Multi-component quasi-crystal component design method based on machine learning

Abstract

The invention relates to a multi-component quasicrystal component design method based on machine learning, which comprises the following steps: S1, collecting data of quasicrystal and components corresponding to the quasicrystal, and carrying out feature mining; s2, determining input and output, and constructing a supervised learning classification model; s3, dividing the original data set into a training set and a test set in proportion; s4, performing random forest model training by using the training set; s5, evaluating the performance of the model through the three indexes; s6, performing feature importance sorting and correlation analysis based on a prediction result; s7, performing high-throughput virtual screening to obtain a target multi-component alloy system; s8, a multi-component alloy system is determined, and a multi-component alloy virtual component complex is generated; s9, generating a ternary phase diagram, and predicting a new quasicrystal according to a quasicrystal criterion; according to the design method, a prediction model is constructed by analyzing the chemical composition, structural characteristics and physical properties of known quasi-crystals, so that the discovery process of new quasi-crystals is accelerated.

Description

Technical Field

[0001] The present invention belongs to the technical field of metal material design and relates to a multi-component quasicrystal composition design method based on machine learning. Background Art

[0002] In the field of materials science, quasicrystals (QCs) are materials with special order. Their electron diffraction patterns exhibit five-fold or ten-fold symmetry, which is forbidden in traditional periodic crystals. Since D. Shechtman discovered quasicrystals in 1984, this field has made remarkable progress. The unique physical properties of quasicrystals, such as abnormal electrical conductivity, thermal conductivity and mechanical strength, have inspired scientists to conduct in-depth research on this type of material. However, the discovery and design of quasicrystals have always relied on experimental trial and error and first-principles calculations, which require a large number of experiments to explore possible alloy combinations to discover new quasicrystals. This method is not only time-consuming but also costly because a large number of synthesis and characterization experiments are required. Although first-principles calculations can provide predictions of quasicrystal properties, they are computationally expensive, especially for multi-component systems. This limits the screening of a large number of potential quasicrystal candidates. As a result, many quasicrystals that may have novel physical phenomena have not yet been discovered.

[0003] With the rapid development of machine learning technology, its application in material design has gradually become a hot topic of research. Machine learning algorithms, especially supervised learning algorithms, can learn and predict the properties of new materials from a large amount of material data. Although machine learning has made some progress in the field of quasicrystal research, there is still no systematic method to use machines to design new quasicrystals in the face of difficult data collection, complex feature mining and difficult to interpret algorithm models. Summary of the invention

[0004] In view of this, in order to solve the problems of high experimental cost and high computational cost in the current use of experimental trial and error and first-principles calculations to discover and design quasicrystals, the present invention provides a multi-component quasicrystal composition design method based on machine learning. This design method constructs a prediction model by analyzing the chemical composition, structural characteristics and physical properties of known quasicrystals, thereby accelerating the discovery process of new quasicrystals.

[0005] In order to achieve the above object, the present invention provides the following technical solutions:

[0006] A method for designing multi-component quasicrystal compositions based on machine learning, comprising the following steps:

[0007] S1. Model building

[0008] S11. Collect chemical composition data of known quasicrystals (QC), approximate crystals (AC) and ordinary periodic crystals (OTHERS), mine the features used to describe the composition, and average each feature value;

[0009] S12, using the sample data collected in step S11 to build a supervised learning classification model, average each eigenvalue, and integrate these averaged eigenvalues, and convert them into a multidimensional descriptor vector that can describe the physical and chemical properties of the constituent elements. This vector will serve as the input of the model; at the same time, the three categories of quasicrystals, approximate crystals and ordinary periodic crystals are used as output labels of the model to build a complete classification model;

[0010] S13, dividing the original data set constructed in step S12 into a training set and a test set according to a ratio of 70-85% of the training set;

[0011] S14, using three supervised learning algorithms, namely, random forest classifier, neural network classifier and support vector machine classifier, to respectively construct classification prediction models, that is, learning the mapping from vectorized synthesis to three different labels of AC, QC and OTHERS, and using the data of the training set in step S13 to train and construct the prediction model and optimize the parameters;

