Machine learning prediction method for dielectric property of ultralow-temperature co-fired ceramic material

Abstract

The invention belongs to the technical field of dielectric ceramic materials, and particularly relates to a machine learning prediction method for dielectric properties of an ultra-low temperature co-fired ceramic material (ULTCC). According to the method, a Materials Project database and material physical / chemical rule statistical calculation based on a first principle are combined, and a feature set related to the dielectric property of the ceramic material is collected, calculated, expanded and generated; then using a summation strategy to comprehensively consider linear features and non-linear features, establishing an automatic feature screening strategy, and carrying out feature importance sorting and screening; the method is utilized to guide training and prediction of a machine learning model, and the dielectric constant, the quality factor and the resonance frequency temperature coefficient of the ULTCC are efficiently and accurately predicted.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of dielectric ceramic materials, and particularly relates to a machine learning prediction method for dielectric properties of ultra-low temperature co-fired ceramic (ULTCC) materials. BACKGROUND

[0002] In recent years, the rise of machine learning (ML) technology has brought revolutionary changes to new material research, realizing a paradigm shift from "experience-driven" to data-driven. The application fields have covered the whole-chain innovation contents such as material performance prediction, material composition design, preparation process optimization and failure analysis, and have been widely applied in 2D materials, drug molecules, catalytic materials and other aspects. However, as one of the three solid materials, ceramic materials, especially dielectric ceramic materials, are subject to mutual constraints of preparation process, composition, microstructure formation and other aspects, resulting in problems such as high cost of related data acquisition, lack of standardization, difficulty in feature quantization and poor repeatability, which seriously restrict the application of ML.

[0003] In order to accelerate the development of new ceramic materials, it is imperative to introduce a new paradigm of ML research. The first condition for realizing the application of ML in the prediction of dielectric properties of ceramic materials is to build the relationship between composition, structure and performance. The difficulty and key point lies in feature engineering, including feature construction and feature selection. However, the characteristics of ceramic materials make the feature engineering of such materials both difficult and expensive. The core parameters of the dielectric properties of ceramic materials are dielectric constant, quality factor and temperature coefficient of resonant frequency. At present, the research on the prediction of dielectric properties of ceramic materials by ML is generally insufficient, especially the prediction of quality factor and temperature coefficient of resonant frequency. Moreover, the existing machine learning research is mostly limited to element composition, ignoring crystal structure features such as bond valence and site distribution, and energy band features.

[0004] Qin J, Liu Z, Ma M, et al. (Machine learning approaches for permittivity prediction and rational design of microwave dielectric ceramics. Journal of Materiomics 2021; 7: 1284-93.) selected 32 chemical and structural features as initial features to establish a dielectric constant prediction model, and the prediction results were better than those of Clausius-Mossotti (C-M) equation. Although structural features were introduced, the selection of initial features was completely based on experience and was not comprehensive enough, resulting in the best determination coefficient R 2Only access 0.6, root mean square error RMSE = 2.58. Mo J, Qin J, Ma M et al.(Machine learning assisted Qxf value prediction of ABO4-type microwave dielectric ceramics.Journal of Materiomics 2025;11;100926) selected 35 structural features as initial features, established a Qxf value prediction model of ABO4 type ceramic, realized R 2 =0.8115 high precision prediction in scheelite structure. Although the calculation expands the structural class features, it is only for ABO4 type ceramics, and lacks universality.

[0005] In summary, at present, in the field of ceramic material dielectric performance prediction, small sample is still the main, and it is mainly concentrated in a certain type (ABO4 type, spinel type, etc.) ceramic. Therefore, how to use feature engineering, model optimization and other means to improve the accuracy and universality of performance prediction in the dilemma of data scarcity and uneven quality while ensuring the calculation cost is a necessary and urgent research direction. SUMMARY

[0006] In view of the above problems or deficiencies, the present application provides a machine learning prediction method for dielectric performance of ultra-low temperature co-fired ceramic material, which combines Materials Project database and statistical calculation based on first principle of material physics / chemistry rules to collect and calculate extended features related to dielectric performance of ceramic material; then the additive strategy is used to comprehensively consider linear features and nonlinear features, and an automatic feature screening strategy is built to screen the features after importance sorting. This method not only reduces the feature dimension and reduces the complexity of model calculation, but also ensures the interpretability of features and models, which can avoid the "black box" problem of ML model.

