Machine learning modeling method based on Mieda theory classification strategy

Abstract

The invention discloses a machine learning modeling method based on a Mieda theory classification strategy, and belongs to the field of machine learning of material science. The method specifically comprises the following steps: firstly, collecting binary compound data, and classifying binary compounds on the basis of a Miedema theory to obtain four material categories; then, constructing a descriptor, and converting the element composition and crystal structure of the binary compound into a series of quantifiable attributes; a machine learning algorithm based on a tree is selected, a corresponding machine learning model is constructed for each material category, and formation energy data and descriptors corresponding to each material category are input for training. And finally, when the binary compound with the new structure is predicted, firstly loading the structure file, generating a corresponding descriptor based on the element composition and the crystal structure, classifying the compound according to the element type, and calling a pre-trained model matched with the classification to obtain an accurate prediction value. According to the invention, the prediction capability of the model for multiple types of materials is improved.

Description

Technical Field

[0001] The present invention belongs to the field of machine learning in materials science, and in particular relates to a machine learning modeling method based on the Miedema theory classification strategy. Background Art

[0002] In the field of materials science, machine learning is gradually becoming a key technology for predicting and evaluating material properties. However, when faced with multiple categories of materials, the prediction accuracy of machine learning models is often unsatisfactory. This is mainly because the properties of materials are ever-changing, and it is difficult for a model to simultaneously capture and accurately predict the properties of all categories of materials. Therefore, improving the model's prediction ability for multiple categories of materials has become a problem that needs to be solved urgently.

[0003] In order to overcome this problem, researchers have begun to seek various optimization methods, among which the classification strategy combined with physical theory is seen as a promising approach. Physical theory, especially classical theories like Miedema, provides researchers with a window to deeply understand the properties of materials.

[0004] Miedema theory has a deep foundation in the analysis and prediction of alloy properties. It comprehensively considers key physical parameters such as electronegativity and electron density, providing a scientific basis for material classification. However, there is a relative lack of practice in integrating Miedema theory with machine learning to improve prediction accuracy, which provides researchers with a new research direction and breakthrough.

[0005] By combining the Miedema theory, it is expected that a more refined material classification system can be constructed, and then a machine learning model can be tailored for each category of material, ultimately achieving a significant improvement in prediction accuracy. Summary of the invention

[0006] The present invention is a machine learning modeling method based on the Miedema theory classification strategy. By integrating the key parameters of the Miedema theory, binary compounds are scientifically classified, and a special machine learning model is constructed for each category, which successfully solves the problem of limited prediction accuracy of traditional machine learning models when dealing with multi-category, complex material properties. This method not only has far-reaching scientific significance, but also provides new ideas and methods for research and application in the field of materials science, and is expected to promote the continuous development and innovation in this field.

[0007] The machine learning modeling method based on Miedema theory classification strategy has the following specific steps:

[0008] Step 1: Collect binary compound data, including the structure files of binary compounds and their corresponding formation energies per unit atom;

[0009] The structure file includes lattice constants, atomic coordinates and element types.

[0010] Step 2: Classify the collected binary compounds based on Miedema theory to obtain four material categories;

[0011] The classification rules are as follows: the IA and IIA group elements in the periodic table are defined as non-transition elements on the left; the IIIB to IB group elements are classified as transition elements; and the IIB to VA group elements are defined as non-transition elements on the right.

[0012] Based on the above classification, four major categories are defined:

[0013] Category a: Binary compounds formed by the combination of non-transition elements on the left and transition elements;

[0014] Category b: binary compounds consisting only of pairs of transition elements, which do not contain non-transition elements;

[0015] Category c: binary compounds composed strictly of non-transition elements;

[0016] Category d: Binary compounds formed by the combination of non-transition elements on the right and transition elements.

[0017] Step 3: Construct descriptors to convert the elemental composition and crystal structure of binary compounds into a series of quantifiable properties.

[0018] Descriptors include: composition descriptors used to characterize chemical composition, and structure descriptors used to describe crystal structure.