[0012] S15, using the data of the test set in step S13 to perform a ten-fold cross-validation on the trained model, evaluating the prediction model effect through the three indicators of precision, recall and F1, and obtaining the optimal prediction model;

[0013] S2. Feature Analysis

[0014] S21, predicting different characteristics of different alloy systems based on the optimal prediction model trained in step S15, evaluating the importance of different characteristics, quantifying the linear relationship between different pairs of characteristics, identifying the key characteristics that have the greatest impact on quasicrystal formation, and revealing the potential relationship between the characteristics;

[0015] S3. Composition design

[0016] S31, using the optimal prediction model trained in step S15 to predict the composition ratios of different alloy systems, using high-throughput virtual screening, screening based on the condition that both the predicted value and the true value are QC as the screening target, and obtaining a multi-element alloy system that meets the condition;

[0017] S32, determining a multi-element alloy system to be studied, and generating a fully covered virtual component complex according to component ratios;

[0018] S33. Draw a ternary phase diagram based on the virtual component complex generated in step S32, and predict new quasicrystals based on the five quasicrystal formation principles of long-range order, non-crystallographic rotational symmetry, incommensurate translational period, cluster line criterion, and equal electron concentration and equal atomic size criterion.

[0019] Furthermore, the features mined in step S11 for describing the components include atomic number, bond radius, van der Waals radius, electronegativity, thermal conductivity, band gap, polarizability, boiling point and melting point.

[0020] Furthermore, the component summary conversion in step S12 adopts the weighted mean, weighted variance, maximum value and minimum value pooling methods.

[0021] Furthermore, in step S13, the training set accounts for 80% of the data set and the test set accounts for 20%.

[0022] Furthermore, the optimal prediction model obtained in step S15 is a random forest classifier.

[0023] Furthermore, the accuracy in step S15 measures the proportion of samples predicted by the model to be positive and actually positive, and the calculation formula is:

[0024]

[0025] TP (True Positives) is the number of samples correctly predicted as positive by the model; FP (False Positives) is the number of negative samples incorrectly predicted as positive by the model.

[0026] The recall rate measures the proportion of all actual positive samples that are correctly predicted as positive by the model. The calculation formula is:

[0027]

[0028] Among them, FN (False Negatives) is the number of false negative examples, which are positive samples that are incorrectly predicted as negative by the model;

[0029] F 1 The score is the harmonic mean of precision and recall, F 1 The score is calculated as:

[0030]

[0031] High precision means fewer false positives, that is, most of the samples predicted by the model as positive are correct; high recall means fewer false negatives, that is, most of the samples actually positive are correctly identified by the model; F 1The score attempts to balance precision and recall, especially in the case of class imbalance. 1 The score provides a performance measure that takes both metrics into account.

[0032] Furthermore, in step S21, the built-in feature importance evaluation function of the random forest classifier prediction model is used to calculate the contribution of each feature to the result and give a ranking, and the Pearson coefficient is used to quantify the linear relationship between the features.

[0033] Furthermore, in step S33, the generated virtual component complex is plotted into a ternary phase diagram, different alloys are distinguished by different colors, and finally a new quasicrystal is predicted according to the quasicrystal criterion principle.

[0034] Furthermore, the quasicrystal criterion principle in step S33 is related to the weighted average value of the van der Waals radius, electronegativity, first ionization energy, the number of valence electrons in the p orbital, and the energy of each atom constituting the ground state of the element.

[0035] The beneficial effects of the present invention are:

[0036] 1. The multi-component quasicrystal composition design method based on machine learning disclosed in the present invention can efficiently identify and analyze the key parameters affecting the performance of quasicrystals by comprehensively utilizing data mining, feature engineering and a variety of machine learning technologies, and construct an accurate prediction model, thereby providing a rapid, precise and economical technological innovation approach for the composition design of quasicrystals.

