Amorphous alloy magnetic heat performance prediction method and system based on interpretable machine learning

Abstract

The application provides an amorphous alloy magnetocaloric performance prediction method and system based on interpretable machine learning, relates to the technical field of material science and engineering, and comprises the following steps: step 1, constructing an amorphous alloy magnetocaloric performance data set, wherein the data set comprises alloy composition data, physical and chemical descriptors, external conditions and structural characteristics of a plurality of amorphous alloy samples and corresponding experimental values of maximum magnetic entropy change and Curie temperature; step 2, screening and optimizing the features in the data set, eliminating the collinearity between the features and performing recursive feature elimination to determine the final feature subsets for predicting the maximum magnetic entropy change and the Curie temperature respectively; and step 3, establishing machine learning models for predicting the maximum magnetic entropy change and the Curie temperature respectively through the final feature subsets, and training and optimizing the models to obtain the trained prediction models. The application realizes a closed loop of high-precision performance prediction, physical mechanism analysis and directional composition design.

Description

Technical Field

[0001] This invention relates to the fields of materials science and engineering technology, and in particular to a method and system for predicting the magnetocaloric properties of amorphous alloys based on interpretable machine learning. Background Technology

[0002] Magnetothermic technology has become an important alternative to traditional refrigeration technology due to its green and environmentally friendly nature. Amorphous alloys have become core candidate materials due to their unique microstructure and excellent magnetocaloric properties. However, the optimization of the magnetocaloric performance of traditional amorphous alloys relies on trial and error based on experience and limited theoretical calculations. This results in problems such as long development cycles, high costs, and difficulty in accurately controlling the complex correlation of multiple factors. Although machine learning has been applied to the prediction of the magnetocaloric performance of amorphous alloys in recent years to improve R&D efficiency, most of these models are black box models.

[0003] For example, a research team attempted to predict the key magnetocaloric properties of rare earth-based amorphous alloys using machine learning. Although they achieved some predictive results, the model could not analyze the intrinsic interaction between composition, physicochemical characteristics and magnetocaloric properties, and could not determine the influence weights and final control range of each factor. As a result, composition optimization could only rely on random adjustments, making it difficult to achieve targeted and synergistic improvement of key magnetocaloric properties. Summary of the Invention

[0004] The technical problem to be solved by this invention is to provide a method and system for predicting the magnetocaloric properties of amorphous alloys based on interpretable machine learning, so as to realize a closed loop of high-precision performance prediction, physical mechanism analysis and directional composition design.

[0005] To solve the above-mentioned technical problems, the technical solution of the present invention is as follows: In a first aspect, a method for predicting the magnetocaloric properties of amorphous alloys based on interpretable machine learning is provided, the method comprising: Step 1: Construct a dataset of magnetocaloric properties of amorphous alloys. The dataset includes alloy composition data, physicochemical descriptors, external conditions and structural characteristics of multiple amorphous alloy samples, as well as the experimental values ​​of the corresponding maximum magnetic entropy change and Curie temperature. Step 2: Filter and optimize the features in the dataset. By eliminating collinearity between features and performing recursive feature elimination, the final feature subsets used to predict the maximum magnetic entropy change and Curie temperature are determined respectively. Step 3: Using the final feature subset, establish machine learning models for predicting the maximum magnetic entropy change and Curie temperature, and train and optimize them to obtain the trained prediction models. Step 4: The interpretability of the trained prediction model is analyzed using the SHAP analysis method to identify the key features and mechanisms that affect the maximum magnetic entropy change and Curie temperature. Step 5: Based on key features and mechanisms of action, design amorphous alloy compositions that meet the preset requirements for maximum magnetic entropy change and Curie temperature. Then, use a prediction model to predict and screen the performance of the designed compositions to obtain the target amorphous alloy compositions.

[0006] Furthermore, a magnetocaloric performance dataset for amorphous alloys was constructed. This dataset includes alloy composition data, physicochemical descriptors, external conditions and structural characteristics of multiple amorphous alloy samples, as well as experimental values ​​for the corresponding maximum magnetic entropy change and Curie temperature. Raw experimental data of amorphous alloys were collected and integrated from multiple published papers to construct an initial dataset covering a variety of alloy systems, including transition metal-based amorphous alloys, rare earth-based amorphous alloys, and gadolinium-based amorphous alloy systems. The amorphous alloy feature data is classified into three categories: alloy composition features, physicochemical descriptors, and external conditions and structural features. The alloy composition features are defined as the atomic percentage of each constituent element and normalized to 100%. Unused elements are set to zero to obtain the classified feature data. Based on the classified feature data and raw experimental data, the maximum magnetic entropy change and Curie temperature experimental values ​​corresponding to each amorphous alloy sample were extracted and associated. The maximum magnetic entropy change was measured under different magnetic field variation conditions, and the Curie temperature was determined by the inflection point of the magnetization and temperature curves to obtain the associated feature and performance data pairs. Based on the associated feature and performance data pairs, the dataset is standardized and outlier detection is performed to eliminate data noise and inconsistencies, ensuring data quality and reliability, and ultimately forming a standardized amorphous alloy magnetocaloric performance dataset.

[0007] Furthermore, the features in the dataset are filtered and optimized. By eliminating collinearity among features and performing recursive feature elimination, the final feature subsets used to predict the maximum magnetic entropy change and Curie temperature are determined, including: Based on the standardized dataset, calculate the Spearman correlation coefficient between all pairs of features to identify patterns of high correlation between features. By using a highly correlated pattern, for each feature pair whose correlation coefficient exceeds a preset threshold, the feature with the larger absolute value of correlation with the target performance is retained, and the other feature is removed, thereby eliminating collinearity interference between features and obtaining a non-redundant feature set optimized for collinearity. Based on a non-redundant feature set, a recursive feature elimination method is used to evaluate feature importance for the maximum magnetic entropy change prediction task and the Curie temperature prediction task, respectively, so as to obtain the recursive feature elimination iterative results. Based on the results of the recursive feature elimination iteration, the final feature subsets for predicting the maximum magnetic entropy change and the final feature subsets for predicting the Curie temperature are determined respectively.

[0008] Furthermore, using the final feature subset, machine learning models for predicting the maximum magnetic entropy change and Curie temperature are established, trained, and optimized to obtain the trained prediction models, including: Based on the final feature subsets used to predict the maximum magnetic entropy change and the final feature subsets used to predict the Curie temperature, multiple ensemble machine learning algorithms were selected as candidate models, including random forest, gradient boosting regression and extreme gradient boosting algorithm. Based on the selected candidate models, a leave-one-out cross-validation strategy is used to train each candidate model. In each iteration, all samples except one sample are used as the training set, and the remaining samples are used as the validation set. The generalization performance of each candidate model under different feature combinations is evaluated through iterative training to obtain the training results. Based on the training results, the prediction accuracy of each candidate model is quantitatively evaluated by calculating the coefficient of determination and root mean square error, and the final model architecture with the best prediction performance is selected based on the evaluation results. Based on the final prediction model architecture, the selected gradient boosting regression model and extreme gradient boosting model are fully trained and optimized by using all training samples in the standardized dataset and the corresponding final feature subsets, ultimately generating a high-precision maximum magnetic entropy change prediction model and Curie temperature prediction model.

[0009] Furthermore, based on the training results, the prediction accuracy of each candidate model is quantitatively evaluated by calculating the coefficient of determination and root mean square error. Based on the evaluation results, the final model architecture with the best prediction performance is selected, including: Based on the training results of each candidate model in leave-one-out cross-validation, the determination coefficient and root mean square error of each candidate model for the maximum magnetic entropy change prediction task and the Curie temperature prediction task are calculated respectively, forming a set of quantitative prediction performance evaluation indicators. Based on the set of prediction performance evaluation metrics, for the maximum magnetic entropy change prediction task, the prediction accuracy of random forest model, gradient boosting regression model and extreme gradient boosting model are compared, and the gradient boosting regression model with the largest coefficient of determination and the smallest root mean square error is selected as the final prediction architecture. Based on the set of prediction performance evaluation metrics, for the Curie temperature prediction task, the prediction accuracy of the random forest model, the gradient boosting regression model, and the extreme gradient boosting model are compared. The extreme gradient boosting model with the largest coefficient of determination and the smallest root mean square error is selected as the final prediction architecture.

[0010] Furthermore, the interpretability of the trained prediction model was analyzed using the SHAP analysis method to identify key features and mechanisms affecting the maximum magnetic entropy change and Curie temperature, including: Based on the trained maximum magnetic entropy change prediction model and Curie temperature prediction model, the SHAP value of each input feature on the prediction result is calculated. The SHAP value quantifies the marginal contribution of each feature to the model prediction in all possible feature combinations through cooperative game theory. Based on the SHAP value, a SHAP summary map is obtained. All features are ranked globally according to the average absolute SHAP value. At the same time, the positive and negative correlation between each feature and the target performance is identified through color coding and point distribution, and the set of key features affecting the maximum magnetic entropy change and Curie temperature is determined. Based on the set of key features, a SHAP dependency graph is generated for each key feature to show the non-linear relationship between a single feature value and the SHAP value. A local weighted regression trend line and a statistical confidence interval are then overlaid on the dependency graph to obtain the SHAP dependency graph analysis results. Based on the SHAP dependency graph analysis results and combined with materials science knowledge, the mechanism of key features on the maximum magnetic entropy change and Curie temperature is decoded, including the final range of influence of the features, nonlinear influence modes, and synergistic or antagonistic effects among multiple features, forming a physical mechanism understanding that can guide the design of amorphous alloy composition.

[0011] Furthermore, based on key characteristics and mechanisms of action, amorphous alloy compositions that meet preset requirements for maximum magnetic entropy change and Curie temperature are designed. The performance of the designed compositions is then predicted and screened using a predictive model to obtain target amorphous alloy compositions, including: Based on the decoding mechanism, the core target parameters and key element selection principles for amorphous alloy composition design are determined. The core target parameters include the preset maximum magnetic entropy change threshold and Curie temperature range. The key element selection principles cover the ratio and functional positioning of core elements, auxiliary elements and control elements. Based on the key element selection principle and combined with the final range of influence of the identified physicochemical characteristics, a set of candidate amorphous alloy compositions that meet the element ratio constraints is obtained. The final range of influence of the physicochemical characteristics includes the range of electronegativity difference, the range of ionization energy, and the range of atomic binding energy. By using the trained maximum magnetic entropy change prediction model and Curie temperature prediction model, the performance of each component in the candidate amorphous alloy composition set is predicted, and the predicted maximum magnetic entropy change value and Curie temperature value corresponding to each candidate component are obtained to obtain the predicted performance results. Based on the set core target parameters, the predicted performance results are screened and evaluated, and candidate components that meet the preset maximum magnetic entropy change threshold and Curie temperature range requirements are retained to form a list of candidate target amorphous alloy components. Based on the multi-feature collaboration of decoding, the candidate target amorphous alloy composition list is optimized and sorted in a second time. Taking into account the process feasibility, element cost and performance stability of the composition, the final target amorphous alloy composition and the corresponding predicted performance parameters are obtained.

