High-entropy ceramic feature determination method and device based on multi-objective optimization

Abstract

The invention relates to a high-entropy ceramic feature determination method and device based on multi-objective optimization. The method comprises the following steps: obtaining candidate feature subsets based on feature subsets respectively corresponding to a plurality of pre-obtained performance prediction models of the high-entropy ceramic; determining the sum of decision coefficients R of the plurality of performance prediction models based on the candidate feature subset to obtain a target decision coefficient, and screening the candidate feature subset based on the target decision coefficient by adopting a genetic algorithm to obtain a target feature subset; and reconstructing a plurality of performance prediction models according to the target feature subset to obtain a target function model, and determining a target feature solution set of the target feature subset by adopting a multi-target algorithm based on the target function model. By adopting the method, introduction of a large number of redundant features can be avoided, generalization ability and precision of the multi-target prediction model determined by the target feature subset are guaranteed, and multi-performance optimization requirements can be considered at the same time.

Description

Technical Field

[0001] This application relates to the field of intelligent material design technology, and in particular to a method and apparatus for determining high-entropy ceramic features based on multi-objective optimization. Background Technology

[0002] High-entropy ceramics, as a new type of multi-component material, exhibit unique performance combinations by integrating multiple metallic elements into a single crystal lattice, showing great promise for applications in extreme environments. However, the performance of high-entropy ceramics is influenced by various characteristics such as the average atomic radius difference and valence electron concentration. These characteristics exhibit complex nonlinear relationships, and the contribution of different characteristics to performance indicators (such as hardness and Young's modulus) varies significantly. Therefore, balancing the constraints among these performance indicators is crucial for the optimized design of high-entropy ceramics.

[0003] In existing technologies, a unified feature subset is constructed by directly splicing features, that is, by directly taking the union of the feature sets of multiple performance prediction models. This easily introduces a large number of redundant features, leading to the expansion of the feature subset dimension and causing the "curse of dimensionality". This reduces the generalization ability and accuracy of the multi-objective prediction model determined by the union of the feature sets, making it impossible to meet the needs of multi-performance optimization design of high-entropy ceramics. Summary of the Invention

[0004] Therefore, it is necessary to provide a method and apparatus for determining high-entropy ceramic features based on multi-objective optimization, which can avoid introducing a large number of redundant features, ensure the generalization ability and accuracy of the multi-objective prediction model for determining the target feature subset, and simultaneously take into account the needs of multiple performance optimizations.

[0005] Firstly, this application provides a method for determining high-entropy ceramic features based on multi-objective optimization, including:

[0006] Based on the feature subsets corresponding to multiple performance prediction models of high-entropy ceramics obtained in advance, a candidate feature subset is obtained;

[0007] The sum of the determination coefficients R² of multiple performance prediction models is determined based on the candidate feature subsets to obtain the target determination coefficients. Then, a genetic algorithm is used to screen the candidate feature subsets based on the target determination coefficients to obtain the target feature subset.

[0008] Multiple performance prediction models are reconstructed based on the target feature subset to obtain the objective function model. Then, a multi-objective algorithm is used based on the objective function model to determine the target feature solution set of the target feature subset.

[0009] In one embodiment, the formula for calculating the coefficient of determination R² is:

[0010]

[0011] Where n is the total number of samples, and the samples are determined by a subset of candidate features. It is the true performance value of the i-th sample. Let i be the predicted performance value for the i-th sample. This represents the average of the actual performance values; performance includes hardness and Young's modulus.

[0012] In one embodiment, the multiple performance prediction models include a hardness prediction model and a Young's modulus prediction model; based on the feature subsets corresponding to the multiple performance prediction models of high-entropy ceramics obtained in advance, a candidate feature subset is obtained, including:

[0013] Obtain the first feature subset of the hardness prediction model and the second feature subset of the Young's modulus prediction model;

[0014] The first feature subset and the second feature subset are combined to obtain the candidate feature subset.

[0015] In one embodiment, the target feature subset includes average valence electron concentration, average density, average first ionization energy, carbon-nitrogen ratio, and comprehensive parameters of the sintering method.

