Machine learning based high temperature superconducting material interpretable prediction method, system, and computer readable storage medium

Abstract

The application discloses a high-temperature superconducting material interpretable prediction method and system based on machine learning and a computer readable storage medium. The method comprises the following steps: constructing a superconducting material dataset to generate material characteristics; constructing a random forest model for training, outputting the importance ranking of the material characteristics through feature_importance, thereby extracting three material characteristics, i.e., ground state atomic volume average deviation, unfilled s orbital electron average deviation and element electronegativity average deviation, as key characteristics for determining the superconducting critical temperature; performing weighted optimization on the trained random forest model by using the key characteristics to form an interpretable prediction model; and predicting candidate materials by using the interpretable prediction model and completing stability verification and screening through Ehull value calculation. The application successfully identifies three key characteristics affecting the superconducting critical temperature through feature importance analysis, thereby ensuring that the prediction result is consistent with the superconducting physical mechanism.

Description

Technical Field

[0001] This invention relates to the intersection of high-temperature superconducting materials technology and machine learning, and particularly to interpretable prediction methods, systems, and computer-readable storage media for high-temperature superconducting materials based on machine learning. Background Technology

[0002] Superconductivity is one of the most complex and fascinating physical phenomena in condensed matter physics. High-temperature superconducting materials, due to their excellent properties such as zero resistance and perfect diamagnetism, have broad application prospects in many key fields such as power transmission, medical imaging, and quantum computing. Since Onnes discovered the superconducting properties of mercury in 1911, researchers have successively discovered thousands of superconducting materials, from simple metals and alloys to complex compounds, and the superconducting critical temperature (Tc) has been continuously broken. However, practical high-temperature superconducting materials are still very limited. Finding materials that achieve superconductivity at higher temperatures (Tc > 70 K) remains the core research direction in this field.

[0003] Currently, the discovery of high-temperature superconducting materials mainly relies on traditional experimental trial-and-error methods and quantum computing methods based on density functional theory (DFT), which have obvious drawbacks: traditional experimental trial-and-error methods require a large amount of material preparation and performance testing work, which is cumbersome, time-consuming, and extremely costly; although quantum computing methods based on DFT can theoretically predict material properties, they have high computational complexity and are time-consuming, making it difficult to achieve large-scale material screening and failing to meet the needs of efficient research and development.

[0004] In recent years, machine learning technology, as the fastest-growing branch of artificial intelligence, has demonstrated enormous potential in the field of materials science, providing a new path for the prediction of high-temperature superconducting materials and thus pioneering the new research direction of materials informatics. Existing machine learning prediction methods largely rely on the chemical composition of materials as input features, neglecting the essential physical roots that determine superconductivity. They also generally suffer from problems such as a lack of uniformity in training datasets, insufficient data leading to model overfitting, and poor interpretability of prediction results, failing to effectively guide the practical research and development of high-temperature superconducting materials. Furthermore, existing methods have not adequately compared the prediction performance of different machine learning algorithms, nor have they optimized for the problem of uneven sample distribution, resulting in limited prediction accuracy and generalization ability for high-temperature superconducting materials. Therefore, there is an urgent need for a method that can overcome these limitations and achieve accurate, efficient, and interpretable prediction of high-temperature superconducting materials. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide an interpretable prediction method, system and computer-readable storage medium for high-temperature superconducting materials based on machine learning.

[0006] The objective of this invention is achieved through the following technical solution: A first aspect of the present invention provides an interpretable prediction method for high-temperature superconducting materials based on machine learning, comprising: Step S1: Construct a superconducting material dataset based on the SuperCon database, generate material features using Magpie software, remove redundancy using Pearson correlation coefficient, retain material features of a preset number of dimensions, and record the superconducting critical temperature Tc value. Step S2: Construct a random forest model for training, and output the importance ranking of material features through feature_importance, thereby extracting three material features as key features that determine the superconducting critical temperature: ground state atom volume average deviation, unfilled s orbital electron average deviation, and element electronegativity average deviation. Step S3: Use the key features to perform weighted optimization on the trained random forest model to form an interpretable prediction model, so that the prediction results are consistent with the superconducting physical mechanism; Step S4: Use an interpretable prediction model to predict candidate materials, and complete stability verification and screening by calculating Ehull values.

[0007] Further, step S1 specifically includes: Collect sample data from the SuperCon database, with a total sample size of no less than 12,000 groups, including oxide superconductors, boride superconductors, iron-based superconductors, and copper-based superconductors; Descriptors were calculated using Magpie software. The descriptors include stoichiometric characteristics, elemental property statistics, and ionic compound characteristics. Samples with Tc=0K and no clear Tc record are removed, as well as duplicates and outliers. The truncated average method is used to correct values ​​with multiple different Tc records. Calculate the Pearson correlation coefficient between each descriptor, and remove or merge descriptors with an absolute correlation coefficient greater than 0.85 as material features, retaining material features of a preset number of dimensions; All material characteristic parameters were normalized, and the preprocessed dataset was divided into training and test sets in an 8:2 ratio.