[0012] Secondly, an amorphous alloy magnetocaloric performance prediction system based on interpretable machine learning includes: The acquisition module is used to construct a dataset of magnetocaloric properties of amorphous alloys. The dataset includes alloy composition data, physicochemical descriptors, external conditions and structural characteristics of multiple amorphous alloy samples, as well as the experimental values ​​of the corresponding maximum magnetic entropy change and Curie temperature. The prediction module is used to filter and optimize the features in the dataset. By eliminating collinearity between features and performing recursive feature elimination, it determines the final feature subsets used to predict the maximum magnetic entropy change and Curie temperature, respectively. The training module is used to build machine learning models for predicting the maximum magnetic entropy change and Curie temperature using the final feature subset, and to train and optimize them to obtain the trained prediction models. The identification module is used to perform interpretability analysis on the trained prediction model using the SHAP analysis method, and to identify the key features and mechanisms that affect the maximum magnetic entropy change and Curie temperature. The processing module is used to design amorphous alloy compositions that meet the preset maximum magnetic entropy change and Curie temperature requirements based on key features and mechanisms of action, and to predict and screen the performance of the designed compositions through a prediction model to obtain the target amorphous alloy composition.

[0013] Thirdly, a computing device, comprising: One or more processors; A storage device for storing one or more programs that, when executed by one or more processors, cause the one or more processors to implement the method.

[0014] Fourthly, a computer-readable storage medium storing a program that, when executed by a processor, implements the method.

[0015] The above-described solution of the present invention has at least the following beneficial effects: By employing a closed-loop technical approach encompassing multidimensional dataset construction, feature selection and optimization, integrated machine learning modeling, SHAP interpretability analysis, and mechanism-guided composition design—specifically including integrating multi-system amorphous alloy data to form a standardized dataset, optimizing feature subsets through collinearity elimination and recursive feature elimination, improving model accuracy by combining gradient boosting regression and extreme gradient boosting algorithms with leave-one-out cross-validation, and utilizing SHAP analysis to decode the mechanisms of key features and guide composition design and selection—this approach overcomes the technical challenges of low R&D efficiency in traditional trial-and-error methods, difficulty in deciphering the nonlinear correlation between amorphous alloy composition and magnetocaloric properties, the inherent trade-off between maximum magnetic entropy change and Curie temperature, and the inability of machine learning models to reveal physical mechanisms due to their black-box nature. This approach achieves high-precision prediction of the maximum magnetic entropy change and Curie temperature of amorphous alloys, realizes the synergistic optimization of these two key magnetocaloric properties, narrows the composition search space, shortens the R&D cycle of room-temperature magnetocaloric materials, and provides a new paradigm combining data-driven and mechanism-supported approaches for the directional design of high-performance amorphous alloys. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating the method for predicting the magnetocaloric properties of amorphous alloys based on interpretable machine learning, as provided in an embodiment of the present invention.

[0017] Figure 2 This is a schematic diagram of an amorphous alloy magnetocaloric performance prediction system based on interpretable machine learning, provided in an embodiment of the present invention.

[0018] Figure 3 It is the distribution of (a) elements and (b) alloy system in the dataset, and (c) Δ S M -T c Scatter plot distribution, and (d)Δ S M The histogram distribution and (e) T c The histogram distribution.

[0019] Figure 4 It is RF, GBR and XGBoost Model R 2 and RMSE Compare (a)∆ S M Prediction, (b) T c Prediction chart.

[0020] Figure 5 It is the input characteristic alloy composition excluding the magnetic and thermal properties Δ S M and T cBetween Spearman (Top right subplot of correlation coefficient heatmap, bottom left subplot of feature selection process).

[0021] Figure 6 yes RFE The model during the process R 2 A graph showing the relationship between the value and the number of features.

[0022] Figure 7 Are (a) and (c) Δ S M and T c The scatter plot compares the experimental and predicted values. The dashed diagonal line in the plot represents the perfect prediction (y=x), and the shaded area represents the 95% confidence interval. (b) and (d) represent Δ... S M and T c Histogram of predicted residual errors.

[0023] Figure 8 It is (a)Δ S M SHAP overview diagram, (b) T c SHAP overview diagram.

[0024] Figure 9 Is it the influence of Δ S M SHAP dependency graph of the first 6 features.

[0025] Figure 10 It is an influence T c SHAP dependency graph of the first 6 features. Detailed Implementation

[0026] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0027] like Figure 1 As shown, embodiments of the present invention propose a method for predicting the magnetocaloric properties of amorphous alloys based on interpretable machine learning. The method includes the following steps: Step 1: Construct a dataset of magnetocaloric properties of amorphous alloys. The dataset includes alloy composition data, physicochemical descriptors, external conditions and structural characteristics of multiple amorphous alloy samples, as well as the experimental values ​​of the corresponding maximum magnetic entropy change and Curie temperature. Step 2: Filter and optimize the features in the dataset. By eliminating collinearity between features and performing recursive feature elimination, the final feature subsets used to predict the maximum magnetic entropy change and Curie temperature are determined respectively. Step 3: Using the final feature subset, establish machine learning models for predicting the maximum magnetic entropy change and Curie temperature, and train and optimize them to obtain the trained prediction models. Step 4: The interpretability of the trained prediction model is analyzed using the SHAP analysis method to identify the key features and mechanisms that affect the maximum magnetic entropy change and Curie temperature. Step 5: Based on key features and mechanisms of action, design amorphous alloy compositions that meet the preset requirements for maximum magnetic entropy change and Curie temperature. Then, use a prediction model to predict and screen the performance of the designed compositions to obtain the target amorphous alloy compositions.

[0028] In this embodiment of the invention, by constructing a multidimensional amorphous alloy magnetocaloric performance dataset covering multiple alloy systems, optimizing feature subsets through collinearity elimination and recursive feature elimination, establishing an integrated machine learning model and training and optimizing it through leave-one-out cross-validation, and utilizing SHAP analysis to decode key features and mechanisms of action, a closed-loop technique for designing and screening target alloy compositions based on mechanisms is adopted. Therefore, this approach overcomes the technical problems of traditional trial-and-error methods, which are time-consuming and labor-intensive, unable to decipher the nonlinear relationship between amorphous alloy composition and magnetocaloric performance, and the inherent trade-off between maximum magnetic entropy change and Curie temperature. Furthermore, existing machine learning models suffer from black-box characteristics, making it difficult to reveal physical mechanisms and guide directional composition design. This approach achieves high-precision prediction of maximum magnetic entropy change and Curie temperature, realizes the synergistic optimization of the two key magnetocaloric properties, narrows the alloy composition search space, and significantly shortens the development cycle of room-temperature magnetocaloric materials. It provides a new paradigm combining data-driven and mechanism-supported approaches for the directional design of high-performance amorphous alloys.

[0029] In a preferred embodiment of the present invention, step 1 above may include: Step 1.1 involves collecting and integrating raw experimental data of amorphous alloys from multiple published literature sources to construct an initial dataset covering various alloy systems. The amorphous alloy samples include transition metal-based amorphous alloys, rare earth-based amorphous alloys, and gadolinium-based amorphous alloys. Specifically, this includes: extensively searching global publications on the magnetocaloric properties of amorphous alloys, including academic papers and research reports, and prioritizing the selection of valid literature containing alloy composition and magnetocaloric performance test data; extracting experimental data from each literature source to ensure comprehensive coverage of the three core alloy systems: transition metal-based amorphous alloys represented by iron, cobalt, and nickel; rare earth-based amorphous alloys represented by erbium, terbium, and dysprosium; and gadolinium-based amorphous alloys. During data extraction, detailed records are kept of the constituent elements, element content, test conditions, and corresponding magnetocaloric performance parameters for each alloy to avoid missing crucial information; and all extracted data are organized and summarized in a unified format to construct the initial dataset, ensuring that the dataset covers amorphous alloy samples with diverse element types and performance characteristics.

[0030] Step 1.2 involves classifying the amorphous alloy feature data into three categories: alloy composition features, physicochemical descriptors, and external condition and structural features. The alloy composition feature is defined as the atomic percentage of each constituent element, standardized to 100%, with unused elements set to zero. This process yields the classified feature data. Specifically, the amorphous alloy feature data in the initial dataset is systematically classified into three categories: The first category is alloy composition features, covering multiple elements such as boron, carbon, aluminum, silicon, phosphorus, titanium, vanadium, chromium, manganese, iron, cobalt, and nickel. The content of each element is expressed as an atomic percentage. The sum of the atomic percentages of all constituent elements is calculated, standardized, and adjusted to 100%. If an element is not used in a particular alloy sample, its atomic percentage is set to zero. The second category is physicochemical descriptors... Based on the inherent properties of each constituent element, parameters are derived through statistical analysis or physical models, including valence electron concentration, melting point, melting point difference, Pauling electronegativity, Pauling electronegativity difference, Mullicken electronegativity, Mullicken electronegativity difference, Christian electronegativity, Christian electronegativity difference, molar volume, atomic radius, atomic size difference, configuration entropy, entropy stability size sensitivity factor, atomic volume, valence electron density, first ionization energy, second ionization energy, electron affinity, atomic mass, electrical conductivity, heat of fusion, and atomic magnetic moment. The third category is external conditions and structural characteristics, where the applied magnetic field changes are recorded as the magnetic field strength values ​​during actual testing. The alloy structural characteristics are classified into three types according to the actual situation: amorphous, amorphous plus nanocrystalline, and crystalline. All characteristics are classified and quantified to obtain standardized and unified classification characteristic data.