[0016] In one embodiment, a genetic algorithm is used to filter candidate feature subsets to obtain a target feature subset based on the target determination coefficient, including:

[0017] The sum of the determination coefficients R² of multiple performance prediction models is used as the fitness function of the genetic algorithm. The target feature subset is obtained by screening the candidate feature subset through selection, crossover, and mutation operations. The population size of the genetic algorithm is set to 30-100 individuals, the crossover probability is set to 0.6-0.9, the mutation probability is set to 0.05-0.2, and the maximum number of iterations is set to 50-200 generations.

[0018] In one embodiment, the multi-objective algorithm employs a second-generation non-dominated sorting genetic algorithm; wherein the population size of the multi-objective algorithm is set to 100, the maximum number of generations is set to 2000, the crossover probability is set to 0.5, and the mutation rate is set to 0.2.

[0019] Secondly, this application also provides a high-entropy ceramic feature determination device based on multi-objective optimization, comprising:

[0020] The first determining module is used to obtain a candidate feature subset based on the feature subsets corresponding to multiple performance prediction models of high-entropy ceramics obtained in advance.

[0021] The filtering module is used to determine the sum of the determination coefficients R² of multiple performance prediction models based on the candidate feature subset, obtain the target determination coefficient, and use a genetic algorithm to filter the candidate feature subset based on the target determination coefficient to obtain the target feature subset;

[0022] The second determination module is used to reconstruct multiple performance prediction models based on the target feature subset, obtain the objective function model, and use a multi-objective algorithm based on the objective function model to determine the target feature solution set of the target feature subset.

[0023] Thirdly, this application also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to perform the following steps:

[0024] Based on the feature subsets corresponding to multiple performance prediction models of high-entropy ceramics obtained in advance, a candidate feature subset is obtained;

[0025] The sum of the determination coefficients R² of multiple performance prediction models is determined based on the candidate feature subsets to obtain the target determination coefficients. Then, a genetic algorithm is used to screen the candidate feature subsets based on the target determination coefficients to obtain the target feature subset.

[0026] Multiple performance prediction models are reconstructed based on the target feature subset to obtain the objective function model. Then, a multi-objective algorithm is used based on the objective function model to determine the target feature solution set of the target feature subset.

[0027] Fourthly, this application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, performs the following steps:

[0028] Based on the feature subsets corresponding to multiple performance prediction models of high-entropy ceramics obtained in advance, a candidate feature subset is obtained;

[0029] The sum of the determination coefficients R² of multiple performance prediction models is determined based on the candidate feature subsets to obtain the target determination coefficients. Then, a genetic algorithm is used to screen the candidate feature subsets based on the target determination coefficients to obtain the target feature subset.

[0030] Multiple performance prediction models are reconstructed based on the target feature subset to obtain the objective function model. Then, a multi-objective algorithm is used based on the objective function model to determine the target feature solution set of the target feature subset.

[0031] Fifthly, this application also provides a computer program product, including a computer program that, when executed by a processor, performs the following steps:

[0032] Based on the feature subsets corresponding to multiple performance prediction models of high-entropy ceramics obtained in advance, a candidate feature subset is obtained;

[0033] The sum of the determination coefficients R² of multiple performance prediction models is determined based on the candidate feature subsets to obtain the target determination coefficients. Then, a genetic algorithm is used to screen the candidate feature subsets based on the target determination coefficients to obtain the target feature subset.

[0034] Multiple performance prediction models are reconstructed based on the target feature subset to obtain the objective function model. Then, a multi-objective algorithm is used based on the objective function model to determine the target feature solution set of the target feature subset.

[0035] The aforementioned method and apparatus for determining features of high-entropy ceramics based on multi-objective optimization includes: obtaining candidate feature subsets based on feature subsets corresponding to multiple performance prediction models of high-entropy ceramics obtained in advance; determining the sum of the determination coefficients R² of multiple performance prediction models based on the candidate feature subsets to obtain target determination coefficients; and using a genetic algorithm to screen the candidate feature subsets based on the target determination coefficients to obtain a target feature subset; reconstructing multiple performance prediction models based on the target feature subsets to obtain an objective function model; and using a multi-objective algorithm based on the objective function model to determine the target feature solution set of the target feature subset. The target feature subset determined by this method avoids introducing a large number of redundant features, ensuring the generalization ability and accuracy of the multi-objective prediction model determined using this target feature subset, effectively solving the problems of feature redundancy and performance degradation of multi-objective prediction models, thereby achieving the goal of simultaneously meeting the requirements of multi-performance optimization design of high-entropy ceramics. Attached Figure Description