[0008] Furthermore, the random forest model constructed in step S2 is a regression model and / or a classification model; The regression model uses the superconducting critical temperature Tc as the label value to predict the specific Tc value of the material. The classification model uses 10K and 77K as the dividing criteria to divide superconducting materials into three categories: low temperature (Tc<10K), medium temperature (10K≤Tc≤77K), and high temperature (Tc>77K).

[0009] Furthermore, the performance validation criteria for the random forest model are: regression prediction R² ≥ 0.93, RMSE ≤ 7.4, average F1 score for classification prediction ≥ 0.91, and average R² for 5-fold cross-validation ≥ 0.92.

[0010] Furthermore, the weighted optimization in step S3 includes: After weighting and enhancing the three key features identified in step S2, they are input together with the remaining features into the random forest model trained in step S2. The hyperparameters of the random forest model—number of decision trees (n_estimators), maximum depth (max_depth), and maximum number of features per tree (max_features)—were optimized using a grid search method to obtain the optimal parameter combination: max_depth = 2~10, max_features = 8~20, and n_estimators = 30~50. The model was then optimized using L2 regularization.

[0011] Further, step S4 includes: ABO3-type compounds were obtained from the Matminer database as candidate materials; Stable and synthesizable high-temperature superconducting materials with predicted Tc values ​​> 70 K and Ehull < 50 meV / atom were selected.

[0012] A second aspect of the present invention provides a machine learning-based interpretable prediction system for high-temperature superconducting materials, comprising: Data acquisition and processing device: used to acquire sample data and candidate material data from the SuperCon database and Matminer database, and to perform feature extraction, data preprocessing and feature screening through Magpie software and Python program; Model training and optimization device: used to run the scikit-learn Python library, build a random forest model, realize model training, grid search hyperparameter optimization and k-fold cross-validation, determine the final prediction model, and output feature importance ranking through feature_importance, extract the ground state atom volume average deviation, unfilled s orbital electron average deviation and element electronegativity average deviation as key features. Prediction and verification device: used to input candidate material characteristics, run the final prediction model to obtain prediction results, verify the stability of key candidate materials through Ehull value calculation, and output a list of high-temperature superconducting materials with practical R&D value.

[0013] Furthermore, the data acquisition and processing device uses the Pearson correlation coefficient to remove redundancy from the features, deleting or merging features with an absolute correlation coefficient greater than 0.85, and retaining 120-dimensional features.

[0014] Furthermore, the model training and optimization device uses a grid search method to optimize the hyperparameters of the random forest model. The optimal parameter range is: maximum depth max_depth = 2~10, maximum number of features per tree max_features = 8~20, and number of decision trees n_estimators = 30~50.

[0015] A third aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the method described in the first aspect.

[0016] The beneficial effects of this invention are: In an exemplary embodiment of the present invention, three key features affecting the superconducting critical temperature were successfully identified through feature importance analysis, breaking through the limitations of traditional black-box prediction in machine learning. Compared with the prior art, this embodiment makes the prediction results clearly interpretable, allowing researchers to adjust the material composition according to the importance ranking of features—reducing atomic volume deviation can reduce lattice mismatch, optimizing the s-orbital electron filling state can enhance superconducting pairing strength, and controlling electronegativity can optimize charge transfer paths.

[0017] After testing, the model of this exemplary embodiment performed well on the test set R. 2 The R² value reached 0.935, with an RMSE of 7.4, compared to existing black-box models (mean R²). 2 (Approximately 0.85) represents an improvement of about 10%. Seven candidate materials with Tc > 70 K were efficiently screened from 4914 ABO3-type compounds. Further Ehull validation confirmed that three of these (CrBO3, Cr2O3, and FeBO3) are stable and synthesizable potential high-temperature superconducting materials. This complete closed-loop system of prediction-interpretation-optimization-validation ensures that the prediction results are consistent with the superconducting physical mechanism and can directly guide the directional design of material composition and structure. Attached Figure Description

[0018] Figure 1 An interpretable prediction method for high-temperature superconducting materials based on machine learning is provided as an exemplary embodiment of the present invention. Figure 2 A feature correlation analysis diagram, namely a Pearson correlation coefficient heatmap, is provided for an exemplary embodiment of the present invention. Figure 3 A graph showing the regression prediction results of a random forest model provided as an exemplary embodiment of the present invention; Figure 4 The graph shows the performance evaluation of the 5-fold cross-validation of the random forest model provided as an exemplary embodiment of the present invention. Detailed Implementation