[0007] A machine learning prediction method for dielectric performance of ultra-low temperature co-fired ceramic material, comprising the following steps:

[0008] S1, collecting the chemical formula, crystal system type, dielectric performance parameters (ε r , Qxf, τ f ) of single-phase ULTCC verified by the industry, and performing data preprocessing work.

[0009] S2, combining Materials Project database and statistical calculation based on first principle of material physics / chemistry rules to collect and calculate extended features related to dielectric performance of ceramic material, the feature types of the feature set include element composition, crystal structure, site and energy band.

[0010] S3. Use the summation strategy to comprehensively consider linear features and nonlinear features, build an automated feature screening strategy, sort the features by importance, and select the top n features in descending order of importance as the final feature subset, where n ≥ 2.

[0011] S4. Use the feature subset obtained by S3 as input feature X and the dielectric performance parameter as output y to construct a data set, and randomly divide the data set into a training set and a test set in proportion.

[0012] S5. Build a machine learning model for hyperparameter optimization.

[0013] S6. After determining the optimal hyperparameters, use the training set to train and evaluate the machine learning model to obtain a trained machine learning model.

[0014] S7: Input the input feature X corresponding to the ULTCC material to be predicted into the machine learning model trained in S6 to output the predicted dielectric performance parameter ε r ,Q×f,τ f .

[0015] Furthermore, the step S3 builds an automatic feature screening strategy, and after receiving the calculated and expanded feature set, the following steps are performed in sequence:

[0016] S31: Variance threshold screening, the variance screening threshold is ≤ 0.1, and the feature columns below the variance screening threshold are deleted;

[0017] S32: Redundancy removal, calculate the Pearson coefficient, delete the redundant features with correlation above the threshold, 0.8≤threshold<1;

[0018] S33: F test, testing the linear correlation between features and targets;

[0019] S34: Mutual information screening, testing the nonlinear correlation between features and targets;

[0020] S35: Use the summation strategy to comprehensively consider linear and nonlinear features, sort the feature importance, and select the top n features in descending order of importance as the final feature subset.

[0021] Furthermore, in the data set of step S4, since the ULTCC materials include Mo salts, V salts, Te salts, W salts and their composite salts, in order to ensure the rationality of sampling and the accuracy of the results, random sampling is first performed from each category in proportion according to the material category, and finally the final training set and test set are merged.

[0022] Furthermore, the machine learning model for hyperparameter optimization in step S5 is any machine learning regression model.

[0023] Further, the step S6 machine learning model training, using the training set, the input of the input feature X (S4 obtained), before input, first to make standardization processing, and then input, to unify the quantization range of all features.

[0024] Further, the step S6 model training and evaluation index is the determination coefficient R 2 , root mean square error RMSE, mean absolute error MAE and Pearson correlation coefficient Pearson; and the evaluation index combination can comprehensively quantify the regression model: the variance explanation ability corresponds to the determination coefficient R 2 , error distribution characteristics correspond to RMSE and MAE, and the prediction trend consistency corresponds to Pearson.

[0025] In summary, the present application combines the Materials Project database and the statistical calculation based on the first principle of material physics / chemistry rules, collects and calculates the extended generation and ceramic material dielectric performance related feature set; then uses the additive strategy to comprehensively consider the linear features and nonlinear features, builds an automated feature screening strategy, sorts and screens the feature importance; and uses this method to guide the machine learning model training and prediction, efficiently and accurately predicts the dielectric constant, quality factor and resonance frequency temperature coefficient of ULTCC. BRIEF DESCRIPTION OF DRAWINGS

[0026] Figure 1 Flowchart for the embodiment.

[0027] Figure 2 F-scores (linear correlation degree) importance ranking chart in the embodiment.

[0028] Figure 3 Mutual information (nonlinear correlation degree) importance ranking chart in the embodiment.

[0029] Figure 4 Comprehensive strategy (additive strategy) importance ranking chart in the embodiment.

[0030] Figure 5 Dielectric constant top25 feature and target (dielectric constant) Pearson coefficient heat map in the embodiment.

