Spinel multi-objective reverse design method based on machine learning and Bayesian optimization algorithm, electronic equipment and storage medium

Abstract

The invention relates to a spinel multi-objective reverse design method based on machine learning and a Bayesian optimization algorithm, electronic equipment and a storage medium, and the design method comprises the steps: firstly extracting related data of a spinel material from a database, and constructing a balanced data set through preprocessing; feature engineering is carried out, a comprehensive feature set is constructed, and key features are reserved; then training a multi-target prediction model through hyper-parameter optimization by using a multi-task gradient elevator model; and finally, integrating to a Bayesian reverse design framework, expanding a design space through a specific encoder, and combining a Gaussian process proxy function and an expected hyper-volume improvement criterion to screen candidate materials meeting conditions and verify performance, thereby completing reverse design optimization. Compared with the prior art, the intelligent and efficient spinel novel multi-target reverse design method can be used for solving the problem of data scarcity, and development of high-performance spinel solar cell materials is accelerated.

Description

Technical Field

[0001] The present invention relates to the technical field of solar cell material design, and in particular to a spinel multi-objective inverse design method, electronic equipment, and storage medium based on machine learning and Bayesian optimization algorithms. Background Art

[0002] Spinel materials, exemplified by AB2X4, show great potential for solar cell applications due to their highly tunable composition and unique structure. However, the scarcity of spinel material data and the requirements for diverse properties pose challenges to the development of efficient and stable spinel solar cells through traditional experiments and data mining.

[0003] In the research of spinel materials, their large band gap has limited related design research. Although performance can be optimized through composition adjustment and doping strategies, traditional trial-and-error methods are costly and time-consuming when faced with a vast composition space, making them difficult to implement effectively.

[0004] The rise of artificial intelligence technology has provided new opportunities for spinel material design, but the Materials Project (MP) database only contains 325 cubic spinel compounds. The amount of data is insufficient to support the algorithm to establish the relationship between composition and performance, which hinders the effective exploration of the composition space.

[0005] Patent CN117952011A provides a novel reverse design method for perovskite devices based on machine learning and Bayesian optimization algorithms. This method uses a machine learning model to quickly identify the optimal parameter combination for achieving the desired device performance, effectively reducing the cost of trial and error. However, this method is primarily targeted at perovskite devices, and its expressiveness and generalization capabilities, particularly for small sample sets, need to be improved when dealing with multi-objective optimization problems.

[0006] Another reference patent, CN119152971A, discloses a method for predicting the chloride ion diffusion coefficient based on a hybrid machine learning model. By combining LASSO regression feature selection with LightGBM and a GPR model, this method improves prediction accuracy and provides uncertainty probability intervals. Although this method performs well in predicting the chloride ion diffusion coefficient, its applicability and efficiency in multi-objective optimization, particularly for the reverse design of spinel materials, remain to be verified.

[0007] Researchers have attempted to address data scarcity through various data-driven approaches, such as using density functional theory (DFT) calculations to generate synthetic datasets for training machine learning models. However, these methods are resource-intensive and rely on large amounts of data acquisition or expensive computational labeling. Therefore, researchers urgently need to develop an intelligent and efficient new multi-objective inverse design method for spinel to address data scarcity. Summary of the Invention

[0008] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and to provide a spinel multi-objective reverse design method, electronic device, and storage medium based on machine learning and Bayesian optimization algorithm. The present invention provides an intelligent and efficient new spinel multi-objective reverse design method, which can be used to solve the problem of data scarcity and accelerate the development of high-performance spinel solar cell materials.

[0009] The purpose of the present invention can be achieved by the following technical solutions:

[0010] A first aspect of the present invention provides a spinel multi-objective inverse design method based on machine learning and Bayesian optimization algorithm, characterized by comprising the following steps:

[0011] S1. Data collection and preprocessing: Extract the band gap values, band gap types, and energy above convex hull data of spinel materials from the Materials Project database, expand the band gap value range to 0.9-2.0 eV, perform standardization preprocessing, and construct a balanced data set;

[0012] S2. Feature Engineering: Based on the balanced dataset constructed in S1, a comprehensive feature set consisting of basic descriptors, calculated descriptors, and composite descriptors is constructed for the AB2X4 chemical formula. Key features are retained through pairwise correlation screening and sequential forward selection.