[0019] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. Furthermore, the technical features involved in the different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0020] See Figure 1 , Figure 1 A flowchart illustrating an exemplary embodiment of the present invention provides a machine learning-based interpretable prediction method for high-temperature superconducting materials, comprising: Step S1: Construct a superconducting material dataset based on the SuperCon database, generate material features using Magpie software, remove redundancy using Pearson correlation coefficient, retain material features of a preset number of dimensions, and record the superconducting critical temperature Tc value. Step S2: Construct a random forest model for training, and output the importance ranking of material features through feature_importance, thereby extracting three material features as key features that determine the superconducting critical temperature: ground state atom volume average deviation, unfilled s orbital electron average deviation, and element electronegativity average deviation. Step S3: Use the key features to perform weighted optimization on the trained random forest model to form an interpretable prediction model, so that the prediction results are consistent with the superconducting physical mechanism; Step S4: Use an interpretable prediction model to predict candidate materials, and complete stability verification and screening by calculating Ehull values.

[0021] Specifically, in this exemplary embodiment, the inherent interpretability mechanism of the random forest algorithm is utilized. A random forest is composed of multiple decision trees, and each decision tree calculates the information gain or Gini impurity reduction of its features when splitting at a node. By weighted averaging the impurity reduction of each feature across all decision trees, the contribution ranking of each feature to the prediction result can be obtained. Unlike traditional black-box machine learning models, the feature_importance mechanism of random forests can reveal the internal logic of the model's decisions, making the prediction results traceable. Specifically, the feature importance calculation in random forests follows the following formula: In the formula, T represents the total number of decision trees. Let f be the set of nodes in the t-th tree that are split using feature f. This represents the reduction in impurity before and after node n splits (typically expressed as Gini impurity or mean square error). This calculation quantifies the contribution of each feature to the prediction of the superconducting critical temperature.

[0022] Furthermore, this exemplary embodiment analyzes the correlation between the importance ranking of features and the physical mechanism of superconductivity. Specifically, the average volume deviation of ground-state atoms reflects the degree of distortion in the crystal structure and directly affects the electron-phonon coupling strength; the average deviation of unfilled s-orbital electrons determines the electronic density of states near the Fermi level; and the average deviation of elemental electronegativity directly affects charge transfer and orbital hybridization. All three are core parameters influencing the superconducting transition temperature in BCS theory and strongly correlated electron systems.

[0023] Furthermore, Ehull (energy convex hull distance) is a key indicator for evaluating the thermodynamic stability of materials. When Ehull < 50 meV / atom, it indicates that the material is thermodynamically stable and synthetically viable. In this embodiment, Ehull verification is used as a stability confirmation step after screening to ensure that the final candidate materials have practical research and development value.

[0024] Specifically, the implementation steps of the entire method include: S1: First, download over 16,000 data points on superconducting materials from the SuperCon database, including chemical formulas, Tc values, crystal structures, and other information. Then, use Python to write a data processing script to convert the original JSON files to CSV format.

[0025] Secondly, Magpie software was used to calculate 132 initial feature descriptors for each sample. The core algorithm of Magpie is as follows: For the chemical formula A_xB_y of a compound, the average value of its elemental property statistics is: In the formula, Represents statistical measures of element properties.

[0026] The mean absolute deviation is: Using the above method, the average value, mean absolute deviation, range, minimum value, and maximum value of 22 elemental properties, including atomic number, atomic radius, electronegativity, and melting point, were calculated.

[0027] Subsequently, the Pearson correlation coefficient r between each feature was calculated. ij When |r ij When |>0.85, two features are determined to be highly redundant, one of which is deleted, and finally 120-dimensional features are retained.

[0028] S2: Several machine learning models were built and compared using the scikit-learn Python library, including multiple linear regression (LR), support vector regression (SVR), artificial neural network (ANN), decision tree (DT), random forest (RF), and gradient boosting decision tree (GBDT). A classification model branch was also constructed, dividing superconducting materials into three categories based on 10K and 77K: low-temperature (Tc < 10K), medium-temperature (10K ≤ Tc ≤ 77K), and high-temperature (Tc > 77K).

[0029] After training, the performance of each model was compared, and the Random Forest (RF) model was ultimately selected as the best performing model (training set R). 2 =0.988, RMSE=3.1). The importance of each feature was output using the feature_importance method of the Random Forest (RF) model. The results showed that the average bias score for ground-state atomic volume was 0.124, the average bias for unfilled s-orbital electrons was 0.108, and the average bias for elemental electronegativity was 0.096, ranking in the top three. This ranking result can be directly used to guide the composition and structure orientation design of high-temperature superconducting materials.

[0030] S3: After weighting and enhancing the three key features identified in step S2, these features, along with the remaining features, are input into the random forest model trained in step S2. The hyperparameters of the random forest model are optimized using GridSearchCV, with the parameter search space being: max_depth=[2,4,6,8,10], max_features=[8,11,14,17,20], n_estimators=[30,40,50]. Five-fold cross-validation is used, with negative mean squared error as the evaluation metric. The search results determine the optimal parameter combination as max_depth=6, max_features=14, n_estimators=40. L2 regularization (λ=0.1) is applied to optimize the model to suppress overfitting.

