Optimization design method and system for material preparation formula and medium

Abstract

The invention provides an optimal design method and system for a material preparation formula and a medium. The optimization design method of the material preparation formula comprises the following steps: acquiring experimental data including different formula combinations and corresponding performance indexes thereof; performing formula variable space design on the basis of the category and value rule of formula variables in the experimental data and formula constraint conditions to determine a formula search boundary comprising discrete variables and continuous variables; based on a target acquisition function, performing search optimization in the formula search boundary by adopting particle swarm optimization in combination with a branch and bound method so as to determine a plurality of candidate formula combinations, the target acquisition function being defined based on performance prediction values and prediction uncertainty of the candidate formula combinations determined by a support vector regression model; and in response to a termination condition meeting search optimization, determining the candidate formula combination with the optimal target acquisition function value as a formula design scheme.

Description

Technical Field

[0001] This invention relates to the field of materials science, and in particular to an optimization design method for material preparation formulations, an optimization design system for material preparation formulations, and a computer-readable storage medium. Background Technology

[0002] In the research and development of chemical materials, formulation design plays a decisive role in material performance. Traditional formulation development relies on empirical experiments and gradual adjustments, which are characterized by long cycles and low efficiency. With the development of machine learning technology, data-driven methods are gradually being applied to the field of chemical formulation optimization. By constructing predictive models between inputs (formulation parameters) and outputs (performance indicators), intelligent formulation screening can be achieved.

[0003] In existing technologies, commonly used prediction models include random forests, support vector machines, and neural networks. However, existing methods often focus on predicting the mean performance, neglecting the important role of prediction uncertainty in the optimization process. This leads to the selected formulations easily getting trapped in local optima or lacking reliability. Furthermore, formulation optimization tasks involve complex constraints where a large number of discrete decision variables (such as material selection switching variables) coexist with continuous variables (such as dosage variables), which traditional optimization methods struggle to handle efficiently.

[0004] In order to overcome the above-mentioned defects of the existing technology, there is an urgent need in the field for an optimization design technology for material preparation formulations that can simultaneously consider the predicted mean of the prediction model output and the uncertainty guidance of the prediction model, and can support the optimization of mixed discrete and continuous variables, thereby improving the efficiency and reliability of formulation screening. Summary of the Invention

[0005] The following provides a brief overview of one or more aspects to offer a basic understanding of them. This overview is not an exhaustive summary of all conceived aspects, nor is it intended to identify key or decisive elements of all aspects, nor to define the scope of any or all aspects. Its sole purpose is to present some concepts of one or more aspects in a simplified form to prepare for the more detailed descriptions that follow.

[0006] To overcome the aforementioned deficiencies in the prior art, this invention provides an optimization design method for material preparation formulations, an optimization design system for material preparation formulations, and a computer-readable storage medium. These methods can simultaneously consider the predicted mean of the prediction model output and the uncertainty guidance of the prediction model, and can support the optimization of mixed discrete and continuous variables, thereby improving the efficiency and reliability of formulation screening.

[0007] Specifically, the optimization design method for the above-mentioned material preparation formulation provided by the first aspect of the present invention includes the following steps: collecting experimental data including different formulation combinations and their corresponding performance indicators; designing the formulation variable space based on the categories and value rules of the formulation variables in the experimental data and the formulation constraints to determine the formulation search boundary including discrete and continuous variables, wherein the formulation constraints are constructed according to the selection rules of the formulation variables and the dosage ratio logic; performing search optimization in the formulation search boundary based on the target acquisition function and using a particle swarm optimization combined with a branch and bound method to determine multiple candidate formulation combinations, wherein the target acquisition function is defined based on the performance prediction value and prediction uncertainty of the candidate formulation combinations determined by the support vector regression model, the support vector regression model is constructed and trained based on the formulation variables in the experimental data, and the prediction uncertainty is estimated by the kernel similarity between the candidate formulation combination and the support vectors in the support vector regression model; and determining the candidate formulation combination with the optimal target acquisition function value as the formulation design scheme in response to satisfying the termination condition of the search optimization.

[0008] Preferably, in one embodiment of the present invention, the step of designing the formulation variable space based on the category and value pattern of the formulation variables in the experimental data and the formulation constraints includes: classifying the variables into continuous parameters and mutually exclusive selection parameters according to the variable category and value pattern in the experimental data, wherein the continuous parameters include component ratios and / or auxiliary agent variables, and the mutually exclusive selection parameters include the selection of main agent type and / or auxiliary agent type; and using the continuous parameters as the continuous variables and the mutually exclusive selection parameters as the discrete variables.

[0009] Preferably, in one embodiment of the present invention, the step of designing the formula variable space based on the category and value rules of the formula variables in the experimental data and the formula constraints further includes: normalizing the continuous variables.

[0010] Preferably, in one embodiment of the present invention, the formulation constraints include the range restriction of the continuous variable, the mutual exclusion selection constraint of the discrete variable, the linkage constraint between the continuous variable and the discrete variable, and / or the overall total amount constraint of the formulation.

[0011] Preferably, in one embodiment of the present invention, the step of designing the formula variable space based on the category and value rules of the formula variables in the experimental data and the formula constraints further includes: reconstructing and grouping the formula variables based on the formula constraints.

[0012] Preferably, in one embodiment of the present invention, the step of using particle swarm optimization combined with branch and bound method to perform search optimization in the recipe search boundary based on the target acquisition function to determine multiple candidate recipe combinations includes: S1: initializing the position and velocity of the particles; S2: performing a search in the recipe search boundary, wherein the discrete variables participate in a continuously relaxed form; S3: updating the position and velocity of the particles according to the value of the target acquisition function of the particles; S4: in response to the current optimal solution being better than the historical optimal solution, processing the discrete variables using the branch and bound method to obtain an improved solution; S5: in response to the improved solution being better than the historical optimal solution, updating the global optimal solution and updating the position and velocity of the particles; and S6: repeating steps S2 to S5 until the termination condition is met.

[0013] Preferably, in one embodiment of the present invention, step S4 includes: selecting the term closest to an integer among the discrete variables as the first discrete variable and performing rounding; and performing local particle swarm optimization in the discrete space where the value of the first discrete variable is 1 and the discrete space where the value of the first discrete variable is 0, respectively, to obtain an improved solution.

[0014] Preferably, in one embodiment of the present invention, the step of constructing and training the support vector regression prediction model includes: constructing and training the support vector regression prediction model based on the formula variable in the experimental data as input and the corresponding performance index as target value, wherein the support vector regression prediction model adopts a polynomial kernel function.