[0036] To more clearly illustrate the technical solutions in the embodiments or related technologies of this application, the drawings used in the description of the embodiments or related technologies will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0037] Figure 1 This is an application environment diagram of a high-entropy ceramic feature determination method based on multi-objective optimization in one embodiment;

[0038] Figure 2 This is a flowchart illustrating a high-entropy ceramic feature determination method based on multi-objective optimization in one embodiment.

[0039] Figure 3 This is a schematic diagram illustrating how fitness changes with the number of features during the feature subset selection process in one embodiment;

[0040] Figure 4 Here is a Pareto front distribution diagram from one embodiment;

[0041] Figure 5 R is the model evaluation metric in one embodiment. 2 A comparison diagram;

[0042] Figure 6 This is a structural block diagram of a high-entropy ceramic feature determination device based on multi-objective optimization in one embodiment;

[0043] Figure 7 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0044] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0045] The design of ceramic materials often requires balancing multiple conflicting performance objectives, such as high hardness and a suitable Young's modulus. How to balance the constraints between these performance indicators has become a critical problem to be solved in the design of high-entropy ceramics. With the development of machine learning technology, the combination of balancing the constraints between high-entropy ceramic performance indicators and multi-objective evolutionary algorithms has become an effective means to solve the problem of optimizing multiple material properties. A typical process includes: first, building a predictive model for each performance objective, and then using a multi-objective optimization algorithm to find the Pareto optimal solution set. However, in this process, the fundamental problem of how to construct a feature space suitable for multi-objective optimization has long been neglected.

[0046] In the field of machine learning research, especially when dealing with multi-objective performance optimization problems, effectively combining numerical feature spaces has become a key approach to improving the performance of multi-objective prediction models. However, existing methods all have significant limitations:

[0047] (1) Direct concatenation method: The optimal feature subsets selected independently by each single performance prediction model are directly merged. Although this method is simple to implement, it ignores the scale differences and interaction relationships between the key features of different performance objectives, which leads to the dimensional expansion of the feature subsets, introduces a large number of redundant features and noise, causes the "curse of dimensionality", and ultimately damages the generalization ability of the multi-objective prediction model.

[0048] (2) Linear weighted method: This method aggregates the predicted values ​​of multiple performance prediction models into a single performance prediction model by weighting them with fixed weights. Although it is widely used, its effectiveness depends strictly on the convexity assumption of the Pareto front, and the fixed weight allocation is difficult to adapt to the dynamic changes of different performance trade-offs during the optimization process, which can easily lead to gradient conflicts.

[0049] (3) Bayesian optimization: As a global optimization strategy, it performs well in black box function optimization, but its computational complexity increases sharply when facing high-dimensional feature spaces. The performance of traditional Gaussian processes decreases significantly after the dimension exceeds 20.

[0050] Therefore, this invention addresses the problem of constructing feature subsets in the multi-objective design of high-entropy ceramics by proposing a feature determination method for high-entropy ceramics based on multi-objective optimization. By optimizing the evolution process and technical parameter configuration, it aims to overcome the shortcomings of existing technologies and improve the effect of multi-objective optimization of high-entropy ceramics.

[0051] The multi-objective optimized high-entropy ceramic feature determination method provided in this application embodiment can be applied to, for example... Figure 1 In the application environment shown, terminal 102 communicates with server 104 via a network. A data storage system can store the data that server 104 needs to process. The data storage system can be integrated onto server 104 or placed on a cloud or other network server. Terminal 102 sends a multi-objective optimized high-entropy ceramic feature determination request to server 104. Server 104 receives the request, obtains candidate feature subsets based on the feature subsets corresponding to multiple pre-acquired performance prediction models of high-entropy ceramics, determines the sum of the determination coefficients R² of multiple performance prediction models based on the candidate feature subsets to obtain the target determination coefficient, and uses a genetic algorithm to filter the candidate feature subsets to obtain the target feature subset based on the target determination coefficient. Multiple performance prediction models are updated according to the target feature subset to obtain the objective function model, and a multi-objective algorithm is used based on the objective function model to determine the target feature solution set of multiple sets of target feature subsets. Terminal 102 can be, but is not limited to, various personal computers, laptops, smartphones, tablets, IoT devices, and portable wearable devices. IoT devices can be smart speakers, smart TVs, smart air conditioners, smart vehicle devices, etc. Portable wearable devices can include smartwatches, smart bracelets, and head-mounted devices. Server 104 can be implemented using a standalone server or a server cluster consisting of multiple servers.

