Machine learning aided design method for SiBCNZr amorphous ceramic performance prediction and component optimization

Abstract

The invention provides a machine learning aided design method for SiBCNZr amorphous ceramic performance prediction and component optimization, which comprises the following steps: constructing a SiBCNZr multi-component amorphous structure model based on first principle calculation and de novo calculation molecular dynamics, and calculating corresponding binding energy and various mechanical property parameters; constructing a sample data set according to the corresponding binding energy and the various mechanical property parameters; the sample data set is preprocessed, and a SiBCN-Zr data set is obtained; constructing a multi-performance prediction model, and optimizing model parameters according to the SiBCN-Zr data set to obtain an optimal multi-performance prediction model; and the optimal multi-performance prediction model outputs an optimal SiBCNZr ceramic component combination meeting performance requirements. According to the machine learning aided design method for performance prediction and component optimization of the SiBCNZr amorphous ceramic, the efficiency and precision of a multi-component amorphous ceramic material in the aspects of performance prediction, mechanism analysis and component optimization can be remarkably improved, and the machine learning aided design method has wide engineering application value and popularization potential.

Description

Technical Field

[0001] The present invention relates to the field of high-performance amorphous ceramic material design, and in particular to a machine learning-assisted design method for performance prediction and component optimization of SiBCNZr amorphous ceramics. Background Art

[0002] Against the backdrop of the development of hypersonic vehicles, thermal protection systems, and advanced propulsion technologies, the service environment poses unprecedented challenges to the thermal, mechanical, and chemical stability of materials. Traditional oxide or carbide ceramics often face problems such as thermal decomposition, loose structure, and decreased antioxidant performance at extreme temperatures exceeding 1500°C, making it difficult to meet stringent application requirements. Quaternary amorphous ceramic materials represented by SiBCN, due to the dense three-dimensional network structure composed of Si-BCN covalent bonds, not only have low density, high hardness, and excellent high-temperature oxidation resistance (up to 1600-2000°C), but also have thermodynamic stability and ablation resistance far exceeding conventional non-oxide ceramics, making them the core candidate materials for the new generation of high-temperature structural ceramics.

[0003] However, SiBCN ceramics still face critical limitations in practical applications. On the one hand, SiBCN amorphous systems are prone to atomic migration, phase separation, and even partial crystallization at high temperatures approaching 2000°C, affecting their structural integrity. On the other hand, the oxide protective layer formed on their surface is insufficiently stable in complex atmospheres, making it difficult to achieve a sustained and effective antioxidant barrier. Therefore, in recent years, research has gradually shifted to the introduction of transition metal elements with high melting points and strong bond energies to manipulate their structure and properties through chemical doping. Zr (zirconium) is an ideal doping component for constructing ultrahigh-temperature amorphous composite systems because its related ceramics (such as ZrB2, ZrC, and ZrN) have extremely high melting points (>3000°C), excellent high-temperature hardness, and potential antioxidant capacity. It can introduce new strong covalent bonds, such as Zr-C, Zr-N, and Zr-B, into the SiBCN network, improving the system's structural stability and mechanical response at high temperatures.

[0004] Although the SiBCN-Zr system theoretically has broad potential for performance optimization, its structure-performance correlation mechanism has not yet been fully revealed. On the one hand, the amorphous structure lacks long-range order, making it difficult to analyze its atomic-scale local configuration using traditional diffraction techniques. On the other hand, the complex bonding relationships between Zr and elements such as B, C, and N are difficult to track and quantify in situ through experiments. At the same time, the component space of the SiBCNZr system is huge, involving a variety of element ratios and combinations, making experimental screening expensive and inefficient. Therefore, establishing a multi-scale, multi-method integrated research strategy has become the key to promoting performance breakthroughs for this type of material.