[0013] S3, model training and optimization: Based on the key features after dimensionality reduction in S2, the multi-task gradient boosting machine (MTGBM) model is used to optimize hyperparameters and train a multi-objective prediction model through the Optuna framework;

[0014] S4. Bayesian inverse design and verification: Integrate the multi-objective prediction model trained in S3 into the Bayesian inverse design framework, expand the spinel design space into a parameterized form through the encoder, combine the Gaussian process surrogate function with the expected hypervolume improvement criterion, screen candidate materials that meet Eg = 1.1-1.5eV, direct band gap and Ehull ≤ 0.025eV / atom, verify the performance of the screened materials, and complete the reverse design optimization of the spinel material.

[0015] Furthermore, in S1, the data collection and preprocessing specifically includes the following steps:

[0016] Data extraction: Obtain the band gap value, band gap type, and energy above convex hull properties of spinel materials from the Materials Project database;

[0017] Data expansion and normalization: The band gap value range was expanded to 0.9-2.0 eV to balance the sample distribution, and all data were normalized;

[0018] Dataset construction: Integrate the expanded data to generate a balanced dataset.

[0019] Furthermore, in S2, the feature engineering specifically includes the following steps:

[0020] Comprehensive feature set construction: Based on the AB2X4 chemical formula, basic descriptors, calculated descriptors, and composite descriptors are extracted from the balanced data set to generate a comprehensive feature set that represents the comprehensive feature set with multidimensional features;

[0021] Feature screening and dimensionality reduction: Based on the comprehensive feature set, redundant features are eliminated through pairwise correlation analysis, and further optimized by combining the sequential forward selection algorithm to retain the key features that contribute most to the prediction of the target attribute.

[0022] Furthermore, in the feature screening and dimensionality reduction process, through pairwise square correlation threshold and sequential forward selection, six key features are finally retained, including maximum melting heat, tolerance factor, LUMO energy, average number of valence electrons, mean value of space group number, and maximum value of element period difference.

[0023] Furthermore, in S3, the model training and optimization specifically includes the following steps:

[0024] Multi-task model configuration and dynamic weight initialization: Based on the key features after S2 dimensionality reduction, a multi-task gradient boosting machine (MTGBM) model framework is constructed. A dynamic weight allocation mechanism is set for the three objectives of band gap value, band gap type, and Ehull. The task weights are dynamically adjusted through the gradient conflict detection function to form the initial multi-objective learning model.

[0025] Dynamically weighted Pareto hyperparameter collaborative optimization: Within the established MTGBM framework, multi-objective joint optimization of hyperparameters is performed using the Optuna framework. The model structure after dynamic weight assignment is used as the optimization constraint to screen the optimal parameter combination that simultaneously meets the band gap prediction accuracy and Ehull stability requirements during the Pareto frontier process.

[0026] Model training and validation: The MTGBM model is trained based on the optimized hyperparameters. Its prediction performance on three objectives, namely, band gap value, band gap type, and Ehull, is verified using the AUC, F1 score, and Hamming loss metrics to generate a multi-objective prediction model.

[0027] Furthermore, in the process of screening the Pareto front, the MTGBM model assigns a 1.2 times weight to the band gap value prediction task through a dynamic weight allocation mechanism, and uses Optuna to optimize the regularization coefficient and the number of leaf nodes to screen the optimal hyperparameter combination of the Pareto front.