[0037] 2. The multi-component quasicrystal composition design method based on machine learning disclosed in the present invention demonstrates how to construct a classification model for quasicrystal prediction, and explores the impact of quantitative features on the prediction results and their potential relationship with each other. Virtual compounds are generated by algorithms, and ternary phase diagrams are drawn, and finally new quasicrystal structures are predicted based on the quasicrystal identification criteria. This method not only improves the efficiency of quasicrystal identification, but also reduces related costs, bringing an innovative quasicrystal design and prediction tool to the field of materials science. Using this method, the discovery of new quasicrystals can be accelerated, promoting the wider application of quasicrystal materials in industry and scientific research.

[0038] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below in conjunction with the accompanying drawings, wherein:

[0040] Figure 1 A flowchart of a method for designing multi-component quasicrystal components based on machine learning according to the present invention;

[0041] Figure 2 This is a distribution diagram of the importance of the top 10 features in the embodiment;

[0042] Figure 3 for Figure 2 Heat map of correlation analysis of top 10 features;

[0043] Figure 4 Ternary phase diagram of a virtual composite generated for an example. DETAILED DESCRIPTION

[0044] The following describes the embodiments of the present invention through specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention.

[0045] like Figure 1 A method for designing multi-component quasicrystal compositions based on machine learning is shown, comprising the following steps:

[0046] S1. Model building

[0047] S11. Collect the chemical composition data of known quasicrystals (QC), approximate crystals (AC) and ordinary periodic crystals (OTHERS), mine the features used to describe the composition, and average each feature value; the features mined to describe the composition include atomic number, bond radius, van der Waals radius, electronegativity, thermal conductivity, band gap, polarizability, boiling point and melting point.

[0048] S12, using the sample data collected in step S11 to build a supervised learning classification model, average each eigenvalue, and integrate these averaged eigenvalues, and convert them into a multidimensional descriptor vector that can describe the physical and chemical properties of the constituent elements. This vector will be used as the input of the model, and the component summary conversion adopts the weighted mean, weighted variance, maximum and minimum pooling methods; at the same time, the three categories of quasicrystals, approximate crystals and ordinary periodic crystals are used as the output labels of the model to build a complete classification model;

[0049] S13, the original data set constructed in step S12 is divided into a training set accounting for 80% and a test set accounting for 20%;

[0050] S14, using three supervised learning algorithms, namely, random forest classifier, neural network classifier and support vector machine classifier, to respectively construct classification prediction models, that is, learning the mapping from vectorized synthesis to three different labels of AC, QC and OTHERS, and using the data of the training set in step S13 to train and construct the prediction model and optimize the parameters;

[0051] S15, using the data of the test set in step S13 to perform a ten-fold cross-validation on the trained model, evaluating the prediction model effect through the three indicators of precision, recall and F1, and obtaining the optimal prediction model;

[0052] S2. Feature Analysis

[0053] S21, predicting different characteristics of different alloy systems based on the optimal prediction model trained in step S15, evaluating the importance of different characteristics, quantifying the linear relationship between different pairs of characteristics, identifying the key characteristics that have the greatest impact on quasicrystal formation, and revealing the potential relationship between the characteristics;

[0054] S3. Composition design

[0055] S31, using the optimal prediction model trained in step S15 to predict the composition ratios of different alloy systems, using high-throughput virtual screening, screening based on the condition that both the predicted value and the true value are QC as the screening target, and obtaining a multi-element alloy system that meets the condition;

[0056] S32, determining a multi-element alloy system to be studied, and generating a fully covered virtual component complex according to component ratios;

[0057] S33. Draw a ternary phase diagram based on the virtual component complex generated in step S32, and predict new quasicrystals based on the five quasicrystal formation principles of long-range order, non-crystallographic rotational symmetry, incommensurate translational period, cluster line criterion, and equal electron concentration and equal atomic size criterion.