[0005] With the rapid development of computational materials science and data-driven methods, first-principles and ab initio molecular dynamics methods have become widely used for amorphous structure modeling and property evaluation. Predictive models based on machine learning have also provided a new paradigm for materials design. The integration of multi-source computational data with machine learning models promises to accurately model complex structure-property relationships while enabling intelligent exploration of the material composition space. Summary of the Invention

[0006] The purpose of the present invention is to provide a machine learning-assisted design method for performance prediction and component optimization of SiBCNZr amorphous ceramics. By systematically constructing an atomic structure model, obtaining key performance parameters, training a high-precision prediction model and introducing a Bayesian optimization algorithm, efficient prediction and directional optimization design of the multi-objective performance of SiBCNZr ceramics can be achieved.

[0007] To achieve the above objectives, the present invention provides a machine learning-assisted design method for performance prediction and composition optimization of SiBCNZr amorphous ceramics, comprising the following steps:

[0008] Based on first-principles calculations and ab initio molecular dynamics, a SiBCNZr multi-component amorphous structure model was constructed, and the corresponding binding energy and various mechanical properties were calculated.

[0009] Construct a sample data set based on the corresponding binding energy and various mechanical property parameters;

[0010] Preprocess the sample data set to obtain the SiBCN-Zr data set;

[0011] Construct a multi-performance prediction model, optimize the model parameters based on the SiBCN-Zr dataset, and obtain the optimal multi-performance prediction model;

[0012] The optimal multi-performance prediction model outputs the optimal SiBCNZr ceramic component combination that meets the performance requirements.

[0013] Preferably, the sample data set includes atomic structure properties, electronic structure and valence electron information, thermodynamic and energy band properties, magnetic and crystallographic characteristics.

[0014] Preferably, a SiBCNZr multi-component amorphous structure model is constructed based on first-principles calculations and ab initio molecular dynamics, and the corresponding binding energy and various mechanical property parameters are calculated, including the following steps:

[0015] The initial crystal structure model of SiBCNZr was constructed according to the set elemental composition, and the geometry of the initial crystal structure model was optimized using the DFT method to obtain the stable structure with the lowest energy.

[0016] AIMD simulation was applied to the optimized structure. The system was heated to 5000K using NVT ensemble and kept at this temperature for a certain period of time before being rapidly cooled to 300K to simulate the amorphization evolution process.

[0017] The formed amorphous structure is optimized for energy minimization, and the total energy is calculated under different volume conditions to determine the thermodynamically optimal configuration;

[0018] The binding energy of the formed amorphous structure is calculated to evaluate the thermodynamic stability of the structure. The binding energy expression is:

[0019] E c =E t -∑n i μ i ;

[0020] Among them, E t is the total energy of each SiBCNZr compound, μ i is the atomic chemical potential of compound i, n i is the number of atoms of the element in the supercell, i includes the elements Si, B, C, N, and Zr;

[0021] Calculation of elastic constant tensor c based on DFT ij , combined with the Voigt-Reuss-Hill averaging method to solve the bulk modulus, shear modulus and Young's modulus, and combined with classical elasticity theory to further obtain Poisson's ratio and Vickers hardness, providing basic calculation data support for subsequent multi-performance data set construction and machine learning modeling.

[0022] Preferably, construct an objective function including

[0023] The SHAP analysis method is used to quantify the marginal contribution of each component descriptor in different target performance outputs, support multi-target performance interpretation, and reveal the positive and negative contribution direction and relative importance of different component features to target performance;

[0024] The Bayesian optimization process randomly generates initial component samples within the set parameter space, combines them with the trained machine learning model to predict target performance, and gradually iterates sampling based on the expected utility function to achieve a global exploration of the optimal component combination.

[0025] The optimization objective can be a single performance or multiple performance joint constraints to achieve personalized goal-oriented design.

[0026] Preferably, constructing a multi-performance prediction model includes the following steps:

[0027] The feature-screened dataset is divided into a training set and a test set in an 80:20 ratio;

[0028] Bayesian optimization strategies (such as hyper_opt) are used to search for hyperparameters of various regression algorithms, with the five-fold cross-validation error as the model performance indicator;

[0029] Select the model with the best performance on the test set from the candidate models. The evaluation indicators include mean absolute error (MAE), mean square error (MSE), and coefficient of determination (R). 2 .