[0052] In one exemplary embodiment, such as Figure 2 As shown, a multi-objective optimization method for determining high-entropy ceramic features is provided, which is then applied to... Figure 1 Taking the server in the example, the explanation includes the following steps 202 to 206. Wherein:

[0053] Step 202: Based on the feature subsets corresponding to the multiple performance prediction models of high-entropy ceramics obtained in advance, a candidate feature subset is obtained.

[0054] Among them, the performance prediction model for high-entropy ceramics is a machine learning model based on feature parameters. It is used to predict the physical, mechanical, and thermal properties of ceramics based on these feature parameters. This includes hardness prediction models, Young's modulus prediction models, and thermal property prediction models. The feature subset corresponding to each performance prediction model refers to the set of features selected from all features of each model that are most helpful in predicting the performance of that model. For example, the feature subset corresponding to the hardness prediction model includes average valence electron concentration, average valence electron concentration difference, melting temperature difference, average mass difference, carbon-nitrogen ratio, and comprehensive parameters of the sintering method.

[0055] Optionally, feature subsets corresponding to multiple performance prediction models of high-entropy ceramics can be obtained by searching literature, and the feature subsets corresponding to all performance prediction models can be merged to obtain candidate feature subsets.

[0056] Step 204: Based on the candidate feature subset, determine the sum of the determination coefficients R² of multiple performance prediction models to obtain the target determination coefficient, and use a genetic algorithm to screen the candidate feature subset to obtain the target feature subset based on the target determination coefficient.

[0057] The coefficient of determination (COD) is an indicator used to measure the performance prediction model. It reflects the correlation between the output of the performance prediction model and the actual experimental data. The closer the COD is to 1, the better the performance prediction model reflects the intrinsic mapping relationship between the input features and the performance. In high-entropy ceramic performance prediction, the COD can be determined by comparing the prediction results of the performance prediction model with the actual experimental data.

[0058] For example, the determination coefficient R² of each performance prediction model is determined, the determination coefficients R² of multiple performance prediction models are summed, and the optimization objective is to maximize the sum of the determination coefficients R² of multiple performance prediction models. A genetic algorithm is used to dynamically evolve and screen the candidate feature subset. By controlling the population size, crossover probability and mutation probability parameters of the genetic algorithm, the target feature subset is obtained.

[0059] Step 206: Reconstruct multiple performance prediction models based on the target feature subset to obtain the objective function model, and use a multi-objective algorithm based on the objective function model to determine the target feature solution set of the target feature subset.

[0060] For example, each performance prediction model is retrained based on the selected target feature subset, resulting in reconstructed performance prediction models. This reduces redundant features and improves the generalization ability of the performance prediction models. The reconstructed performance prediction models are then logically or computationally integrated to obtain the objective function model. A multi-objective evolutionary algorithm (such as NSGA-II) is used to search and iterate within the target feature subset. By simultaneously optimizing each performance prediction model, a set of feature combinations that achieve a trade-off between different performance metrics is obtained, i.e., a Pareto optimal solution set for multiple target performance metrics. Optionally, this Pareto optimal solution set may include the specific values ​​of multiple target feature subsets (target feature solution sets).

[0061] Based on the determined Pareto optimal solution set, the objective function model is reconstructed to obtain a multi-objective prediction model. This Pareto optimal solution set can ensure that the multi-objective prediction model has high prediction accuracy on different performance objectives, thus providing a basis for the multi-performance optimization and design of high-entropy ceramics.

