A material composition design method based on feature gradient

Abstract

The application belongs to the technical field of material science, and discloses a material composition design method based on feature gradient, which calculates the gradient of a performance function with respect to material composition in an end-to-end differentiable calculation model from material composition to material features, to a Gaussian process regression model prediction, and finally to the performance function value; maximizes the performance function based on the gradient of the material composition to obtain material composition optimization results; obtains performance experimental results of the material composition optimization results, adds the performance experimental results to a training data set of the end-to-end differentiable calculation model, updates the end-to-end differentiable calculation model; and selects the material composition with the best experimental result from all the material composition optimization results, and takes the material composition as the final composition of the material. The application can greatly improve the efficiency of material composition design.

Description

Technical Field

[0001] This invention belongs to the field of materials science and technology, and specifically relates to a material composition design method based on feature gradients. Background Technology

[0002] With the rapid development of materials science and artificial intelligence, materials informatics methods, especially Bayesian optimization (BO), have become powerful tools for accelerating the design of new material compositions. Due to its high efficiency, lack of need for large amounts of training data, and ease of implementation, Bayesian optimization is widely used in the development of advanced materials such as high-entropy alloys, metallic glasses, electronic ceramics, and perovskites. In the material composition design process, Bayesian optimization balances exploration and utilization by defining an acquisition function (AF) that includes the predicted mean and uncertainty, thereby screening for the best candidate materials. However, as the number of material components increases, the composition space grows rapidly exponentially, posing a significant challenge to traditional acquisition function maximization methods.

[0003] Current mainstream material composition design work mainly relies on exhaustively enumerating the entire design space to identify optimal candidate materials. This method becomes computationally too complex and impractical as the number of components increases. For example, in the design of high-entropy alloys, the possible combinations of components exceed 10^ 10 The number of possibilities far exceeds the capabilities of current computing power. Furthermore, a common practice in materials informatics is to convert raw compositions into material features to improve the performance of machine learning models, but these conversions also complicate the definition and propagation of gradients. While some research has attempted to optimize performance functions using gradient methods, applying gradients to end-to-end processes involving feature engineering remains technically challenging, forcing many studies to employ enumeration or heuristic methods, which are inefficient and make it difficult to explore large design spaces. Therefore, developing a method that can efficiently utilize feature gradients to maximize performance functions has significant theoretical and practical value for accelerating material composition design, reducing experimental costs, and expanding the feasible design space. Summary of the Invention

[0004] To address the shortcomings of the existing technology, the present invention aims to provide a material composition design method based on feature gradients, which can greatly improve the efficiency of material composition design.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A material composition design method based on feature gradients includes the following process:

[0007] The gradient of the efficiency function with respect to the material composition is calculated in the pre-established end-to-end differentiable calculation model, which ranges from material composition to material characteristics, then to Gaussian process regression model prediction, and finally to efficiency function value.

[0008] Based on the gradient of material composition, the efficiency function is maximized to obtain the material composition optimization result;

[0009] Obtain the performance experimental results of the material composition optimization results, add the performance experimental results to the training dataset of the end-to-end differentiable computation model, and update the end-to-end differentiable computation model;

[0010] The material composition with the best experimental results is selected from all the material composition optimization results, and this material composition is taken as the final composition of the material.

[0011] Preferably, the training process of the Gaussian process regression model includes:

[0012] Obtain experimental datasets of material composition and corresponding properties, and establish a composition and property training database;

[0013] The material composition in the database is converted into material features using a feature transformation function; wherein, the feature transformation function combines the elemental properties of the material with the mole fraction to generate material features;

[0014] Based on the material characteristics and the corresponding material performance data in the database, a Gaussian process regression model is trained to obtain a well-trained Gaussian process regression model.

[0015] When establishing the end-to-end differentiable computational model, an end-to-end differentiable computational model is established, which starts from material composition, material characteristics, and then to the prediction of a trained Gaussian process regression model, and finally to the performance function value.

[0016] Preferably, the gradient of the performance function with respect to the material composition is calculated using a numerical differential method.

[0017] Preferably, the numerical differentiation method employs an automatic differentiation framework based on PyTorch.