[0030] Preferably, the model parameters are optimized based on the SiBCN-Zr dataset, including

[0031] Randomly extract samples from the sample dataset with replacement to generate multiple sub-datasets. The size of each sub-dataset is the same as the original dataset, but samples are allowed to be repeated.

[0032] When each decision tree node splits, some features are randomly selected as candidate split features;

[0033] At each node, the optimal split point is selected based on the principle of minimizing the mean square error (MSE);

[0034] Repeat the above splitting process until the stopping condition is met (such as the tree reaches the maximum depth, the number of node samples is less than the threshold, etc.), and generate multiple independent regression trees;

[0035] For a new input sample, each decision tree independently predicts a value, and the final result is the mean of the predictions of all trees;

[0036] By averaging multiple trees, the variance of single tree predictions is reduced, and the model's robustness to noise and outliers is improved.

[0037] Therefore, the present invention adopts the above-mentioned machine learning-assisted design method for SiBCNZr amorphous ceramic performance prediction and component optimization, and the technical effects are as follows:

[0038] (1) By introducing first-principles calculations and ab initio molecular dynamics methods, we systematically constructed multiple sets of SiBCNZr amorphous structure models and evaluated their binding energies and mechanical properties, achieving high-precision calculations of structural configurations and multiple performance parameters.

[0039] (2) Combining computational results with literature information, a training sample set integrating Magpie descriptors was constructed, and a prediction model was established using multiple machine learning algorithms, significantly improving the prediction accuracy of target performance. The SHAP interpretability method was used to quantitatively identify key descriptors, clarifying the primary control mechanisms of the physicochemical properties of various elements on properties such as binding energy, elastic modulus, and hardness, thus enhancing the physical explanatory power of the model.

[0040] (3) Based on the constructed prediction model and Bayesian optimization strategy, a multi-objective performance-oriented SiBCNZr ceramic component design method was proposed, which can achieve a reverse search for a specific Young's modulus target value while meeting the thermodynamic stability, greatly improving the component optimization efficiency and having good engineering adaptability. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 A flowchart of a machine learning-assisted design method for property prediction and composition optimization of SiBCNZr amorphous ceramics.

[0042] Figure 2 The configuration diagram of the amorphous model obtained based on DFT and AIMD calculations in the present invention; Figure 2 (a) is SiBCN; Figure 2 (b) is Si2B3C3NZr; Figure 2 (c) is Si2B7C3NZr3; Figure 2 (d) is Si3B8C4N2Zr3; Figure 2 (e) is Si3B 11 C4N3Zr4; Figure 2 (f) is Si 30 B5C 20 N9; Figure 2 (g) is Si4BC2N; Figure 2 (h) is Si4BC2N3; Figure 2 (i) is Si7B3C4N6;

[0043] Figure 3 It is the density distribution diagram of each target parameter in the machine learning data set of the present invention; Figure 3 (a) is the binding energy Ec; Figure 3 (b) is the bulk modulus B; Figure 3 (c) is the shear modulus G; Figure 3 (d) is Young's modulus E; Figure 3 (e) is the Vickers hardness Hv; Figure 3 (f) is Poisson's ratio ν;

[0044] Figure 4 is the Pearson correlation graph between any two features after feature removal in the (binding energy dataset) of the present invention;

[0045] Figure 5 A comparison chart of the prediction performance of different machine learning models in the present invention (binding energy dataset); Figure 5 (a) MSE and MAE values of each regression model; Figure 5 (b) is the R of each regression model 2 value;

[0046] Figure 6 This is the fitting diagram of the best performing model in the present invention in different target performance predictions: Figure 6 (a) is the binding energy Ec; Figure 6 (b) Bulk modulus B; Figure 6 (c) shear modulus G; Figure 6 (d) Young's modulus E; Figure 6 (e) Vickers hardness Hv; Figure 6 (f) Poisson's ratio ν;

[0047] Figure 7 is the SHAP value distribution of each feature in the binding energy dataset of the present invention. DETAILED DESCRIPTION

[0048] The technical solution of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0049] Unless otherwise defined, technical or scientific terms used in the present invention shall have the same meaning as commonly understood by one of ordinary skill in the art to which the present invention belongs.