[0015] Preferably, in one embodiment of the present invention, the step of estimating prediction uncertainty by the kernel similarity between candidate formulation combinations and support vectors in the support vector regression model includes: calculating the standard deviation of the residuals as a basic error estimation index based on the residuals between the true and predicted values ​​of the performance indicators corresponding to different formulation combinations in the experimental data; calculating the kernel similarity between each candidate formulation combination and each support vector in the support vector regression model; calculating the average of the kernel similarities between each candidate formulation combination and all support vectors to determine the local confidence index of each candidate formulation combination; and determining the prediction uncertainty of each candidate formulation combination based on the local confidence index of each candidate formulation combination and the standard deviation of the residuals.

[0016] Preferably, in one embodiment of the present invention, the expression of the target acquisition function is: ,in, The predicted mean is determined by the support vector regression prediction model. The prediction uncertainty is estimated by the kernel similarity between candidate recipe combinations and support vectors in the support vector regression model. Hyperparameters for balancing exploration and utilization.

[0017] Preferably, in one embodiment of the present invention, the method further includes the step of: performing dual verification of the formulation design scheme at both the model level and the experimental level.

[0018] Furthermore, the material preparation formulation optimization design system provided by the second aspect of the present invention includes a memory and a processor. The memory stores computer instructions. The processor is connected to the memory and configured to execute the computer instructions stored in the memory to implement the material preparation formulation optimization design method provided in any of the above embodiments.

[0019] Furthermore, the computer-readable storage medium provided according to the third aspect of the present invention stores computer instructions. When the computer instructions are executed by a processor, the optimized design method for the material preparation formulation provided in any of the above embodiments is implemented. Attached Figure Description

[0020] The above-described features and advantages of the present invention will be better understood after reading the following detailed description of embodiments of the present disclosure in conjunction with the accompanying drawings. In the drawings, components are not necessarily drawn to scale, and components having similar related characteristics or features may have the same or similar reference numerals.

[0021] Figure 1 A schematic diagram of an optimized design system for material preparation formulations according to some embodiments of the present invention is shown;

[0022] Figure 2 A flowchart illustrating an optimized design method for material preparation formulations according to some embodiments of the present invention is shown;

[0023] Figure 3 A flowchart illustrating an optimized design method for material preparation formulations according to some embodiments of the present invention is shown;

[0024] Figure 4 The diagram illustrates the structure of support vector regression modeling and target acquisition function value calculation according to some embodiments of the present invention;

[0025] Figure 5 A flowchart illustrating a search optimization using particle swarm optimization combined with branch and bound, according to some embodiments of the present invention, is shown.

[0026] Figure 6 The convergence trend diagram of the particle swarm optimization combined with branch-and-bound method provided according to a preferred embodiment of the present invention is shown; and

[0027] Figure 7The experimental-level verification results of the formulation design scheme provided according to a preferred embodiment of the present invention are shown.

[0028] Figure label:

[0029] 100: Optimization design system for material preparation formulations;

[0030] 110: Memory;

[0031] 111: Computer-readable storage medium;

[0032] 120: Processor; and

[0033] S210~S240: Steps. Detailed Implementation

[0034] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. It should be noted that the aspects described below with reference to the accompanying drawings and specific embodiments are merely exemplary and should not be construed as limiting the scope of protection of the present invention in any way.

[0035] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0036] Furthermore, the terms "upper," "lower," "left," "right," "top," "bottom," "horizontal," and "vertical" used in the following description should be understood as the orientations shown in the relevant paragraphs and accompanying drawings. These relative terms are for illustrative purposes only and do not imply that the described apparatus must be manufactured or operated in a specific orientation, and therefore should not be construed as limiting the invention.

[0037] It is understood that although terms such as "first," "second," and "third" may be used herein to describe various components, regions, layers, and / or parts, these components, regions, layers, and / or parts should not be limited by these terms, and these terms are only used to distinguish different components, regions, layers, and / or parts. Therefore, the first components, regions, layers, and / or parts discussed below may be referred to as second components, regions, layers, and / or parts without departing from some embodiments of the present invention.

[0038] As mentioned above, existing methods mostly focus on predicting the average performance, neglecting the important role of prediction uncertainty in the optimization process. This leads to the selected formulations easily getting trapped in local optima or lacking reliability. In addition, formulation optimization tasks involve complex constraints where a large number of discrete decision variables (such as material selection switching variables) coexist with continuous variables (such as dosage variables), which traditional optimization methods struggle to handle efficiently.

[0039] To overcome the aforementioned deficiencies in the prior art, this invention provides an optimization design method for material preparation formulations, an optimization design system for material preparation formulations, and a computer-readable storage medium. These methods can simultaneously consider the predicted mean of the prediction model output and the uncertainty guidance of the prediction model, and can support the optimization of mixed discrete and continuous variables, thereby improving the efficiency and reliability of formulation screening.

[0040] In some non-limiting embodiments, the optimization design method for the material preparation formulation provided in the first aspect of the present invention can be implemented via the optimization design system for the material preparation formulation provided in the second aspect of the present invention.

[0041] Please refer to Figure 1 , Figure 1 A schematic diagram of an optimized design system for material preparation formulations provided according to some embodiments of the present invention is shown.

[0042] like Figure 1 As shown, the material preparation formulation optimization design system 100 may be configured with a memory 110 and a processor 120. The memory 110 includes, but is not limited to, the computer-readable storage medium 111 provided in the third aspect of the present invention, which stores computer instructions thereon. The processor 120 is connected to the memory 110 and is configured to execute the computer instructions stored in the memory 110 to implement the material preparation formulation optimization design method provided in the first aspect of the present invention.

[0043] The working principle of the above-mentioned material preparation formulation optimization design system will be described below with reference to some embodiments of the material preparation formulation optimization design methods. Those skilled in the art will understand that these embodiments of the material preparation formulation optimization design methods are merely non-limiting implementations provided by the present invention, intended to clearly demonstrate the main concepts of the invention and provide some specific solutions convenient for public implementation, rather than limiting all functions or all working methods of the material preparation formulation optimization design system. Similarly, the material preparation formulation optimization design system is also only one non-limiting implementation provided by the present invention, and does not constitute a limitation on the executing entity and execution order of each step in these material preparation formulation optimization design methods.

[0044] Please refer to Figure 2 and Figure 3 , Figure 2 and Figure 3 A flowchart is shown of an optimized design method for material preparation formulations provided according to some embodiments of the present invention.