[0031] Model performance validation: Regression prediction R on the test set 2 =0.935, RMSE=7.4, average F1 score for classification prediction=0.935, average R-squared value for 5-fold cross-validation 2 =0.9216, with a standard deviation of only 0.0057. All indicators meet the preset standard (R²). 2 With scores of ≥0.93, RMSE≤7.4, and F1≥0.91, this model is confirmed as the final prediction model for high-temperature superconducting materials.

[0032] S4: Obtain 4914 ABO3-type compounds from the Matminer database as candidate materials, extract 120-dimensional features using the same method as the training data, and perform standardization.

[0033] The candidate material features are input into the final RF prediction model obtained in step S3, and the predicted Tc value and temperature range classification results are output. Based on the analysis of feature importance ranking, seven candidate materials with predicted Tc values ​​> 70K are selected: AuSrO3 (76.62K), CrBO3 (72.91K), AuBaO3 (71.89K), KPtO3 (71.56K), Cr2O3 (70.81K), FeBO3 (70.35K), and MnCrO3 (70.16K).

[0034] Ehull values ​​were calculated for the seven candidate materials mentioned above. For the selected key candidate materials, the thermodynamic stability of the materials was assessed by calculating their Ehull values ​​(energy on the convex hull). Three of these materials had Ehull values ​​of [value missing]. hull Materials with a strength of < 50 meV / atom are stable and synthesizable (CrBO3, Cr2O3, FeBO3), confirming their potential high-temperature superconductivity and completing the prediction process.

[0035] This exemplary embodiment successfully identified three key features affecting the superconducting critical temperature through feature importance analysis, breaking through the limitations of traditional black-box prediction in machine learning. Compared with existing technologies, this embodiment makes the prediction results clearly interpretable, allowing researchers to adjust the material composition according to the importance ranking of features—reducing atomic volume deviation can reduce lattice mismatch, optimizing the s-orbital electron filling state can enhance superconducting pairing strength, and controlling electronegativity can optimize charge transfer paths.

[0036] After testing, the model of this exemplary embodiment performed well on the test set R. 2 The R² value reached 0.935, with an RMSE of 7.4, compared to existing black-box models (mean R²). 2 (Approximately 0.85) represents an improvement of about 10%. Seven candidate materials with Tc > 70 K were efficiently screened from 4914 ABO3-type compounds. Further Ehull validation confirmed that three of these (CrBO3, Cr2O3, and FeBO3) are stable and synthesizable potential high-temperature superconducting materials. This complete closed-loop system of prediction-interpretation-optimization-validation ensures that the prediction results are consistent with the superconducting physical mechanism and can directly guide the directional design of material composition and structure.

[0037] More preferably, in an exemplary embodiment, step S1 specifically includes: Collect sample data from the SuperCon database, with a total sample size of no less than 12,000 groups, including oxide superconductors, boride superconductors, iron-based superconductors, and copper-based superconductors; Descriptors were calculated using Magpie software. The descriptors include stoichiometric characteristics, elemental property statistics, and ionic compound characteristics. Samples with Tc=0K and no clear Tc record are removed, as well as duplicates and outliers. The truncated average method is used to correct values ​​with multiple different Tc records. Calculate the Pearson correlation coefficient between each descriptor, and remove or merge descriptors with an absolute correlation coefficient greater than 0.85 as material features, retaining material features of a preset number of dimensions; All material characteristic parameters were normalized, and the preprocessed dataset was divided into training and test sets in an 8:2 ratio.

[0038] Specifically, in this exemplary embodiment, a specific implementation of step S1 is disclosed, which is as follows: S101: Collection of high-temperature superconducting material sample data: The sample data comes from the SuperCon database (created and maintained by the National Institute for Materials Science of Japan, and is the largest database of its kind), covering all reported superconductors and related non-superconducting compounds. The total number of sample data is no less than 12,000 sets, of which high-temperature superconducting materials account for no less than 10%. It covers various types such as oxide superconductors, boride superconductors, iron-based superconductors, and copper-based superconductors, and includes data related to potential candidate materials such as ABO3-type compounds. The original JSON files are processed into CSV files using Python programs for subsequent processing.

[0039] S102: Extracting core feature parameters: Using Magpie software, 132 descriptors were calculated for each sample, covering four major categories: stoichiometric features, elemental property statistics, electronic structure attributes, and ionic compound features. (i) Stoichiometric characteristics: Depends only on the proportion of elements, not on the specific types of elements; (ii) Statistical data on element properties: average value, mean absolute deviation, range, minimum value, maximum value and mode of 22 different element properties (including period / group in the periodic table, atomic number, atomic radius, melting point, electronegativity, etc.); (iii) Electronic structure properties: the average fraction of s, p, d and f valence shell electrons in all existing elements; (iv) Characteristics of ionic compounds: Assuming all elements exhibit a single oxidation state, determine whether it is possible to form ionic compounds.