[0031] Step 1.3: Based on the categorized feature data and original experimental data, extract and associate the experimental values ​​of the maximum magnetic entropy change and Curie temperature for each amorphous alloy sample. The maximum magnetic entropy change is measured under different magnetic field variations, and the Curie temperature is determined by the inflection point of the magnetization and temperature curves to obtain associated feature and performance data pairs. Specifically, this includes: based on the obtained categorized feature data and combined with the test records in the original experimental data, extracting the two core magnetocaloric performance parameters for each amorphous alloy sample; for the maximum magnetic entropy change, extracting the values ​​measured under different magnetic field variations to ensure performance is covered under different magnetic field environments; for the Curie temperature, locating the inflection point in the magnetization and temperature curve test data from the original experiment, and the temperature corresponding to this inflection point is the Curie temperature of the sample; during the extraction process, strictly verify the feature data and performance data of each sample to ensure a one-to-one correspondence and avoid data misalignment or confusion, ultimately forming a unique and complete pair of feature and performance data for each amorphous alloy sample.

[0032] Step 1.4: Based on the associated feature and performance data pairs, the dataset is standardized and outlier detected to eliminate data noise and inconsistencies, ensuring data quality and reliability, ultimately forming a standardized amorphous alloy magnetocaloric performance dataset. Specifically, this includes: performing data standardization and outlier detection on the obtained associated feature and performance data pairs; data standardization using a unified scaling method to transform all feature and performance data, eliminating dimensional differences between different parameters and ensuring all data are on the same order of magnitude, facilitating unified calculation and analysis in subsequent models; outlier detection using statistical analysis methods to identify anomalous data points deviating from the normal data range by observing the overall data distribution, such as by analyzing data dispersion and drawing data distribution histograms, filtering out values ​​that significantly exceed most data distribution ranges; verifying each detected anomalous data point individually, confirming that the anomaly is due to experimental measurement errors, data recording errors, etc., and then removing or correcting them to effectively eliminate data noise and inconsistencies; after standardization and outlier correction, integrating all valid data to form a standardized amorphous alloy magnetocaloric performance dataset with reliable data quality, standardized parameters, and accurate correlations.

[0033] In this embodiment of the invention, by employing technical means such as integrating multiple literature data to construct an initial dataset covering various alloy systems, classifying features into alloy composition features, physicochemical descriptors and external conditions and structural features, associating the maximum magnetic entropy change and Curie temperature experimental values ​​corresponding to the samples, and optimizing data quality through standardization processing and outlier detection, the technical problems of limited coverage, chaotic feature classification without unified standards, high data noise and insufficient reliability of traditional amorphous alloy datasets are overcome. Thus, the technical effect of forming a standardized amorphous alloy magnetocaloric performance dataset that is comprehensive, features are standardized and unified, data association is clear, and quality is reliable is achieved.

[0034] In a preferred embodiment of the present invention, step 2 above may include: Step 2.1: Based on the standardized dataset, calculate the Spearman correlation coefficients between all pairs of features to identify highly correlated patterns among features. Specifically, this includes: using the constructed standardized amorphous alloy magnetocaloric property dataset as a basis, focusing on all classified and standardized features in the dataset; calculating the Spearman correlation coefficients between each pair of different features to quantify the strength and direction of the linear correlation between features; fully considering the diversity of features during the calculation process, covering all categories such as alloy composition features, physicochemical descriptors, and external conditions and structural features to ensure that no pair of features is overlooked in the correlation analysis; organizing the correlation coefficient results between all pairs of features to form a complete correlation matrix, and identifying feature combinations with large absolute values ​​of correlation coefficients and highly correlated patterns among features by analyzing the numerical distribution in the matrix.

[0035] Step 2.2: Using a high correlation model, for each feature pair with a correlation coefficient exceeding a preset threshold, retain the feature with the larger absolute value of correlation with the target performance and remove the other feature to eliminate collinearity interference between features, resulting in a non-redundant feature set optimized for collinearity. Specifically, this includes: referencing the feature correlation analysis results, setting the correlation coefficient threshold to 0.9, and identifying feature pairs with a correlation coefficient greater than or equal to 0.9 as feature combinations with severe collinearity; for each identified collinear feature pair, calculating the correlation coefficient between each feature in the pair and the maximum magnetic entropy change and Curie temperature of the two target performance parameters, and comparing the absolute values; retaining the feature with the larger absolute value of correlation with the target performance, as this feature can more effectively reflect the influence law on magnetocaloric performance and contains more valuable information; removing the other feature with a relatively weak correlation with the target performance from the dataset to avoid information redundancy and collinearity interference with the retained feature; performing the above retention and removal operations on all collinear feature pairs one by one to complete the collinearity optimization processing of all features, ultimately obtaining a non-redundant feature set without severe collinearity and with low information redundancy.

[0036] Step 2.3: Based on the non-redundant feature set, a recursive feature elimination method is used to evaluate feature importance for both the maximum magnetic entropy change prediction task and the Curie temperature prediction task, to obtain the recursive feature elimination iterative results. Specifically, this includes: designing independent recursive feature elimination processes for the maximum magnetic entropy change prediction task and the Curie temperature prediction task based on the obtained non-redundant feature set; for the maximum magnetic entropy change prediction task, a gradient boosting regression algorithm is selected as the basic estimator; for the Curie temperature prediction task, an extreme gradient boosting algorithm is selected as the basic estimator. Both algorithms are suitable for the nonlinear relationship between the corresponding magnetocaloric properties and features; firstly, the corresponding basic estimator model is trained using all features in the non-redundant feature set, and then the gradient boosting algorithm is used to evaluate feature importance. The feature gain metric for ascending regression or the feature weight metric for extreme gradient boosting are used to rank all features by importance, determining the contribution of each feature to the model's prediction results. Then, the feature with the lowest importance ranking is removed, and the base estimator model is retrained using the remaining features. A leave-one-out cross-validation strategy is used to evaluate the predictive performance of the new model. This process of ranking feature importance, removing the least important feature, retraining the model, and evaluating performance is repeated, removing only one feature per iteration to ensure the precision of the selection process, until the model performance shows significant fluctuations or the preset iteration limit is reached. The changes in the feature set and the corresponding model performance data during each iteration are recorded to form a complete recursive feature elimination iteration result.

[0037] Step 2.4: Based on the results of the recursive feature elimination iteration, determine the final feature subsets for predicting the maximum magnetic entropy change and the final feature subsets for predicting the Curie temperature, respectively. Specifically, analyze the obtained recursive feature elimination iteration results, focusing on the trend of model performance as the number of features decreases. For the maximum magnetic entropy change prediction task, observe the change in the coefficient of determination of the gradient boosting regression model. When the number of features is gradually reduced from 59 in the non-redundant feature set to 16, the model's coefficient of determination remains at a high level and tends to stabilize. If the number of features is further reduced to 15, the coefficient of determination drops sharply, indicating that 16 features represent the final balance between model accuracy and feature dimensionality. For the Curie temperature prediction task, track the change in the coefficient of determination of the extreme gradient boosting model. When the number of features is reduced to 17, the model can still maintain high prediction accuracy. Further reduction of features leads to a significant decline in accuracy; therefore, 17 features are determined as the final number. Based on the above analysis results, a corresponding number of features were extracted to form the final feature subsets. The final feature subset for maximum magnetic entropy change prediction includes 16 features such as aluminum, iron, dysprosium, erbium, and melting point, while the final feature subset for Curie temperature prediction includes 17 features such as aluminum, silicon, manganese, iron, and cobalt. The two subsets are adapted to their respective prediction task requirements.

[0038] In this embodiment of the invention, by employing the technical means of first identifying highly correlated patterns by calculating the Spearman correlation coefficient between pairs of features, retaining features more strongly correlated with the target performance to eliminate collinearity interference, and then using a recursive feature elimination method to evaluate feature importance and determine the final feature subset for the two prediction tasks of maximum magnetic entropy change and Curie temperature, the technical problems of high model complexity and easy overfitting caused by collinear features in the original feature set, and the impact of feature dimensional redundancy on training efficiency, as well as the lack of targeted feature selection for different magnetocaloric performance prediction tasks, which affects prediction accuracy, are overcome. Thus, the technical effect of obtaining a non-redundant final feature subset adapted to different prediction tasks is achieved, which simplifies the model structure, improves training efficiency, and effectively retains key information.

[0039] In a preferred embodiment of the present invention, step 3 above may include: Step 3.1: Based on the final feature subsets used to predict the maximum magnetic entropy change and the final feature subsets used to predict the Curie temperature, several ensemble machine learning algorithms are selected as candidate models. These ensemble machine learning algorithms include random forest, gradient boosting regression, and extreme gradient boosting. Specifically, based on the determined final feature subsets, three representative ensemble machine learning algorithms are carefully selected as candidate models for the two different prediction tasks: maximum magnetic entropy change and Curie temperature. These three algorithms are random forest, gradient boosting regression, and extreme gradient boosting. The core reason for selecting these three algorithms is that they are all adept at handling nonlinear data relationships and accurately capturing the relationship between the amorphous alloy composition and its magnetocaloric properties. Complex nonlinear relationships effectively compensate for the limitations of traditional linear models. Among them, random forest, by constructing multiple decision trees and integrating voting results, has strong anti-overfitting ability and stability, and can be used as a basic comparison model. Gradient boosting regression adopts a sequential residual correction strategy to gradually optimize prediction errors, which is suitable for capturing the smooth trend of maximum magnetic entropy change with composition. Extreme gradient boosting adds a regularization term to the gradient boosting, which can better handle the Curie temperature mutation problem caused by small changes in rare earth element content and improve the model's adaptability to complex fluctuating data. The three algorithms complement each other, comprehensively covering the performance change patterns of different types, and providing sufficient basis for subsequent selection of the final model.

[0040] Step 3.2: Based on the selected candidate models, a leave-one-out cross-validation strategy is used to train each candidate model. In each iteration, all samples except one are used as the training set, and the remaining samples are used as the validation set. The generalization performance of each candidate model under different feature combinations is evaluated through iterative training to obtain the training results. Specifically, this includes: For the three selected candidate models, a leave-one-out cross-validation strategy is used for system training to maximize the use of information from every sample in the dataset and improve the model's generalization performance. Firstly, the dataset contains 490 valid amorphous alloy samples, therefore the leave-one-out cross-validation needs to be iterated 490 times. During each iteration, the remaining 48 samples (excluding the single sample) are used as the validation set. Nine samples are used as the training set, and the remaining single sample is used as an independent validation set. This ensures that each sample can be evaluated independently as a validation set, avoiding bias in generalization performance evaluation caused by improper sample partitioning. During each training iteration, the final feature subset of the corresponding prediction task is used as the model input, and the consistency of training parameters is strictly controlled, such as the number of decision trees and the initial learning rate, to ensure that the training conditions are comparable for different models and different iteration numbers. After training, the prediction error of the model is calculated using the validation set, and the performance index of each iteration is recorded. Finally, the average performance index of 490 iterations is used to comprehensively evaluate the generalization ability of each candidate model under different feature combinations, forming a complete training result dataset.