[0045] like Figure 2 As shown, the material preparation formulation optimization design method 200 may include step S210: collecting experimental data including different formulation combinations and their corresponding performance indicators.

[0046] The material preparation formulation optimization design system (hereinafter referred to as the optimization design system) can first collect a dataset consisting of the proportion of each chemical raw material, the amount of additives, process parameters and target performance indicators.

[0047] Then, the optimization design system can perform step S220: design the recipe variable space based on the category and value rules of the recipe variables in the experimental data and the recipe constraints, so as to determine the recipe search boundary including discrete and continuous variables.

[0048] Formulation constraints can be constructed based on the selection rules of each formulation variable and the dosage ratio logic in the experimental data.

[0049] Recipe variable space design can be implemented based on recipe constraints, thereby determining the recipe search boundary, which includes both discrete and continuous variables. Recipe variable space design can include discrete variable design and continuous variable standardization. For example... Figure 3 As shown, discrete variable design can be the encoding of discrete variables, while continuous variable standardization can be the normalization of continuous variables.

[0050] To accurately model the discrete and continuous mixed decision-making characteristics contained in chemical material formulations, the optimization design system can encode and process the formulation variables contained in the dataset. By introducing logical structure constraints on the basis of the original formulation variables, it can realize feature construction based on the joint encoding of discrete selection variables and continuous dosage variables, so that the selection behavior of each component in the formulation and the application amount are co-expressed, thereby reflecting the process logic and constraint rules in the real formulation design scenario.

[0051] Specifically, the optimization design system can first perform unified modeling of discrete and continuous variables based on the categories and value patterns of formulation variables. The optimization design system can classify variables in chemical formulation design according to their characteristics, with some variables being continuous parameters (such as component ratios and auxiliary agent dosages), and others being mutually exclusive selection parameters (such as the type of main agent and the selection of auxiliary agent categories). Continuous parameters can be represented by continuous variables, while mutually exclusive selection parameters need to be represented by discrete decision variables.

[0052] For mutually exclusive selection problems, a 0-1 discrete variable is introduced to control that each group can only select one or two active options, while a corresponding continuous variable is designed to represent the specific value of the selected option; the continuous variable of the unselected option is automatically set to zero. This hybrid modeling approach ensures both the physical rationality of the formulation design and a clear variable definition for the optimization problem.

[0053] For example, if a component is indicated by a discrete variable as "use", the optimization design system can provide a set of continuous dosage variables to describe the specific amount of the selected component to be added. This combination strategy can represent process requirements such as "selecting only one component and limiting the dosage range" or "allowing the simultaneous selection of hydrophilic and hydrophobic components but requiring the dosage to be matched".

[0054] Subsequently, the optimization design system can further introduce formulation constraints that must be satisfied during the optimization search process, based on the constructed mixed variables. These formulation constraints can be defined according to the selection rules for formulation variables and the dosage ratio logic.

[0055] In some embodiments, formulation constraints may include, but are not limited to: range restrictions for continuous variables, such as single-component ratio constraints within a specified range; mutually exclusive selection constraints for discrete variables, such as only one active component can be selected from a specific category; linkage constraints between continuous and discrete variables, such as the requirement that the mass ratio of the main agent and the auxiliary agent be equal; and / or total constraints on the overall formulation, such as the requirement that the sum of all components be controlled within a specified range.

[0056] The optimization design system can refactor and group recipe variables based on recipe constraints.

[0057] In some examples, optimization design systems can map problems involving multiple material selection, such as a set of variables (e.g., a master material or base component) that uniquely selects one from multiple components, to discrete sets of selection variables. These are represented by 0-1 binary codes indicating whether each material is selected; a value of 1 indicates selection, and a value of 0 indicates non-selection. Only a specific number of materials (e.g., one or two) can be selected within a set to satisfy "choose one of several" or "choose several of several" combination constraints.

[0058] In some examples, the optimization design system can treat variables representing numerical information such as material dosage and additive ratio as continuous variables, setting upper and lower limits as value range constraints. Here, for fixed formulation components and special functional additives in the material, the optimization design system can set them as constant input variables, not treating them as free variables during the optimization process. Other free variables are set as continuous variables varying within a certain range to adjust performance-related proportioning strategies.

[0059] In some examples, for component groups that require joint selection (such as a combination of principal and auxiliary components), the optimization design system can design conditional selection rules that allow the selection of only one from the principal component, or the selection of one from both the principal and auxiliary components, while mandating that the dosages of both are equal.

[0060] In some examples, the formulation constraints also include an overall formulation total constraint, that is, the total amount of all formulation components added must meet a specified range.

[0061] Through the above-mentioned meticulous design of discrete variables, it is ensured that the generated formulation scheme always conforms to the basic logic and constraints of chemical formulation design during the optimization process.

[0062] In this way, the optimization design system, through a unified variable construction method, is compatible with the expression methods of various types of components in chemical formulations. Combined with the introduced formulation constraints, it can flexibly represent various engineering constraints such as "optional components", "dosage balance", and "proportion matching", thus providing a structurally complete and semantically clear input feature system for subsequent optimization modeling.

[0063] Furthermore, the formulation variable space design also includes the standardization of continuous variables. Specifically, the optimization design system can normalize continuous variables to unify the scale of data with different dimensions, facilitating model training and optimization search. For discrete variables with selected feature types, the original binary representation of 0-1 is maintained without normalization to preserve the categorical properties of discrete variables.

[0064] Based on the results of the above recipe variable space design, the optimization design system can construct the recipe search boundary of the particle swarm optimizer.

[0065] Please continue to refer to this. Figure 2 The optimization design system can execute step S230: based on the target acquisition function, it uses particle swarm optimization combined with branch and bound method to perform search optimization in the formula search boundary to determine multiple candidate formula combinations.

[0066] The target acquisition function is based on the performance predictions and prediction uncertainties of candidate formulation combinations determined by the support vector regression model. The support vector regression model is constructed and trained based on the formulation variables in the experimental data, and the prediction uncertainty is estimated by the kernel similarity between the candidate formulation combinations and the support vectors in the support vector regression model.

[0067] exist Figure 3In the illustrated embodiment, before constructing the recipe search boundary, the optimization design system can build and train a Support Vector Regression (SVR) model (hereinafter referred to as the SVR model) based on the original variables in the collected experimental dataset, which includes recipes and performance indicators. All original input variables in the experimental data are continuous expressions. Based on the construction and training of the SVR model, a target acquisition function is then constructed for the subsequent optimization search process.

[0068] The optimization design system can define an objective acquisition function that considers the prediction mean and prediction uncertainty of the SVR model to guide the optimization search. In some embodiments, the objective acquisition function can be the Upper Confidence Bound (UCB) criterion in Bayesian optimization.