[0040] S103: Data Preprocessing First, samples with Tc=0K, no clear Tc record, and duplicates were removed. Then, the truncated average method was used to correct values ​​with multiple different Tc records (after sorting the Tc values, the highest and lowest values ​​were removed, and the average of the remaining values ​​was taken). Outliers were removed through data visualization and literature tracing, and finally 12,439 valid data were retained (including 4,403 copper-based compounds, 1,557 iron-based compounds, and 6,479 other compounds).

[0041] Secondly, calculate the Pearson correlation coefficient between each descriptor, such as... Figure 2 The Pearson correlation coefficient heatmap shown visually illustrates the correlation between features. Darker colors indicate higher correlation coefficients, providing a basis for subsequent feature reduction and merging. This graph allows for the rapid identification of redundant features. Features with an absolute correlation coefficient greater than 0.85 were reduced and merged, ultimately retaining 120 features to avoid feature redundancy that could lead to model overfitting.

[0042] Next, all feature parameters are normalized to map the feature values ​​to a uniform range, eliminating the influence of units and ensuring the stability of model training. Optionally, to address the issue of uneven sample distribution, the number of superconducting material samples in different temperature zones (low temperature, medium temperature, and high temperature) can be kept consistent by randomly splitting the samples, thereby improving the accuracy of model classification and prediction.

[0043] Finally, the 12,439 valid data points were divided into a training set (9,951 data points) and a test set (2,488 data points) in an 8:2 ratio. At the same time, a 5-fold cross-validation method was used to divide the samples into 5 equal parts for subsequent model performance evaluation.

[0044] More preferably, in an exemplary embodiment, the random forest model constructed in step S2 is a regression model and / or a classification model; The regression model uses the superconducting critical temperature Tc as the label value to predict the specific Tc value of the material. The classification model uses 10K and 77K as the dividing criteria to divide superconducting materials into three categories: low temperature (Tc<10K), medium temperature (10K≤Tc≤77K), and high temperature (Tc>77K).

[0045] Specifically, in this exemplary embodiment, a dual-branch prediction architecture is constructed: a regression model directly predicts continuous values ​​of Tc, while a classification model predicts the temperature zone category of the material. The two models complement each other—the regression model provides accurate Tc estimates, while the classification model provides temperature zone classification judgments; cross-validation between the two improves prediction reliability. Furthermore, the use of 10K and 77K as classification thresholds in the classification model has clear physical meaning, corresponding to different cooling costs and application scenarios, respectively.

[0046] In practical applications, the regression model is constructed as follows: using 120-dimensional features as input X and Tc values ​​as output y, a random forest (RF) model is built. All model parameters are initialized to the default values ​​from scikit-learn. The classification model is constructed by discretizing the Tc values ​​into three labels: 0 represents low temperature (Tc < 10K), 1 represents moderate temperature (10K ≤ Tc ≤ 77K), and 2 represents high temperature (Tc > 77K), and then constructing the random forest (RF) model.

[0047] More preferably, in an exemplary embodiment, the performance validation criteria for the random forest model are: regression prediction R² ≥ 0.93, RMSE ≤ 7.4, average F1 score for classification prediction ≥ 0.91, and average R² for 5-fold cross-validation ≥ 0.92.

[0048] Specifically, in this exemplary embodiment, the Random Forest (RF) model is optimized. This model can learn complex nonlinear dependencies from large amounts of data without assuming a functional form between the predictor and target variables. It has good tolerance for heterogeneity in training data, can handle both numerical and categorical data, requires minimal targeted preprocessing, and can estimate the importance of each predictor, thus improving model interpretability. Prediction output settings: The regression model outputs the predicted Tc value of the material, and the classification model outputs the temperature range classification result of the material; the feature_importance command provided by scikit-learn is used to extract the features that contribute the most to the prediction of superconducting temperature, generate the feature importance ranking, and identify the core factors affecting superconductivity, that is, automatically extract the three key features that contribute the most to the superconducting critical temperature: including the average deviation of ground state atomic volume, the average deviation of unfilled s orbital electrons, and the average deviation of element electronegativity.

[0049] It should be noted that in practical applications, the feature_importance command extracts the most significant features from both regression and classification models: the average deviation of ground-state atom volume, the average deviation of unfilled s orbital electrons, and the average deviation of element electronegativity.