[0031] Figure 6 Real value-predicted value scatter plot (dielectric constant).

[0032] Figure 7 Quality factor top25 feature and target (quality factor) Pearson coefficient heat map.

[0033] Figure 8 Real value-predicted value scatter plot (quality factor).

[0034] Figure 9 The Pearson coefficient heat map of the top 25 features of the resonant frequency temperature coefficient and the target (resonant frequency temperature coefficient).

[0035] Figure 10 It is a scatter plot of actual value-predicted value (resonant frequency temperature coefficient). DETAILED DESCRIPTION

[0036] The present invention is described below using specific embodiments. Those skilled in the art will readily appreciate the other advantages and benefits of the present invention from the disclosure herein. The present invention may also be implemented or applied through various other specific embodiments, and the details in this specification may be modified and altered based on different perspectives and applications without departing from the spirit of the present invention.

[0037] Example:

[0038] A machine learning prediction method for the dielectric properties of ultra-low temperature co-fired ceramic materials, such as Figure 1 As shown, the following steps are included:

[0039] S1. This example collects the chemical formula, crystal system type, dielectric performance parameters (ε r ,Q×f,τ f ) and perform data preprocessing.

[0040] The data used in this example strictly follow the original data published in the literature, and the data used are pre-processed as follows:

[0041] For repeated materials, only one is retained; for materials with the same chemical formula but different dielectric performance parameters, the performance parameters are averaged to ensure that the data strictly follows the original data.

[0042] S2. Combined with the Materials Project database, a preliminary collection of 19 features was conducted. Based on first-principles material physics / chemistry rules, statistical calculations were performed to generate a feature set related to the dielectric properties of ceramic materials. The feature types of the feature set included elemental composition, crystal structure, site, and energy band. The final number of features after expansion was 16,118.

[0043] S3, using the additive strategy to comprehensively consider linear and nonlinear features, building an automated feature screening strategy, performing feature importance ranking, and screening the top n features in importance as the final feature subset. Different targets result in different screening results, but the same screening strategy is executed, and the significant correlation feature columns screened are different according to different targets. The target can be any one of the dielectric performance parameters (ε r , f, τ f . This embodiment takes the dielectric constant ε r as an example.

[0044] When the expanded feature set and the target are received, the following steps are executed in turn:

[0045] S31: variance threshold screening, deleting low-variance feature columns; the variance screening threshold is 0.1, and the variance screening retains 1038 / 16118 features.

[0046] S32: redundancy removal, calculating the Pearson coefficient, and deleting high-correlation redundant features; the threshold is 0.85, and the redundancy removal retains 430 / 1038 features.

[0047] S33: F-test, testing the linear correlation degree of the feature and the target, and the linear score is represented by S linear .

[0048] S34: mutual information screening, testing the nonlinear correlation degree of the feature and the target, and the nonlinear score is represented by S nonlinear .

[0049] S35: using the additive strategy to comprehensively consider linear and nonlinear features, the formula is as follows, where S linear and S nonlinear have been standardized.

[0050] S add =S linear +S nonlinear

[0051] Then, according to the additive strategy score from large to small, this embodiment selects the top 25 features as the final significant correlation feature subset, and applies the same screening strategy to the training set and the test set. The final retained features are 25 / 430. The linear, nonlinear, and additive strategy feature score importance ranking visualization graphs (taking the dielectric constant as an example) of steps S33, S34, and S35 are shown in Figure 2 , Figure 3 , Figure 4 .

[0052] Figure 2Importance ranking plot for F-scores (linear correlation degree) (take dielectric constant as an example), in which blue is positive PCC (Pearson coefficient) and orange is negative PCC. Figure 3 Importance ranking plot for mutual information (nonlinear correlation degree) (take dielectric constant as an example), in which blue is positive PCC and orange is negative PCC. Figure 4 Importance ranking plot for comprehensive strategy (additive strategy) (take dielectric constant as an example), in which blue is linear and orange is nonlinear.

[0053] S4, taking the feature subset screened in S3 as input features X and the dielectric performance parameter as output y, a data set is constructed, and the data set is randomly divided into a training set and a test set in proportion. Since the ULTCC material used in this embodiment includes molybdate, vanadate, tellurite, tungstate and their composite salts, in order to ensure the rationality of sampling and the accuracy of results, first, according to the material categories, 8:2 proportion is randomly sampled from each category, and finally, the final training set and test set are formed respectively.