[0041] Step 3.3: Based on the training results, the prediction accuracy of each candidate model is quantitatively evaluated by calculating the coefficient of determination and root mean square error (RMSE). The final model architecture with the best prediction performance is selected based on the evaluation results. Specifically, this includes: Based on the training results obtained using leave-one-out cross-validation, the prediction accuracy of the three candidate models is quantitatively evaluated by calculating the coefficient of determination and RMSE, two core indicators. The coefficient of determination measures the goodness of fit between the model's predicted and experimental values, ranging from 0 to 1; a value closer to 1 indicates a better fit. The RMSE measures the average deviation between the predicted and experimental values; a smaller value indicates higher prediction accuracy. For the maximum magnetic entropy change prediction task, the coefficient of determination and RMSE of the random forest, gradient boosting regression, and extreme gradient boosting models are calculated respectively, and compared. The gradient boosting regression model achieved a determination coefficient of 92.21% and a root mean square error (RMSE) of 1.168, which is superior to the random forest model (88.7% determination coefficient, RMSE 1.408) and the extreme gradient boosting model (89.2% determination coefficient, RMSE 1.373). Therefore, the gradient boosting regression model was selected as the final architecture for maximum magnetic entropy change prediction. For the Curie temperature prediction task, the metrics of the three models were also calculated. The extreme gradient boosting model performed best, achieving a determination coefficient of 91.60% and a RMSE of 42.212, which is superior to the gradient boosting regression model (90.2% determination coefficient, RMSE 45.464) and the random forest model (90.4% determination coefficient, RMSE 45.005). Therefore, the extreme gradient boosting model was selected as the final architecture for Curie temperature prediction.

[0042] Step 3.4: Based on the final prediction model architecture, the selected gradient boosting regression model and extreme gradient boosting model are fully trained and optimized using all training samples in the standardized dataset and the corresponding final feature subset. This ultimately generates a high-precision maximum magnetic entropy change prediction model and a Curie temperature prediction model. Specifically, this includes: initiating the complete parameter training and optimization process based on the determined final prediction model architecture; firstly, calling all 490 samples in the standardized amorphous alloy magnetocaloric performance dataset and the corresponding final feature subset determined in Step 2, where 16 features are used for maximum magnetic entropy change prediction and 17 features are used for Curie temperature prediction, ensuring the completeness and relevance of the model training data; for the selected gradient boosting regression model, the core parameters, including the learning rate and decision tree depth, are gradually adjusted for the maximum magnetic entropy change prediction task. The model's performance was observed through multiple iterations of training, including adjusting parameters such as the degree of change and the number of leaf nodes per tree. Parameter adjustments were stopped when the coefficient of determination stabilized above 92.21% and the root mean square error (RMSE) dropped below 1.168, ensuring the model reached final convergence. For the selected extreme gradient boosting model, the focus was on optimizing regularization parameters, subsample ratios, and column sampling ratios to address the abrupt changes in Curie temperature. Repeated adjustments were made to stabilize the coefficient of determination above 91.60% and the RMSE below 42.212. During training, the model's training and validation errors were monitored in real time to prevent overfitting or underfitting, ensuring stable high-precision prediction performance on both the training set and unknown data. Finally, two high-precision models were generated to adapt to both maximum magnetic entropy change and Curie temperature prediction.

[0043] In this embodiment of the invention, by employing three ensemble machine learning algorithms—random forest, gradient boosting regression, and extreme gradient boosting—as candidate models, and by fully evaluating the generalization performance of each model through leave-one-out cross-validation, quantitatively selecting the final model architecture using the coefficient of determination and root mean square error, and completing model parameter training and optimization based on all samples of the standardized dataset and the corresponding final feature subset, the technical problems of single algorithms being unable to adapt to the nonlinear variation law of different magnetocaloric properties of amorphous alloys, the weak generalization ability of traditional training methods, and insufficient prediction accuracy are overcome. This achieves the technical effect of generating high-precision prediction models that adapt to the smooth change of maximum magnetic entropy and the abrupt change characteristics of Curie temperature, ensuring the accuracy and reliability of the prediction of these two key magnetocaloric properties.

[0044] In a preferred embodiment of the present invention, step 3.1 above may include: Step 3.31: Based on the training results of each candidate model in leave-one-out cross-validation, calculate the coefficient of determination and root mean square error (RMSE) of each candidate model for the maximum magnetic entropy change prediction task and the Curie temperature prediction task, forming a quantitative set of prediction performance evaluation indicators. Specifically, this includes: collecting all training results of the three candidate models—random forest, gradient boosting regression, and extreme gradient boosting—in leave-one-out cross-validation, including the maximum magnetic entropy change prediction value and Curie temperature prediction value for each model for 490 amorphous alloy samples, as well as the corresponding experimental measurements; calculating the coefficient of determination and RMSE of each candidate model for the maximum magnetic entropy change prediction task, whereby the coefficient of determination measures the degree of fit between the predicted and experimental values, and the RMSE reflects the average deviation between the predicted and experimental values; using the same calculation logic, calculating the coefficient of determination and RMSE of the three candidate models for the Curie temperature prediction task; and systematically organizing all calculation results according to the correspondence between model type, prediction task, coefficient of determination, and RMSE to form a complete set of quantitative prediction performance evaluation indicators.

[0045] Step 3.32: Based on the set of prediction performance evaluation metrics, for the maximum magnetic entropy change prediction task, compare the prediction accuracy of the random forest model, gradient boosting regression model, and extreme gradient boosting model, and select the gradient boosting regression model with the largest coefficient of determination and the smallest root mean square error as the final prediction architecture. Specifically, this includes: extracting all data corresponding to the maximum magnetic entropy change prediction task from the quantitative prediction performance evaluation metric set, and focusing on comparing the coefficients of determination and root mean square errors of the three models; among them, the random forest model has a coefficient of determination of 88.7% and a root mean square error of 1.408; the gradient boosting regression ... The coefficient of determination (COP) of the gradient boosting regression model was 92.21%, and the root mean square error (RMSE) was 1.168. The COP of the extreme gradient boosting model was 89.2%, and the RMSE was 1.373. Comparing the models one by one according to the selection criteria of the largest COP and the smallest RMSE, the gradient boosting regression model showed a significantly higher COP and a significantly lower RMSE, indicating a higher fit and smaller bias in predicting the maximum magnetic entropy change. Furthermore, considering the smooth change in maximum magnetic entropy change with the amorphous alloy composition, the sequential residual correction capability of the gradient boosting regression model better suited this change pattern. Therefore, the gradient boosting regression model was selected as the final architecture for predicting the maximum magnetic entropy change.

[0046] Step 3.33: Based on the set of prediction performance evaluation metrics, for the Curie temperature prediction task, compare the prediction accuracy of the random forest model, gradient boosting regression model, and extreme gradient boosting model, and select the extreme gradient boosting model with the largest coefficient of determination and the smallest root mean square error as the final prediction architecture. Specifically, this includes: extracting relevant data for the Curie temperature prediction task from the quantitative prediction performance evaluation metric set, and conducting a detailed comparison of the performance metrics of the three candidate models; the coefficient of determination of the random forest model is 90.4%, and the root mean square error is 45.005; the coefficient of determination of the gradient boosting regression model is 90.2%, and the root mean square error is 45.464; the coefficient of determination of the extreme gradient boosting model is 91.60%, and the root mean square error is 42.212. Based on the core selection principle of maximizing the coefficient of determination and minimizing the root mean square error, the extreme gradient boosting model performs best in both metrics, with the highest degree of fit between its predictions and experimental values ​​and the smallest average deviation. Considering that the Curie temperature is easily affected by small changes in the content of rare earth elements and can cause abrupt changes, the regularization term of the extreme gradient boosting model can effectively handle this abrupt change characteristic and improve the stability of the prediction. Therefore, the extreme gradient boosting model is selected as the final architecture for Curie temperature prediction.

[0047] In this embodiment of the invention, because the coefficient of determination and root mean square error are calculated from the training results using leave-one-out cross-validation, a set of quantitative prediction performance evaluation indicators is formed. Then, for two different prediction tasks, namely maximum magnetic entropy change and Curie temperature, the accuracy of three models, namely random forest, gradient boosting regression, and extreme gradient boosting, is compared. The model with the largest coefficient of determination and the smallest root mean square error is selected as the final prediction architecture for the corresponding task. Therefore, this invention overcomes the technical problems of lacking a unified quantitative standard to evaluate model performance, the difficulty of a single model to adapt to the nonlinear variation law of different magnetocaloric properties, the smooth change of maximum magnetic entropy change and the abrupt change characteristics of Curie temperature, and the insufficient prediction accuracy caused by subjective and one-sided model selection. Thus, it achieves the technical effect of matching the final model architecture for the two types of magnetocaloric performance prediction tasks respectively, ensuring the accuracy and specificity of the prediction of maximum magnetic entropy change and Curie temperature.

[0048] In a preferred embodiment of the present invention, step 4 above may include: Step 4.1: Based on the trained maximum magnetic entropy change prediction model and Curie temperature prediction model, calculate the SHAP value of each input feature for the prediction result. The SHAP value quantifies the marginal contribution of each feature to the model prediction in all possible feature combinations using cooperative game theory. Specifically, this includes: calculating the SHAP value for the input features of the two models based on the trained maximum magnetic entropy change prediction model and Curie temperature prediction model; using a cooperative game theory-based calculation logic, considering the role of each feature in all possible feature combinations to quantify its marginal contribution to the model prediction result; for the gradient boosting regression model for maximum magnetic entropy change prediction, the input features include 16 final features such as aluminum, iron, dysprosium, and erbium; for the extreme gradient boosting model for Curie temperature prediction, the input features include 17 final features such as aluminum, silicon, manganese, and iron; during the calculation process, comprehensively cover the combination scenarios of each feature with all features to ensure that the contribution value calculation of each feature is not limited by the feature combination method, and finally assign a unique SHAP value to each input feature of each model. The numerical value intuitively reflects the degree and direction of the corresponding feature's influence on the prediction result.

