Machine learning modeling method based on miedema theory classification strategy

Abstract

The application discloses a machine learning modeling method based on a Miedema theory classification strategy, and belongs to the machine learning field of material science; specifically, first, binary compound data are collected, and the binary compounds are classified based on the Miedema theory to obtain four material categories; then, descriptors are constructed to convert the element composition and crystal structure of the binary compounds into a series of quantifiable attributes. By selecting a tree-based machine learning algorithm, a corresponding machine learning model is constructed for each material category, and the formation energy data and the descriptors corresponding to each material category are input for training. Finally, when predicting a new structure binary compound, first, a structure file is loaded, and corresponding descriptors are generated based on the element composition and the crystal structure; the compound is classified according to the element type, and by calling a pre-trained model matched with the classification, accurate prediction values can be obtained. The application improves the prediction ability of the model for multi-category materials.

Description

Technical Field

[0001] This invention belongs to the field of machine learning in materials science, specifically relating to a machine learning modeling method based on a classification strategy of Miedema theory. Background Technology

[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 types of materials, the prediction accuracy of machine learning models is often unsatisfactory. This is mainly because the properties of materials are highly variable, and it is difficult for a single model to simultaneously capture and accurately predict the characteristics of all types of materials. Therefore, improving the predictive ability of models for multiple types of materials has become an urgent problem to be solved.

[0003] To overcome this challenge, researchers have begun to explore various optimization methods, among which the classification strategy combining physical theories is seen as a promising approach. Physical theories, especially classical theories like Miedema, provide researchers with a window into the deep understanding of material properties.

[0004] Miedema theory has a long history of expertise 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 currently 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 Miedema theory, it is hoped that a more refined material classification system can be constructed, and machine learning models can be tailored for each category of materials, ultimately achieving a significant improvement in prediction accuracy. Summary of the Invention

[0006] This invention presents a machine learning modeling method based on the Miedema theory classification strategy. By integrating key parameters of the Miedema theory, it scientifically classifies binary compounds and constructs a specialized machine learning model for each category. This successfully solves the problem of limited prediction accuracy in traditional machine learning models when dealing with multi-category, complex materials. This method not only has profound scientific significance but also provides new ideas and approaches for research and applications in materials science, and is expected to promote the continuous development and innovation of this field.

[0007] The specific steps of the machine learning modeling method based on the Miedema theory classification strategy are as follows:

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

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

[0010] Step 2: Based on Miedema theory, the collected binary compounds are classified into four material categories;

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

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

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

[0014] Category b: Binary compounds consisting only of paired transition elements, without any non-transition elements;

[0015] Category c: Binary compounds consisting strictly of non-transition elements;

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

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

[0018] The descriptors include: composition descriptors for characterizing chemical components, and structure descriptors for describing crystal structures.

[0019] 3.1 The specific calculation process for the 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, using the properties of various elements, six derived values ​​are calculated as component descriptors for the current binary compound.

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

[0023]

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

[0025]

[0026] In the formula, N represents the total number of atoms, and both the element type and the number of atoms are obtained from the crystal structure file of the binary compound; X i Let represent the relevant attribute values ​​of the i-th atom, where i ranges from 1 to N. The superscripts a, v, r, s, k, and u represent the mean, variance, range, skewness, kurtosis, and summation, respectively.

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

[0028] Step 3.2.1: Determine the nearest neighbor relationships between atoms in the binary compound using the Voronoi diagram method, identify the nearest neighbor atom of each atom and record its coordinates. The number of neighbors of an atom is the coordination number χ. CN .

[0029] Step 3.2.2: Take each atom as the center point and combine it with the coordinate information of its nearest neighbor atom to calculate the bond length R of each center point and the angle θ between the chemical bonds and the adjacent chemical bonds. For convenience, the cosine value of the chemical bond angle, cosθ, is used to indirectly describe the magnitude of θ.

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

[0031]

[0032] In the formula, the values ​​of j and k both range from 1 to x. CN And j is not equal to k

[0033] Similarly, for the remaining nearest neighbor atoms at the center point, calculate the bond length R and the cosine of the bond angle cosθ with the i-th atom; calculate the average of all bond lengths R and cosine of the bond angle cosθ to obtain the average bond length. Average value of key angle cosine As the bond length and bond angle cosine of the i-th atom;

[0034] Similarly, taking the next atom as the center point, the above average value is calculated again 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 attribute 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, and the j-th atom is the nearest neighbor atom. The corresponding attributes of the two atoms are subtracted to obtain the attribute difference value Δχ. Similarly, the corresponding attributes of the i-th atom at the center point and each of the other nearest neighbor atoms are subtracted to obtain the attribute difference value Δχ.