[0028] Furthermore, in S4, the Bayesian inverse design includes the following specific steps:

[0029] Multi-objective model integration and design space initialization: Based on the multi-objective prediction model MTGBM trained on S3, it is embedded in the Bayesian inverse design framework as the core predictor, and the design space of the spinel chemical formula AB2X4 is expanded to the parameterized form A through the encoder. a B_bX_x(a∈(0,1), b∈(0,2), x∈(0,4)), establishes a candidate material space that can be quantified for search;

[0030] Surrogate model-driven multi-objective optimization: Using the quantitative search candidate material space as input, a Gaussian process surrogate function is constructed. Combined with the expected hypervolume improvement criterion, three objectives, Eg = 1.1-1.5eV, direct band gap, and Ehull ≤ 0.025eV / atom, are jointly modeled to balance exploration and development through adaptive sampling.

[0031] Candidate material screening and iterative verification: Based on multi-objective optimization, the MTGBM model is used to impose a penalty function on candidate materials that exceed the Ehull standard, eliminate invalid solutions and generate a set of high-potential materials.

[0032] Furthermore, in S4, the process of verifying the performance of the screened materials includes: analyzing the contribution of key features in S2 through the SHAP interpretable model, and combining the doping mechanism with density functional theory to verify the performance of the materials screened in S4, thereby completing the reverse design optimization of the spinel material.

[0033] A second aspect of the present invention provides an electronic device comprising a memory and a processor, wherein the processor is configured to execute a program in the memory, thereby implementing the spinel multi-objective inverse design method based on machine learning and Bayesian optimization algorithm as described above.

[0034] A third aspect of the present invention provides a storage medium containing computer-executable instructions, which, when executed by a computer processor, is used to execute the spinel multi-objective inverse design method based on machine learning and Bayesian optimization algorithm as described above.

[0035] Compared with the prior art, the present invention has the following beneficial effects:

[0036] 1) The closed-loop data-model-design framework breaks through the limitations of small samples

[0037] The present invention uses an active learning (AL)-driven Bayesian optimization (BO) paradigm to construct a closed-loop system of "data generation-model iteration-inverse design": adopting a Gaussian process (GP) proxy function and the expected hypervolume improvement (EHI) criterion to achieve a dynamic balance between exploration and utilization in the candidate material space; using the MTGBM multi-task prediction model to pre-screen invalid solutions that exceed the Ehull standard (applying a penalty function), 80% of the optimization resources are focused on the high-potential region of Eg=1.1-1.5eV and direct band gap, reducing the experimental trial and error cost by 65%.

[0038] 2) Multi-task dynamic fusion mechanism achieves accurate reverse mapping

[0039] The present invention establishes a quantification system for spinel feature contribution, and uses the SHAP interpretable model to analyze the physical regulation law of key features (such as tolerance factor τ, LUMO energy le) on multi-objective performance; combines sequential forward selection (SFS) with Optuna hyperparameter optimization to construct a 6-dimensional key feature space (h max ,τ,le,e mean 、s mean 、p max ), enabling MTGBM to achieve a prediction accuracy of AUC>0.85 with a small sample data of 325 items; based on the material gene expansion strategy (such as the optimization of the Zr / Be / Se doping ratio), the candidate material ZrBe2Se4 with an SLME of 32.4% was reversely designed, approaching the Shockley-Queisser (SQ) theoretical limit. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 is a flow chart of an application example of the present invention;

[0041] Figure 2 It is the parameterized bit element diagram of the encoder in the application example of the present invention;

[0042] Figure 3 This is a schematic diagram of the exploration-exploitation balance of Bayesian optimization in the reverse design in the application example of the present invention;

[0043] Figure 4 It is a dynamic weight allocation path diagram in an application example of the present invention;

[0044] Figure 5 is a hyperparameter optimization path diagram in an application example of the present invention;

[0045] Figure 6 This is a simplified diagram of the overall process of the spinel multi-objective reverse design method based on machine learning and Bayesian optimization algorithm in the present invention. DETAILED DESCRIPTION

[0046] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments. Component models, material names, connection structures, circuit structures, control methods, algorithms, and other features not explicitly described in this technical solution are considered common technical features disclosed in the prior art.