[0049] Step 4.2: Based on the SHAP values, obtain the SHAP summary map. Sort all features globally by their average absolute SHAP value. Simultaneously, identify the positive and negative correlations between each feature and the target performance using color coding and point distribution to determine the set of key features affecting the maximum magnetic entropy change and Curie temperature. Specifically, this includes: generating corresponding SHAP summary maps based on the calculated SHAP values ​​of all features; first, sorting each feature in descending order by its average absolute SHAP value, where a higher average absolute SHAP value indicates stronger global importance of the feature to the prediction result; and then using color coding to distinguish feature values. The blue area represents lower eigenvalues, and the red area represents higher eigenvalues. The distribution of data points in the graph indicates the positive or negative correlation between the eigenvalue and the target performance. When data points are concentrated in areas with positive SHAP values, it indicates a positive correlation between the eigenvalue and the target performance, which will improve the target performance. When data points are concentrated in areas with negative SHAP values, it indicates a negative correlation, which will reduce the target performance. The key eigenvalue set affecting the maximum magnetic entropy change is selected, including iron, magnetic field changes, aluminum, first ionization energy, Christian electronegativity difference, and atomic binding energy. The key eigenvalue set affecting the Curie temperature is determined, including heat capacity, first ionization energy, aluminum, cobalt, iron, average atomic weight, and melting point differences.

[0050] Step 4.3: Based on the key feature set, generate a SHAP dependency graph for each key feature to display the non-linear relationship between a single feature value and the SHAP value. Overlay a locally weighted regression trend line and statistical confidence interval onto the dependency graph to obtain the SHAP dependency graph analysis results. Specifically, this includes: generating a separate SHAP dependency graph for each key feature based on the defined key feature set; the SHAP dependency graph uses the feature value as the horizontal axis and the corresponding SHAP value as the vertical axis to clearly display the non-linear relationship between changes in a single feature value and changes in the SHAP value; to more accurately capture this relationship trend, [further details are needed for the dependency graph analysis]. A smooth trend line generated by a locally weighted regression method is overlaid, which visually represents the average marginal effect of the feature on the prediction result. Simultaneously, a 95% confidence interval is added. The width of the interval reflects the reliability of the feature's marginal effect within that range; a narrower interval indicates a denser data distribution and a more reliable marginal effect, while a wider interval indicates sparser data and greater uncertainty in the marginal effect. Through systematic analysis of the dependency graph of each key feature, the nonlinear variation pattern between the feature and the SHAP value, the trend line's direction, and the distribution of confidence intervals are recorded, forming a complete SHAP dependency graph analysis result.

[0051] Step 4.4: Based on the SHAP dependency graph analysis results and combined with materials science knowledge, decode the mechanism of key features' influence on the maximum magnetic entropy change and Curie temperature. This includes identifying the final range of influence of the features, nonlinear influence modes, and synergistic or antagonistic effects among multiple features, forming a physical mechanism understanding that can guide the design of amorphous alloy compositions. Specifically, this includes: deeply interpreting the SHAP dependency graph analysis results using professional knowledge in materials science to decode the intrinsic mechanism of key features' influence on the maximum magnetic entropy change and Curie temperature; for the maximum magnetic entropy change, iron is negatively correlated with the magnetic entropy change because excessive iron increases the amorphous alloy... The magnetic inhomogeneity weakens the magnetic exchange interaction between magnetic moments; the magnetic field change is strongly positively correlated with the magnetic entropy change, which conforms to Maxwell's relation, and a larger magnetic field change can promote a more significant reorientation of magnetic moments; aluminum is generally positively correlated because it can optimize atomic packing density and enhance the cooperative magnetic behavior of adjacent magnetic atoms; at the same time, the final range of the effects of each key feature, such as the Christian electronegativity difference being most favorable to the improvement of magnetic entropy change when it is between 0.08 and 0.10, the first ionization energy being the strongest positive contribution to the magnetic entropy change when it is around 6.5 electron volts, and the atomic binding energy being no less than 400 kJ / mol can ensure the stability of the magnetic domain structure. For Curie temperature, cobalt and iron are positively correlated because of the strong ferromagnetic exchange interaction between their atoms, which can maintain the ferromagnetic state at higher temperatures; aluminum is negatively correlated, as excess aluminum dilutes the concentration of magnetic elements; heat capacity above 28 joules per kilogram of Kelvin promotes the increase of Curie temperature; in addition, in-depth analysis of the synergistic or antagonistic effects among multiple characteristics, such as iron being negatively correlated with the maximum magnetic entropy change but positively correlated with Curie temperature, and aluminum having opposite effects on the two properties, ultimately leads to a systematic understanding of the physical mechanism.

[0052] In this embodiment of the invention, by employing a cooperative game theory approach to calculate the SHAP value of each input feature, generating a summary map based on the SHAP value to complete the global importance ranking of features and the identification of positive and negative correlations, generating a SHAP dependency map for key features with superimposed local weighted regression trend lines and statistical confidence intervals, and decoding the mechanism of feature action by combining materials science knowledge, the technical problems caused by the black box nature of traditional machine learning models—such as the inability to influence key features that affect the maximum magnetic entropy change and Curie temperature of amorphous alloys, the difficulty in revealing the intrinsic mechanism of interaction between features and performance, and the inability to provide physical mechanism support for composition design—are overcome. This achieves the technical effect of accurately identifying key regulatory features, clearly analyzing the nonlinear regulatory law and core physical mechanism of features on magnetocaloric performance, and forming a physical mechanism understanding that can directly guide the directional design of amorphous alloy composition, thus building a bridge between data association and the principles of materials science.

[0053] In a preferred embodiment of the present invention, step 5 above may include: Step 5.1: Based on the decoding mechanism, determine the core target parameters and key element selection principles for amorphous alloy composition design. The core target parameters include the preset maximum magnetic entropy change threshold and Curie temperature range. The key element selection principles cover the proportions and functional positioning of core elements, auxiliary elements, and regulating elements. Specifically, this includes: determining the core target parameters and key element selection principles for amorphous alloy composition design based on the decoding key characteristic mechanism; focusing on room temperature cooling requirements, setting the maximum magnetic entropy change threshold to 7.5 J / (kg・K) to ensure sufficient cooling capacity; limiting the Curie temperature range to 280 to 320 K to ensure suitability for room temperature applications; and selecting key elements. The principle revolves around performance synergistic optimization, with gadolinium identified as the core element. Its unique electronic structure can balance the maximum magnetic entropy change and Curie temperature, overcoming the inherent trade-off between the two. Erbium and dysprosium are used as auxiliary elements, leveraging their high atomic magnetic moments to enhance the maximum magnetic entropy change, but their content needs to be controlled to prevent the Curie temperature from deviating from the target range. Iron and aluminum are used as regulating elements. Iron stabilizes the Curie temperature through strong ferromagnetic exchange interaction, while aluminum enhances the synergistic effect of magnetic moments by optimizing atomic packing density to improve the maximum magnetic entropy change. At the same time, iron and aluminum need to be added at low concentrations to prevent excessive amounts from causing performance degradation. In addition, the ratio of core elements, auxiliary elements, and regulating elements must meet the basic requirement that the total atomic percentage is 100% to ensure the rationality of the alloy composition.

[0054] Step 5.2: Based on the key element selection principles and the final effective range of the identified physicochemical characteristics, a set of candidate amorphous alloy compositions that meet the elemental ratio constraints is obtained. The final effective range of the physicochemical characteristics includes the electronegativity difference range, ionization energy range, and atomic binding energy range. Specifically, this includes: based on the determined key element selection principles and the final effective range of the identified physicochemical characteristics, formulating elemental ratio constraints and generating a set of candidate amorphous alloy compositions; the final range of the physicochemical characteristics is a Christian electronegativity difference between 0.08 and 0. Between 0.10 and 0.10, the first ionization energy is approximately 6.5 electron volts, and the atomic binding energy is not less than 400 kilojoules per mole. These ranges ensure suitable chemical affinity between elements, optimized magnetic moment alignment, and stable magnetic domain structure. Specific elemental ratio constraints include: the total atomic percentage of the core element gadolinium, auxiliary elements erbium and dysprosium, and controlling elements aluminum and iron must be 100%; the content of each element is adjusted in 2% increments to ensure precise control of component content; and at least two elements must have non-zero atomic percentages to ensure sufficient glass-forming ability of the alloy and avoid amorphous phase decomposition. Based on these constraints, the system combines the content ratios of each element, ultimately generating a set containing 31,624 candidate compositions.

[0055] Step 5.3 involves using the trained maximum magnetic entropy change prediction model and Curie temperature prediction model to predict the performance of each component in the candidate amorphous alloy composition set, obtaining the predicted maximum magnetic entropy change and Curie temperature values ​​for each candidate component to obtain the predicted performance results. Specifically, this includes: calling the trained high-precision prediction model to predict the magnetocaloric performance of each component in the candidate amorphous alloy composition set; wherein, the maximum magnetic entropy change prediction adopts a gradient boosting regression model, and the Curie temperature prediction adopts an extreme gradient boosting model, with prediction accuracies of 92.21% and 91.60% respectively, ensuring the reliability of the prediction results; for each candidate component, extracting 16 maximum magnetic entropy change prediction features and 17 Curie temperature prediction features, and inputting them into the corresponding models; the models calculate and output the predicted maximum magnetic entropy change and Curie temperature values ​​for each candidate component through the nonlinear correlation between the learned features and performance; and recording the element ratio, predicted maximum magnetic entropy change, and predicted Curie temperature values ​​for each candidate component to form a complete dataset of predicted performance results.

[0056] Step 5.4: Based on the set core target parameters, the predicted performance results are screened and evaluated, retaining candidate components that meet the preset maximum magnetic entropy change threshold and Curie temperature range requirements, forming a candidate target amorphous alloy composition list. Specifically, this includes: systematically screening and evaluating the obtained predicted performance results based on the set core target parameters; verifying the maximum magnetic entropy change prediction value and Curie temperature prediction value of each candidate component one by one, with the screening criteria being a maximum magnetic entropy change prediction value not less than 7.5 J / (kg・K) and a Curie temperature prediction value between 280 and 320 K; for candidate components that meet the above two conditions, retaining their complete information, including elemental ratios and the two performance prediction values; for candidate components that do not meet either of the conditions, directly removing them from the dataset to avoid invalid components occupying subsequent optimization resources; after screening, a candidate target amorphous alloy composition list containing 12 candidate components is formed, and all components in the list have initially met the core performance requirements for room temperature cooling.