[0039] The average of all attribute differences at the center point is calculated to obtain the average attribute difference for the i-th atom as the center point.

[0040]

[0041] Where n i This represents the nearest neighbor number of the i-th atom.

[0042] Step 3.2.5, determine the coordination number χ of the i-th atom. CN bond length Key angle cosine value Attribute Difference Average The updated attribute of this atom is used in the formula for calculating the derived value to obtain the corresponding structure descriptor;

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

[0044] Step 5: When predicting binary compounds with 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 obtain accurate prediction values ​​by calling the pre-trained model that matches the classification.

[0045] The advantages of this invention are:

[0046] This invention presents a machine learning modeling method based on the Miedema theory classification strategy, which improves the model's predictive ability for multiple types of materials and solves the problem of limited prediction accuracy of traditional machine learning models when dealing with multiple types of complex materials. Attached Figure Description

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

[0048] Figure 2 The machine learning model constructed for this invention. Detailed Implementation

[0049] To facilitate understanding and implementation of the present invention by those skilled in the art, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Obviously, the described embodiments are merely some, not all, embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort should fall within the scope of protection of the present invention.

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

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

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

[0053] Step 2: Based on Miedema theory, the collected binary compounds are classified into four material categories;

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

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

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

[0057] Category b: Binary compounds consisting only of paired transition elements, without any non-transition elements;

[0058] Category c: Binary compounds consisting strictly of non-transition elements;

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

[0060] It should be noted that this classification strategy is applicable only to elements in the first five periods of the periodic table, excluding Groups VIA and VIIA and all noble gas elements.

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

[0062] To improve the accuracy of machine learning models in predicting material properties, the chemical composition and crystal structure of compounds are transformed into a series of quantifiable attributes. Specifically, this includes two descriptor systems: one for characterizing chemical composition, called composition descriptors; and the other for describing crystal structure, called structure descriptors.

[0063] These descriptors will be used as input to the model to predict the physical and chemical properties of the material;

[0064] 3.1 Component Descriptor

[0065] Composition descriptors focus on the composition of compounds. Common composition descriptors contain a list of properties used in various models, covering periodic table information, atomic radius measurements, electronic 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 default element property library used in this method was obtained by summarizing and categorizing various books and literature.

[0069] Then, six mathematical statistics are calculated using the properties of various elements: 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] In the formula, N represents the total number of atoms, and both the element type and the number of atoms are obtained from the crystal structure file of the binary compound; X i Let represent the relevant attribute values ​​of the i-th atom, where i ranges from 1 to N. The superscripts a, v, r, s, k, and u represent the mean, variance, range, skewness, kurtosis, and summation, respectively.

[0073] Based on the calculation formula defined above, six related derived values ​​can be calculated from a single element property as part of the composition descriptor. Taking B3N4 as an example, assuming there are 3 B atoms and 4 N atoms in a unit cell, and the electron affinity (EA) value of the B atom is 1.6 and the electron affinity (EA) value of the N atom is 1.4, substituting into formula (1) gives (1.6*3+1.4*4) / 7=1.49, from which 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] Structural descriptors are extracted from the local environment of each atom in the structure. The local environment of an atom represents the interaction between the atom and its nearest neighbor and directly affects the formation energy of the compound. By default, structural descriptors include descriptors related to chemical bonds (CB) and coordination number (CN). The descriptor for chemical bonds is represented by a function that takes into account the bond length R and the angle θ with adjacent chemical bonds. That is, CB can be represented as the function CB = (R, θ).

[0076] Common structure 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 interatomic interactions.

[0077] The specific calculation process is as follows:

[0078] Step 3.2.1: Obtain the local atomic environment and its coordination number: Using the CrystalNN function in the pymatgen package, based on Voronoi diagram theory, determine the nearest neighbor relationships between atoms in the binary compound, identify the nearest neighbor atom of each atom and record its coordinates. The number of neighbors of an atom is the coordination number χ. CN .