[0018] Preferably, the efficiency function is maximized using an optimization algorithm based on the gradient of material composition.

[0019] Preferably, the optimization algorithm employs a sequential least squares programming method.

[0020] Preferably, the initial material composition is generated using a rejection sampling method when maximizing the efficiency function based on the gradient of the material composition.

[0021] Preferably, the Gaussian process regression model uses the Matern 2.5 kernel function.

[0022] Preferably, the performance function is an expected improvement function, an improvement probability function, or a confidence upper bound function.

[0023] The present invention also provides a material composition design system based on feature gradients, used to implement the material composition design method based on feature gradients described above. The system includes:

[0024] The gradient calculation module is used to calculate the gradient of the efficiency function with respect to the material composition in a pre-established end-to-end differentiable calculation model that goes from material composition to material characteristics, then to Gaussian process regression model prediction, and finally to efficiency function value.

[0025] Composition optimization module: used to maximize the efficiency function based on the gradient of material composition to obtain the material composition optimization result;

[0026] Model update module: Used to obtain the performance experimental results of the material composition optimization results, add the performance experimental results to the training dataset of the end-to-end differentiable computation model, and update the end-to-end differentiable computation model;

[0027] The screening module is used to select the material composition with the best experimental results from all the material composition optimization results, and use this material composition as the final composition of the material.

[0028] The present invention has the following beneficial effects:

[0029] This invention significantly improves the efficiency of material composition design by utilizing the characteristic gradient optimization process to maximize the efficiency function in Bayesian optimization. Compared to traditional exhaustive enumeration methods, this invention reduces the complexity of the internal optimization problem from a rapid polynomial increase with the number of components to an experimentally observed linear relationship, making it possible to explore ultra-large-scale design spaces. This reduction in complexity is particularly advantageous in the composition design of multi-component materials such as high-entropy alloys, ceramics, and perovskites, and can handle problems exceeding 10^... 10 The design space for possible combinations of components.

[0030] This invention establishes an end-to-end differentiable computational process from raw material composition to material characteristics, then to model prediction, and finally to the performance function value, overcoming the technical bottleneck of integrating feature engineering and gradient optimization in materials informatics. By using numerical differentiation techniques to calculate the gradient of the performance function relative to the material composition, it enables efficient use of gradient information to guide the composition optimization process. This method not only accelerates the Bayesian optimization process but also reduces the number of experiments, significantly lowering the cost and time of materials research and development.

[0031] This invention employs a random initial component sampling strategy, promoting a more diverse solution space exploration and effectively avoiding the component concentration problem common in traditional methods. Experimental results show that the component state entropy obtained by this method decays more slowly, demonstrating the diversity of its exploration space. This characteristic is significant for discovering new material formulations, helping researchers discover potential high-performance materials in a broader component space. This invention is highly flexible and scalable; by adjusting key hyperparameters, such as the number of initial components, the choice of performance function, the surrogate model type, and the feature calculation formula, it can be customized and optimized according to the characteristics of different material systems. This modular design allows the method to be easily transferred to different material design problems, providing a general optimization framework for the field of materials informatics.

[0032] Furthermore, this invention can form a closed-loop optimization process with material preparation and characterization experiments, where the results of each round of experiments can be fed back into the model for updates, continuously improving prediction accuracy. This human-machine collaborative material design approach greatly accelerates the material development process, providing a powerful tool for the rapid discovery and optimization of new materials, and has significant practical application value in promoting the research and development of high-performance materials. Attached Figure Description

[0033] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this application, do not constitute an undue limitation of the invention. In the drawings:

[0034] Figure 1 This is a schematic diagram of the overall process of the material composition design method based on feature gradient of the present invention.

[0035] Figure 2 This is a schematic diagram comparing the impact of different performance functions (UCB, POI, and EI) on optimization performance in embodiments of the present invention.

[0036] Figure 3 This diagram illustrates a comparison of computation time between the feature gradient-based method and the traditional exhaustive search method under different numbers of components, according to an embodiment of the present invention.

[0037] Figure 4 This is a schematic diagram comparing the prediction performance of the machine learning model when directly using the original components and when using the transformed material features as input in an embodiment of the present invention.