[0062] Based on the feature combinations selected from the Pareto optimal solution set, a new prediction model is constructed for each performance index. Each model uses the selected feature set as input variables to predict the value of the corresponding performance index. By comprehensively applying the reconstructed prediction models, synergistic prediction and evaluation of high-entropy ceramics across multiple performance indices can be achieved. Furthermore, based on the prediction results of each performance and their interrelationships, the optimal feature combination is selected to guide the composition design, process parameter control, and material ratio optimization of high-entropy ceramics. This ensures that all performance indices remain at excellent levels, thereby achieving synergistic optimization and performance improvement of the material's multiple properties.

[0063] In the aforementioned method for determining the features of high-entropy ceramics based on multi-objective optimization, candidate feature subsets are obtained based on the feature subsets corresponding to multiple performance prediction models of high-entropy ceramics obtained in advance. The sum of the determination coefficients R² of multiple performance prediction models is determined based on the candidate feature subsets to obtain the target determination coefficient. A genetic algorithm is then used to screen the candidate feature subsets to obtain the target feature subset. This avoids introducing a large number of redundant features, which would lead to feature subset dimensionality expansion and the "curse of dimensionality" problem. Multiple performance prediction models are reconstructed based on the target feature subset to obtain the objective function model. A multi-objective algorithm is then used based on the objective function model to determine the target feature solution set of the target feature subset. This ensures the generalization ability and accuracy of the multi-objective prediction model determined using this target feature subset, effectively solving the problems of feature redundancy and performance degradation of multi-objective prediction models, thereby meeting the requirements of multi-performance optimization design for high-entropy ceramics.

[0064] In an exemplary embodiment, the multiple performance prediction models include a hardness prediction model and a Young's modulus prediction model; based on the feature subsets corresponding to the multiple performance prediction models of high-entropy ceramics obtained in advance, a candidate feature subset is obtained, including: obtaining a first feature subset of the hardness prediction model and a second feature subset of the Young's modulus prediction model; and taking the union of the first feature subset and the second feature subset to obtain the candidate feature subset.

[0065] Optionally, the hardness prediction model is the Vickers hardness prediction model. The first feature subset (Subset_H) of the Vickers hardness prediction model and the second feature subset (Subset_E) of the Young's modulus prediction model are obtained by searching the literature. Subset_H contains 5 features: average valence electron concentration, average valence electron concentration difference, melting temperature difference, average mass difference, carbon-nitrogen ratio, and comprehensive sintering method parameters. Subset_E contains 8 features: carbon-nitrogen ratio, average valence electron concentration, average Pauling electronegativity difference, average first ionization energy, average melting temperature, average radius, average first ionization energy difference, and comprehensive sintering method parameters. The union of Subset_H and Subset_E yields a candidate feature subset containing 11 features: carbon-nitrogen ratio, average valence electron concentration, average Pauling electronegativity difference, average first ionization energy, average melting temperature, average radius, average first ionization energy difference, comprehensive sintering method parameters, average valence electron concentration difference, melting temperature difference, and average mass difference.

[0066] In this embodiment, the feature subsets corresponding to multiple performance prediction models are combined to form a general feature subset containing all key features. This ensures the integrity of multiple performance information, facilitates comprehensive consideration of the mutual constraints between various performances, and thus achieves multi-performance synergistic optimization of high-entropy ceramics.

[0067] In an exemplary embodiment, a genetic algorithm is used to screen candidate feature subsets to obtain a target feature subset based on the target determination coefficient. This includes: using the sum of the determination coefficients R² of multiple performance prediction models as the fitness function of the genetic algorithm, and screening the candidate feature subsets through selection, crossover, and mutation operations to obtain the target feature subset; wherein the population size of the genetic algorithm is set to 30-100 individuals, the crossover probability is set to 0.6-0.9, the mutation probability is set to 0.05-0.2, and the maximum number of iterations is set to 50-200 generations.

[0068] For example, the population size of the genetic algorithm in this embodiment is set to 50 individuals, the crossover probability is set to 0.8, the mutation probability is set to 0.1, and the maximum number of iterations is set to 100 generations. The fitness function of the genetic algorithm is defined as Fitness = Σ(R²_i). Here, R²_i represents the determination coefficient of the i-th target performance prediction model trained using the current target feature subset. Multiple target performances include Vickers hardness and Young's modulus. That is, the fitness function is to maximize the sum of the determination coefficients R² of all performance prediction models. The feature combination is iteratively optimized through selection, crossover, and mutation operations to obtain the target feature subset.