[0050] Example 1

[0051] like Figure 1 As shown, a machine learning-assisted design method for performance prediction and composition optimization of SiBCNZr amorphous ceramics includes the following steps:

[0052] S1. Construct amorphous structures and evaluate properties based on first principles and ab initio molecular dynamics:

[0053] The present invention first performs geometric optimization of the crystal structure based on density functional theory (DFT), employing the PBE functional combined with the projected augmented plane wave (PAW) method to describe electron-ion interactions to ensure structural convergence. Subsequently, ab initio molecular dynamics (AIMD) simulations are performed on the optimized crystal structure. Heat treatment at 5000 K disrupts the initially ordered structure, followed by rapid cooling to 300 K to form a stable amorphous structure in the NVT ensemble.

[0054] The obtained amorphous structure was further subjected to static geometry optimization to obtain the most thermodynamically stable configuration, such as Figure 2 Based on the optimized model, the total energy of the system is calculated to obtain the binding energy, and the elastic constant tensor c is solved through the stress-strain response. ij , and then calculate the bulk modulus (B), shear modulus (G), Young's modulus (E), Poisson's ratio (ν) and Vickers hardness (Hv), providing multi-objective performance data support for subsequent machine learning.

[0055] S2. Build a training sample set and extract Magpie descriptors:

[0056] The binding energy and mechanical property data calculated above were integrated with selected literature data to establish a training dataset. For descriptor extraction, the Magpie descriptor extraction tool was used to characterize the physicochemical properties of each component. The extracted features included, but were not limited to, statistical quantities such as atomic radius, melting point, first ionization energy, number of valence electrons, atomic volume, energy band width, and filled state density. The mean, range, standard deviation, and dispersion of these features were calculated and ultimately used as model input variables.

[0057] S3. Data preprocessing and feature screening:

[0058] The data preprocessing process was systematically preprocessed, including key steps such as outlier removal, constant feature deletion, feature normalization, and feature dimensionality reduction to minimize the impact of potential bias on the prediction model.

[0059] Step 1: Draw the target variable distribution graph and kernel density estimation curve, and use the box plot to identify and eliminate outlier samples with significant deviation from the trend. Figure 3 is the density distribution of each target parameter;

[0060] Step 2: Remove Magpie features whose values are constant across all samples to avoid invalid effects on the model;

[0061] Step 3: Use the MinMaxScaler method to normalize the remaining numerical features. The normalization formula is as follows:

[0062]

[0063] Among them, X new is the normalized value obtained after MinMaxScaler; X is the original data from the dataset; X max and X min are the maximum and minimum values of the data set respectively;

[0064] Step 4: Calculate the Pearson correlation coefficient between any two features, and use |ρ|>0.9 as the threshold to identify feature pairs with strong linear correlation, and only retain one representative feature. Take the dataset with binding energy as an example, Figure 4 is the Pearson correlation graph between any two features after feature removal. The linear correlation calculation formula is as follows:

[0065]

[0066] Among them, X i With X j For two sets of data features, and The data Xi and data X j The mean of The data X i The standard deviation of The data X j The standard deviation of cov(X i , X j ) is the variable X i and X j The covariance of .

[0067] The Pearson correlation coefficient ranges from -1 to 1; negative values indicate negative correlation, positive values indicate positive correlation, and an absolute value close to 1 indicates a significant linear correlation.