[0019] 3.1 The specific calculation process of component descriptor is as follows:

[0020] First, for each element type of the current binary compound, the corresponding properties are searched in the element property library, and the attribute values ​​of each element are obtained;

[0021] Then, six derived values ​​are calculated using the properties of each element as the composition descriptors of the current binary compound.

[0022] The derived values ​​include mean, variance, range, skewness, kurtosis and sum; the specific calculation formula is as follows:

[0023]

[0024] X r =max(X i )-min(X i ) (3)

[0025]

[0026] Where N is the total number of atoms, and the element type and the number of atoms are obtained from the crystal structure file of the binary compound; X i is the relevant property value of the i-th atom, i ranges from 1 to N, and the superscripts a, v, r, s, k, and u are the mean, variance, range, skewness, kurtosis, and sum, respectively.

[0027] 3.2 The specific calculation process of the structure descriptor is as follows:

[0028] Step 3.2.1, determine the closest distance relationship between the atoms of the binary compound by the Voronoi diagram method, identify the nearest neighbor atoms of each atom and record their coordinates. The number of neighbors of an atom is the coordination number of the atom χ CN .

[0029] Step 3.2.2, taking each atom as the center point, and combining the coordinate information of its nearest neighboring atoms, calculate the chemical bond length R corresponding to each center point and the adjacent chemical bond angle θ. For convenience, the cosine value of the chemical bond angle cosθ is used to indirectly describe the size of θ;

[0030] When the i-th atom is the center point, the j-th atom and the k-th atom are the nearest neighbor atoms, the calculation formula for the bond length R and the cosine value of the bond angle cosθ is as follows:

[0031]

[0032] In the formula, the value range of j and k is 1 to x CN , and j is not equal to k

[0033] Similarly, for the remaining nearest neighbor atoms of the center point, calculate the bond length R and the bond angle cosine value cosθ with the i-th atom respectively; calculate the average value of all bond lengths R and bond angle cosine values ​​cosθ to obtain the average bond length The average value of the bond angle cosine as the bond length and bond angle cosine of the ith atom;

[0034] Similarly, take the next atom as the center point and repeat the calculation of the above average values ​​to obtain the bond length and bond angle cosine value of each center point atom;

[0035] Step 3.2.3, by consulting the element property library, mark the property values ​​of all elements in the current binary compound as χ.

[0036] Step 3.2.4, substitute the property value χ of each atom into the following formula:

[0037] ΔX i,j =|X i -X j | (9)

[0038] The i-th atom is the center point, the j-th atom is the nearest neighbor atom, and the corresponding attributes of the two atoms are subtracted to obtain the attribute difference value Δχ; similarly, the attributes of the i-th atom of the center point and each of the remaining nearest neighbor atoms are subtracted to obtain the attribute difference value Δχ with the remaining nearest neighbor atoms;

[0039] Calculate the average value of all the attribute difference values ​​of the center point to get the average attribute difference value of the i-th atom as the center point

[0040]

[0041] where n i represents the number of neighbors of the ith atom.

[0042] Step 3.2.5: Set the coordination number χ of the i-th atom to CN , bond length Bond angle cosine Attribute Difference Average Substitute the updated properties of the atom into the derivative value calculation formula to obtain the corresponding structural descriptor;

[0043] Step 4: By selecting appropriate machine learning algorithms, four machine learning models are constructed for the four material categories respectively, and the formation energy data and descriptors corresponding to the four material categories are input for training;

[0044] Step 5: When predicting binary compounds of new structures, first load the structure file and generate corresponding descriptors based on its elemental composition and crystal structure. Classify the compounds according to the type of elements, and by calling a pre-trained model that matches the classification, accurate prediction values ​​can be obtained.

[0045] The advantages of the present invention are:

[0046] The present invention provides a machine learning modeling method based on the Miedema theory classification strategy, which improves the model's prediction ability for multiple categories of materials; and solves the problem of limited prediction accuracy of traditional machine learning models when processing multiple categories and complex materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 This is a flow chart of a machine learning modeling method based on the Miedema theory classification strategy of the present invention.

[0048] Figure 2 Machine learning models built for the present invention. DETAILED DESCRIPTION

[0049] In order to facilitate those skilled in the art to understand and implement the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. Obviously, the described embodiments are only partial embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative work should fall within the scope of protection of the present invention.