[0038] Figure 5 This is a box plot showing the impact of the initial number of random components on the final optimization result in an embodiment of the present invention.

[0039] Figure 6 This represents the trend and standard deviation of the mean of the final performance index as the initial component quantity increases in the embodiments of the present invention. Detailed Implementation

[0040] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. The illustrative embodiments and descriptions of the present invention are used to explain the present invention, but are not intended to limit the present invention.

[0041] Reference Figure 1 The present invention provides a material composition design method based on feature gradients, comprising the following steps:

[0042] Obtain experimental datasets of material composition and corresponding properties, and establish a composition and property training database;

[0043] The material composition in the database is transformed into material features through a feature transformation function, which combines elemental properties with mole fraction to generate material features.

[0044] Based on the material characteristics and the corresponding performance data in the database, a Gaussian Process Regression (GPR) model is trained.

[0045] Establish an end-to-end differentiable calculation model that goes from material composition to material characteristics, then to Gaussian process regression model prediction, and finally to the performance function value;

[0046] The gradient of the efficiency function with respect to the material composition is calculated using numerical differentiation methods;

[0047] Based on the gradient of material composition, the efficiency function is maximized using an optimization algorithm to obtain the optimized result of material composition;

[0048] The optimal material composition was verified by performance experiments, and the experimental results were added to the training dataset for end-to-end differentiable computation model updates.

[0049] The material composition with the best experimental results is selected from all the material composition optimization results, and this material composition is taken as the final composition of the material.

[0050] In the above-described scheme of the present invention, the data processing procedure of the feature transformation function includes:

[0051] The calculation is based on the weighted average of the characteristics of each element in the periodic table, including the atomic radius, the number of valence electrons, and electronegativity.

[0052] Maximum and minimum value operations based on element properties are used to capture the extreme value characteristics of the constituent elements;

[0053] It is calculated based on the differences and ratios between the constituent elements and is used to characterize the interaction properties between elements.

[0054] In the above-described scheme of the present invention, the Gaussian process regression model adopts the Matern 2.5 kernel function, and its mathematical expression is as follows:

[0055]

[0056] Where r represents the Euclidean distance between the two points, l is the length scale parameter, and σ 2 This is the variance parameter.

[0057] In the above-described scheme of the present invention, the performance function includes:

[0058] The Expected Improvement (EI) function is used to balance exploration and exploitation.

[0059] The Probability of Improvement (POI) function focuses on regions with high probability of improvement.

[0060] Alternatively, the Upper Confidence Bound (UCB) function balances exploration and exploitation through weighted mean and uncertainty.

[0061] In the above-described scheme of the present invention, the numerical differentiation method adopts an automatic differentiation framework based on PyTorch, and its process includes:

[0062] The gradient of the performance function is calculated using posterior sample reparameterization techniques.

[0063] The end-to-end gradient from material composition to performance function value is calculated using the chain rule;

[0064] Gradient calculation is achieved using a forward computation graph and backward gradient propagation.

[0065] In the above-described scheme of the present invention, the optimization algorithm employs the Sequential Least Squares Programming (SLSQP) method, the process of which includes:

[0066] Supports linear constraint handling to ensure that the total mole fraction of components is 100%;

[0067] Consider additional constraints such as elemental composition limitations;

[0068] The Hessian matrix is ​​approximated using the quasi-Newton method, which improves convergence efficiency.

[0069] In the above-described scheme of the present invention, when maximizing the efficiency function using an optimization algorithm based on the gradient information, the initial material composition is generated using a rejection sampling method. The process of generating the initial material composition using the rejection sampling method includes:

[0070] Randomly generate candidate components that satisfy the condition that the total component value is 100%;

[0071] Effective ingredients are screened based on elemental composition and other constraints.

[0072] Ensure that the initial components are evenly distributed within the feasible design space.

[0073] In the above-described scheme of the present invention, the Bayesian optimization process is as follows:

[0074] The optimization process is initiated simultaneously from multiple random initial components;

[0075] Parallel search can be performed using different performance function definitions or different random seeds;

[0076] By combining the results of multiple optimizations, more diverse optimal ingredient recommendations are obtained.