[0057] Step 5.5: Based on the multi-feature synergy of decoding, the candidate target amorphous alloy composition list is further optimized and sorted. Taking into account the process feasibility, element cost, and performance stability of the composition, the final target amorphous alloy composition and corresponding predicted performance parameters are obtained. Specifically, this includes: Based on the multi-feature synergy effect of decoding, the candidate target amorphous alloy composition list is further optimized and sorted, comprehensively considering three key factors: process feasibility, element cost, and performance stability. Regarding process feasibility, the element ratios of each composition are evaluated to ensure they meet the requirements of the actual smelting process, eliminating compositions with excessively low element content that makes precise control difficult or excessively high content that significantly increases smelting difficulty. Regarding element cost, the total content of rare earth elements gadolinium, erbium, and dysprosium in each composition is compared, and rare earth elements are prioritized for use under the premise of comparable performance. Fewer components reduce material preparation costs. Regarding performance stability, a multi-feature synergistic mechanism is used to analyze whether the proportions of key elements in each component are within their final effective range, ensuring that the magnetocaloric properties of the alloy are not easily affected by environmental factors during long-term use. A comprehensive scoring standard is established based on these factors to rank candidate target components, ultimately selecting target amorphous alloy components with excellent performance, feasible processes, controllable costs, and strong stability. Among them, the Gadolinium 82Aluminum 2Iron 6Erbium 10 component exhibits the most outstanding performance with a maximum magnetic entropy change of 7.82 J / (kg・K) and a Curie temperature of 280.3 K. The maximum magnetic entropy changes of the remaining target components are maintained between 7.54 and 7.63 J / (kg・K), and the Curie temperatures are between 280.8 and 281.2 K, all meeting the practical application requirements for room temperature cooling.

[0058] In this embodiment of the invention, the core target parameters and key element selection principles for amorphous alloy composition design are determined based on the SHAP decoding mechanism. Combined with the physicochemical characteristics such as electronegativity differences, ionization energy, and atomic binding energy, a set of candidate compositions that satisfy element ratio constraints is generated. The performance of the candidate compositions is predicted using a trained maximum magnetic entropy change and Curie temperature prediction model. After screening according to preset targets, secondary optimization and ranking are performed considering process feasibility, element cost, and performance stability. Therefore, this approach overcomes the technical problems of traditional composition design, which is characterized by strong blindness, difficulty in overcoming the inherent trade-offs of maximum magnetic entropy change and Curie temperature, and neglect of key factors such as process adaptability and economy in practical applications. This achieves the technical effect of efficiently obtaining target amorphous alloy compositions that possess excellent magnetocaloric performance, meet preset threshold and room temperature adaptability requirements, are process-feasible, cost-controllable, and have stable performance. It realizes directional synergistic optimization of key magnetocaloric performance, shortens the material development cycle, and provides a practical composition scheme for the industrial application of room temperature magnetocaloric refrigeration materials.

[0059] like Figure 2 As shown, embodiments of the present invention also provide an amorphous alloy magnetocaloric performance prediction system based on interpretable machine learning, comprising: The acquisition module is used to construct a dataset of magnetocaloric properties of amorphous alloys. The dataset includes alloy composition data, physicochemical descriptors, external conditions and structural characteristics of multiple amorphous alloy samples, as well as the experimental values ​​of the corresponding maximum magnetic entropy change and Curie temperature. The prediction module is used to filter and optimize the features in the dataset. By eliminating collinearity between features and performing recursive feature elimination, it determines the final feature subsets used to predict the maximum magnetic entropy change and Curie temperature, respectively. The training module is used to build machine learning models for predicting the maximum magnetic entropy change and Curie temperature using the final feature subset, and to train and optimize them to obtain the trained prediction models. The identification module is used to perform interpretability analysis on the trained prediction model using the SHAP analysis method, and to identify the key features and mechanisms that affect the maximum magnetic entropy change and Curie temperature. The processing module is used to design amorphous alloy compositions that meet the preset maximum magnetic entropy change and Curie temperature requirements based on key features and mechanisms of action, and to predict and screen the performance of the designed compositions through a prediction model to obtain the target amorphous alloy composition.

[0060] Appendix Figure 3 This is a visualization chart showcasing the core features of the research dataset, comprehensively presenting the elemental composition, system classification, magnetocaloric property correlations, and distribution patterns of amorphous alloys. This lays the data foundation for subsequent machine learning modeling and performance analysis. The following is a detailed explanation of each of the five sub-charts: Figure 3 (a): Element distribution This subplot illustrates the distribution characteristics of the 38 elements covered in the dataset. The elements include transition metals such as Fe, Co, and Ni; rare earth elements such as Gd, Er, Tb, and Dy; and glass-forming elements such as B, Al, and Si. The elements cover key categories in the periodic table related to amorphous alloy formation and magnetocaloric properties. The distribution of each element corresponds to its atomic percentage range in the alloy, with unused elements accounting for 0%. This reflects the elemental diversity of the dataset, providing a foundation for subsequent analysis of the correlation between elemental composition and magnetocaloric properties, and also demonstrating that the model can adapt to prediction scenarios involving multiple elemental combinations.

[0061] Figure 3 (b): Alloy system distribution This subplot presents the classification and proportion of alloy systems in the dataset, mainly including three core systems: transition metal-based (TM-based), primarily Fe-based, Co-based, and Ni-based, which are the traditional systems for magnetocaloric alloys; rare earth-based (RE-based), primarily Er-based, Tb-based, Dy-based, and Ho-based, known for their high magnetic entropy changes; and Gd-based, which stands alone as an intermediate system, while also including the Highentropyserials series and a small number of other systems. Fe-based and Gd-based alloys account for the largest proportion in the dataset, reflecting the representativeness of these two systems in magnetocaloric material research. Clearly defining the system coverage of the dataset provides a classification basis for subsequent comparisons of the differences in magnetocaloric performance of different systems.

[0062] Figure 3 (c): Δ S M - T c Scatter plot distribution This subgraph is a core performance correlation diagram, showing the maximum magnetic entropy change Δ. S M With Curie temperature T c The collaborative distribution relationship exhibits tri-directional clustering characteristics; Transition metal-based clusters, such as Fe-based and Co-based, exhibit low performance characteristics (Δ). S M ≤3.3J / (kg・K), High T c 200-650K; Physical essence: Transition metals such as Fe have a stable magnetically ordered structure due to strong ferromagnetic exchange interactions between atoms. T c However, the low atomic magnetic moments and local structural disorder limit the decrease in magnetic entropy Δ. S M Rare earth-based clusters, such as Er-based, Tb-based, and Dy-based, exhibit high performance characteristics. S M 5-18J / (kg・K), low T c ≤110K; Physically, rare earth elements such as Dy and Er have high atomic magnetic moments (Dy ~ 10.6 μB, Er ~ 9.6 μB). Under a magnetic field, the magnetic moment reorientation produces a significant entropy change Δ. S M However, due to their large atomic radii, weak magnetic exchange interactions, and low magnetic order, they are easily disrupted by thermal disturbances. T c .

[0063] Gd-based clustering, performance characteristics, intermediate equilibrium state Δ S M =3-8J / (kg・K), Tc =250-320K; Its core advantage, bridging the performance gap between the first two types of systems, is that Gd's seven unpaired 4f electrons give it both a moderate atomic magnetic moment and strong magnetic exchange interaction. T c It is adapted to the room temperature cooling range of 280-320K, becoming the core research system of room temperature magnetocaloric materials.

[0064] Figure 3 (d): Δ S M histogram distribution This subgraph illustrates the maximum magnetic entropy change Δ S M The numerical distribution pattern and key statistical information are as follows. Sample size Num 487 valid samples; numerical range 0.011-18.3 J / (kg·K); statistical characteristics: mean Mean =4.33 J / (kg・K), standard deviation Stdev =4.18 J / (kg・K); The distribution characteristics are generally right-skewed, and the Δ of most samples is... S M The concentrations are concentrated in the range of 0-8 J / (kg·K), with a few rare earth-based samples reaching high values ​​of 10-18 J / (kg·K); reflecting Δ S M The range of regulation is extremely wide, proving that the magnetic entropy change can be significantly altered through component design, and also providing data span support for high-precision prediction by machine learning models.

[0065] Figure 3 (e): T c histogram distribution This subgraph shows the Curie temperature. T c The numerical distribution pattern is as follows, with a range of 26-650K covering the low to medium-high temperature range; the distribution characteristics exhibit a multi-peak distribution, corresponding to trigonal clustering. T c Concentrated rare earth-based low T c Peaks, high transition metal-based T c Peaks, mid-temperature peaks of Gd-based alloys; visually representing different alloy systems. T c The differences provide data reference for component screening within the target temperature range, such as room temperature 280-320K.

[0066] Appendix Figure 4 It consists of three ensemble machine learning algorithms: Random Forest (RF), Gradient Boosting Regression (GRIR), and Gradient Boosting Regression (GRIR). GBR Extreme gradient boosting XGBoost The performance comparison visualization in the prediction of magnetocaloric properties of amorphous alloys is mainly used to screen the optimal prediction model and determine the coefficients. R 2 and root mean square error RMSE The quantitative indicators are divided into two main forecasting tasks.

[0067] Figure 4 (a): Maximum magnetic entropy change Δ S M Predictive performance comparison This subgraph focuses on Δ S M The prediction accuracy of the core indicator of cooling capacity, key information is as follows: indicator meaning. R 2 The closer to 1, RMSE The smaller the value, the higher the model prediction accuracy. RMSE Units and Δ S M Consistent, J / (kg・K); Algorithm performance ranking, GBR algorithm R 2 =0.922, RMSE =1.167, the best performance; RF algorithm R 2 =0.892, RMSE =1.373; XGBoost algorithm R 2 =0.887, RMSE =1.408, GBR Its sequential residual correction characteristics are more suitable for capturing Δ S M The smooth nonlinear relationship between alloy composition and magnetic entropy change can accurately fit the gradual correlation between composition and magnetic entropy change.

[0068] Figure 4 (b): Curie temperature T c Predictive performance comparison This subgraph focuses T c The prediction accuracy of the core indicator for adapting to application temperature is as follows, along with key information: the meaning of the indicator and Δ. S M Consistent with predictions R 2 The closer to 1, RMSE smaller RMSE Units and T c Consistency, denoted by K, indicates better prediction performance; algorithm performance ranking, XGBoost algorithm, R 2 =0.910, RMSE =43.620, the best performance; RF algorithm, R 2 =0.904, RMSE =45.005; GBR algorithm, R 2 =0.902, RMSE =45.464; XGBoost The regularization term design can better handle the effects of minute variations in rare earth element content. T c The abrupt nonlinear relationship avoids overfitting and improves the stability of temperature prediction.