[0050] The present invention provides a machine learning modeling method based on the Miedema theory classification strategy, such as Figure 1 As shown, the specific steps are as follows:

[0051] Step 1: Collect binary compound data, including the structure files of binary compounds and their corresponding formation energies per unit atom;

[0052] The structure file includes lattice constants, atomic coordinates and element types.

[0053] Step 2: Classify the collected binary compounds based on Miedema theory to obtain four material categories;

[0054] The present invention adopts a classification strategy based on Miedema theory to systematically classify binary compounds. The classification rules are as follows: the IA and IIA group elements in the periodic table are defined as non-transition elements on the left; the IIIB to IB group elements are classified as transition elements; and the IIB to VA group elements are defined as non-transition elements on the right.

[0055] Based on the above classification, four major categories are defined:

[0056] Category a: Binary compounds formed by the combination of non-transition elements on the left and transition elements;

[0057] Category b: binary compounds consisting only of pairs of transition elements, which do not contain non-transition elements;

[0058] Category c: binary compounds composed strictly of non-transition elements;

[0059] Category d: Binary compounds formed by the combination of non-transition elements on the right and transition elements.

[0060] It should be noted that the scope of application of this classification strategy is limited to the elements in the first five periods of the periodic table, excluding Groups VI A and VII A and all rare gas elements.

[0061] Step 3: Construct descriptors to convert the elemental composition and crystal structure of binary compounds into a series of quantifiable properties.

[0062] In order to improve the accuracy of machine learning models in predicting material properties, the chemical composition and crystal structure of the compound are converted into a series of quantifiable properties; specifically, it includes two descriptor systems: one is used to characterize the chemical composition, called compositional descriptors; the other is used to describe the crystal structure, called structural descriptors.

[0063] These descriptors will serve as input to models to predict the physical and chemical properties of materials;

[0064] 3.1 Composition Descriptors

[0065] Composition descriptors focus on the composition of a compound. Common composition descriptors contain lists of properties used in various models, covering periodic table information, measurements of atomic radius, electron-related properties, and physical properties.

[0066] The specific calculation process is as follows:

[0067] First, for each element type of the current binary compound, the corresponding properties are searched in the element property library, and the attribute values ​​of each element are obtained;

[0068] The element property library used by this method by default is obtained by searching various books and summarizing literature.

[0069] Then, six mathematical statistics are calculated using the properties of each element: mean, variance, range, skewness, kurtosis and sum, to comprehensively evaluate the performance of each element's various properties in the compound.

[0070] The specific calculation formula is as follows:

[0071]

[0072] Where N is the total number of atoms, and the element type and the number of atoms are obtained from the crystal structure file of the binary compound; X i is the relevant property value of the i-th atom, i ranges from 1 to N, and the superscripts a, v, r, s, k, and u are the mean, variance, range, skewness, kurtosis, and sum, respectively.

[0073] According to the calculation formula defined above, six related derivative values ​​can be calculated from the single element properties as part of the component descriptor. 3 N 4 For example, assuming that there are 3 B atoms and 4 N atoms in a unit cell, and the electron affinity (EA) value of B atoms is 1.6, and the electron affinity (EA) value of N atoms is 1.4, substituting into formula (1) is (1.6*3+1.4*4) / 7=1.49, and the composition descriptor EA of the compound can be obtained. a The specific value is 1.49, and so on.

[0074] 3.2 Structure Descriptor

[0075] The structural descriptor is extracted from the local environment of each atom in the structure, and the local environment of the atom represents the interaction between the atom and its neighbors and directly affects the formation energy of the compound. The structural descriptor contains descriptors related to chemical bonds CB and coordination numbers CN by default, where the descriptor of chemical bonds is expressed by considering the bond length R and the angle θ with adjacent chemical bonds. That is, CB can be expressed as the function CB = (R, θ).

[0076] Common structural descriptors also include Allred-Rochow, Pauling, Martynov-Batsanov, Gordy and Mulliken electronegativity, as well as Miedema electronegativity and Miedema electron density, which can describe the properties of interactions between atoms.