[0068] Table 1 Names and meanings of features retained after feature elimination

[0069]

[0070]

[0071] S4. Multi-objective performance prediction model construction and SHAP analysis:

[0072] Based on the filtered feature data, a variety of mainstream supervised learning regression models (including linear regression, random forest, gradient boosting tree, XGBoost, etc.) are used for training. The parameters are adjusted by Bayesian optimization algorithm, and the MAE, MSE and R 2 As an evaluation index to evaluate the prediction accuracy of each model. The formula is:

[0073]

[0074] Where N is the number of samples, f i is the predicted value, y i is the exact value, is the average value of the accurate value. MAE is the average value of the absolute difference between the predicted value and the actual value, and MSE is the average square difference between the predicted value and the actual value. The smaller the two parameters are, the better the model performance is. 2 The value range of is 0 to 1, and higher values (closer to 1) indicate that the model fits the input data better.

[0075] In this example, the kernel ridge regression model (KRR) shows the best prediction performance on the binding energy dataset (Ec), as shown in Figure 5 As shown in Figure 2, the KRR model achieves the lowest values in both MSE and MAE, and R 2 The value is the highest. Among the other output features, the best performing models are mainly concentrated in integrated algorithms such as RF and XGB. The fitting diagram of the best performing model in different target performance predictions is shown in the figure below. Figure 6 shown.

[0076] The SHAP (Shapley Additive Explanations) algorithm was further introduced to perform global and local interpretability analysis on the trained optimal machine learning model. The results showed that atomic volume, number of valence electrons, melting point, and filling state density are the main controlling features affecting binding energy and Young's modulus. This analysis clarified the role of elements such as Si, B, C, N, and Zr in regulating the structural stability and mechanical rigidity of the material. Figure 7 is the SHAP value distribution of each feature in the binding energy dataset.

[0077] S5. Component inverse design based on Bayesian optimization:

[0078] By randomly generating initial component samples within the set parameter space, combining the trained machine learning model to predict target performance, and gradually iterating sampling based on the expected utility function, a global exploration of the optimal component combination is achieved.

[0079] In this example, the search targets SiBCNZr ceramics with a Young's modulus closest to 139 GPa, where the content range of the five elements is limited to Si 30-60 B 1-15 C 15-30 N 5-30 Zr 0-30 By constructing initial sampling points within a set space, a Bayesian optimization strategy was employed, with the expected improvement function employed to continuously iteratively optimize the predicted results, ultimately finding the optimal component configuration that met the performance requirements. Optimization results showed that when the Zr content was zero, the system's binding energy and Young's modulus were closer to the target values. However, when the Zr content was restricted to ≥1%, although Zr enhanced the rigidity and the Young's modulus increased to 159 GPa, the deviation from the target value was significant, verifying the rationality of the algorithm's output and the physical significance of the predictions.

[0080] Therefore, the present invention adopts the above-mentioned machine learning-assisted design method for SiBCNZr amorphous ceramic performance prediction and component optimization. By constructing and optimizing multiple groups of amorphous structure models based on density functional theory and ab initio molecular dynamics, the system obtains thermodynamic and mechanical property data, and constructs a training data set in combination with Magpie descriptors to further establish a high-precision performance prediction model. On this basis, a Bayesian optimization algorithm is introduced to perform a global search of the set component space, and the optimal component combination that meets multiple performance constraints is output. This method has both theoretical rigor and engineering practicality, can significantly improve the design efficiency and prediction accuracy of complex ceramic materials, and provide a reliable theoretical basis and technical path for amorphous ceramic performance regulation and structural optimization.

[0081] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A machine learning-assisted design method for performance prediction and component optimization of SiBCNZr amorphous ceramics, characterized in that: The following steps are involved: Based on first-principles calculations and ab initio molecular dynamics, a multi-component amorphous structure model of SiBCNZr was constructed, and the corresponding binding energy and various mechanical properties were calculated. Construct a sample data set based on the corresponding binding energy and various mechanical property parameters; Preprocess the sample data set to obtain the SiBCN-Zr data set; Construct a multi-performance prediction model, optimize the model parameters based on the SiBCN-Zr dataset, and obtain the optimal multi-performance prediction model; The optimal multi-performance prediction model outputs the optimal SiBCNZr ceramic component combination that meets the performance requirements.