[0069] Appendix Figure 5 This is the core visualization chart for feature optimization. Its main function is to identify collinearity among features and filter key features that are strongly correlated with magnetocaloric properties. This lays the foundation for subsequent dimensionality reduction, accuracy improvement, and interpretability enhancement of machine learning models. It consists of two main sub-charts: Top right corner sub-image: Spearman Correlation coefficient heatmap This subgraph quantifies the relationship between input feature alloy composition and feature and target magnetocaloric properties Δ. S M and T c The nonlinear correlation; adopting Spearman The correlation coefficient is suitable for capturing nonlinear associations, with a numerical range of -1 to 1; the larger the absolute value, the stronger the correlation. It identifies collinear features; if the pairwise correlation coefficient of two features is ≥0.9, it is considered highly collinear, which increases model complexity and leads to overfitting. For each pair of collinear features, features with Δ are removed. S M or T c Features with lower absolute correlation coefficients retain variables with richer information; six redundant features are eliminated, including atomic volume, atomic radius, second ionization energy, valence electron density, Pauling electronegativity, and Mullicken electronegativity.

[0070] Bottom left sub-image: Feature selection process diagram This subgraph visually illustrates the logic of feature retention and removal, focusing on the priority of feature relevance to target performance; feature removal refers to Δ... S M or T cRedundant features with weak correlation and collinearity were identified; retained features refer to those with stronger correlation to the target performance and no significant collinearity, totaling 59, providing a basis for subsequent recursive feature elimination; the target performance Δ was clearly labeled. S M and T c This ensures that the screening process always revolves around improving the accuracy of magnetocaloric performance prediction.

[0071] Appendix Figure 6 Elimination of recursive features RFE During the process, the relationship curve of the model's coefficient of determination with the number of features is used to screen the optimal feature set for predicting the magnetocaloric properties of amorphous alloys. Horizontal axis Num The number of input features used in beroffeatures for model training ranges from 0 to 60, with the number of features decreasing from the highest to the lowest. RFE The process of gradually eliminating unimportant features; vertical axis R 2 Quantitative metrics for model prediction accuracy R 2 The closer the value is to 1, the higher the agreement between the predicted and experimental values, and the better the accuracy. The two curves correspond to the prediction models of the two core magnetocaloric performance indicators, with the blue curve Δ representing the prediction results. S M Maximum magnetic entropy change GBR Model; Orange Curve T c Curie temperature XGBoost Model.

[0072] Based on the research logic of feature selection, the core function of this graph is to find a balance between high prediction accuracy and low feature dimensionality, Δ S M The blue curve in the prediction model shows how the number of features decreases from the original 59 to 16. R 2 The fact that the 16 features remained stable without a significant decrease indicates that they already included the predicted Δ. S M The required core information; when the number of features is further reduced to 15, R 2 The sharp drop indicates that excessive feature removal led to the loss of key information, resulting in a significant decrease in model accuracy. The conclusion is: Δ S M The optimal feature set for prediction is 16.

[0073] T c The orange curve of the prediction model represents the change in the number of features as the number of features gradually decreases from 59 to 17. R2 The value remained consistently high, close to 0.91, without significant decay, indicating that the 17 features provide sufficient support. T c High-precision prediction; when the number of features is less than 17. R 2 The slow decline indicates that some key regulatory features have been eliminated. Conclusion: T c The optimal feature set for prediction is 17.

[0074] Simplify model complexity by RFE Through screening, the original 65 features, which contained redundancy, were ultimately reduced to 16 / 17 optimal features. This reduced the computational cost of model training and avoided the risk of overfitting caused by redundant features; the optimal feature set... R 2 Comparable to the full-feature model, the selected features were found to retain key information regarding the composition-magnetothermal properties; supporting subsequent interpretability analysis: the simplified feature set provides a basis for further analysis. SHAP Analyzing and decoding the mechanism of key features provides convenience and avoids interference from high-dimensional features in disassembling the black box.

[0075] Appendix Figure 7 It contains four subgraphs, where a and c represent the maximum magnetic entropy change Δ. S M And Curie temperature T c A scatter plot comparing predicted experimental values ​​and predicted values. The dashed diagonal line represents the perfect prediction y=x, and the shaded area is the 95% confidence interval. Δ S M Coefficient of determination for prediction R 2 =0.9221, root mean square error RMSE =1.1680 J / (kg・K), T c Predicted R 2 =0.9160、 RMSE =42.2120K, all demonstrating the high accuracy of the optimized model; b and d are Δ S M and T c The predicted residual error histogram shows that the difference between the predicted and experimental residual values ​​follows a normal distribution with a mean close to 0, indicating no significant systematic error. This confirms that the model can effectively capture key components and performance relationships after feature selection, while also simplifying computational complexity.

[0076] Appendix Figure 8 The explanation includes (a) the maximum magnetic entropy change Δ SM and Curie temperature T c of SHAP Summary diagrams; both diagrams use the y-axis to arrange features in descending order of importance and the x-axis to represent features. SHAP Positive values ​​improve target performance, while negative values ​​decrease it; the color gradient from blue to red corresponds to a higher feature value. Among these, the influence of Δ... S M The key characteristics are Fe, μ 0 ΔH, Al, I 1 , Δχ c And Ecoh, Fe and Ecoh with respect to Δ S M Negative correlation μ 0 ΔH, Al and Δ χ c Positive correlation, I 1 The influencing relationships are quite complex; T c Key features include Cp, I 1 Al, Co, Fe, AW and ΔTmelt, Cp, Al, AW and ΔTmelt and T c Negative correlation I 1 Co and Fe are positively correlated, and each point represents the corresponding feature in a single sample. SHAP The values ​​clearly show the direction of influence of each key feature on the two types of magnetocaloric properties and the distribution of feature values.

[0077] Appendix Figure 9 To influence the maximum magnetic entropy change Δ of amorphous alloys S M The first 6 key features SHAP Dependency graph, including (a) Fe, (b) μ 0 ΔH, change in applied magnetic field, (c)Al, (d) I 1 First ionization energy, (e)Δ χ c Christian electronegativity difference, (f)Ecoh atomic binding energy, 6 subplots; the horizontal axis of each subplot represents the eigenvalue, and the vertical axis represents the eigenvalue. SHAP A positive value indicates that the feature is boosted by Δ. S M Negative values ​​represent a decrease of Δ S MThe color bars reflect the eigenvalues: blue corresponds to higher eigenvalues, and red corresponds to lower eigenvalues. The pink shaded area in the graph represents the eigenvalues ​​obtained through locally weighted regression. LOWESS The narrower the 95% confidence interval of the generated trend line, the more reliable the marginal utility of that range characteristic. R 2 LOWESS This indicates the goodness of fit between the trend line and the actual marginal effect; specifically, Fe, as the most important feature, is related to Δ S M Significantly negative correlation R 2 LOWESS =0.900, especially when the Fe atomic percentage is less than 0.3, the negative effect is more obvious, because excess Fe will increase the magnetic inhomogeneity of amorphous alloys and weaken the magnetic exchange interaction; μ 0 ΔH and Δ S M Strong positive correlation R 2 LOWESS =0.968, which conforms to Maxwell's relation; a larger magnetic field change can promote a more significant reorientation of the magnetic moment to increase the magnetic entropy change; Al totality and ΔS S M Positive correlation R 2 LOWESS =0.901, the cooperative magnetic behavior of magnetic atoms can be enhanced by optimizing the atomic packing density, but the confidence interval widens significantly when the percentage of Al atoms exceeds 0.3, which is due to the increased uncertainty of marginal effects caused by the sparse data in the high Al content region. I 1 Nonlinear effect R 2 LOWESS =0.681, at I 1 At approximately 6.5 eV SHAP The value reaches its maximum for Δ S M The strongest positive contribution, too high or too low I 1 It will disrupt magnetic order; Δ χ c It can promote Δ in the range of 0.08-0.10 S M promote R 2 LOWESS =0.331, a moderate difference in electronegativity can enhance the chemical affinity between elements, stabilize the amorphous phase, and maintain strong magnetic interactions; Ecoh, on the other hand, inhibits Δ at <400 kJ / mol. S MR 2 LOWESS =0.812, because low binding energy weakens atomic bonding, reduces the stability of magnetic domain structure, and limits the magnetic entropy change under an external magnetic field; this figure quantifies the characteristic -Δ S M The correlation and uncertainty of the Δ clearly reveal the regulation of each key feature. S M The physical mechanism.

[0078] Appendix Figure 10 explain one, Figure 10 To influence the Curie temperature of amorphous alloys T c The first 6 key features SHAP Dependency graph, including (a) heat capacity C p (b) First ionization energy I 1 (c) Aluminum (Al), (d) Cobalt (Co), (e) Iron (Fe), (f) Average atomic weight (AW) are presented in six subplots. The horizontal axis of each subplot represents the eigenvalue, and the vertical axis represents the eigenvalue. SHAP A positive value indicates an improvement in this feature. T c Negative values ​​represent a decrease T c The color bars reflect the eigenvalues: blue corresponds to higher eigenvalues, red to lower eigenvalues, and the pink shaded area represents eigenvalues ​​obtained through locally weighted regression. LOWESS The narrower the 95% confidence interval of the generated trend line, the more reliable the marginal utility of the feature. R 2 LOWESS This indicates the goodness of fit between the trend line and the actual marginal effect; specifically, C p right T c The effect exhibits a nonlinear pattern of first decreasing and then increasing. R 2 LOWESS =0.912, at that time, the higher C p By enhancing high-temperature heat dissipation, thermal motion can be prevented from disrupting magnetic order, thereby promoting... T c promote; I 1 and T c Positive correlation R 2 LOWESS =0.900, and I 1 >7.8 eV SHAP The value rose rapidly due to higher I 1It can enhance the localization of valence electrons and stabilize ferromagnetic order at high temperatures; Al... T c Negative correlation RLOWESS =0.766, excessive Al will dilute the concentration of magnetic elements such as Fe and Co, weakening magnetic exchange interactions, leading to T c Reduce; Co R 2 LOWESS =0.661 and Fe R 2 LOWESS =0.797 and T c They are positively correlated, and there is a strong ferromagnetic exchange interaction between their atoms, which can resist thermal motion at higher temperatures, maintain the ferromagnetic state of the alloy, and thus improve... T c AW in the range of 60-110 g / mol with T c There is a significant negative correlation, and the correlation tends to stabilize beyond this range. R 2 LOWESS =0.806, the initial negative correlation stems from the decrease in atomic diffusion rate and the stabilization of magnetic structure due to the increase in atomic weight. Subsequent saturation occurs because the magnetic exchange interaction reaches its upper limit. This figure quantifies the relationship between key features and... T c The correlation and uncertainty clearly reveal the regulation of different characteristics. T c The intrinsic physical mechanism enables precise adjustment in the design of amorphous alloy composition. T c It provides evidence.