[0054] S5, a machine learning model for automatic hyperparameter optimization of genetic algorithm is built.

[0055] This embodiment takes XGBoost regression model as an example, and its hyperparameters and search space (empirical values) include: number of trees (200-400), tree depth (4-8), learning rate (0.01-0.1), subsampling rate (0.2-0.8), and feature sampling rate (0.2-0.8).

[0056] S6, determine the best hyperparameters, then train and evaluate the machine learning model using the training set, and get the trained machine learning model.

[0057] The genetic algorithm is used to automatically optimize the parameters of the machine learning model, and the parameter optimization includes: using genetic algorithm to automatically search the hyperparameter space of the machine learning model, and generating the optimal hyperparameter combination by iteratively performing the following operations:

[0058] (a) initialize the population, randomly generate a combination of hyperparameters as the initial population;

[0059] (b) fitness evaluation: use the machine learning model to evaluate the performance of each hyperparameter combination (such as the determination coefficient R2 of the regression task, the root mean square error RMSE, etc.), and use these performance indicators as fitness values, and this embodiment uses the determination coefficient R2 as the evaluation index;

[0060] (c) genetic operation: through selection, crossover and mutation operations, new hyperparameter combinations are constantly generated, and their fitness is evaluated;

[0061] (d) Iterative optimization: repeat steps (b)-(c) until the maximum number of iterations is reached or the fitness value no longer improves, and output the globally optimal hyperparameter combination.

[0062] When training the machine learning model, the input features X (obtained in S4) are standardized before being inputted to unify the quantization range of all features.

[0063] The indicators for training and evaluating the machine learning model are the determination coefficient R 2 , the root mean square error RMSE, the mean absolute error MAE, and the Pearson correlation coefficient. The combination of evaluation indicators can comprehensively quantify the regression model: the variance explanation capability corresponds to the determination coefficient R 2 , the error distribution characteristic corresponds to the RMSE and the MAE, and the prediction trend consistency corresponds to the Pearson.

[0064] Finally, the trained machine learning model is obtained.

[0065] S7, input the input features X corresponding to the UL TCC material to be predicted into the trained machine learning model in S6, and output the predicted dielectric performance parameters (ε r , Qxf, τ f ).

[0066] This embodiment uses the test set that does not participate in the model training to verify the prediction of the dielectric performance parameters (ε r , Qxf, τ f ) and evaluate the prediction accuracy. For the performance of the model prediction results, the comparison scatter plot of the true value and the predicted value (including the dielectric constant, the quality factor, and the resonance frequency temperature coefficient) is shown in Figure 6 , Figure 8 , Figure 10 .

[0067] Figure 6 The true value-predicted value scatter plot (dielectric constant): the blue points are the training set sample points, the orange points are the test set sample points, the dashed line is the ideal line y=x, and the blue and orange lines are the prediction fitting lines of the training set and the test set, respectively; Figure 8 The true value-predicted value scatter plot (quality factor): the blue points are the training set sample points, the orange points are the test set sample points, the dashed line is the ideal line y=x, and the blue and orange lines are the prediction fitting lines of the training set and the test set, respectively; Figure 10 The true value-predicted value scatter plot (resonance frequency temperature coefficient): the blue points are the training set sample points, the orange points are the test set sample points, the dashed line is the ideal line y=x, and the blue and orange lines are the prediction fitting lines of the training set and the test set, respectively.

[0068] In addition, in order to intuitively show the correlation degree of the screened feature subset and the target attribute, the embodiment adopts the form of a Pearson coefficient heat map for display. The Pearson coefficient heat maps of the screened feature subset and the target attribute (dielectric constant, quality factor, resonant frequency temperature coefficient) are shown in Figure 5 , Figure 7 , Figure 9 .

[0069] Figure 5 The Pearson coefficient heat map of the dielectric constant top25 features and the target (dielectric constant) in the embodiment. Figure 7 The Pearson coefficient heat map of the quality factor top25 features and the target (quality factor). Figure 9 The Pearson coefficient heat map of the resonant frequency temperature coefficient top25 features and the target (resonant frequency temperature coefficient).