[0069] Specifically, in this embodiment, the binary codes of the 11 candidate feature subsets determined above are iteratively evolved using a genetic algorithm. The goal is to maximize the sum of the determination coefficients R² of the Vickers hardness model and the Young's modulus model, i.e., the fitness function, and finally select the optimal general feature subset (target feature subset) containing 5 core features.

[0070] In the previous exemplary embodiment, the formula for calculating the coefficient of determination R² is:

[0071]

[0072] Where n is the total number of samples, and the samples are determined by a subset of candidate features. It is the true performance value of the i-th sample. Let i be the predicted performance value for the i-th sample. This represents the average of the true performance values; performance includes hardness and Young's modulus. Optionally, the true performance values ​​of the sample can be obtained by searching relevant literature, and the predicted performance values ​​of the sample are determined by the performance prediction model.

[0073] For example, in this embodiment, the screening process for candidate feature subsets is as follows: Figure 3 As shown, when the number of features in the feature subset is 5, the fitness function value of the genetic algorithm reaches its maximum. Subsequently, as the number of features increases, the fitness function value continuously decreases. Finally, the target feature subset determined by the genetic algorithm is: average valence electron concentration, average density, average first ionization energy, carbon-nitrogen ratio, and comprehensive parameters of the sintering method.

[0074] Since the candidate feature subset obtained by combining the feature subsets corresponding to multiple performance prediction models may contain features that have little impact on some performance or duplicate features, leading to the "curse of dimensionality", this embodiment uses the global search capability of genetic algorithms to screen the candidate feature subsets and automatically evolves a concise feature combination (target feature subset) that has high interpretability for multiple performance targets. This effectively overcomes the curse of dimensionality and information redundancy problems of the traditional "direct splicing method", reduces the dimension of the feature space, and retains multiple key performance features.

[0075] In an exemplary embodiment, the multi-objective algorithm employs a second-generation non-dominated sorting genetic algorithm; wherein the population size of the multi-objective algorithm is set to 100, the maximum number of generations is set to 2000, the crossover probability is set to 0.5, and the mutation rate is set to 0.2.

[0076] For example, based on the target feature subset obtained above, the Vickers hardness performance prediction model and the Young's modulus performance prediction model are reconstructed to obtain the objective function model for multi-objective optimization. A multi-objective evolutionary algorithm is then used to solve this model, obtaining a Pareto optimal solution set for multiple objective performances. Preferably, the NSGA-II algorithm is used for multi-objective optimization, with the following parameters set: population size 100, maximum number of generations 2000, crossover probability 0.5, and mutation rate 0.2.

[0077] In this embodiment, a multi-objective algorithm is adopted based on the objective function model to determine the target feature solution set of the target feature subset. This can improve the generalization ability and prediction accuracy of the multi-objective prediction model determined by the target feature subset, effectively solve the problems of feature redundancy and performance degradation of the multi-objective prediction model, and thus achieve the requirement of balancing the multi-performance optimization design of high-entropy ceramics.

[0078] In one exemplary embodiment, to verify the effectiveness of the Pareto front, this invention retrieved multiple sets of actual performance data of high-entropy ceramics from relevant literature as verification points. For example... Figure 4 As shown, most of these verification points are located within the Pareto front obtained by the method of this invention, indicating that this invention can effectively predict the performance limits of real materials. The verification data are as follows:

[0079]

[0080] In comparison, Figure 4 The Pareto fronts obtained from the comparative examples (using the direct splicing method, the linear weighting method, and the Bayesian optimization method) are more discrete and sparse.

[0081] Performance comparison experiments show that the present invention improves the average performance of the multi-objective prediction model compared to the direct splicing method, the linear weighting method, and the Bayesian optimization method. Specifically, the comparison of the model evaluation index R² is shown below. Figure 5 As shown.