[0077] In the above-described solution of the present invention, the optimization results are verified through experimental testing, including:

[0078] The recommended optimal composition was used for material preparation and performance testing;

[0079] The test results are compared with the prediction performance, and the prediction error is calculated.

[0080] The Gaussian process regression model is updated based on the newly added experimental data to improve the accuracy of subsequent predictions.

[0081] Example

[0082] Please refer to Figure 1 The material composition design method based on feature gradient in this embodiment includes the following steps:

[0083] Step 1: Perform differentiable feature transformation on the components;

[0084] Specifically, this embodiment uses a feature transformation function ε(·) to convert the original material composition c into material features. In materials informatics, the original elemental composition is usually not directly used as input to a machine learning model, but rather transformed into feature descriptors that better characterize the material properties through feature engineering. The feature transformation function used in this embodiment combines elemental features with mole fractions to generate a series of material features, including weighted average, maximum, and minimum value operations on elemental properties. For example, for an alloy composed of multiple elements, features such as average atomic radius, average valence electron number, and average electronegativity are calculated, which can more accurately characterize the physical and chemical properties of the material.

[0085] Specifically, the feature transformation function in this embodiment is fully differentiable, which ensures the end-to-end gradient calculation from material composition to performance function. To achieve this, this embodiment performs an approximate transformation of the feature transformation function; the approximate functions for the argmax / argmin function and the non-zero filtering function are as follows:

[0086] w = softmax(τ·x)

[0087] mask = sigmoid(τ·(c-ε))

[0088] We also implemented the feature transformation function ourselves using the PyTorch framework and ensured that all operations (such as weighted average and maximum / minimum value calculation) are differentiable.

[0089] Step 2: Construct a Gaussian process regression model and calculate the predicted values;

[0090] Specifically, this embodiment uses Gaussian Process Regression (GPR) as a surrogate model and constructs the model using the Matern 2.5 kernel function. The GPR model takes the material characteristic ε(c) calculated in step 1 as input and outputs the predicted value of the target material properties and its uncertainty estimate. The expression for the Matern 2.5 kernel function is:

[0091]

[0092] Where r represents the Euclidean distance between the two points, l is the length scale parameter, and σ 2 These are the variance parameters. These kernel function parameters are determined by optimizing the marginal likelihood of the training data.

[0093] This embodiment uses the BoTorch framework to implement the training and prediction process of a Gaussian process regression model. This framework is built on top of GPyTorch and PyTorch and supports automatic gradient calculation and GPU acceleration. The training process of the Gaussian process regression model includes: constructing a training set based on existing experimental data, optimizing kernel function parameters, and using the optimized model for prediction.

[0094] Step 3: Construct a framework for calculating the numerical gradient of the efficiency function;

[0095] Specifically, this embodiment establishes a complete computational model from material composition and characteristics to Gaussian process regression prediction results, and finally to the performance function value. The performance function employs Expected Improvement (EI), Probability of Improvement (POI), or Upper Confidence Bound (UCB). For example, the mathematical expression for EI is: α EIg(x) = E[max(g(x)-μ,0)], where g(x) is the Gaussian process regression prediction value and μ is the currently observed best performance value.

[0096] This embodiment calculates the gradient of the efficiency function with respect to the material composition using a numerical differentiation method. Specifically, based on the fundamental properties of Gaussian process regression, this embodiment expresses the efficiency function as the expectation of the posterior sample:

[0097]

[0098] in Let h be a sample of a function drawn from the posterior distribution. Through reparameterization techniques, the random function samples are transformed into a deterministic function h. D (x,∈), finally we get the gradient expression:

[0099]

[0100] Step 4: Perform gradient ascent on the performance function;

[0101] Specifically, this embodiment uses the Sequential Least Squares Programming (SLSQP) optimization algorithm to maximize the gradient-based efficiency function. Starting with random initial composition guessing, the SLSQP algorithm iteratively updates the material composition based on the calculated efficiency function gradient, moving in the direction of increasing efficiency function value until a local optimum is found.

[0102] During the optimization process, this embodiment considers common constraints in material composition design, such as the total mole fraction of elements must be 100% and element solubility limitations. These constraints are explicitly integrated into the SLSQP optimization algorithm to ensure that all recommended compositions are within the feasible design space.