[0069] The expression for the target acquisition function is:

[0070] ,

[0071] in, The predicted mean determined by the support vector regression prediction model. To estimate the prediction uncertainty by using the kernel similarity between the sample to be predicted and the support vectors in the support vector regression model, To balance exploration and utilization, the hyperparameter is an adjustment factor that weighs the contributions of the mean and standard deviation, and is usually taken as a small positive number.

[0072] The target acquisition function not only considers the predicted values ​​of the SVR model but also incorporates its uncertainty assessment results, thereby providing dual guidance for performance improvement and risk control during the search. In the optimization search process, by maximizing the value of the target acquisition function, the performance indicators of the target material can be maximized. Furthermore, the optimization process balances high predicted values ​​and high-potential regions, balancing exploration and exploitation, to more effectively find the formulation design scheme that maximizes performance indicators.

[0073] Please refer to Figure 4 , Figure 4 A structural diagram illustrating the support vector regression modeling and target acquisition function value calculation provided by some embodiments of the present invention is shown.

[0074] like Figure 4 As shown, the optimization design system can normalize continuous formulation variables in the experimental dataset and extract the target performance index as the prediction object of the model. A support vector regression prediction model is constructed using the continuous formulation variables from the experimental data to learn the nonlinear mapping relationship between the formulation variables and the target performance.

[0075] Specifically, the optimization design system can first standardize the formula data so that the variables are distributed on the same scale, ensuring that the formula features with different dimensions and value ranges have a consistent numerical scale in the support vector regression modeling process, thereby improving the training effect, stability and prediction performance of the model.

[0076] In some embodiments, the optimization design system uses the MinMaxScaler method to linearly transform all continuous feature values ​​to a fixed interval, so as to ensure that the numerical distribution of different feature dimensions is within the same scale range, which facilitates numerical stability and convergence in the subsequent modeling process.

[0077] Then, using the normalized continuous dosage or concentration values ​​of each component as input features and the performance index as the target value, the SVR model is trained to fit the nonlinear relationship between the formulation parameters and the performance response.

[0078] The SVR model fits the mapping relationship between formulation variables and target performance in a regression manner, and can capture the nonlinear correlation between formulation variables and performance response in a high-dimensional feature space. The trained SVR model can quickly predict the corresponding performance value given any normalized input, providing an efficient and reliable performance evaluation tool for subsequent formulation optimization.

[0079] like Figure 4 As shown, by constructing and training the SVR model, the trained SVR prediction model and the SVR support vectors can be output.

[0080] SVR models can employ polynomial kernels to capture the complex nonlinear mapping between formulation and performance, and to balance the model's fitting and generalization abilities by optimizing the penalty parameter. The polynomial kernel is defined as follows:

[0081] .

[0082] in, Indicates sample With support vectors The inner product, The scaling function of the kernel function. For kernel bias term, Let be the order of the polynomial.

[0083] like Figure 4As shown, during the search optimization process, the optimization design system can predict the performance of new formulations based on the SVR model, and estimate the uncertainty of the prediction results based on the kernel similarity between the support vectors and the prediction points (i.e., the candidate formulation combinations obtained during the search optimization process). The estimated prediction uncertainty can be used as optimization guidance information.

[0084] In some embodiments, the optimization design system can obtain prediction uncertainty through a dynamic standard deviation adjustment method based on training residuals and kernel similarity.

[0085] First, the optimization design system can calculate the standard deviation of the overall training residuals based on the residuals between the true values ​​of the performance indicators corresponding to different formulation combinations in the experimental data used for training and the predicted values ​​determined by the SVR model. As a basic error estimation index.

[0086] Then, the kernel similarity between each sample to be predicted (e.g., candidate recipe combinations in the search optimization process) and each support vector in the SVR model is calculated. Here, the optimization design system can determine the kernel similarity between each sample to be predicted and each support vector in the SVR model based on the aforementioned polynomial kernel function. .

[0087] Preferably, to eliminate the differences in kernel similarity distribution among different input samples, the optimization design system can normalize the kernel similarity matrix, mapping the numerical range to the [0,1] interval, thereby standardizing the local similarity measure. Here, the normalization formula is:

[0088] ,

[0089] in, The minimum value in the kernel similarity matrix. This represents the maximum value in the kernel similarity matrix.

[0090] The normalized kernel matrix can standardize the local similarity measure and eliminate the bias caused by different sample feature distributions.

[0091] Then, the mean of the kernel similarity between each sample to be predicted and all support vectors is calculated to determine the local confidence index of each sample to be predicted.

[0092] Specifically, for each sample to be predicted, the average of its normalized kernel values ​​with all support vectors is calculated, and this average is defined as the local similarity. :

[0093] ,

[0094] in, This indicates the number of support vectors.

[0095] Local similarity As a local confidence index.

[0096] Subsequently, the optimization design system can be based on the local confidence index of each sample to be predicted. and the standard deviation of the residuals The prediction uncertainty estimate for each sample to be predicted is dynamically adjusted.

[0097] In some embodiments, the optimization design system can dynamically estimate the prediction standard deviation corresponding to different input samples to be predicted by multiplying the standard deviation of the training residuals by a function of the normalized kernel distance. The estimated prediction standard deviation is used as the prediction uncertainty of each sample to be predicted. The following formula can be used for calculation:

[0098] ,

[0099] It can be seen that local similarity The higher the value (i.e., the closer it is to the support vectors of the SVR model), the lower the prediction uncertainty; conversely, the lower the value, the greater the uncertainty.

[0100] Please continue to refer to this. Figure 4 Based on the predicted mean of the SVR model of the determined sample to be predicted and the calculated prediction uncertainty of the sample to be predicted, the target acquisition function value of the sample to be predicted can be determined.

[0101] Understandably, such as Figure 3 As shown, in some embodiments, those skilled in the art can first establish and train the SVR model and construct the target acquisition function based on the collected experimental data, and then design a representation method for discrete decision variables based on the category and value rules of the formulation variables in the experimental data, and construct an optimization problem according to the formulation constraints. The order of steps for establishing and training the SVR model and constructing the target acquisition function is not restrictive; that is, in the above embodiments, this process can be performed before or after step S220.

[0102] The optimization design system uses a support vector regression model to learn the nonlinear mapping relationship between recipe variables and performance indicators, and combines kernel similarity to dynamically estimate the prediction uncertainty. This makes the performance prediction results not only highly accurate, but also provides reliable prediction uncertainty quantification for optimization search, which significantly improves the reliability and exploration efficiency of subsequent optimization.