[0050] More preferably, in an exemplary embodiment, the weighted optimization in step S3 includes: After weighting and enhancing the three key features identified in step S2, they are input together with the remaining features into the random forest model trained in step S2. The hyperparameters of the random forest model—number of decision trees (n_estimators), maximum depth (max_depth), and maximum number of features per tree (max_features)—were optimized using a grid search method to obtain the optimal parameter combination: max_depth = 2~10, max_features = 8~20, and n_estimators = 30~50. The model was then optimized using L2 regularization.

[0051] Specifically, in this exemplary embodiment, key feature weights are first assigned. Based on the feature importance score output by feature_importance in step S2, the three key features are weighted differently: the ground-state atom volume average deviation importance score is 0.124, and a weight of 1.24 (α1) is assigned; the unfilled s orbital electron average deviation importance score is 0.108, and a weight of 1.08 (α2); the element electronegativity average deviation importance score is 0.096, and a weight of 0.96 (α3); the remaining non-key features are uniformly assigned a basic weight of 1.0. During model training, the feature values ​​of key features are amplified according to their weights, strengthening the dominant role of core physical features in the prediction results. Then, the weighted feature input is used to input the 120-dimensional features (X′=[α1x1,α2x2,α3x3,x4,x5,…,x120]) into the original trained random forest model, replacing the original feature input. This allows the model to prioritize learning key features that are strongly related to the physical mechanism of superconductivity during training and prediction, thereby improving the interpretability of the model from the feature level.

[0052] It should be noted that the average deviation of element electronegativity is assigned a weight of <1, which means that although this feature itself is important, it is compressed and weighted to a certain extent to avoid it dominating the model (this feature has large numerical fluctuations, a lot of noise, and is prone to overfitting).

[0053] Random forest models contain multiple hyperparameters, the values ​​of which directly affect model performance. In this exemplary embodiment, a grid search method is used for system optimization: by traversing preset hyperparameter combinations, cross-validation is used to evaluate the performance of each parameter group, and the optimal combination is selected. This method is more systematic and efficient than manual hyperparameter tuning. Furthermore, L2 regularization adds a penalty term of the sum of squared weights to the loss function. L2 regularization can constrain excessively large weights, preventing the model from over-relying on certain features, thereby mitigating overfitting. Specifically: First, all initial model parameters use the system default values. The initial hyperparameters for the RF model include n_estimators (number of decision trees), max_depth (maximum depth of decision trees), and max_features (number of features used per decision tree). The learning rate is set to 0.001-0.01 (preferably 0.005), the number of iterations is 100-500 (preferably 300), and the batch size (number of samples per training iteration) is 32-128 (preferably 64). The root mean square error (RMSE) and linear fit coefficient (R²) are used. 2 For regression models, precision, recall, and F1 score are used as evaluation metrics, while for classification models, precision, recall, and F1 score are used as evaluation metrics.

[0054] The model was trained using the training set partitioned in step S1. Its performance was evaluated using cross-validation samples every 10 iterations. The results showed that the RF model performed optimally, with a training set R² = 0.988 and RMSE = 3.1 (see attached image). Figure 3 ).

[0055] Then, the hyperparameters n_estimators, max_depth, and max_features of the RF model were optimized and adjusted using the grid search method (GridSearchCV) to obtain the optimal parameter combination (the preferred range is max_depth=2~10, max_features=8~20, n_estimators=30~50); the L2 regularization method was used to optimize the model to avoid overfitting and improve the model's generalization ability.

[0056] The optimized RF model was validated using the test set partitioned in step S1. The results showed that the regression prediction R² = 0.935 (e.g., Figure 4 The RMSE was 7.4; the R² values ​​for 5-fold cross-validation were 0.929, 0.914, 0.927, 0.918, and 0.920, respectively, with a mean precision of 0.921 (see attached). Figure 3 The average F1 score for classification prediction was 0.91, which met the preset criteria, and the RF model was determined as the final prediction model.

[0057] It's important to note that the principle behind weighted augmentation lies in amplifying the numerical range of key features in the feature space. This makes the random forest model more inclined to select features strongly correlated with the physical mechanisms of superconductivity when splitting nodes. This guides the model to prioritize learning the physical mapping relationships between atomic volume bias, electron occupancy states, electronegativity bias, and the superconducting critical temperature, improving the model's interpretability at the feature level rather than the post-processing level. Furthermore, weighted features have higher information gain potential during the decision tree node splitting process in the random forest, causing the model to prioritize the three key features as splitting nodes when constructing the tree structure.

[0058] More preferably, in an exemplary embodiment, step S4 includes: ABO3-type compounds were obtained from the Matminer database as candidate materials; Stable and synthesizable high-temperature superconducting materials with predicted Tc values ​​> 70 K and Ehull < 50 meV / atom were selected.