[0103] To enhance the diversity of the exploration and avoid premature convergence to suboptimal solutions, this embodiment employs a rejection sampling method to generate multiple random initial components, which are uniformly distributed throughout the feasible design space. Initiating multiple optimization processes in parallel from different initial points allows for a more comprehensive exploration of the design space, identifying diverse local optima. By comparing the performance function values ​​of these local optima, this embodiment can determine the globally optimal component. Experimental results demonstrate that this random initial sampling strategy effectively prevents premature convergence to specific regions, resulting in a slower decay rate of component state entropy, thus proving a broader design space exploration capability.

[0104] Table 1 is the pseudocode for the performance function maximization method in this embodiment.

[0105] Please refer to Table 1. The algorithm implementation in this embodiment can be divided into the following core steps:

[0106] The first line represents the input conditions of the algorithm, including the existing component-performance dataset D. comp and design space D space Dataset D comp The data, including known material compositions and their corresponding experimentally measured performance values, will be used to train the surrogate model; while the design space D... space The range of values ​​and constraints for component variables are defined, such as the range of element content and the restriction on the miscibility between elements.

[0107] The second line defines the algorithm's iterative process, where i represents the current iteration number and T is the maximum number of iterations. In each iteration, the algorithm updates the model based on existing data and selects new experimental points. This embodiment supports setting different iteration termination conditions, including a fixed number of iterations, a computational budget constraint, or a convergence criterion.

[0108] Line 3 indicates that a surrogate model is built at the beginning of each iteration. This embodiment uses Gaussian process regression as the surrogate model, which can predict the performance and uncertainty of unknown points based on limited observation data. The construction of the Gaussian process regression model includes the following steps: kernel function selection (this invention uses the Matern 2.5 kernel function), hyperparameter optimization (by maximizing marginal likelihood), and model training.

[0109] The fourth line represents the calculation of material characteristics for candidate points in the design space. For design space D... space For each component c in the model, its corresponding material characteristics are calculated using the feature transformation function ε(·). The feature transformation process includes steps such as element property lookup (e.g., atomic radius, electronegativity), statistical calculation (e.g., weighted average, standard deviation), and feature combination (e.g., element pair interaction characteristics). The feature transformation function implemented in this embodiment is fully differentiable, which is crucial for subsequent gradient calculations.

[0110] Line 5 indicates training a differentiable Gaussian process regression (GP) model. This embodiment uses the BoTorch framework to implement a Gaussian process regression model. This framework is built on PyTorch and supports automatic differentiation. In this step, the GP model uses the material features calculated in line 4 as input and the observed performance values ​​as output for training. The training process includes kernel function parameter optimization and posterior distribution calculation.

[0111] Line 6 represents the calculation of the gradient of the performance function, which is the core innovation of this embodiment. This is achieved by calculating the gradient of the performance function α(g(ε(c))) with respect to the component c. The algorithm can efficiently determine the optimal direction for component adjustment. Gradient calculation utilizes the chain rule, decomposing the end-to-end gradient from component to performance function into three parts:

[0112]

[0113] These correspond to the gradients of the performance function, GP prediction, and feature transformation, respectively.

[0114] Lines 7-8 initialize an empty candidate component set c. set Then, it begins to iterate through gradient optimization until the computational budget limit (such as 50 guesses) or other termination conditions are met.

[0115] Lines 9-11 represent the gradient-based optimization process. Specifically, the algorithm starts from the current component c0 and uses the SLSQP optimization algorithm to maximize the efficiency function value α(g(ε(c))). The optimization process uses the gradient information calculated in line 6. It also considers compositional constraints, such as a total mole fraction of elements of 100% and limitations on the range of element content. The SLSQP algorithm can effectively handle this type of constrained nonlinear optimization problem. Its working principle is to construct a quadratic approximation of the objective function and a linear approximation of the constraints, and iteratively solve the subproblems until convergence.

[0116] Line 12 indicates that the optimized component c' is added to the candidate component set c. set In this embodiment, the optimization process can be initiated in parallel from multiple random initial points to obtain a more diverse range of candidate components and effectively avoid local optima traps.