[0047] Example 1

[0048] This embodiment combines machine learning, active learning (AL) and Bayesian optimization (BO) algorithms to provide an intelligent and efficient new multi-objective inverse design method for spinel to solve the problem of data scarcity and accelerate the development of high-performance spinel solar cell materials.

[0049] See also Figure 6 In the simplified process diagram, a novel multi-objective reverse design method of spinel based on machine learning and Bayesian optimization algorithm in this embodiment includes the following steps:

[0050] Step 1: Data collection and preprocessing. Extract spinel related data from the Materials Project (MP) database, focusing on the band gap value (E g ), band gap type (“is_gap_direct”), and energy above the convex hull (E hull ) These three key attributes. Given that the data in the initial dataset that meets the expected characteristics are scarce and unevenly distributed, the continuous values are discretized into two categories (True(1) or False(0)) for binary classification, and E is expanded. g The selection range is 0.9-2.0eV to alleviate the sample imbalance problem and provide a high-quality data foundation for subsequent feature engineering and model training.

[0051] Step 2: Feature Engineering. Using the preprocessed data from Step 1, a feature extractor was developed to calculate a comprehensive descriptor set consisting of 62 basic descriptors, 10 calculated descriptors, and 274 integrated descriptors to better characterize material properties from chemical formulas. A pairwise squared correlation cutoff of 0.90 was applied to the training set for preliminary feature selection, reducing the number of variables and providing more targeted and effective features for model training.

[0052] Step 3: Model Training and Selection. Based on the feature dataset obtained after feature engineering in Step 2, multiple machine learning models are evaluated, including neural networks (NN), classification boosting (CatBoost), extreme gradient boosting (XGBoost), and multi-task gradient boosting machines (MTGBM). Model evaluation is performed by calculating metrics such as accuracy, F1 score, Hamming loss, and area under the curve (AUC), and the best-performing model is selected. Sequential forward selection is used to optimize the learning ability of the selected model, identify key features, and perform hyperparameter optimization using the Optuna framework. Finally, the model is trained and validated to obtain a well-performing prediction model.

[0053] Step 4: Active learning-driven Bayesian inverse design process. An inverse design framework is constructed, consisting of an encoder, the MTGBM component trained in Step 3, and Optuna. The encoder expands the design space of the spinel formula. The MTGBM is used to predict multiple properties of new synthetic components and assist Bayesian optimization (BO) in narrowing the search space. Optuna, as the BO framework, integrates a Gaussian process (GP) model as a surrogate function and the expected hypervolume improvement (EHI) criterion to balance exploration and exploitation, efficiently identifying the most suitable candidate materials within a limited number of trials.

[0054] Step 5: Results Analysis and Application. The spinel material obtained through the inverse design framework in Step 4 is analyzed, including doping mechanism analysis and feature importance analysis using the SHAP interpretable model. Leveraging the key features identified during the model training process in Step 3, this provides more targeted guidance for spinel material design.

[0055] In specific implementation, the specific process of data collection and preprocessing in step 1 is as follows:

[0056] Step A1: Extract 325 spinel data from the MP database, focusing on the band gap value (E g ), band gap type (“is_gap_direct”), and energy above the convex hull (E hull ))These three properties are crucial for solar cell applications.

[0057] Step A2: Since the initial dataset meets all the expected characteristics (E g In the range of 1.1-1.5eV, direct band gap, E hull ≤0.025eV / atom) is scarce and the data distribution is uneven, so the continuous values are discretized into two categories (True(1) or False(0)) for binary classification.

[0058] Step A3: To alleviate the sample imbalance problem, E g The selection range is expanded to 0.9-2.0eV.

[0059] In specific implementation, the specific steps of feature engineering in step 2 are:

[0060] Step B1: Based on the preprocessed data obtained in Step 1, a feature extractor is developed to calculate a comprehensive descriptor set including 62 basic descriptors, 10 calculated descriptors, and 274 integrated descriptors to better characterize material properties from chemical formulas.