[0079] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for predicting the magnetocaloric properties of amorphous alloys based on interpretable machine learning, characterized in that, The method includes: Step 1: Construct a dataset of magnetocaloric properties of amorphous alloys. The dataset includes alloy composition data, physicochemical descriptors, external conditions and structural characteristics of multiple amorphous alloy samples, as well as the experimental values ​​of the corresponding maximum magnetic entropy change and Curie temperature. Step 2: Filter and optimize the features in the dataset. By eliminating collinearity between features and performing recursive feature elimination, the final feature subsets used to predict the maximum magnetic entropy change and Curie temperature are determined respectively. Step 3: Using the final feature subset, establish machine learning models for predicting the maximum magnetic entropy change and Curie temperature, and train and optimize them to obtain the trained prediction models. Step 4: The interpretability of the trained prediction model is analyzed using the SHAP analysis method to identify the key features and mechanisms that affect the maximum magnetic entropy change and Curie temperature. Step 5: Based on key features and mechanisms of action, design amorphous alloy compositions that meet the preset requirements for maximum magnetic entropy change and Curie temperature. Then, use a prediction model to predict and screen the performance of the designed compositions to obtain the target amorphous alloy compositions.

2. The method for predicting the magnetocaloric properties of amorphous alloys based on interpretable machine learning according to claim 1, characterized in that, Step 1: Construct a magnetocaloric performance dataset for amorphous alloys. The dataset includes alloy composition data, physicochemical descriptors, external conditions and structural characteristics of multiple amorphous alloy samples, as well as experimental values ​​for the corresponding maximum magnetic entropy change and Curie temperature, including: Raw experimental data of amorphous alloys were collected and integrated from multiple published papers to construct an initial dataset covering a variety of alloy systems, including transition metal-based amorphous alloys, rare earth-based amorphous alloys, and gadolinium-based amorphous alloy systems. The amorphous alloy feature data is classified into three categories: alloy composition features, physicochemical descriptors, and external conditions and structural features. The alloy composition features are defined as the atomic percentage of each constituent element and normalized to 100%. Unused elements are set to zero to obtain the classified feature data. Based on the classified feature data and raw experimental data, the maximum magnetic entropy change and Curie temperature experimental values ​​corresponding to each amorphous alloy sample were extracted and associated. The maximum magnetic entropy change was measured under different magnetic field variation conditions, and the Curie temperature was determined by the inflection point of the magnetization and temperature curves to obtain the associated feature and performance data pairs. Based on the associated feature and performance data pairs, the dataset is standardized and outlier detection is performed to eliminate data noise and inconsistencies, ensuring data quality and reliability, and ultimately forming a standardized amorphous alloy magnetocaloric performance dataset.

3. The method for predicting the magnetocaloric properties of amorphous alloys based on interpretable machine learning according to claim 2, characterized in that, The features in the dataset are filtered and optimized. By eliminating collinearity among features and performing recursive feature elimination, the final feature subsets used to predict the maximum magnetic entropy change and Curie temperature are determined, including: Based on the standardized dataset, calculate the Spearman correlation coefficient between all pairs of features to identify patterns of high correlation between features. By using a highly correlated pattern, for each feature pair whose correlation coefficient exceeds a preset threshold, the feature with the larger absolute value of correlation with the target performance is retained, and the other feature is removed, thereby eliminating collinearity interference between features and obtaining a non-redundant feature set optimized for collinearity. Based on a non-redundant feature set, a recursive feature elimination method is used to evaluate feature importance for the maximum magnetic entropy change prediction task and the Curie temperature prediction task, respectively, so as to obtain the recursive feature elimination iterative results. Based on the results of the recursive feature elimination iteration, the final feature subsets for predicting the maximum magnetic entropy change and the final feature subsets for predicting the Curie temperature are determined respectively.

4. The method for predicting the magnetocaloric properties of amorphous alloys based on interpretable machine learning according to claim 3, characterized in that, Using the final feature subset, machine learning models for predicting the maximum magnetic entropy change and Curie temperature were established, trained, and optimized to obtain the trained prediction models, including: Based on the final feature subsets used to predict the maximum magnetic entropy change and the final feature subsets used to predict the Curie temperature, multiple ensemble machine learning algorithms were selected as candidate models, including random forest, gradient boosting regression and extreme gradient boosting algorithm. Based on the selected candidate models, a leave-one-out cross-validation strategy is used to train each candidate model. In each iteration, all samples except one sample are used as the training set, and the remaining samples are used as the validation set. The generalization performance of each candidate model under different feature combinations is evaluated through iterative training to obtain the training results. Based on the training results, the prediction accuracy of each candidate model is quantitatively evaluated by calculating the coefficient of determination and root mean square error, and the final model architecture with the best prediction performance is selected based on the evaluation results. Based on the final prediction model architecture, the selected gradient boosting regression model and extreme gradient boosting model are fully trained and optimized by using all training samples in the standardized dataset and the corresponding final feature subsets, ultimately generating a high-precision maximum magnetic entropy change prediction model and Curie temperature prediction model.

5. The method for predicting the magnetocaloric properties of amorphous alloys based on interpretable machine learning according to claim 4, characterized in that, Based on the training results, the prediction accuracy of each candidate model is quantitatively evaluated by calculating the coefficient of determination and root mean square error. The final model architecture with the best prediction performance is selected based on the evaluation results, including: Based on the training results of each candidate model in leave-one-out cross-validation, the determination coefficient and root mean square error of each candidate model for the maximum magnetic entropy change prediction task and the Curie temperature prediction task are calculated respectively, forming a set of quantitative prediction performance evaluation indicators. Based on the set of prediction performance evaluation metrics, for the maximum magnetic entropy change prediction task, the prediction accuracy of random forest model, gradient boosting regression model and extreme gradient boosting model are compared, and the gradient boosting regression model with the largest coefficient of determination and the smallest root mean square error is selected as the final prediction architecture. Based on the set of prediction performance evaluation metrics, for the Curie temperature prediction task, the prediction accuracy of the random forest model, the gradient boosting regression model, and the extreme gradient boosting model are compared. The extreme gradient boosting model with the largest coefficient of determination and the smallest root mean square error is selected as the final prediction architecture.

6. The method for predicting the magnetocaloric properties of amorphous alloys based on interpretable machine learning according to claim 5, characterized in that, The interpretability of the trained prediction model was analyzed using the SHAP analysis method to identify key features and mechanisms affecting the maximum magnetic entropy change and Curie temperature, including: Based on the trained maximum magnetic entropy change prediction model and Curie temperature prediction model, the SHAP value of each input feature on the prediction result is calculated. The SHAP value quantifies the marginal contribution of each feature to the model prediction in all possible feature combinations through cooperative game theory. Based on the SHAP value, a SHAP summary map is obtained. All features are ranked globally according to the average absolute SHAP value. At the same time, the positive and negative correlation between each feature and the target performance is identified through color coding and point distribution, and the set of key features affecting the maximum magnetic entropy change and Curie temperature is determined. Based on the set of key features, a SHAP dependency graph is generated for each key feature to show the non-linear relationship between a single feature value and the SHAP value. A local weighted regression trend line and a statistical confidence interval are then overlaid on the dependency graph to obtain the SHAP dependency graph analysis results. Based on the SHAP dependency graph analysis results and combined with materials science knowledge, the mechanism of key features on the maximum magnetic entropy change and Curie temperature is decoded, including the final range of influence of the features, nonlinear influence modes, and synergistic or antagonistic effects among multiple features, forming a physical mechanism understanding that can guide the design of amorphous alloy composition.

7. The method for predicting the magnetocaloric properties of amorphous alloys based on interpretable machine learning according to claim 6, characterized in that, Step 5 above includes: Based on the decoding mechanism, the core target parameters and key element selection principles for amorphous alloy composition design are determined. The core target parameters include the preset maximum magnetic entropy change threshold and Curie temperature range. The key element selection principles cover the ratio and functional positioning of core elements, auxiliary elements and control elements. Based on the key element selection principle and combined with the final range of influence of the identified physicochemical characteristics, a set of candidate amorphous alloy compositions that meet the element ratio constraints is obtained. The final range of influence of the physicochemical characteristics includes the range of electronegativity difference, the range of ionization energy, and the range of atomic binding energy. By using the trained maximum magnetic entropy change prediction model and Curie temperature prediction model, the performance of each component in the candidate amorphous alloy composition set is predicted, and the predicted maximum magnetic entropy change value and Curie temperature value corresponding to each candidate component are obtained to obtain the predicted performance results. Based on the set core target parameters, the predicted performance results are screened and evaluated, and candidate components that meet the preset maximum magnetic entropy change threshold and Curie temperature range requirements are retained to form a list of candidate target amorphous alloy components. Based on the multi-feature collaboration of decoding, the candidate target amorphous alloy composition list is optimized and sorted in a second time. Taking into account the process feasibility, element cost and performance stability of the composition, the final target amorphous alloy composition and the corresponding predicted performance parameters are obtained.

8. A system for predicting the magnetocaloric properties of amorphous alloys based on interpretable machine learning, the system implementing the method as described in any one of claims 1 to 7, characterized in that, include: The acquisition module is used to construct a dataset of magnetocaloric properties of amorphous alloys. The dataset includes alloy composition data, physicochemical descriptors, external conditions and structural characteristics of multiple amorphous alloy samples, as well as the experimental values ​​of the corresponding maximum magnetic entropy change and Curie temperature. The prediction module is used to filter and optimize the features in the dataset. By eliminating collinearity between features and performing recursive feature elimination, it determines the final feature subsets used to predict the maximum magnetic entropy change and Curie temperature, respectively. The training module is used to build machine learning models for predicting the maximum magnetic entropy change and Curie temperature using the final feature subset, and to train and optimize them to obtain the trained prediction models. The identification module is used to perform interpretability analysis on the trained prediction model using the SHAP analysis method, and to identify the key features and mechanisms that affect the maximum magnetic entropy change and Curie temperature. The processing module is used to design amorphous alloy compositions that meet the preset maximum magnetic entropy change and Curie temperature requirements based on key features and mechanisms of action, and to predict and screen the performance of the designed compositions through a prediction model to obtain the target amorphous alloy composition.

9. A computing device, characterized in that, include: One or more processors; A storage device for storing one or more programs, which, when executed by one or more processors, cause the one or more processors to implement the method as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a program that, when executed by a processor, implements the method as described in any one of claims 1 to 7.

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