[0117] Lines 13-14 indicate the selection of the next experimental point from the candidate component set. The algorithm uses the efficiency function value as the selection criterion, choosing the component with the highest efficiency function value: c*←argmax. c∈cset α(g(ε(c))) is chosen as the next experimental point. This selection strategy balances exploration and exploitation, taking into account both regions with high predictive performance and regions with high uncertainty.

[0118] Line 15 indicates that the actual experiment is performed, the true performance value of the selected component c* is obtained, and this new data point is added to the experimental dataset D. comp In practical applications, this step may involve experimental processes such as material synthesis and performance testing, or it may utilize high-precision computational simulations to replace experiments.

[0119] Line 16 indicates that the component c with the highest performance value is returned. After all iterations are completed, the algorithm selects the component with the best performance from historical data as the final recommendation. Furthermore, this embodiment also supports returning multiple high-performing components for researchers to choose from, providing a more diverse range of solutions.

[0120] Table 1

[0121]

[0122]

[0123] Figure 2 The optimization effect of the method in this embodiment under different performance functions is demonstrated.

[0124] Please refer to Figure 2 , Figure 2 This paper illustrates the performance index (FOM) trends of the material composition design method based on feature gradients as the number of iterations increases, using different performance functions (UCB, POI, or EI). The horizontal axis represents the number of iterations, and the vertical axis represents the normalized performance index value.

[0125] Specifically, this embodiment evaluates three commonly used performance functions: expected improvement (EI, red curve), improvement probability (POI, pink curve), and confidence upper bound (UCB, blue curve). Figure 2 The solid line represents the average value of multiple optimization runs, while the shaded area represents the corresponding standard deviation, reflecting the stability of the optimization process. From... Figure 2 As can be observed, all three performance functions can improve material properties with increasing iteration number, which verifies the effectiveness and robustness of the method in this embodiment under different performance function settings.

[0126] It is noteworthy that in the early iteration stages (0-10 iterations), UCB and EI exhibit faster convergence speeds, attributed to their advantages in exploring and exploiting the balance. However, in later iterations (more than 25 iterations), the performance differences among the three efficiency functions gradually decrease, eventually stabilizing. This result demonstrates that the characteristic gradient optimization method of this embodiment can work well with various efficiency functions, providing materials designers with a flexible selection space. In practical applications, appropriate efficiency functions can be selected based on the specific problem characteristics and preferences.

[0127] Figure 3 The paper presents a comparative analysis of the computation time between the method of this embodiment and the traditional method.

[0128] Please refer to Figure 3 , Figure 3 The computation time consumption of the efficiency function maximization method based on feature gradient (green) and the traditional exhaustive enumeration method (red) was compared under different component numbers. The horizontal axis represents the number of material components, and the vertical axis shows the computation time (seconds) in logarithmic proportions.

[0129] Specifically, the red dashed line represents the computation time of the traditional exhaustive enumeration method, which exhibits a rapid polynomial growth trend as the number of components increases. When the number of components reaches 6, the computation time is approximately 10^3 seconds; while when the number of components increases to 11, the computation time surges to 10^... 12 Seconds. This rapidly increasing computational complexity severely limits the application of traditional methods in the design of multi-component materials.

[0130] In contrast, the feature gradient method in this embodiment (green horizontal line) exhibits a significant computational efficiency advantage. Regardless of the increase in the number of components, its computation time remains at approximately 10^60^6. 2 The computational complexity remains relatively stable at a level of approximately 1.7 seconds (about 1.7 minutes). This significant reduction in computational complexity (from rapid polynomial growth to an approximately linear relationship) makes it possible to explore large design spaces. The purple dashed line in the figure marks the intersection of the two methods when the number of components is equal to 6, indicating that the method in this embodiment has a significant computational efficiency advantage when dealing with material design problems with 6 or more components.

[0131] The efficiency of this method stems from directly guiding the search direction using gradient information, avoiding exhaustive calculations of the entire design space. This characteristic makes this method particularly suitable for the composition design of complex multi-component materials such as high-entropy alloys and multi-element ceramics.