[0079] This function automatically constructs a Voronoi diagram by reading the atomic coordinates (x, y, z) from 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 there is 1 B atom and 1 N atom in a unit cell, if the CrystalNN function identifies 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: Take each atom as the center point and combine it with the coordinate information of its nearest neighbor atom to calculate the bond length R of each center point and the angle θ between the chemical bonds and the adjacent chemical bonds. For convenience, the cosine value of the chemical bond angle, cosθ, is used to indirectly describe the magnitude of θ.

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

[0083]

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

[0085] Similarly, for the remaining nearest neighbor atoms at the center point, calculate the bond length R and the cosine of the bond angle cosθ with the i-th atom; calculate the average of all bond lengths R and cosine of the bond angle cosθ to obtain the average bond length. Key angle cosine average value As the bond length and bond angle cosine of the i-th atom;

[0086] Similarly, taking the next atom as the center point, the above average value is calculated again to obtain the bond length and cosine value of the bond angle of each center point atom;

[0087] Step 3.2.3: By consulting the element property library, mark the attribute 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, and the j-th atom is the nearest neighbor atom. The corresponding attributes of the two atoms are subtracted to obtain the attribute difference value Δχ. Similarly, the corresponding attributes of the i-th atom at the center point and each of the other nearest neighbor atoms are subtracted to obtain the attribute difference value Δχ.

[0091] The average of all attribute differences at the center point is calculated to obtain the average attribute difference for the i-th atom as the center point.

[0092]

[0093] Where n i This represents the nearest neighbor number of the i-th atom.

[0094] Step 3.2.5, determine the coordination number χ of the i-th atom. CN bond length Key angle cosine value Attribute Difference Average The updated attribute of the atom is used as the basis for the derived value calculation formula to obtain the corresponding structure descriptor.

[0095] Step 4: By selecting appropriate tree-based machine learning algorithms, construct four machine learning models for the four material categories respectively, and input the formation energy data and descriptors corresponding to the four material categories for training.

[0096] The XGBoost algorithm is used by default to build the model. Before training the model, the formation energy data and descriptors corresponding to the four material categories are used as the input data for model training. The data are randomly divided into training set and test set, with the training set accounting for 80% by default, in order 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 For the sample true value, For the sample predicted value, This is the sample average.

[0100] Step 5: When predicting binary compounds with 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 obtain accurate prediction values ​​by calling the pre-trained model that matches the classification.

[0101] Example:

[0102] (1) Data collection of binary compounds: Using Python programming, DFT relaxation structure and formation energy data of binary compounds were collected from public databases AFLOW, OQMD and MP, and a total of 343,506 data points were obtained;

[0103] These compounds were divided into binary chemical systems, and outliers were detected for each binary chemical system using the z-score method with a threshold of 5, resulting in 341,382 data points.

[0104] (2) Classification strategy based on Miedema theory: Based on the differences in electronegativity, discontinuities in electron density and differences in atomic size, and following the rules proposed by Miedema et al., the 341,382 binary compounds collected were divided into four categories: category a has 50,120 data points; category b has 105,208 data points; category c has 67,439 data points; and category d has 118,615 data points.

[0105] (3) Construct explanatory descriptors, including component descriptors and structure descriptors;

[0106] This example selects 35 elemental properties to generate composition descriptors, covering periodic table information, atomic radius measurements, electron-related properties, and physical properties, etc. See Table 1 for details;

[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 is obtained, corresponding to the component descriptor of a compound.

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

[0111] First, obtain the atomic nearest neighbor information and the coordination number χ. CN Then, obtain the chemical bond length R and the cosine value of the bond angle cosθ; by referring to 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, cosine value of the bond angle cosθ and element property value χ into formulas (9) and (10) respectively to obtain the corresponding average value of attribute difference. 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] Thus, we obtain a two-dimensional array with dimensions of 341382×270, which can be stored as a CSV file for subsequent machine learning modeling.

[0113] (4) Machine learning modeling:

[0114] In choosing the machine learning algorithm, this example uses Extreme Gradient Boosting (XGBoost) to build a predictive model with strong generalization capabilities. To ensure the consistency and reproducibility of the data partition, the dataset is divided into an 80% training set and a 20% test set using the `train_test_split` function from Python's Scikit-Learn library, with the `random_state` parameter set to 420.