[0103] Then, the optimization design system can efficiently search and optimize within the high-dimensional formula search boundary containing discrete and continuous variables designed in step S220, based on the objective acquisition function, using a hybrid optimization strategy combining particle swarm optimization (PSO) and branch and bound (BB) methods (hereinafter referred to as PSO-BB method), to collaboratively complete the search of high-dimensional, strongly constrained variable space and determine multiple candidate formula combinations.

[0104] By constructing the aforementioned target acquisition function that integrates the predicted mean and the upper confidence bound (UCB) of the prediction uncertainty, the optimization design system can balance performance improvement and exploration potential during the optimization process, avoid getting trapped in local optima, and enhance the globality and robustness of the optimization search.

[0105] During the optimization process, continuous variables are updated and explored using the particle swarm optimization algorithm, while discrete variables are prioritized based on how close their values ​​are to integers in the current solution of the particles. Discrete decision variables that are close to having determined values ​​are locked first, and the search space is dynamically reduced, thereby accelerating the optimization convergence process and selecting the formulation design scheme that satisfies all formulation constraints and has the optimal UCB index.

[0106] Please refer to Figure 5 , Figure 5 A flowchart illustrating a search optimization method using particle swarm optimization combined with branch and bound, according to some embodiments of the present invention, is shown.

[0107] In the initial optimization phase, to facilitate unified modeling and continuous space exploration, the optimization design system can first set upper and lower limits for continuous variables based on the recipe search boundary, according to the originally set physical range, while the discrete variables are given continuous relaxation between 0 and 1. That is, the discrete variables are modeled in floating-point form, and their values ​​are relaxed to the [0,1] interval, so that the discrete variables can be initially searched in the continuous interval.

[0108] Building upon this, a standard particle swarm optimization (PSO) algorithm is employed for a global search in a continuous space. PSO guides candidate solutions to continuously update the search space by simulating the velocity and position evolution of particles, thus exploring a region with superior performance output.

[0109] In some embodiments, the optimization design system may also employ a dynamic constraint screening mechanism during the search optimization process. During the particle swarm optimization and branch-and-bound search stages, the optimization design system can monitor the legality of generated solutions in real time, eliminating or adjusting candidate solutions that do not meet the constraints, thereby improving search efficiency and ensuring that the search space always meets the feasibility requirements of the chemical formulation.

[0110] like Figure 5As shown, the optimization design system can set hyperparameters such as the number of particles, inertia weight, self-learning factor and social learning factor of the particle swarm optimizer, set the iteration number t=1, the target acquisition function value to positive infinity, and initialize the continuous position vector and velocity of the particles.

[0111] Then, the optimization design system can initiate iterative optimization of particles. During the search within the recipe search boundary, continuous variables are directly optimized according to the standard particle swarm optimization (PSO) update rules, while discrete variables participate in the search in PSO with continuous relaxation. Particles can update their position and velocity based on feedback information from the target acquisition function UCB to explore potential better recipe combinations.

[0112] like Figure 5 As shown, the optimization design system can decompose the current particle's position vector into discrete and continuous parts, then construct a complete solution vector and evaluate the target acquisition function. Based on the target acquisition function values ​​of each particle, the individual optimal position and the global optimal position of each particle are updated.

[0113] As the search progresses, to ensure reasonable convergence of discrete variables, the optimization design system gradually introduces rounding constraints based on the convergence of variables during the optimization process. It gradually constructs a solution space that satisfies integer constraints by building subproblems. After each round of optimization iteration, a branch and bound mechanism is introduced to dynamically process the discrete variables. Finally, under the premise that both continuous and discrete variables satisfy the formulation constraints, the optimal chemical formulation design scheme is obtained.

[0114] like Figure 5 As shown, for each round of PSO search, the values ​​of discrete variables are identified. The optimization design system can determine whether the current optimal solution is better than the historical optimal solution, then perform an approximate rounding operation on the discrete variable part, transforming the discrete variables into discrete feasible solutions, and then constructing a complete solution vector and evaluating the target acquisition function.

[0115] Specifically, before each round of branching and bounding, the optimization design system can select the variable whose value is closest to an integer (0 or 1) from all discrete variables as the most "deterministic" first discrete variable. This first discrete variable is then preferentially subjected to a rounding branch, fixing its value to either 0 or 1. Then, the system splits the problem into two subproblems based on this first discrete variable, thereby gradually locking down discrete decision variables and narrowing the search space. Preferably, the optimization design system can remove the locked variables from the subsequent search space, reducing the degrees of freedom of the optimization problem. Finally, based on the discrete feasible solutions transformed from the first discrete variable, a complete solution vector is constructed, and the objective acquisition function is evaluated.

[0116] Next, the optimization design system determines whether the current optimal solution is better than the historical optimal solution. If the current optimal solution is better than the historical optimal solution, the optimization design system uses a branch-and-bound method to perform local particle swarm optimization in both the discrete space where the first discrete variable has a value of 1 and the discrete space where the first discrete variable has a value of 0, to obtain an improved solution. Figure 5 In the embodiment shown, the optimization design system can use the current optimal solution as the initial point of the branch and bound submodule, and call the branch and bound module to search for the current optimal solution in the formed discrete space to obtain an improved solution.

[0117] By employing this dynamic discrete variable locking strategy, the optimization design system can gradually narrow down the recipe search space, avoiding the combinatorial explosion problem caused by discrete choices and improving search efficiency and convergence speed. Compared to traditional continuous optimization or simple discretization strategies, the optimization design system can more accurately handle complex combinatorial constraints in recipe design.

[0118] Next, the optimization design system determines whether the improved solution is superior to the historical best solution. In response to the improved solution being superior to the historical best solution, the optimization design system can update the global best solution and update the position and velocity of each particle.

[0119] like Figure 5 As shown, the optimization design system repeats the above search and optimization steps until the termination condition is met, at which point the final solution is output.

[0120] The optimized design system learns the relationship between formulation and performance by introducing a support vector regression model, while combining kernel function estimation to predict uncertainty. It also utilizes particle swarm optimization algorithm combined with branch and bound strategy to maximize the upper confidence bound (UCB) target acquisition function within the Bayesian optimization framework. This approach balances exploration and utilization, effectively improving the efficiency and accuracy of reverse design of chemical formulations.

[0121] Please refer to Figure 2 The optimization design system can execute step S240: in response to satisfying the termination condition of the search optimization, determine the candidate formula combination with the optimal target acquisition function value as the formula design scheme.