[0061] Step B2: A pairwise squared correlation cutoff of 0.90 was applied to perform preliminary feature selection on the training set, reducing the number of variables from 344 to 88.

[0062] In specific implementation, the specific process of model training and selection in step 3 is as follows:

[0063] Step C1: Based on the dataset obtained after feature selection in step 2, multiple machine learning models are evaluated, including neural network (NN), classification boosting (CatBoost), extreme gradient boosting (XGBoost), and multi-task gradient boosting machine (MTGBM).

[0064] Step C2: Evaluate each model by calculating indicators such as accuracy, F1 score, Hamming loss, and area under the curve (AUC), and select a model that performs well among various indicators, such as MTGBM.

[0065] Step C3: Use the sequential forward selection method to further optimize the learning ability of the selected model (such as MTGBM). Combined with the feature information obtained in step 2, six key features are determined to improve the AUC score of the model.

[0066] Step C4: Use the Optuna framework to optimize the hyperparameters of the selected model. Step C5: Finally, train and validate the selected model (such as MTGBM) to achieve good prediction results on the three objectives of "is_gap_direct", Ehull) and Eg.

[0067] In specific implementation, the specific steps of the active learning-driven Bayesian inverse design process in step 4 are:

[0068] Step D1: Build the inverse design framework, which contains the encoder, the MTGBM component trained in step 3, and Optuna.

[0069] Step D2: The encoder encodes the candidate elements into a list of A, B, and X sites and element ratios, expanding the design space of the spinel formula from AB2X4 to A′ a A″ 1-a B′ b B″ 2-b X′ x X″4-x , the range of a is (0,1), the range of b is (0,2), and the range of c is (0,4).

[0070] Step D3: Utilize the prediction capability of the MTGBM model in step 3 to predict multiple properties of the newly synthesized component and assist Bayesian optimization (BO) to narrow the search space.

[0071] Step D4: Optuna is used as a BO framework, integrating the Gaussian process (GP) model as a proxy function to impose a penalty function on candidates that exceed the Ehull standard, thereby accelerating the elimination of invalid solutions.

[0072] Adaptive sampling is used to efficiently identify the most suitable candidate materials within a limited number of trials.

[0073] In specific implementation, the specific content of the result analysis and application in step 5 is as follows:

[0074] Step E1: Analyze the doping mechanism of the spinel material obtained through the inverse design framework in Step 4, combined with the material property relationships learned by the model in Step 3, such as analyzing the impact of doping certain elements in a specific spinel material on the band gap and stability.

[0075] Step E2: Analyze the feature importance using the SHAP interpretable model. Using the features identified in Step 2 and the results of the model training in Step 3, construct a detailed contribution graph to highlight the impact of key features in composition regulation and provide guidance for spinel material design.

[0076] Step E3: The SLME method combined with DFT was used to verify some of the designed materials, among which the SLME calculation of ZrBe2Se4 reached 32.4%, close to the SQ limit.

[0077] Application Example 1

[0078] like Figure 1 As shown in the figure, a new multi-objective inverse design method for spinel based on machine learning and Bayesian optimization algorithm is proposed. The specific steps are as follows:

[0079] Step 1: Data collection and preprocessing

[0080] Step A1: Extract data of 325 spinel compounds from the Materials Project (MP) database, focusing on three key properties: band gap value (Eg), band gap type (direct / indirect), and energy above the convex hull (Ehull).

[0081] Step A2: Since the data that meet the target characteristics (Eg = 1.1-1.5eV, direct band gap, Ehull ≤ 0.025eV / atom) are scarce and unevenly distributed, the continuous values are discretized into binary labels (True / False) and the Eg range is expanded to 0.9-2.0eV to balance the samples (e.g. Figure 3 As shown, the data distribution is more even after expansion).

[0082] Step A3: Perform data standardization on Eg, bandgap type, and Ehull to construct a preprocessed data set containing 325 samples.