[0058] Example

[0059] The database established by the embodiment of the present invention is mainly based on ternary alloys to predict new aluminum-based ternary quasicrystals. The specific steps are as follows:

[0060] S1. Collect chemical composition data of known quasicrystals, approximate phase crystals and ordinary periodic crystals. 47 thermodynamically stable quasicrystals (QCs) and 59 approximate phase crystals (ACs) were collected from the Handbook of Quasicrystallometry, and 5863 periodic crystal chemical compositions were randomly extracted from the Materials Project database as other ordinary periodic crystals (OTHERS);

[0061] S2. The constituent elements in a given composition are characterized by 58 elemental features, including atomic number, bond radius, van der Waals radius, electronegativity, thermal conductivity, band gap, polarizability, boiling point and melting point. Each feature value is averaged and the final input composition is converted into a 58-dimensional descriptor vector representing the physicochemical characteristics of the constituent elements. The three classification labels of QC, AC and OTHERS are used as output to build a complete supervised learning classification model.

[0062] S3. Divide the dataset. For each category, randomly select about 80% of the total samples as the training set to train the model (the number of QC, AC, and OTHERS are 34, 45, and 4673, respectively), and use the remaining 20% ​​of the samples as the test set to evaluate the prediction performance (the number of QC, AC, and OTHERS are 13, 14, and 1190, respectively);

[0063] S4. Use various supervised learning algorithms, such as random forest, neural network, support vector machine, etc., to build a classification prediction model. The classification model takes components and features as inputs and three labels, AC, QC, and OTHERS, as outputs. Random forest has the best effect, so the random forest classifier is used to build the prediction model;

[0064] S5. Perform ten-fold cross validation on the test set to evaluate the prediction model. The evaluation indicators we use are precision, recall and F 1 .

[0065] Precision measures the proportion of samples that are actually positive among those predicted by the model. Its calculation formula is:

[0066]

[0067] Among them, TP (True Positives) is the true positive example, which is the number of samples correctly predicted by the model as the positive class; FP (False Positives) is the false positive example, which is the number of negative class samples incorrectly predicted by the model as the positive class.

[0068] Recall measures the proportion of all actual positive samples that are correctly predicted as positive by the model. Its calculation formula is:

[0069]

[0070] Among them, FN (False Negatives) is the number of false negative examples, which are positive samples that are incorrectly predicted as negative samples by the model.

[0071] F 1 The score is the harmonic mean of precision and recall, which attempts to find a balance between precision and recall.1 The score is calculated as:

[0072]

[0073] High precision means fewer false positives, that is, most of the samples predicted by the model as positive are correct. High recall means fewer false negatives, that is, most of the samples actually positive are correctly identified by the model. 1 The score attempts to balance precision and recall, especially in the case of class imbalance. 1 The score can provide a performance measure that takes these two indicators into consideration. Table 1 shows the evaluation results of the random forest classifier model prediction, where the prediction accuracy of QC can be as high as 0.86, indicating that the model effect is good.

[0074] Table 1

[0075] QC AC OTHERS Precision 0.86 0.73 0.99 Recall 0.46 0.67 1.00 <![CDATA[F 1 ]]> 0.60 0.70 1.00

[0076] S6. Since random forest is selected as the classification model in this embodiment, the built-in feature importance evaluation function of the random forest model can be used. Random forest evaluates the importance of features by constructing multiple decision trees and calculating the average impurity reduction of each feature in all trees. Figure 2 What is shown is the importance percentage of the top 10 features, from which it can be seen that the number of valence electrons is the main factor affecting the formation of quasicrystals.

[0077] S7. Use the Pearson correlation coefficient to quantify the linear relationship between different features. Through the correlation matrix heat map, highly correlated feature pairs can be intuitively identified, such as Figure 3 As shown. The correlation between each feature and the target variable is analyzed to determine which features have a stronger correlation with the formation of quasicrystals. The results of the correlation analysis can help us understand how different physicochemical properties jointly affect the formation of quasicrystals. In addition, it can also be used for feature selection, that is, to select the features with the strongest correlation with the target variable when building a prediction model.