[0115] During model training, the XGBRegressor class from the XGBoost library was used to construct the model, and the n_estimators hyperparameter was set to 200 to enhance the model's prediction accuracy. Other hyperparameters were kept at their default values ​​to preserve the original performance of the algorithm. The determination coefficients (R²) of the model were calculated using formulas (11) to (14). 2 The root mean square error (RMSE), mean absolute error (MAE), and maximum absolute error (MaxError) are used to comprehensively evaluate the model's predictive performance. The model built in this example performs as follows: Figure 2 As shown.

[0116] Through the specific implementation methods described above, this 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 profound scientific significance but also provides new ideas and approaches for research and applications in the field of materials science.

Claims

1. A machine learning modeling method based on a classification strategy according to Miedema theory, characterized in that, The specific steps are as follows: Step 1: Collect binary compound data, including the structural files of the binary compounds and their corresponding formation energy per unit atom; Step 2: Based on Miedema theory, the collected binary compounds are classified into four material categories; Step 3: Construct descriptors to transform the elemental composition and crystal structure of binary compounds into a series of quantifiable properties; Descriptors include: composition descriptors for characterizing chemical components, and structure descriptors for describing crystal structures; 3.1 The specific calculation process for the 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, using the properties of various elements, six derived values ​​are calculated as component descriptors for the current binary compound; The derived values ​​include the mean, variance, range, skewness, kurtosis, and sum; the specific calculation formulas are as follows: In the formula, N represents the total number of atoms, and both the element type and the number of atoms are obtained from the crystal structure file of the binary compound; X i Let be the relevant attribute value of the i-th atom, where i ranges from 1 to N. The superscripts a, v, r, s, k, and u are the mean, variance, range, skewness, kurtosis, and summation, respectively. 3.2 The specific calculation process of the structure descriptor is as follows: Step 3.2.1: Determine the nearest neighbor relationships between atoms in the binary compound using the Voronoi diagram method, identify the nearest neighbor atom of each atom and record its coordinates. The number of neighbors of an atom is the coordination number χ. CN ; Step 3.2.2: Take each atom as the center point and combine it with the coordinate information of its nearest neighbor atom to calculate the bond length R of each center point and the angle θ between the chemical bonds and the adjacent chemical bonds. For convenience, the cosine value of the chemical bond angle, cosθ, is used to indirectly describe the magnitude of θ. When the i-th atom is the center point, and the j-th and k-th atoms are the nearest neighbors, the formulas for calculating the bond length R and the cosine of the bond angle cosθ are as follows: In the formula, the values ​​of j and k both range from 1 to x. CN And j is not equal to k; Similarly, for the remaining nearest neighbor atoms at the center point, calculate the bond length R and the cosine of the bond angle cosθ with the i-th atom; calculate the average of all bond lengths R and cosine of the bond angle cosθ to obtain the average bond length. Average value of key angle cosine As the bond length and bond angle cosine of the i-th atom; Similarly, taking the next atom as the center point, the above average value is calculated again 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 attribute 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, and the j-th atom is the nearest neighbor atom. The corresponding attributes of the two atoms are subtracted to obtain the attribute difference value Δχ. Similarly, the corresponding attributes of the i-th atom at the center point and each of the other nearest neighbor atoms are subtracted to obtain the attribute difference value Δχ. The average of all attribute differences at the center point is calculated to obtain the average attribute difference for the i-th atom as the center point. Where n i This represents the nearest neighbor number of the i-th atom; Step 3.2.5, determine the coordination number χ of the i-th atom. CN bond length Key angle cosine value Attribute Difference Average The updated attribute of this atom is used in the formula for calculating the derived value to obtain the corresponding structure descriptor; Step 4: By selecting appropriate machine learning algorithms, construct four machine learning models for the four material categories respectively, and input the formation energy data and descriptors corresponding to the four material categories for training; Step 5: When predicting binary compounds with 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 obtain accurate prediction values ​​by calling the pre-trained model that matches the classification.

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

3. The machine learning modeling method based on the Miedema theory classification strategy as described in claim 1, characterized in that, In step two, the classification rules are as follows: elements in groups IA and IIA of the periodic table are defined as non-transitional elements on the left; elements in groups IIIB to IB are classified as transitional elements; elements in groups IIB to VA are defined as non-transitional elements on the right. Based on the above classification, four main categories are defined: Category a: Binary compounds formed by the combination of non-transition elements and transition elements on the left; Category b: Binary compounds consisting only of paired transition elements, without any non-transition elements; Category c: Binary compounds consisting strictly of non-transition elements; Category d: Binary compounds formed by the combination of non-transition elements and transition elements on the right.

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