[0059] Specifically, in this exemplary embodiment, the specific implementation of step S4 regarding the screening of ABO3-type compounds and Ehull verification is described: First, chemical formulas and crystal structure information of 4914 ABO3 compounds were obtained from the Matminer database, including A-site elements (alkali metals, alkaline earth metals, rare earth elements, etc.) and B-site elements (transition metals, main group metals, etc.). Candidate material feature extraction: Following the same method as the training data, 132 initial features were calculated using Magpie, and 120-dimensional features were retained after Pearson filtering. Z-score standardization was then performed to ensure that the feature distribution of the candidate materials remained consistent with the training set.

[0060] The model then predicts: the features of 4914 candidate materials are input into the optimized RF model to obtain the Tc prediction value and temperature range classification results for each compound.

[0061] Screening of key candidate materials: Based on the ranking of feature importance, analysis revealed that the average volume deviation of ground-state atoms, electron occupancy, and electronegativity are the core factors affecting superconductivity. Meanwhile, the prediction results identified seven candidate materials with Tc > 70 K: AuSrO3 (76.62 K), CrBO3 (72.91 K), AuBaO3 (71.89 K), KPtO3 (71.56 K), Cr2O3 (70.81 K), FeBO3 (70.35 K), and MnCrO3 (70.16 K).

[0062] Ehull Calculation: For the seven key candidate materials selected above, the Ehull calculation for each material was performed. hull Values ​​are used to assess the thermodynamic stability of materials, including three types with E values. hullMaterials with a strength of < 50 meV / atom are stable and synthesizable (CrBO3, Cr2O3, FeBO3), confirming their potential high-temperature superconductivity and completing the prediction process.

[0063] In summary, the above exemplary embodiments have the following advantages: (1) Strong interpretability: The core influence features are extracted by using the feature_importance command of the RF model, which clarifies the key influences of ground state atomic volume, electron occupancy, and element electronegativity on superconducting temperature. This breaks the limitation of the "black box" prediction of traditional machine learning models. Moreover, the extracted core features are consistent with the conclusions of existing superconducting mechanism research, providing a clear theoretical basis for the structural optimization and performance improvement of high-temperature superconducting materials. (2) High prediction efficiency: The high-temperature superconducting materials can be predicted quickly through machine learning models. The prediction time for a single sample is shortened to the second level. Compared with the traditional experimental trial and error method and DFT quantum computing method, the efficiency is improved by more than 100 times. It can realize high-throughput screening of large-scale candidate materials, greatly shorten the research and development cycle, and is especially suitable for rapid screening of large-scale material libraries such as the Matminer database. (3) High prediction accuracy: This invention constructs a unified and rich dataset based on the SuperCon database, and removes redundant features through Pearson correlation coefficient. The optimized RF model has high R in regression prediction. 2 The accuracy is as high as 0.93 or above, the RMSE is as low as 7.4 or below, the average F1 score for classification prediction is ≥0.91, and the low prediction accuracy caused by the small number of high-temperature superconducting samples is solved by sample equalization. The prediction accuracy is better than that of existing similar methods. (4) Low cost and strong practicality: This invention does not require a large amount of experimental preparation and complex quantum calculation. Screening can be completed by feature extraction and model prediction alone, which greatly reduces the research and development cost of high temperature superconducting materials. At the same time, the dataset covers a variety of superconducting materials, the model has strong generalization ability, and can be applied to the prediction of different types of high temperature superconducting materials such as copper-based, iron-based, oxide, and borides. It can also accurately screen specific types of compounds such as ABO3, and has a wide range of practical application value. (5) High model reliability: The optimal RF model is selected by comparing multiple machine learning models. Combined with grid search hyperparameter optimization and 5-fold cross-validation, the model overfitting is effectively avoided, ensuring the stability and reliability of the model. At the same time, the unified SuperCon database is used as the data source, which solves the problems of insufficient data volume and poor uniformity of the existing dataset, further improving the credibility of the model prediction.

[0064] Having the same inventive concept as the exemplary embodiments described above, another exemplary embodiment of the present invention provides a machine learning-based interpretable prediction system for high-temperature superconducting materials, comprising: Data acquisition and processing device: used to acquire sample data and candidate material data from the SuperCon database and Matminer database, and to perform feature extraction, data preprocessing and feature screening through Magpie software and Python program; Model training and optimization device: used to run the scikit-learn Python library, build a random forest model, realize model training, grid search hyperparameter optimization and k-fold cross-validation, determine the final prediction model, and output feature importance ranking through feature_importance, extract the ground state atom volume average deviation, unfilled s orbital electron average deviation and element electronegativity average deviation as key features. Prediction and verification device: used to input candidate material characteristics, run the final prediction model to obtain prediction results, verify the stability of key candidate materials through Ehull value calculation, and output a list of high-temperature superconducting materials with practical R&D value.

[0065] Correspondingly, the data acquisition and processing device uses the Pearson correlation coefficient to remove redundancy from the features, and deletes or merges features with an absolute correlation coefficient greater than 0.85, retaining 120-dimensional features.