[0083] Step 2: Feature Engineering

[0084] Step B1: Construct a 346-dimensional feature set based on the chemical formula (AB2X4), including: basic descriptors (62 dimensions): ionic radius, electronegativity, and atomic mass of the elements at the A / B / X sites; computational descriptors (10 dimensions): tolerance factor (τ), LUMO energy (l e ), octahedral factor; composite descriptor (274 dimensions): generate electron cloud overlap energy and valence electron distribution statistics between elements through Matminer.

[0085] Step B2: Through pairwise correlation screening (threshold 0.90) and stepwise forward selection (SFS), 6 key features (such as Figure 2 As shown, encoder parameterization expands the design space): Key characteristics: Maximum melting heat (h max ), τ, le, average valence electron number (e mean ), mean value of space group number (s mean ), the maximum value of the element period difference (p max ).

[0086] Step 3: Model training and selection

[0087] Step C1: Compare the neural network (NN), CatBoost, XGBoost, and MTGBM models. The evaluation metrics include AUC, F1 score, and Hamming loss.

[0088] Step C2: Figure 4 As shown, MTGBM uses dynamic weight allocation (G n =w1G1+…+w n G n ) Solve the multi-task gradient conflict and give E g The task has a higher weight (w1=1.2), and the AUC in Eg prediction reaches 0.86, which is significantly better than the single-task model.

[0089] Step C3: Optimize the regularization coefficient (λ using the Optuna framework 11= 0.001), the number of leaf nodes (num_leaves = 168) and other parameters (optimization path such as Figure 5 As shown), screen the optimal combination of Pareto frontier.

[0090] Step 4: Bayesian optimization reverse design, build a reverse design framework, integrate the encoder, MTGBM model and Optuna optimizer. The encoder expands the spinel design space to parameterize the site element ratio (a∈(0,1),b∈(0,2),x∈(0,4)) (e.g. Figure 2 Step D2: Pre-screening E by MTGBM hull Candidate materials that exceed the standard, combined with Bayesian optimization (such as Figure 3 As shown, the Gaussian process proxy function and the expected hypervolume improvement criterion balance exploration and utilization), quickly positioning E g =1.1-1.5eV, high potential material with direct band gap.

[0091] Step 5: Result Verification and Application

[0092] Step E1: Inverse design generates the candidate material ZrBe2Se4, which is predicted to have an SLME of 32.4%, and is close to the Shockley-Queisser limit as verified by DFT.

[0093] Step E2: Analyze the key feature contributions through the SHAP interpretable model (such as Figure 4 As shown in the dynamic weight path, τ and l e Contributes to Eg regulation by over 70%) and guides the optimization of material composition.

[0094] In summary, the present invention provides a spinel material reverse design method based on machine learning and Bayesian optimization, which builds a "data-model-design" closed-loop system for the multi-objective optimization problem of small samples. Data is extracted from the Materials Project database, and a descriptor set is constructed through discretization and feature engineering. Six key features (h max , τ, etc.); train the multi-task gradient boosting machine (MTGBM), and combine it with Optuna hyperparameter optimization to predict the band gap type, E g / E hull (AUC>0.85); the Bayesian optimization framework was used to integrate Gaussian process and EHI criterion, and the feature contribution was analyzed by SHAP to eliminate E hull >0.025eV / atom invalid solution, 80% of resources focused on E g = 1.1-1.5eV high potential zone. Reverse engineering has resulted in materials such as ZrBe2Se4, achieving a SLME of 32.4%, approaching the SQ limit and providing new solutions for the development of high-efficiency solar cells.

[0095] The above description of the embodiments is intended to facilitate understanding and use of the invention by those skilled in the art. It will be apparent that those skilled in the art can readily make various modifications to these embodiments and apply the general principles described herein to other embodiments without requiring inventive effort. Therefore, the present invention is not limited to the above-described embodiments. Improvements and modifications made by those skilled in the art based on the disclosure of the present invention, without departing from the scope of the present invention, should be within the scope of protection of the present invention.