[0078] S8. Then use the trained model to perform virtual screening on any composition. The screening basis is a system where the true value is QC and the predicted value is also QC. In addition, in this embodiment, we focus on ternary systems, and Table 1 is several systems that were finally screened. For convenience, this embodiment selects an Al-Cu-Fe system from the final screening results, which is observed and predicted to have QC compounds.

[0079] Table 2

[0080] elements label prediction Al 65 Cu20 Os 15 (Al, Cu, Os) QC QC Zn 72 Sc 16 Cu 12 (Cu, Sc, Zn) QC QC Al 65 Cu 20 Fe 15 (Al, Cu, Fe) QC QC Al 65 Cu 20 Ru 15 (Al, Cu, Ru) QC QC

[0081] S9. Generate virtual complexes using algorithms to cover all combinations, such as Al a Cu b Fe c , where a, b, and c are ratios. The total value of the ratio is set to 100, the step size is set to 0.5, and 20298 combinations are finally generated. This example uses the function make_virtual compounds to implement the above process.

[0082] S10, draw the generated virtual composite using a ternary phase diagram, such as Figure 4 As shown, the yellow area is OTHERS, the orange area is AC, and the red area is QC. Finally, this example extracts five rules: long-range order, non-crystallographic rotational symmetry, incommensurate translation period, cluster line criterion, and isoelectronic concentration and isoatomic size criterion. These criteria are related to the weighted average of the van der Waals radius, electronegativity, first ionization energy, the number of valence electrons in the p orbital, and the energy of each atom that constitutes the ground state of the element. The five rules are then plotted in a ternary phase diagram. In aluminum alloys, most quasicrystal phases appear near the intersection of the five straight lines. The blue dots in the figure represent the composition ratio of the new quasicrystal predicted in this example.

[0083] The present invention demonstrates how to construct a classification model for quasicrystal prediction through examples, and analyzes the impact of features on results and the potential connections between features; then uses an algorithm to generate a virtual complex, draws a ternary phase diagram, and finally predicts new quasicrystals based on quasicrystal criteria. The method of the present invention not only improves the efficiency of quasicrystal discovery, but also reduces costs, providing an innovative quasicrystal design and prediction tool for the field of materials science. Through this method, the discovery process of new quasicrystals can be accelerated, promoting the application of quasicrystal materials in industry and scientific research.

[0084] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution, which should be included in the scope of the claims of the present invention.

Claims

1. A multi-component quasicrystal composition design method based on machine learning, characterized in that: The following steps are involved: S1. Model building S11. Collect chemical composition data of known quasicrystals (QC), approximate crystals (AC) and ordinary periodic crystals (OTHERS), mine the features used to describe the composition, and average each feature value; S12, using the sample data collected in step S11 to build a supervised learning classification model, average each eigenvalue, and integrate these averaged eigenvalues, and convert them into a multidimensional descriptor vector that can describe the physical and chemical properties of the constituent elements. This vector will serve as the input of the model; at the same time, the three categories of quasicrystals, approximate crystals and ordinary periodic crystals are used as output labels of the model to build a complete classification model; S13, dividing the original data set constructed in step S12 into a training set and a test set according to a ratio of 70-85% of the training set; S14, using three supervised learning algorithms, namely, random forest classifier, neural network classifier and support vector machine classifier, to respectively construct classification prediction models, that is, learning the mapping from vectorized synthesis to three different labels of AC, QC and OTHERS, and using the data of the training set in step S13 to train and construct the prediction model and optimize the parameters; S15, using the data of the test set in step S13 to perform a ten-fold cross-validation on the trained model, evaluating the prediction model effect through the three indicators of precision, recall and F1, and obtaining the optimal prediction model; S2. Feature Analysis S21, predicting different characteristics of different alloy systems based on the optimal prediction model trained in step S15, evaluating the importance of different characteristics, quantifying the linear relationship between different pairs of characteristics, identifying the key characteristics that have the greatest impact on quasicrystal formation, and revealing the potential relationship between the characteristics; S3. Composition design S31, using the optimal prediction model trained in step S15 to predict the composition ratios of different alloy systems, using high-throughput virtual screening, screening based on the condition that both the predicted value and the true value are QC as the screening target, and obtaining a multi-element alloy system that meets the condition; S32, determining a multi-element alloy system to be studied, and generating a fully covered virtual component complex according to component ratios; S33. Draw a ternary phase diagram based on the virtual component complex generated in step S32, and predict new quasicrystals based on the five quasicrystal formation principles of long-range order, non-crystallographic rotational symmetry, incommensurate translational period, cluster line criterion, and equal electron concentration and equal atomic size criterion.