[0122] The final solution output by step S230 is the candidate recipe combination with the optimal target acquisition function value. The optimization design system uses this final solution as the recipe design scheme.

[0123] Furthermore, after selecting the optimal formulation design scheme, to ensure its reliability and practical application value, the optimization design system can perform dual validation at both the model level and the experimental level. Model-level validation involves using different regression models to perform performance predictions on the selected optimal formulation, assessing the consistency of its target performance. Experimental-level validation is achieved by those skilled in the art through actual chemical experiments to prepare and test the optimal formulation. By comprehensively comparing the model prediction results with experimental measurements, those skilled in the art can verify the effectiveness and engineering feasibility of the proposed optimization method in formulation design.

[0124] Here, the optimization design system uses a variety of different prediction models to independently verify the selected formulas. The verification models used include, but are not limited to, performance predictors trained based on regression methods such as decision trees, gradient boosting, and support vector machines, in order to avoid the problem of error accumulation caused by the bias of a single model and enhance the objectivity and robustness of the verification results.

[0125] During the validation process, the optimized and screened formulations were used as inputs and fed into various validation models for performance prediction. The consistency of the prediction results and the deviation from the output results of the SVR model during the optimization process were compared. If the performance prediction results of different prediction models for the screened formulations maintained high consistency and the prediction indicators met the preset performance requirements, the optimization results were considered to have good consistency validation at the machine learning model level.

[0126] In some embodiments, the optimization design system can input the searched formulation design scheme into the SVR model to back-produce the target performance, thereby confirming that it has reached the optimal design objective under model estimation. Next, to enhance the robustness verification between models, the optimization design system can introduce commonly used machine learning predictors (such as CatBoost) to compare the performance predictions of the same formulation combination. By comparing the consistency prediction results of different models for this formulation design scheme horizontally, the model robustness and generalization performance of the optimization scheme can be further evaluated.

[0127] To further confirm the practical feasibility of the screened formulations in real-world application environments, those skilled in the art can select representative formulations from the optimization results and conduct chemical experiments for preparation and performance testing.

[0128] In some embodiments, the optimization design system can conduct actual chemical synthesis experiments based on the structural parameters and additive ratios of the formulation design scheme. Samples are prepared under controlled experimental conditions, and target performance indicators are determined using standard testing procedures.

[0129] Then, the experimental results are quantitatively compared with the model predictions to calculate the range of deviations and analyze the systematic and random sources of model prediction errors.

[0130] By comparing the experimentally measured performance indicators with the model predictions, the accuracy and applicability of the optimization method in actual material synthesis are verified. If the experimental error is within the acceptable range, the model is reliable and the optimal design is worth implementing; if the experimental error has a large deviation, the optimization design system can further correct the model or expand the sample dataset based on the experimental feedback data, forming a closed-loop iterative optimization mechanism.

[0131] When the experimental results are consistent with the model predictions and meet or exceed the design indicators, it indicates that the optimization design system can effectively guide the reverse design of chemical material formulations and has significant engineering application potential.

[0132] By conducting dual verification of the formulation design scheme at both the model and experimental levels, a closed loop was ensured throughout the entire process from model prediction to experimental verification, demonstrating the practical guiding capability and engineering implementation value of the data-driven design methodology.

[0133] The formulation design schemes finally selected by the optimization design system have shown excellent performance after being verified by various prediction models and tested by actual chemical experiments, which fully demonstrates the effectiveness and wide application potential of this invention in the field of reverse engineering of chemical material formulations.

[0134] In summary, this invention provides a chemical formulation reverse design method based on a support vector regression model and a hybrid optimization algorithm of particle swarm optimization and branch-bound, which overcomes the problems of low efficiency of traditional exhaustive search, difficulty of gradient methods in handling discrete constraints, and poor scalability of Gaussian process Bayesian optimization. For the mixed optimization problem in formulation design where discrete variables (such as raw material selection) and continuous variables (such as addition amounts) coexist, a clear and expressive optimization framework is constructed. The confidence upper bound criterion from Bayesian optimization is introduced into the optimization process, comprehensively considering the predicted mean and uncertainty of the SVR model, guiding the search direction in the optimization process to achieve a balance between performance improvement and uncertainty exploration. It possesses both global search capability and feasible solution construction capability, and can efficiently handle chemical formulation design tasks under high-dimensional and complex constraints.

[0135] The following is a specific, non-limiting preferred embodiment, which will be used to further elaborate on the optimized design method of the material preparation formulation proposed in this invention.

[0136] In this preferred embodiment, experimental data on the formulation of a certain water-based organosilicon material were selected for testing and evaluation. The optimization design system can collect experimental data on the formulation of water-based organosilicon materials.

[0137] Statistical analysis of the dataset shows that the target performance index ranges from 0.32 to 2.07, with a mean of 1.17 and a median of 1.15. This indicates that the data distribution is skewed to the left, suggesting significant room for optimization.

[0138] However, the supervised learning regression model (SVR model) built based on this dataset theoretically cannot exceed the maximum predicted value of 2.07 in historical experiments. Therefore, the objective of the optimization task of the optimized design system is set to maximize this target performance index, and the performance of the obtained formulation is verified through actual experiments to see if it is better than the current average level.

[0139] The original dataset contains 28-dimensional input variables, representing raw material ratios, additive contents, and related process parameters. Optionally, the optimization design system can design the formulation variable space based on the categories and value patterns of the 28-dimensional formulation variables in the experimental data, as well as the formulation constraints.

[0140] The original dataset is classified, including the main polymer region ( to Crosslinking agent and solvent region ( to ), performance additive area ( to ), packing selection area ( to ) and catalyst region ( and ).

[0141] In the main polymer region, to This represents six optional reactive polymers, which are mutually exclusive selected through discrete selection variables. Only one of them can be selected for formulation design, and its corresponding dosage is in the range of [93,100]. The term represents non-reactive polymers, and its value is obtained through calculation as the main dose balance term:

[0142] ,

[0143] in, Indicates non-reactive polymers The value, Indicates the first The values ​​of these variables are determined, thus the optimized design system can ensure that the total amount of the main polymer is fixed at 100.

[0144] In the crosslinking agent and solvent region, This indicates the presence of a cross-linking agent; it is an adjustable continuous variable with a value range of [0.5, 3.0]. Indicates surfactant; to These represent different levels of water content and are collectively referred to as water series components. Here, to All components are fixed, i.e., constant input variables, whose values ​​remain unchanged in the experimental design.