[0096] Example 2

[0097] This embodiment provides an electronic device for spinel multi-objective reverse design. Its core components include a memory and a processor. The memory is used to store data and programs, while the processor is responsible for executing the programs in the memory, thereby implementing a spinel multi-objective reverse design method based on machine learning and Bayesian optimization algorithms.

[0098] In actual operation, the device first uses machine learning algorithms to learn and analyze spinel-related data, building a preliminary predictive model. Subsequently, leveraging the efficient global optimization capabilities of the Bayesian optimization algorithm, it performs reverse design on the spinel's multiple objectives, continuously adjusting parameters to search for optimal solutions and achieve precise optimization of multiple aspects, including spinel performance. Throughout this process, the memory and processor work closely together to ensure a smooth design process, efficient algorithm operation, and accurate design results.

[0099] Example 3

[0100] The present embodiment provides a storage medium containing computer-executable instructions, and the storage medium of the computer-executable instructions is used to execute the spinel multi-objective inverse design method based on machine learning and Bayesian optimization algorithm as described above when executed by a computer processor. The storage medium has the characteristics of high storage capacity, high read and write speed, etc., and can quickly load and execute large amounts of data and program codes required for complex algorithms. It is not only compatible with a variety of operating systems and hardware platforms, making it convenient to apply the design method on different devices, but also has good scalability, which is convenient for subsequent optimization and upgrading of the spinel multi-objective inverse design method, further improving design efficiency and accuracy, so as to adapt to the diverse needs of spinel materials in different application scenarios, and provide strong software support and data guarantee for the research and development and innovation of spinel materials.

Claims

1. A spinel multi-objective inverse design method based on machine learning and Bayesian optimization algorithm, characterized in that: The following steps are involved: S1. Data collection and preprocessing: Extract the band gap values, band gap types, and energy above convex hull data of spinel materials from the Materials Project database, expand the band gap value range to 0.9-2.0 eV, perform standardization preprocessing, and construct a balanced data set; S2. Feature Engineering: Based on the balanced dataset constructed in S1, a comprehensive feature set consisting of basic descriptors, calculated descriptors, and composite descriptors is constructed for the AB2X4 chemical formula. Key features are retained through pairwise correlation screening and sequential forward selection. S3, model training and optimization: Based on the key features after dimensionality reduction in S2, the multi-task gradient boosting machine (MTGBM) model is used to optimize hyperparameters and train a multi-objective prediction model through the Optuna framework; S4. Bayesian inverse design and verification: Integrate the multi-objective prediction model trained in S3 into the Bayesian inverse design framework, expand the spinel design space into a parameterized form through the encoder, combine the Gaussian process surrogate function with the expected hypervolume improvement criterion, screen candidate materials that meet Eg = 1.1-1.5eV, direct band gap and Ehull ≤ 0.025eV / atom, verify the performance of the screened materials, and complete the reverse design optimization of the spinel material.

2. The spinel multi-objective inverse design method based on machine learning and Bayesian optimization algorithm according to claim 1, characterized in that: In S1, the data collection and preprocessing specifically include the following steps: Data extraction: Obtain the band gap value, band gap type, and energy above convex hull properties of spinel materials from the Materials Project database; Data expansion and normalization: The band gap value range was expanded to 0.9-2.0 eV to balance the sample distribution, and all data were normalized; Dataset construction: Integrate the expanded data to generate a balanced dataset.

3. The spinel multi-objective inverse design method based on machine learning and Bayesian optimization algorithm according to claim 1, characterized in that: In S2, the feature engineering specifically includes the following steps: Comprehensive feature set construction: Based on the AB2X4 chemical formula, basic descriptors, calculated descriptors, and composite descriptors are extracted from the balanced data set to generate a comprehensive feature set that represents the comprehensive feature set with multidimensional features; Feature screening and dimensionality reduction: Based on the comprehensive feature set, redundant features are eliminated through pairwise correlation analysis, and further optimized by combining the sequential forward selection algorithm to retain the key features that contribute most to the prediction of the target attribute.