[0077] The specific calculation process is as follows:

[0078] Step 3.2.1, obtain the local environment of the atom and its coordination number: use the CrystalNN function in the pymatgen software package, based on the Voronoi diagram theory, to determine the closest distance relationship between the atoms of the binary compound, identify the nearest neighbor atoms of each atom and record their coordinates. The number of neighbors of an atom is the coordination number of the atom χ CN .

[0079] This function automatically constructs the Voronoi diagram by reading the atomic coordinates (x, y, z) in the binary compound crystal structure file. Through this systematic analysis process, CrystalNN can identify the nearest neighbor atoms of each atom and record their coordinates.

[0080] Taking BN as an example, assuming that there is 1 B atom and 1 N atom in a unit cell, if the CrystalNN function recognizes that the B atom has three nearest neighbor atoms (denoted as N1 N2 N3) and the N atom has two nearest neighbor atoms (denoted as B1 B2), then the coordination number of the B atom is 3 and the coordination number of the N atom is 2.

[0081] Step 3.2.2, taking each atom as the center point, and combining the coordinate information of its nearest neighboring atoms, calculate the chemical bond length R corresponding to each center point and the adjacent chemical bond angle θ. For convenience, the cosine value of the chemical bond angle cosθ is used to indirectly describe the size of θ;

[0082] When the i-th atom is the center point, the j-th atom and the k-th atom are the nearest neighbor atoms, the calculation formula for the bond length R and the cosine value of the bond angle cosθ is as follows:

[0083]

[0084] In the formula, the value range of j and k is 1 to x CN , and j is not equal to k; through the above calculation, we can obtain the specific values ​​representing the chemical bond length R and the bond angle cosθ.

[0085] Similarly, for the remaining nearest neighbor atoms of the center point, calculate the bond length R and the bond angle cosine value cosθ with the i-th atom respectively; calculate the average value of all bond lengths R and bond angle cosine values ​​cosθ to obtain the average bond length Bond angle cosine mean as the bond length and bond angle cosine of the ith atom;

[0086] Similarly, take the next atom as the center point and repeat the calculation of the above average values ​​to obtain the bond length and bond angle cosine value of each center point atom;

[0087] Step 3.2.3, by consulting the element property library, mark the property values ​​of all elements in the current binary compound as χ.

[0088] Step 3.2.4, substitute the property value χ of each atom into the following formula:

[0089] ΔX i,j =|X i -X j | (9)

[0090] The i-th atom is the center point, the j-th atom is the nearest neighbor atom, and the corresponding attributes of the two atoms are subtracted to obtain the attribute difference value Δχ; similarly, the attributes of the i-th atom of the center point and each of the remaining nearest neighbor atoms are subtracted to obtain the attribute difference value Δχ with the remaining nearest neighbor atoms;

[0091] Calculate the average value of all the attribute differences of the center point to get the average attribute difference value of the i-th atom as the center point

[0092]

[0093] Where n i represents the number of neighbors of the ith atom.

[0094] Step 3.2.5: Set the coordination number χ of the i-th atom to CN , bond length Bond angle cosine Attribute Difference Average The updated property of the atom is substituted into the derivative value calculation formula to obtain the corresponding structural descriptor.

[0095] Step 4: By selecting a suitable tree-based machine learning algorithm, four machine learning models are constructed for the four material categories respectively, and the formation energy data and descriptors corresponding to the four material categories are input for training.

[0096] By default, the XGBoost algorithm is used to build the model. Before starting to train the model, the formation energy data and the obtained descriptors corresponding to the four material categories are used as input data for model training, and they are randomly divided into training sets and test sets. The training set accounts for 80% by default to verify the generalization ability of the model.

[0097] The trained model is evaluated using formulas (11) to (14):

[0098]

[0099] Where n is the number of samples, y i is the true value of the sample, is the sample prediction value, is the sample mean.

[0100] Step 5: When predicting binary compounds of new structures, first load the structure file and generate corresponding descriptors based on its elemental composition and crystal structure. Classify the compounds according to the type of elements, and by calling a pre-trained model that matches the classification, accurate prediction values ​​can be obtained.