[0082] This invention defines the determination of high-entropy ceramic features as a multi-objective optimization problem. Utilizing the global search capability of a genetic algorithm, it automatically evolves a concise feature combination (target feature subset) that has high interpretability for multiple performance objectives, effectively overcoming the dimensionality curse and information redundancy problems of the traditional "direct splicing method." It does not rely on the shape assumption of the Pareto front and does not require manual weighting, avoiding the inherent limitations of the "linear weighting method." By directly optimizing the comprehensive prediction accuracy of the multi-objective model, it ensures the fundamental reliability of the feature space. Compared with traditional methods, the universal feature space (target feature subset) determined by this invention significantly improves the efficiency and quality of multi-objective optimization. Experiments show that the multi-objective prediction model constructed based on the method of this invention has improved comprehensive prediction performance compared to the traditional union method, and the obtained Pareto front distribution is more uniform and has better convergence. Furthermore, by introducing literature verification points, this invention can effectively verify the degree of matching between the Pareto front and actual material properties, enhancing the reliability and practicality of the optimization results. Furthermore, this invention provides a general feature space optimization framework, the ideas of which can be transferred to other material systems or engineering fields involving multi-objective modeling, providing a referable technical path for promoting intelligent design to a new stage of "system optimization".

[0083] It should be understood that although the steps in the flowcharts of the above embodiments are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the above embodiments may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0084] Based on the same inventive concept, this application also provides a device for determining high-entropy ceramic features based on multi-objective optimization to implement the aforementioned method for determining high-entropy ceramic features based on multi-objective optimization. The solution provided by this device is similar to the solution described in the above method. Therefore, the specific limitations of one or more embodiments of the device for determining high-entropy ceramic features based on multi-objective optimization provided below can be found in the limitations of the method for determining high-entropy ceramic features based on multi-objective optimization described above, and will not be repeated here.

[0085] In one exemplary embodiment, such as Figure 6As shown, a high-entropy ceramic feature determination device based on multi-objective optimization is provided, comprising: a first determination module 602, a filtering module 604, and a second determination module 606, wherein:

[0086] The first determining module 602 is used to obtain a candidate feature subset based on the feature subsets corresponding to multiple performance prediction models of high-entropy ceramics obtained in advance.

[0087] The screening module 604 is used to determine the sum of the determination coefficients R² of multiple performance prediction models based on the candidate feature subset, obtain the target determination coefficient, and use a genetic algorithm to screen the candidate feature subset based on the target determination coefficient to obtain the target feature subset.

[0088] The second determining module 606 is used to reconstruct multiple performance prediction models based on the target feature subset, obtain the objective function model, and use a multi-objective algorithm based on the objective function model to determine the target feature solution set of the target feature subset.

[0089] In one exemplary embodiment, the formula for calculating the coefficient of determination R² is:

[0090]

[0091] Where n is the total number of samples, and the samples are determined by the candidate feature subset. It is the true performance value of the i-th sample. Let i be the predicted performance value for the i-th sample. This represents the average of the actual performance values; the performance includes hardness and Young's modulus.

[0092] In an exemplary embodiment, the plurality of performance prediction models include a hardness prediction model and a Young's modulus prediction model; the first determining module 602 is further configured to obtain a first feature subset of the hardness prediction model and a second feature subset of the Young's modulus prediction model; and to perform union processing on the first feature subset and the second feature subset to obtain a candidate feature subset.

[0093] In one exemplary embodiment, the target feature subset includes average valence electron concentration, average density, average first ionization energy, carbon-nitrogen ratio, and comprehensive parameters of the sintering method.

[0094] In an exemplary embodiment, the second determining module 606 is further configured to use the sum of the determination coefficients R² of the multiple performance prediction models as the fitness function of the genetic algorithm, and to obtain a target feature subset by selecting, crossing over, and mutating the candidate feature subset; wherein, the population size of the genetic algorithm is set to 30-100 individuals, the crossover probability is set to 0.6-0.9, the mutation probability is set to 0.05-0.2, and the maximum number of iterations is set to 50-200 generations.

[0095] In an exemplary embodiment, the multi-objective algorithm employs a second-generation non-dominated sorting genetic algorithm; wherein the population size of the multi-objective algorithm is set to 100, the maximum number of generations is set to 2000, the crossover probability is set to 0.5, and the mutation rate is set to 0.2.