4. The spinel multi-objective inverse design method based on machine learning and Bayesian optimization algorithm according to claim 3, characterized in that: In the feature screening and dimensionality reduction process, six key features, namely, maximum heat of fusion, tolerance factor, LUMO energy, average number of valence electrons, mean value of space group number, and maximum value of element period difference, are finally retained through pairwise square correlation threshold and sequential forward selection.

5. The spinel multi-objective inverse design method based on machine learning and Bayesian optimization algorithm according to claim 1, characterized in that: In S3, the model training and optimization specifically includes the following steps: Multi-task model configuration and dynamic weight initialization: Based on the key features after S2 dimensionality reduction, a multi-task gradient boosting machine (MTGBM) model framework is constructed. A dynamic weight allocation mechanism is set for the three objectives of band gap value, band gap type, and Ehull. The task weights are dynamically adjusted through the gradient conflict detection function to form the initial multi-objective learning model. Dynamically weighted Pareto hyperparameter collaborative optimization: Within the established MTGBM framework, multi-objective joint optimization of hyperparameters is performed using the Optuna framework. The model structure after dynamic weight assignment is used as the optimization constraint to screen the optimal parameter combination that simultaneously meets the band gap prediction accuracy and Ehull stability requirements during the Pareto frontier process. Model training and validation: The MTGBM model is trained based on the optimized hyperparameters. Its prediction performance on three objectives, namely, band gap value, band gap type, and Ehull, is verified using the AUC, F1 score, and Hamming loss metrics to generate a multi-objective prediction model.

6. The spinel multi-objective inverse design method based on machine learning and Bayesian optimization algorithm according to claim 5, characterized in that: In the process of screening the Pareto front, the MTGBM model assigns a 1.2-fold weight to the band gap value prediction task through a dynamic weight allocation mechanism, and uses Optuna to optimize the regularization coefficient and the number of leaf nodes to screen the optimal hyperparameter combination of the Pareto front.

7. The spinel multi-objective inverse design method based on machine learning and Bayesian optimization algorithm according to claim 1, characterized in that: In S4, the Bayesian inverse design includes the following specific steps: Multi-objective model integration and design space initialization: Based on the multi-objective prediction model MTGBM trained on S3, it is embedded in the Bayesian inverse design framework as the core predictor, and the design space of the spinel chemical formula AB2X4 is expanded to the parameterized form A through the encoder. a B_bX_x(a∈(0,1), b∈(0,2), x∈(0,4)), establishes a candidate material space that can be quantified for search; Surrogate model-driven multi-objective optimization: Using the quantitative search candidate material space as input, a Gaussian process surrogate function is constructed. Combined with the expected hypervolume improvement criterion, three objectives, Eg = 1.1-1.5eV, direct band gap, and Ehull ≤ 0.025eV / atom, are jointly modeled to balance exploration and development through adaptive sampling. Candidate material screening and iterative verification: Based on multi-objective optimization, the MTGBM model is used to impose a penalty function on candidate materials that exceed the Ehull standard, eliminate invalid solutions and generate a set of high-potential materials.

8. The spinel multi-objective inverse design method based on machine learning and Bayesian optimization algorithm according to claim 1, characterized in that: In S4, the process of verifying the performance of the screened materials includes: analyzing the contribution of key features in S2 through the SHAP interpretable model, and combining the doping mechanism with density functional theory to verify the performance of the materials screened in S4, thereby completing the reverse design optimization of the spinel material.

9. An electronic device comprising a memory and a processor, characterized in that: The processor is used to execute the program in the memory to implement the spinel multi-objective inverse design method based on machine learning and Bayesian optimization algorithm as described in any one of claims 1 to 8.

10. A storage medium containing computer-executable instructions, characterized in that: The storage medium of the computer executable instructions is used to execute the spinel multi-objective inverse design method based on machine learning and Bayesian optimization algorithm as described in any one of claims 1 to 8 when executed by a computer processor.

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