[0145] In the performance additives section, to This represents five fixed additives that are used as fixed numerical inputs to the model in the experiment and do not participate in the adjustment of optimization variables.

[0146] In the packing selection area, to as well as These represent six types of hydrophilic fillers. and This indicates two hydrophobic fillers that can be selectively combined with a hydrophilic filler to form a combined filling scheme. The formulation design allows the use of only one hydrophilic filler, or the addition of a hydrophobic filler, provided that the dosages of both are strictly equal. The total dosage of all fillers must meet the process requirements, i.e., be controlled within the range of [90, 110].

[0147] In the catalyst region, and These represent two fixed-component catalysts, whose values ​​remain constant in the experimental system to ensure the activity regulation of the reaction process.

[0148] The experimental data described above were used as input to the SVR model, with the target output performance as the metric Y, to construct and train the SVR model.

[0149] Based on the 28-dimensional formula variables and formula constraints mentioned above, the formula search boundary can be determined. The optimization problem constructed based on the formula search boundary and the objective acquisition function can be:

[0150] .

[0151] in, For the discrete variable part of the i-th type of variable, The value can be 0 or 1.

[0152] Subsequently, based on the target acquisition function, a combination of particle swarm optimization (PSO) and branch-and-bound methods is used to search and optimize within the recipe search boundary to determine multiple candidate recipe combinations. In this preferred embodiment, the PSO stage uses 50 particles, iterating 10 steps per round; a total of 30 rounds of iteration are performed; after each run, the branch-and-bound (BB) algorithm is called to perform a rounding branch on the discrete variable closest to an integer in the current solution. The PSO-BB optimization process is repeated 20 times independently to improve robustness and record multiple sets of optimization results.

[0153] The entire optimization process uses the UCB objective acquisition function as the evaluation metric, combining the predicted mean and uncertainty to balance exploratory and conservative approaches. The convergence of the objective function value is recorded in each iteration, ultimately yielding a set of optimal formulations under feasible constraints.

[0154] Please refer to Figure 6 , Figure 6 The diagram shows the convergence trend of a particle swarm optimization combined with a branch-and-bound method provided according to a preferred embodiment of the present invention.

[0155] like Figure 6 As shown, the performance index of the particle swarm optimization combined with the branch and bound method improves rapidly in the initial rounds and reaches convergence around the 9th round, indicating that the particle swarm optimization combined with the branch and bound method can locate high-performance solutions in the early stage and has strong search efficiency.

[0156] The optimized formulation design, predicted by the SVR model, achieved a performance index (Y) of 1.84, which is among the highest in the current dataset. To further verify the reliability of the SVR model's prediction, a CatBoost regression model trained on the same dataset was used to predict the formulation design. The results showed a performance index (Y) of 1.76, which is highly consistent with the SVR model's prediction.

[0157] Please refer to Figure 7 , Figure 7 The experimental-level verification results of the formulation design scheme provided according to a preferred embodiment of the present invention are shown.

[0158] The top-ranked formulation design from 20 PSO-BB optimizations was selected for actual chemical experimental verification. The experimental results are as follows: Figure 7 As shown, the final measured performance index Y value is 1.50, which is significantly higher than the average level of the dataset (1.17), verifying that the proposed optimization method has strong practicality and engineering guidance value.

[0159] In summary, the material preparation formulation optimization design method provided by this invention can efficiently screen out formulation design schemes that meet the constraints of chemical formulation variables and have the best performance. Compared with the prior art, it shows significant advantages in the speed of finding the optimal solution, feasibility verification capability, and convergence. This indicates that the material preparation formulation optimization design method provided by this invention can achieve reverse optimization in a more efficient and accurate manner in complex formulation systems, significantly improving the R&D efficiency of chemical products and providing an innovative technical approach for various material and formulation optimization and performance prediction applications.

[0160] Although the methods described above are illustrated and depicted as a series of actions for the sake of simplicity, it should be understood and appreciated that these methods are not limited by the order of the actions, as some actions may occur in a different order and / or concurrently with other actions from the illustrations and descriptions herein or not illustrated and described herein but which may be understood by those skilled in the art, according to one or more embodiments.

[0161] Those skilled in the art will understand that information, signals, and data can be represented using any of a variety of different techniques and skills. For example, the data, instructions, commands, information, signals, bits, symbols, and chips described throughout the above description can be represented by voltage, current, electromagnetic waves, magnetic fields or magnetic particles, light fields or optical particles, or any combination thereof.

[0162] Those skilled in the art will further appreciate that the various illustrative logic blocks, modules, circuits, and algorithm steps described in conjunction with the embodiments disclosed herein can be implemented as electronic hardware, computer software, or a combination of both. To clearly illustrate this interchangeability between hardware and software, the various illustrative components, blocks, modules, circuits, and steps are described above in a generalized manner in terms of their functionality. Whether such functionality is implemented as hardware or software depends on the specific application and the design constraints imposed on the overall system. Those skilled in the art may implement the described functionality in different ways for each specific application, but such implementation decisions should not be construed as departing from the scope of the invention.

[0163] The various illustrative logic modules and circuits described in conjunction with the embodiments disclosed herein may be implemented or performed using a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA) or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. The general-purpose processor may be a microprocessor, but in alternatives, it may be any conventional processor, controller, microcontroller, or state machine. The processor may also be implemented as a combination of computing devices, such as a combination of a DSP and a microprocessor, multiple microprocessors, one or more microprocessors cooperating with a DSP core, or any other such configuration.

[0164] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein may be embodied directly in hardware, in a software module executed by a processor, or in a combination of both. The software module may reside in RAM memory, flash memory, ROM memory, EPROM memory, EEPROM memory, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium known in the art. An exemplary storage medium is coupled to a processor such that the processor can read and write information to / from the storage medium. In an alternative, the storage medium may be integrated into the processor. The processor and storage medium may reside in an ASIC. The ASIC may reside in a user terminal. In an alternative, the processor and storage medium may reside as discrete components in the user terminal.