[0070] As can be seen from the above embodiments, the present application combines the Materials Project database and the statistical calculation based on the first principle of material physics / chemistry rules, collects and calculates the extended generated feature set related to the dielectric performance of ceramic materials; then uses the additive strategy to comprehensively consider the linear features and nonlinear features, builds an automated feature screening strategy, and screens after sorting the feature importance; and uses this method to guide the training and prediction of the machine learning model, efficiently and accurately predicts the dielectric constant, quality factor and resonant frequency temperature coefficient of the ULTCC.

Claims

1. A machine learning prediction method for the dielectric properties of ultra-low temperature co-fired ceramic materials, comprising the following steps: S1, collect the chemical formula, crystal system type, dielectric performance parameters of the single-phase ULTCC verified by the industry, and make data preprocessing; wherein the dielectric performance parameters include ε r , Q×f, τ f ; S2. Collect and calculate an extended feature set related to the dielectric properties of ceramic materials by combining the Materials Project database and statistical calculations based on first-principle material physics / chemistry rules, the feature types of the feature set including element composition, crystal structure, site, and energy band; S3. Use an additive strategy to comprehensively consider linear and nonlinear features, build an automated feature screening strategy, perform feature importance ranking, and select the top n features in terms of importance as the final feature subset, n≥2; S4. Use the feature subset obtained in S3 as the input feature X and the dielectric property parameter as the output y to build a dataset, and randomly divide the dataset into a training set and a test set according to a proportion; S5. Build a machine learning model for hyperparameter optimization; S6. After determining the best hyperparameters, use the training set to train and evaluate the machine learning model, obtaining a trained machine learning model; S7. Using the test set that did not participate in the model training, predict the dielectric performance parameter ε of the ULTCC material r Q x f, τ f and evaluate its prediction accuracy.

2. The machine learning prediction method of dielectric properties of ultra-low temperature co-fired ceramic material according to claim 1, characterized in that: The step S3 builds an automated feature screening strategy, which performs the following steps in sequence when receiving the extended feature set: S31. Variance threshold screening, variance screening threshold ≤0.1, delete feature columns below the variance screening threshold; S32. Remove redundancy, calculate the Pearson coefficient, and delete redundant features with a correlation above a threshold value, 0.8≤threshold<1; S33. F-test, test the linear correlation degree of the feature and the target; S34. Mutual information screening, test the nonlinear correlation degree of the feature and the target; S35. Use an additive strategy to comprehensively consider linear and nonlinear features, perform feature importance ranking, and select the top n features in terms of importance as the final feature subset. 3.The method of claim 1, wherein the method further comprises: determining a plurality of dielectric properties of the ultra-low temperature co-fired ceramic material; and determining a plurality of dielectric properties of the ultra-low temperature co-fired ceramic material using the machine learning model. In the step S4, the dataset is first randomly sampled from each category according to a proportion based on the material category, and finally merged to form the final training set and test set. 4.The method of claim 1, wherein the method further comprises: determining a plurality of dielectric properties of the ultra-low temperature co-fired ceramic material; and determining a plurality of dielectric properties of the ultra-low temperature co-fired ceramic material using the machine learning model. The machine learning model for hyperparameter optimization in step S5 is any machine learning regression model. 5.The method of claim 1, wherein the method further comprises: determining a plurality of dielectric properties of the ultra-low temperature co-fired ceramic material; and determining a plurality of dielectric properties of the ultra-low temperature co-fired ceramic material using the machine learning model. In the step S6, the machine learning model is trained using the training set, and the input feature X obtained in S4 is standardized before input.

6. The machine learning prediction method of dielectric properties of ultra-low temperature co-fired ceramic materials of claim 1, wherein: The index for the step S6 model training and evaluation is the determination coefficient R 2 , the root mean square error RMSE, the mean absolute error MAE and the Pearson correlation coefficient Pearson; and the evaluation index combination can comprehensively quantify the regression model: wherein the variance explanation ability corresponds to the determination coefficient R 2 , the error distribution characteristic corresponds to the RMSE and the MAE, and the prediction trend consistency corresponds to the Pearson.

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