is expressed as: Where VIF i is the variance inflation factor value of the i-th feature, R i is the multiple correlation coefficient between the ith feature and all other features.

2. The method for obtaining the peeling energy of two-dimensional nanomaterials by using machine learning according to claim 1, characterized in that: In step 1, the peeling energy is expressed as: E exf = E 2D -E bulk Formula 1, In the formula, E exf is the peeling energy, E 2D is the energy of each atom in the 2D nanomaterial, E bulk is the energy of each atom in the layered bulk material.

3. The method for obtaining the peeling energy of two-dimensional nanomaterials by using machine learning according to claim 1, characterized in that: The mutual information value I(X i ; Y), expressed as: In the formula, x i Represents feature X i The value of y represents the value of the peeling energy Y, p(x i ,y) is X i The joint probability distribution of and Y, p(x i ) and p(y) are respectively X i and the marginal probability distribution of Y.

4. The method for obtaining the stripping energy of two-dimensional nanomaterials by using machine learning according to claim 1, characterized in that: In step 2, multiple prediction models are trained using the data set and grid search hyperparameter optimization is performed to obtain multiple trained prediction models, and multiple candidate prediction models are pre-screened from the prediction models. The specific process is as follows: The data set is divided into 10 parts equally, and each part is used as a validation set, and the remaining 9 parts are used as training sets, forming a total of 10 validation and training sets; Use 10 training sets from the 10 validation training sets to train each prediction model in turn and perform grid search hyperparameter optimization to obtain each training completed model; The AB-type 2D nanomaterials in 10 validation training sets were input into each training completed model in turn, and the root mean square error of each training completed model was calculated. A total of 10 root mean square errors were obtained for each training completed model. The 10 root mean square errors obtained for each training completed model were averaged, and the average was used as the ten-fold cross-validation error of the corresponding training completed model. The ten-fold cross-validation error of each training completed model was compared with the preset error, and the training completed model corresponding to the closest preset error was selected as the candidate prediction model.

5. The method for obtaining the stripping energy of two-dimensional nanomaterials by using machine learning according to claim 1, characterized in that: In steps 4 and 5, the optimal prediction model is selected from multiple trained candidate prediction models. The specific process is as follows: The n features and stripping energies or the features and stripping energies obtained after the j-1th round of screening are divided into a training set and a test set; Using the training set to train multiple candidate prediction models and perform random search hyperparameter optimization to obtain each trained candidate prediction model; The AB-type 2D nanomaterials in the test set are input into each trained candidate prediction model, and each trained candidate prediction model outputs a prediction value; based on the prediction value of each trained candidate prediction model and the stripping energy in the test set, multiple performance evaluation indicators of each trained candidate prediction model are calculated, and the trained candidate prediction model whose multiple performance evaluation indicators all meet the preset performance evaluation indicators is selected as the optimal prediction model.

6. The method for obtaining the stripping energy of two-dimensional nanomaterials by using machine learning according to claim 5, characterized in that: Various performance evaluation metrics include coefficient of determination, root mean square error, mean square error, and mean absolute error.

7. The method for obtaining the peeling energy of two-dimensional nanomaterials by using machine learning according to claim 6, characterized in that: The coefficient of determination is expressed as: In the formula, m is the total number of data, is the machine learning prediction value of sample i, is the DFT calculated value of sample i, is the average value of the DFT calculated value; The root mean square error is expressed as: The mean square error is expressed as: The mean absolute error is expressed as:

8. The method for obtaining the peeling energy of two-dimensional nanomaterials by using machine learning according to claim 1, characterized in that: Contribution of each characteristic of the tested AB-type 2D nanomaterial to the stripping energy in the optimal prediction model It is expressed as: Where n represents the number of features, S is the subset of all features that does not include feature x, and p(S∪x) represents the predicted value of the selected machine learning prediction model when feature x is taken into account, while p(S) is the predicted value when feature x is not taken into account.

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