[0101] Example:

[0102] (1) Collect binary compound data: Use Python programming to collect DFT relaxed structure and formation energy data of binary compounds from the public databases AFLOW, OQMD, and MP, and obtain a total of 343,506 data;

[0103] These compounds were divided into binary chemical systems, and the z-score method was used to detect outliers for each binary chemical system. The threshold was set to 5, and finally 341,382 data were obtained.

[0104] (2) Develop a classification strategy based on Miedema theory: Based on the difference in electronegativity, discontinuity in electron density, and difference in atomic size, and following the rules proposed by Miedema et al., the 341,382 binary compounds collected were divided into four major categories: Category A had a total of 50,120 data; Category B had a total of 105,208 data; Category C had a total of 67,439 data; and Category D had a total of 118,615 data.

[0105] (3) construct explanatory descriptors, including component descriptors and structural descriptors;

[0106] In this example, 35 element properties were selected to generate composition descriptors, covering periodic table information, atomic radius measurements, electron-related properties, and physical attributes, etc. Detailed information is shown in Table 1;

[0107] Table 1

[0108]

[0109] First, by querying the element property library, the specific values ​​X of the above 35 properties of the constituent elements of the binary compound are obtained. Then, X is substituted into the derivative value calculation formulas (1) to (6) to obtain the value of the corresponding component descriptor of the compound. Finally, an array of size 1×210 can be obtained, which corresponds to the component descriptor of a compound.

[0110] Construction of structural descriptors: Allred-Rochow, Pauling, Martynov-Batsanov, Gordy and Mulliken electronegativities, as well as Miedema electronegativity and Miedema electron density were selected to generate relevant structural descriptors.

[0111] First, obtain the atomic neighbor information and coordination number χ CN , then obtain the chemical bond length R and the bond angle cosine value cosθ; by querying Table 1, obtain the specific values ​​χ of the above 7 properties of the constituent elements of the binary compound; substitute the obtained chemical bond length R, bond angle cosine value cosθ and element property value χ into formulas (9) and (10) respectively, and the corresponding property difference average value can be obtained: and Finally, χ CN , and Substituting into formulas (1) to (6), the corresponding structural descriptors are calculated; finally, an array of size 1×60 is obtained, corresponding to the structural descriptor of a compound.

[0112] From this, we can see that we have obtained a two-dimensional array with a dimension of 341382×270, which is stored as a csv file for subsequent machine learning modeling.

[0113] (4) Machine Learning Modeling:

[0114] In terms of the choice of machine learning algorithm, this example uses the extreme gradient boosting algorithm (XGBoost) to build a prediction model with strong generalization ability. In order to ensure the consistency and repeatability of data division, the data set is divided into 80% training set and 20% test set through the train_test_split function in Python's Scikit-Learn library, and the random_state parameter is set to 420.

[0115] During the model training process, the XGBRegressor class in the XGBoost library was used to build the model, and the n_estimators hyperparameter was set to 200 to enhance the prediction accuracy of the model. Other hyperparameters were kept at the default values ​​to preserve the original performance of the algorithm. The coefficient of determination (R) of the model was calculated using formulas (11) to (14). 2 ), root mean square error (RMSE), mean absolute error (MAE), and maximum absolute error (MaxError) to comprehensively evaluate the prediction effect of the model. The effect of the model constructed in this example is as follows Figure 2 shown.

[0116] Through the above specific implementation, the present invention successfully combines Miedema theory with machine learning, improving the accuracy and reliability of machine learning models in predicting material properties. This method not only has far-reaching scientific significance, but also provides new ideas and methods for research and application in the field of materials science.