[0066] Correspondingly, the model training and optimization device uses a grid search method to optimize the hyperparameters of the random forest model. The optimal parameter range is: maximum depth max_depth = 2~10, maximum number of features per tree max_features = 8~20, and number of decision trees n_estimators = 30~50.

[0067] Having the same inventive concept as the exemplary embodiments described above, another exemplary embodiment of the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method described in the first aspect.

[0068] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A machine learning based interpretable prediction method for high temperature superconducting materials, characterized in that, include: Step S1: Construct a superconducting material dataset based on the SuperCon database, generate material features using Magpie software, remove redundancy using Pearson correlation coefficient, retain material features of a preset number of dimensions, and record the superconducting critical temperature Tc value. Step S2: Construct a random forest model for training, and output the importance ranking of material features through feature_importance, thereby extracting three material features as key features that determine the superconducting critical temperature: ground state atom volume average deviation, unfilled s orbital electron average deviation, and element electronegativity average deviation. Step S3: Use the key features to perform weighted optimization on the trained random forest model to form an interpretable prediction model, so that the prediction results are consistent with the superconducting physical mechanism; Step S4: Use an interpretable prediction model to predict candidate materials, and complete stability verification and screening by calculating Ehull values.

2. The method of claim 1, wherein: Step S1 specifically includes: Collect sample data from the SuperCon database, with a total sample size of no less than 12,000 groups, including oxide superconductors, boride superconductors, iron-based superconductors, and copper-based superconductors; Descriptors were calculated using Magpie software. The descriptors include stoichiometric characteristics, elemental property statistics, and ionic compound characteristics. Samples with Tc=0K and no clear Tc record are removed, as well as duplicates and outliers. The truncated average method is used to correct values ​​with multiple different Tc records. Calculate the Pearson correlation coefficient between each descriptor, and remove or merge descriptors with an absolute correlation coefficient greater than 0.85 as material features, retaining material features of a preset number of dimensions; All material characteristic parameters were normalized, and the preprocessed dataset was divided into training and test sets in an 8:2 ratio.

3. The method according to claim 1, characterized in that: The random forest model constructed in step S2 is a regression model and / or a classification model; The regression model uses the superconducting critical temperature Tc as the label value to predict the specific Tc value of the material. The classification model uses 10K and 77K as the dividing criteria to divide superconducting materials into three categories: low temperature (Tc<10K), medium temperature (10K≤Tc≤77K), and high temperature (Tc>77K).

4. The method according to claim 1, characterized in that: The performance validation criteria for the random forest model are: regression prediction R² ≥ 0.93, RMSE ≤ 7.4, average F1 score for classification prediction ≥ 0.91, and average R² for 5-fold cross-validation ≥ 0.

92.

5. The method according to claim 1, characterized in that: The weighted optimization in step S3 includes: After weighting and enhancing the three key features identified in step S2, they are input together with the remaining features into the random forest model trained in step S2. The hyperparameters of the random forest model—number of decision trees (n_estimators), maximum depth (max_depth), and maximum number of features per tree (max_features)—were optimized using a grid search method to obtain the optimal parameter combination: max_depth = 2~10, max_features = 8~20, and n_estimators = 30~50. The model was then optimized using L2 regularization.

6. The method according to claim 1, characterized in that: Step S4 includes: ABO3-type compounds were obtained from the Matminer database as candidate materials; Stable and synthesizable high-temperature superconducting materials with predicted Tc values ​​> 70 K and Ehull < 50 meV / atom were selected.

7. A machine learning-based interpretable prediction system for high-temperature superconducting materials, characterized in that, include: Data acquisition and processing device: used to acquire sample data and candidate material data from the SuperCon database and Matminer database, and to perform feature extraction, data preprocessing and feature screening through Magpie software and Python program; Model training and optimization device: used to run the scikit-learn Python library, build a random forest model, realize model training, grid search hyperparameter optimization and k-fold cross-validation, determine the final prediction model, and output feature importance ranking through feature_importance, extract the ground state atom volume average deviation, unfilled s orbital electron average deviation and element electronegativity average deviation as key features. Prediction and verification device: used to input candidate material characteristics, run the final prediction model to obtain prediction results, verify the stability of key candidate materials through Ehull value calculation, and output a list of high-temperature superconducting materials with practical R&D value.

8. The system according to claim 7, characterized in that: The data acquisition and processing device uses the Pearson correlation coefficient to remove redundancy from the features, and deletes or merges features with an absolute correlation coefficient greater than 0.85, retaining 120-dimensional features.

9. The system according to claim 7, characterized in that: The model training and optimization device uses a grid search method to optimize the hyperparameters of the random forest model. The optimal parameter range is: maximum depth max_depth = 2~10, maximum number of features per tree max_features = 8~20, and number of decision trees n_estimators = 30~50.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1 to 6.

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