2. The method for designing multi-component quasicrystal composition based on machine learning as claimed in claim 1, characterized in that: The features mined in step S11 for describing the components include atomic number, bond radius, van der Waals radius, electronegativity, thermal conductivity, band gap, polarizability, boiling point, and melting point.

3. The multi-component quasicrystal composition design method based on machine learning as claimed in claim 1, characterized in that: The component summary conversion in step S12 adopts the weighted mean, weighted variance, maximum value and minimum value pooling methods.

4. The method for designing multi-component quasicrystal composition based on machine learning as claimed in claim 1, characterized in that: In step S13, the training set accounts for 80% of the data set and the test set accounts for 20%.

5. The method for designing multi-component quasicrystal composition based on machine learning as claimed in claim 4, characterized in that: The optimal prediction model obtained in step S15 is the random forest classifier.

6. The method for designing multi-component quasicrystal composition based on machine learning as claimed in claim 5, characterized in that: The accuracy in step S15 measures the proportion of samples predicted by the model to be positive and actually positive. The calculation formula is: TP (True Positives) is the number of samples correctly predicted as positive by the model; FP (False Positives) is the number of negative samples incorrectly predicted as positive by the model. The recall rate measures the proportion of all actual positive samples that are correctly predicted as positive by the model. The calculation formula is: Among them, FN (False Negatives) is the number of false negative examples, which are positive samples that are incorrectly predicted as negative by the model; The F1 score is the harmonic mean of precision and recall. The calculation formula of the F1 score is: High precision means fewer false positives, that is, most of the samples predicted by the model as positive are correct; high recall means fewer false negatives, that is, most of the samples that are actually positive are correctly identified by the model; the F1 score attempts to balance precision and recall, especially in the case of class imbalance. The F1 score provides a performance metric that comprehensively considers these two indicators.

7. The method for designing multi-component quasicrystal composition based on machine learning as claimed in claim 6, characterized in that: In step S21, the built-in feature importance evaluation function of the random forest classifier prediction model is used to calculate the contribution of each feature to the result and give a ranking, and the Pearson coefficient is used to quantify the linear relationship between the features.

8. The method for designing multi-component quasicrystal composition based on machine learning as claimed in claim 7, characterized in that: In step S33, the generated virtual component complex is drawn into a ternary phase diagram, and different colors are used to distinguish different alloys, and finally new quasicrystals are predicted according to the quasicrystal criterion principle. The criterion principle of quasicrystals mainly includes the following aspects: First, quasicrystals have long-range quasi-periodic translation order and long-range directional order, which is the basic feature that distinguishes them from traditional crystals and amorphous solids. Secondly, quasicrystals can exhibit non-crystallographic rotational symmetry, such as five-fold or ten-fold symmetry, which does not exist in ordinary crystals. In addition, the atomic arrangement of quasicrystals is not repeated in space, showing the characteristics of incommensurate translation period. Finally, when analyzing the composition law of alloy phases, the isoelectronic concentration and isoatomic size criteria are used as guidance to further confirm whether there is a multi-electron quasicrystal.

9. The method for designing multi-component quasicrystal composition based on machine learning as claimed in claim 8, characterized in that: The quasicrystal criterion principle in step S33 is related to the weighted average value of the van der Waals radius, electronegativity, first ionization energy, the number of valence electrons in the p orbital, and the energy of each atom constituting the ground state of the element.

Images