[0096] The modules in the aforementioned high-entropy ceramic feature determination device based on multi-objective optimization can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the corresponding operations of each module.

[0097] In one exemplary embodiment, a computer device is provided, which may be a server, and its internal structure diagram may be as follows: Figure 7 As shown, this computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides the environment for the operating system and computer programs in the non-volatile storage media to run. The database stores a subset of candidate features. The I / O interfaces are used for exchanging information between the processor and external devices. The communication interface is used for communicating with external terminals via a network connection. When executed by the processor, the computer program implements a high-entropy ceramic feature determination method based on multi-objective optimization.

[0098] Those skilled in the art will understand that Figure 7 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0099] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps in the above method embodiments.

[0100] In one embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above method embodiments.

[0101] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0102] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments of the above methods. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM). The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0103] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0104] The above embodiments are merely illustrative of several implementation methods of this application, and their descriptions are relatively specific and detailed. However, they should not be construed as limiting the scope of this application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A method for determining high-entropy ceramic features based on multi-objective optimization, characterized in that, The method includes: Based on the feature subsets corresponding to multiple performance prediction models of high-entropy ceramics obtained in advance, a candidate feature subset is obtained; The sum of the determination coefficients R² of multiple performance prediction models is determined based on the candidate feature subset to obtain the target determination coefficient. Based on the target determination coefficient, a genetic algorithm is used to filter the candidate feature subset to obtain the target feature subset. Multiple performance prediction models are reconstructed based on the target feature subset to obtain an objective function model. Based on the objective function model, a multi-objective algorithm is used to determine the target feature solution set of the target feature subset.

2. The method according to claim 1, characterized in that, The formula for calculating the coefficient of determination R² is as follows: Where n is the total number of samples, and the samples are determined by the subset of candidate features. It is the true performance value of the i-th sample. Let i be the predicted performance value for the i-th sample. This represents the average of the actual performance values; the performance includes hardness and Young's modulus.

3. The method according to claim 1, characterized in that, The multiple performance prediction models include a hardness prediction model and a Young's modulus prediction model; the candidate feature subset is obtained by considering the feature subsets corresponding to the multiple performance prediction models of high-entropy ceramics obtained in advance, including: Obtain the first feature subset of the hardness prediction model and the second feature subset of the Young's modulus prediction model; The first feature subset and the second feature subset are combined to obtain the candidate feature subset.

4. The method according to claim 1, characterized in that, The target feature subset includes average valence electron concentration, average density, average first ionization energy, carbon-nitrogen ratio, and comprehensive parameters of the sintering method.

5. The method according to claim 1, characterized in that, The step of using a genetic algorithm to filter the candidate feature subset based on the target determination coefficient to obtain the target feature subset includes: The sum of the determination coefficients R² of multiple performance prediction models is used as the fitness function of the genetic algorithm. The target feature subset is obtained by screening the candidate feature subset through selection, crossover, and mutation operations. The population size of the genetic algorithm is set to 30-100 individuals, the crossover probability is set to 0.6-0.9, the mutation probability is set to 0.05-0.2, and the maximum number of iterations is set to 50-200 generations.

6. The method according to claim 1, characterized in that, The multi-objective algorithm adopts the second-generation non-dominated sorting genetic algorithm; wherein, the population size of the multi-objective algorithm is set to 100, the maximum number of generations is set to 2000, the crossover probability is set to 0.5, and the mutation rate is set to 0.

2.

7. A high-entropy ceramic feature determination device based on multi-objective optimization, characterized in that, The device includes: The first determining module is used to obtain a candidate feature subset based on the feature subsets corresponding to multiple performance prediction models of high-entropy ceramics obtained in advance. The filtering module is used to determine the sum of the determination coefficients R² of multiple performance prediction models based on the candidate feature subset, to obtain the target determination coefficient, and to use a genetic algorithm to filter the candidate feature subset based on the target determination coefficient to obtain the target feature subset; The second determining module is used to reconstruct multiple performance prediction models based on the target feature subset to obtain an objective function model, and to determine the target feature solution set of the target feature subset using a multi-objective algorithm based on the objective function model.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 6.

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

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 6.

Images