[0132] Figure 4 This verifies the necessity of feature transformation in material composition design.

[0133] Please refer to Figure 4 , Figure 4 The predictive performance of machine learning models was compared across three different material systems: shape memory alloy (SMA), titanium alloy (Ti Alloy), and high entropy alloy (HEA), using the original composition (blue) as input and using the transformed material features (red). The vertical axis in each subplot represents the mean absolute error (MAE) or root mean square error (RMSE) of 10-fold cross-validation, in units of K, GPa, and MPa, respectively.

[0134] Specifically, for each material system, Figure 4 The prediction error distributions for the two input methods are illustrated using box plots. The blue box plots represent results using the original elemental components directly as model input, while the red box plots represent results using the transformed material features as input. In all three cases, the p-values ​​of the T-tests were less than 0.01, indicating that the performance difference between the two methods is statistically significant.

[0135] In all three material systems, using the transformed material features as input significantly reduced the model prediction error. Specifically, in the SMA system, the prediction error decreased from approximately 27 K to approximately 19 K; in the Ti alloy system, from approximately 45 GPa to approximately 39 GPa; and in the HEA system, from approximately 100 MPa to approximately 95 MPa. These results clearly demonstrate that converting the original composition into material features through feature engineering can significantly improve the prediction accuracy of machine learning models.

[0136] This performance improvement can be attributed to the material's ability to better capture the physicochemical interactions between elements, such as differences in atomic size, electronegativity, and mixing enthalpy, which directly affect the material's structure and properties. Therefore, the differentiable feature transformation step employed in the method of this invention not only improves the model's prediction accuracy but also lays the foundation for subsequent gradient optimization.

[0137] Figure 5 This demonstrates the impact of the key hyperparameter, the number of initial random components, on the optimization performance in the method of this embodiment.

[0138] Please refer to Figure 5 , Figure 5 The impact of different initial random component numbers on the final optimization results was analyzed. Figure 5 The box plot shows the final performance metrics (Final Component Analysis) for initial component counts of 10, 20, 40, and 80. max Distribution.

[0139] Specifically, from Figure 5 It can be observed that as the number of initial components increases, the distribution of the final performance index gradually shifts upward and the distribution range narrows. This indicates that increasing the number of initial random components can improve the quality and stability of the optimization results. When the number of initial components increases from 10 to 80, the median performance index increases from approximately 0.67 to approximately 0.69, and the interquartile range (box height) decreases significantly, indicating that the results are more concentrated in the high-performance region.

[0140] This result can be attributed to the following reasons: more initial random components provide a wider range of search starting points, increasing the probability of finding the global optimum; multiple parallel optimization processes can explore the design space more comprehensively and avoid getting trapped in local optima; the random distribution of a large number of starting points helps to overcome the complexity and non-convexity of the design space.

[0141] In practical applications, users can flexibly choose an appropriate number of initial components based on computational resources and time constraints. For complex material systems or high-dimensional design spaces, it is recommended to use more initial components to obtain more reliable optimization results; while for situations with limited computational resources or simpler design spaces, using an initial component number of 20 × the number of components obtained from a large number of experiments can also achieve satisfactory results.

[0142] Figure 6 It shows the trend of the mean of the final performance index and its standard deviation as the number of initial components increases.

[0143] The graph further quantifies the data intuitively. Figure 5 The trend shows the relationship between the mean (points) and standard deviation (error bar) of the final performance index and the number of initial components. It can be seen that as the number of initial components increases, the mean of the performance index continuously improves, while the standard deviation gradually decreases. This verifies that increasing the number of initial random points can improve the reliability and effectiveness of optimization.