Claims

1. A machine learning modeling method based on Miedema theory classification strategy, characterized in that: The specific steps are as follows: Step 1: Collect binary compound data, including the structure files of binary compounds and their corresponding formation energies per unit atom; Step 2: Classify the collected binary compounds based on Miedema theory to obtain four material categories; Step 3: Construct descriptors to convert the elemental composition and crystal structure of binary compounds into a series of quantifiable properties; Descriptors include: compositional descriptors for characterizing chemical composition, and structural descriptors for describing crystal structure; 3.1 The specific calculation process of component descriptor is as follows: First, for each element type of the current binary compound, the corresponding properties are searched in the element property library, and the attribute values ​​of each element are obtained; Then, six derived values ​​are calculated using the properties of each type of element as the composition descriptors of the current binary compound; The derived values ​​include mean, variance, range, skewness, kurtosis and sum; the specific calculation formula is as follows: Where N is the total number of atoms, and the element type and the number of atoms are obtained from the crystal structure file of the binary compound; X i is the relevant property value of the i-th atom, i ranges from 1 to N, and the superscripts a, v, r, s, k, and u are the mean, variance, range, skewness, kurtosis, and sum, respectively; 3.2 The specific calculation process of the structure descriptor is as follows: Step 3.2.1, determine the closest distance relationship between the atoms of the binary compound by the Voronoi diagram method, identify the nearest neighbor atoms of each atom and record their coordinates. The number of neighbors of an atom is the coordination number of the atom χ CN ; Step 3.2.2, taking each atom as the center point, and combining the coordinate information of its nearest neighboring atoms, calculate the chemical bond length R corresponding to each center point and the adjacent chemical bond angle θ. For convenience, the cosine value of the chemical bond angle cosθ is used to indirectly describe the size of θ; When the i-th atom is the center point, the j-th atom and the k-th atom are the nearest neighbor atoms, the calculation formula for the bond length R and the cosine value of the bond angle cosθ is as follows: In the formula, the value range of j and k is 1 to x CN , and j is not equal to k; Similarly, for the remaining nearest neighbor atoms of the center point, calculate the bond length R and the bond angle cosine value cosθ with the i-th atom respectively; calculate the average value of all bond lengths R and bond angle cosine values ​​cosθ to obtain the average bond length The average value of the bond angle cosine as the bond length and bond angle cosine of the ith atom; Similarly, take the next atom as the center point and repeat the calculation of the above average values ​​to obtain the bond length and bond angle cosine value of each center point atom; Step 3.2.3, by consulting the element property library, mark the property values ​​of all elements in the current binary compound as χ; Step 3.2.4, substitute the property value χ of each atom into the following formula: ΔX i,j =|X i -X j | (9) The i-th atom is the center point, the j-th atom is the nearest neighbor atom, and the corresponding attributes of the two atoms are subtracted to obtain the attribute difference value Δχ; similarly, the attributes of the i-th atom of the center point and each of the remaining nearest neighbor atoms are subtracted to obtain the attribute difference value Δχ with the remaining nearest neighbor atoms; Calculate the average value of all the attribute difference values ​​of the center point to get the average attribute difference value of the i-th atom as the center point where n i represents the number of neighbors of the ith atom; Step 3.2.5: Set the coordination number χ of the i-th atom to CN , bond length Bond angle cosine Attribute Difference Average Substitute the updated properties of the atom into the derivative value calculation formula to obtain the corresponding structural descriptor; Step 4: By selecting appropriate machine learning algorithms, four machine learning models are constructed for the four material categories respectively, and the formation energy data and descriptors corresponding to the four material categories are input for training; Step 5: When predicting binary compounds of new structures, first load the structure file and generate corresponding descriptors based on its elemental composition and crystal structure. Classify the compounds according to the type of elements, and by calling a pre-trained model that matches the classification, accurate prediction values ​​can be obtained.

2. A machine learning modeling method based on Miedema theory classification strategy as claimed in claim 1, characterized in that: In the step 1, the structure file of the binary compound includes lattice constants, atomic coordinates and element types.

3. A machine learning modeling method based on Miedema theory classification strategy as claimed in claim 1, characterized in that: In the step 2, the classification rules are as follows: the elements of groups IA and IIA in the periodic table are defined as non-transition elements on the left; the elements of groups IIIB to IB are classified as transition elements; the elements of groups IIB to VA are defined as non-transition elements on the right; Based on the above classification, four major categories are defined: Category a: Binary compounds formed by the combination of non-transition elements on the left and transition elements; Category b: binary compounds consisting only of pairs of transition elements, which do not contain non-transition elements; Category c: binary compounds composed strictly of non-transition elements; Category d: Binary compounds formed by the combination of non-transition elements on the right and transition elements.

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