[0165] In one or more exemplary embodiments, the described functionality may be implemented in hardware, software, firmware, or any combination thereof. If implemented in software as a computer program product, the functionality may be stored or transmitted as one or more instructions or code on or through a computer-readable medium. A computer-readable medium includes both computer storage media and communication media, encompassing any medium that facilitates the transfer of a computer program from one location to another. A storage medium may be any available medium accessible to a computer. By way of example and not limitation, such a computer-readable medium may include RAM, ROM, EEPROM, CD-ROM or other optical disc storage, disk storage or other magnetic storage devices, or any other medium that can be used to carry or store desired program code in the form of instructions or data structures and is accessible to a computer. Any connection is also legitimately referred to as a computer-readable medium. For example, if the software is transmitted from a website, server, or other remote source using coaxial cable, fiber optic cable, twisted pair, digital subscriber line (DSL), or wireless technologies such as infrared, radio, and microwave, then the coaxial cable, fiber optic cable, twisted pair, DSL, or wireless technologies such as infrared, radio, and microwave are included in the definition of a medium. As used in this article, disk and disc include compact discs (CDs), laser discs, optical discs, digital multi-purpose discs (DVDs), floppy disks, and Blu-ray discs. Disks typically reproduce data magnetically, while discs reproduce data optically using lasers. Combinations of these should also be included within the scope of computer-readable media.

[0166] The prior description of this disclosure is provided to enable any person skilled in the art to make or use this disclosure. Various modifications to this disclosure will be apparent to those skilled in the art, and the general principles defined herein may be applied to other variations without departing from the spirit or scope of this disclosure. Therefore, this disclosure is not intended to be limited to the examples and designs described herein, but should be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for the optimal design of a material preparation recipe, characterized in that, The method comprises the steps of: collecting experimental data comprising different formula combinations and their corresponding performance indicators; designing a formula variable space based on the categories and value rules of the formula variables in the experimental data and formula constraint conditions to determine formula search boundaries comprising discrete variables and continuous variables, wherein the formula constraint conditions are constructed according to the selection rules and dosage ratio logic of the formula variables; based on a target collection function, searching and optimizing in the formula search boundaries by using a particle swarm optimization combined with a branch and bound method to determine a plurality of candidate formula combinations, wherein the target collection function is defined based on the performance prediction value and prediction uncertainty of the candidate formula combinations determined by a support vector regression model, the support vector regression model is constructed and trained based on the formula variables in the experimental data, and the prediction uncertainty is estimated by the kernel similarity between the candidate formula combinations and the support vectors in the support vector regression model; and in response to satisfying the termination condition of the search and optimization, determining the candidate formula combination with the optimal value of the target collection function as the formula design scheme.

2. The method of claim 1, wherein the material preparation formulation is optimized for a desired property. The step of designing the formula variable space based on the categories and value rules of the formula variables in the experimental data and formula constraint conditions comprises: according to the variable categories and value rules in the experimental data, dividing the variables into continuous parameters and mutually exclusive selection parameters, wherein the continuous parameters comprise component proportions and / or auxiliary variable, and the mutually exclusive selection parameters comprise main agent types and / or auxiliary category selection; and taking the continuous parameters as the continuous variables and the mutually exclusive selection parameters as the discrete variables.

3. The method of claim 1, wherein the material preparation formulation is optimized for a desired property. The step of designing the formula variable space based on the categories and value rules of the formula variables in the experimental data and formula constraint conditions further comprises: normalizing the continuous variables.

4. The method of claim 1, wherein the material preparation formulation is optimized for a desired property. The formula constraint conditions comprise the value interval limitation of the continuous variables, the mutually exclusive selection constraint of the discrete variables, the linkage constraint between the continuous variables and the discrete variables, and / or the overall formula total amount constraint.

5. The method of claim 1, wherein the material preparation formulation is optimized for a desired property. The step of designing the formula variable space based on the categories and value rules of the formula variables in the experimental data and formula constraint conditions further comprises: reconstructing and grouping the formula variables based on the formula constraint conditions.

6. The method of claim 1, wherein the material preparation formulation is optimized for a desired property. The step of searching and optimizing in the formula search boundaries based on the target collection function by using the particle swarm optimization combined with the branch and bound method to determine a plurality of candidate formula combinations comprises: S1: initializing the position and speed of the particles; S2: searching in the formula search boundaries, wherein the discrete variables participate in the form of continuous relaxation; S3: updating the position and speed of the particles according to the value of the target collection function of the particles; S4: in response to the current optimal solution being better than the historical optimal solution, processing the discrete variables by the branch and bound method to obtain an improved solution; S5: in response to the improved solution being better than the historical optimal solution, updating the global optimal solution and updating the position and speed of the particles; and S6: repeating steps S2-S5 until the termination condition is met.

7. The method of claim 6, wherein the material preparation formulation is optimized for a desired property. Step S4 comprises: selecting one of the discrete variables closest to an integer as a first discrete variable and performing an integer operation; and performing local particle swarm optimization in a discrete space where the first discrete variable has a value of 1 and a discrete space where the first discrete variable has a value of 0, respectively, to obtain an improved solution.

8. The method of claim 1, wherein the material preparation formulation is optimized for a desired property. The step of constructing and training the support vector regression prediction model comprises: Based on the formula variables in the experimental data as input and the corresponding performance indicators as target values, the support vector regression prediction model is constructed and trained, and the support vector regression prediction model adopts a polynomial kernel function.

9. The method of claim 8, wherein the material preparation formulation is optimized for a desired property. The step of estimating the prediction uncertainty by the kernel similarity between the candidate formula combination and the support vectors in the support vector regression model comprises: Based on the residuals between the true values and the predicted values of the performance indicators corresponding to different formula combinations in the experimental data, the standard deviation of the residuals is calculated as a basic error estimation indicator; calculating the kernel similarity between each candidate formula combination and each support vector in the support vector regression model; calculating the average of the kernel similarity between each candidate formula combination and all support vectors to determine the local confidence indicator of each candidate formula combination; and Based on the local confidence indicator of each candidate formula combination and the standard deviation of the residuals, the prediction uncertainty of each candidate formula combination is determined.

10. The method of claim 9, wherein the material preparation formulation is optimized for a desired property. The expression of the target acquisition function is: ， wherein, the predicted mean determined for a support vector regression prediction model, the predicted uncertainty estimated for the support vector regression model by kernel similarity between candidate formula combinations and support vectors, a hyperparameter balancing exploration and exploitation.

11. The method of claim 1, wherein the material preparation formulation is optimized for a desired property. Further comprising the steps of: double verification of the formula design scheme at the model level and the experimental level.

12. A system for the optimal design of a formulation of a material, characterized in that, including: a memory having computer instructions stored thereon; and a processor connected to the memory and configured to execute the computer instructions stored on the memory to implement the optimization design method of the material preparation formula according to any one of claims 1-11.

13. A computer readable storage medium having stored thereon computer instructions, wherein, The computer instructions are executed by the processor to implement the optimization design method of the material preparation formula according to any one of claims 1-11. The computer instructions are executed by the processor to implement the optimization design method of the material preparation formula according to any one of claims 1-11.

Images