2. A machine learning-assisted design method for performance prediction and component optimization of SiBCNZr amorphous ceramics according to claim 1, characterized in that: Sample datasets include atomic structure properties, electronic structure and valence electron information, thermodynamic and energy band properties, magnetic and crystallographic features.

3. The machine learning-assisted design method for performance prediction and component optimization of SiBCNZr amorphous ceramics according to claim 1, characterized in that: A SiBCNZr multi-component amorphous structure model was constructed based on first-principles calculations and ab initio molecular dynamics, and the corresponding binding energy and various mechanical property parameters were calculated, including the following steps: The initial crystal structure model of SiBCNZr was constructed according to the set elemental composition, and the geometry of the initial crystal structure model was optimized using the DFT method to obtain the stable structure with the lowest energy. AIMD simulation was applied to the optimized structure. The system was heated to 5000K using NVT ensemble and kept at this temperature for a certain period of time before being rapidly cooled to 300K to simulate the amorphization evolution process. The formed amorphous structure is optimized for energy minimization, and the total energy is calculated under different volume conditions to determine the thermodynamically optimal configuration; The binding energy of the formed amorphous structure is calculated to evaluate the thermodynamic stability of the structure. The binding energy expression is: AND c =And t -∑n i μ i ; Among them, E t is the total energy of each SiBCNZr compound, μ i is the atomic chemical potential of compound i, n i is the number of atoms of the element in the supercell, i includes the elements Si, B, C, N, and Zr; Calculation of elastic constant tensor c based on DFT ij , combined with the Voigt-Reuss-Hill averaging method to solve the bulk modulus, shear modulus and Young's modulus, and combined with classical elasticity theory to further obtain Poisson's ratio and Vickers hardness, providing basic calculation data support for subsequent multi-performance data set construction and machine learning modeling.

4. A machine learning-assisted design method for performance prediction and component optimization of SiBCNZr amorphous ceramics according to claim 1, characterized in that: Construct the objective function, including The SHAP analysis method is used to quantify the marginal contribution of each component descriptor in different target performance outputs, support multi-target performance interpretation, and reveal the positive and negative contribution direction and relative importance of different component features to target performance; The Bayesian optimization process randomly generates initial component samples within a set parameter space, combines them with a trained machine learning model to predict target performance, and then iterates the sampling step by step based on the expected utility function to achieve a global exploration of the optimal component combination. The optimization goal is a single performance or multiple performance joint constraints to achieve personalized goal-oriented design.

5. The machine learning-assisted design method for performance prediction and component optimization of SiBCNZr amorphous ceramics according to claim 1, characterized in that: Building a multi-performance prediction model includes the following steps: The feature-screened dataset is divided into a training set and a test set in an 80:20 ratio; Bayesian optimization strategy is used to search for hyperparameters of various regression algorithms, with 50% cross-validation error as the model performance indicator; Select the model with the best performance on the test set from the candidate models. The evaluation indicators include mean absolute error (MAE), mean square error (MSE), and coefficient of determination (R). 2 .

6. The machine learning-assisted design method for performance prediction and component optimization of SiBCNZr amorphous ceramics according to claim 1, characterized in that: Optimize model parameters based on SiBCN-Zr dataset, including Randomly extract samples from the sample dataset with replacement to generate multiple sub-datasets. The size of each sub-dataset is the same as the original dataset, but samples are allowed to be repeated. When each decision tree node splits, some features are randomly selected as candidate split features; At each node, the optimal split point is selected based on the principle of minimizing the mean square error (MSE); Repeat the above splitting process until the stopping condition is met to generate multiple independent regression trees; For a new input sample, each decision tree independently predicts a value, and the final result is the mean of the predictions of all trees; By averaging multiple trees, the variance of single tree predictions is reduced, and the model's robustness to noise and outliers is improved.

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