[0144] As can be seen from the above embodiments, this invention provides a material composition design method based on feature gradients. By establishing an end-to-end differentiable computational process from material composition to material features, then to surrogate model prediction, and finally to the performance function value, it achieves gradient calculation and efficient optimization of the performance function relative to the material composition. This invention reduces the computational complexity of the internal optimization problem from a rapid polynomial increase with the number of components to an experimentally observed linear relationship, making it possible to explore large-scale material design spaces. Experimental verification shows that the method of this invention can work effectively under various performance function settings, and its computational efficiency far exceeds that of traditional exhaustive methods, especially when the number of components is large. At the same time, this invention demonstrates the important role of feature transformation in improving the prediction accuracy of machine learning models and analyzes the impact of hyperparameters such as the initial number of random components on optimization performance. The method of this invention is applicable to the composition design of complex multi-component materials such as high-entropy alloys, multi-component ceramics, and perovskites, which can significantly accelerate the development process of new materials and greatly reduce experimental costs and R&D cycles. Compared with the traditional "trial and error method," this invention provides a systematic and intelligent material design method, offering new ideas and solutions for efficient optimization in the field of materials informatics, with broad application prospects and important practical value.

[0145] Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort should fall within the scope of protection of the present invention.

[0146] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method of material composition design based on feature gradient, characterized in that, The process includes the following: The gradient of the efficiency function relative to the material composition is calculated in a pre-established end-to-end differentiable computational model, which ranges from material composition and characteristics to Gaussian process regression model prediction, and finally to the efficiency function value. Specifically, the gradient of the efficiency function relative to the material composition is calculated using numerical differentiation methods. In practice, based on the fundamental properties of Gaussian process regression, the efficiency function is expressed as the expectation of the posterior samples. where, are function samples drawn from the posterior distribution, the stochastic function samples are converted into deterministic function samples by the reparameterization trick and finally the gradient expression is obtained Based on the gradient of material composition, the efficiency function is maximized to obtain the material composition optimization result; Obtain the performance experimental results of the material composition optimization results, add the performance experimental results to the training dataset of the end-to-end differentiable computation model, and update the end-to-end differentiable computation model; The material composition with the best experimental results is selected from all the material composition optimization results, and this material composition is used as the final composition of the material. The training process of the Gaussian process regression model includes: Obtain experimental datasets of material composition and corresponding properties, and establish a composition and property training database; The material composition in the database is converted into material features using a feature transformation function; wherein, the feature transformation function combines the elemental properties of the material with the mole fraction to generate material features; Based on the material characteristics and the corresponding material performance data in the database, a Gaussian process regression model is trained to obtain a well-trained Gaussian process regression model. When establishing the end-to-end differentiable computational model, an end-to-end differentiable computational model is established, which starts from material composition, material characteristics, and then to the prediction of a trained Gaussian process regression model, and finally to the performance function value.

2. The method of claim 1, wherein, The gradient of the efficiency function with respect to the material composition is calculated using numerical differentiation methods.

3. The material composition design method based on feature gradient according to claim 2, characterized in that, The numerical differentiation method adopts the PyTorch automatic differentiation framework.

4. The material composition design method based on feature gradient according to claim 1, characterized in that, Based on the gradient of material composition, an optimization algorithm is used to maximize the efficiency function.

5. The material composition design method based on feature gradient according to claim 1, characterized in that, The optimization algorithm employs the sequential least squares programming method.

6. The material composition design method based on feature gradient according to claim 5, characterized in that, Based on the gradient of material composition, the initial material composition is generated using a rejection sampling method when maximizing the efficiency function.

7. The material composition design method based on feature gradient according to claim 1, characterized in that, The Gaussian process regression model uses the Matern 2.5 kernel function.

8. The material composition design method based on feature gradient according to claim 1, characterized in that, The performance function is the expected improvement function, the improvement probability function, or the confidence upper bound function.

9. A material composition design system based on feature gradients, characterized in that, The system for implementing the material composition design method based on feature gradient as described in any one of claims 1-8 comprises: The gradient calculation module is used to calculate the gradient of the efficiency function with respect to the material composition in a pre-established end-to-end differentiable calculation model that goes from material composition to material characteristics, then to Gaussian process regression model prediction, and finally to efficiency function value. Composition optimization module: used to maximize the efficiency function based on the gradient of material composition to obtain the material composition optimization result; Model update module: Used to obtain the performance experimental results of the material composition optimization results, add the performance experimental results to the training dataset of the end-to-end differentiable computation model, and update the end-to-end differentiable computation model; The screening module is used to select the material composition with the best experimental results from all the material composition optimization results, and use this material composition as the final composition of the material.

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