An adaptive sampling method for multi-model decision making based on weighted approximation to ideal points
Through the multi-model decision-making adaptive sampling method based on approximation ideal point weighting, the problem of long time to build a proxy model and high computational cost is solved, and more efficient proxy model construction and lower computational cost are achieved, which is suitable for complex optimization design problems. .
Patent Information
- Application Number
- CN202410467230.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-04-18
- Publication Date
- 2024-12-31
- Estimated Expiration
- 2044-04-18
AI Technical Summary
In the complex optimization design problem of the prior art, the construction of the agent model and the training sample set are long, and relying on prior knowledge and high computing costs, the computing efficiency and cost have not been effectively improved.
Adaptive sampling method for multi-model decision-making based on approximation ideal point weighting is adopted. The initial sample set is built through parameterized simulation modeling, the initial weight is calculated, the region of interest with the maximum prediction error is found for sampling, and the sample set and model weight are updated until the Stop condition.
It improves computing efficiency, reduces computing costs, achieves faster iterative convergence and better stability and generalization, and is suitable for complex engineering optimization design problems.
Smart Images
Figure CN118378521B_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of efficient proxy modeling, and in particular relates to a multi-model decision-making adaptive sampling method based on approximate ideal point weighting. Background Art
[0002] A surrogate model, also known as a metamodel, is a method of building an approximate model of a real model using a small amount of data. In recent decades, surrogate modeling technology has flourished, and many classic surrogate model methods have emerged, such as polynomial regression (PRS), radial basis function (RBF), Kriging model (KRG), support vector regression (SVR) and other classic methods, as well as new methods represented by deep neural networks (DNN). However, in the face of complex optimization design problems, surrogate models still require a lot of time to build training sample sets. In theory, the more precise the sample set, the better the fitting performance of the surrogate model obtained by training, but this also leads to a geometric increase in the time it takes to build the sample set.
[0003] In recent years, proxy modeling of complex problems is developing from one-time sampling methods, such as classic Latin hypercube sampling (LHD) and uniform design (UD), to sequential adaptive sampling techniques. The one-time sampling method refers to distributing sample points throughout the input space to build a proxy model. Adaptive sampling refers to collecting more sample points in areas where the model prediction error is large (region of interest), and then continuously adding new sample points in an iterative manner to update the proxy model until the stopping criteria are met. This method can build a more accurate proxy model with fewer sample points. Therefore, the present invention attempts to use an adaptive sampling method to solve the above problems.
[0004] A training method for a target detection model with data adaptive resampling is proposed in the prior art. The method randomly screens a pre-acquired sample data set to obtain a first training set, and then adaptively samples the data based on prior knowledge to obtain a second training set. Finally, the two training sets are used to complete the training of the target detection model. However, the subsequent resampling process and model update of this method are based on the second training set, which is very dependent on the acquisition of prior knowledge and the performance of the second training set. How to obtain accurate and sufficient prior knowledge becomes the key to the problem.
[0005] A method for adaptive structural optimization design is proposed in the prior art. The method obtains the initial sampling points through Latin hypercube sampling and constructs a proxy model using the radial basis function method. Finally, a genetic algorithm is used to perform multi-objective inexact search and update the proxy model. However, the performance of this method mainly depends on the performance of the genetic algorithm, and after the inexact search, a finite element analysis simulation model needs to be called for further evaluation, which still requires a high computational cost.
[0006] Although relevant patents have proposed adaptive sampling methods for solving and calculating various models, there are still some problems, especially in terms of computing efficiency and computing cost, which need to be improved. Summary of the invention
[0007] In order to solve the above technical problems, the present invention proposes a multi-model decision-making adaptive sampling method based on weighted approximation to ideal points, which can optimize the weights of multiple models by weighted approximation to ideal points, and then quickly and efficiently construct a proxy model through the adaptive sampling method of multi-model decision-making.
[0008] To achieve the above-mentioned object, the present invention provides a multi-model decision adaptive sampling method based on approximate ideal point weighting, comprising: according to the actual problem requirements, using a parameterized simulation modeling method to build an initial sample set, and using an approximate ideal point weighting model to calculate the initial weights;
[0009] Based on the initial sample set, initial parameters are input and an initial multi-model decision model is built in combination with the initial weights;
[0010] The prediction error is calculated using the initial multi-model decision model, and an area of interest with a maximum prediction error is found, sampling is performed in the area of interest to obtain a sampling point set; the sampling point set processing specifically includes:
[0011] The sampling point set is used to calculate the output response, and then the sampling points and their responses are added to the initial sample set to update the sample set;
[0012] Based on the updated sample set, the training set and test set are randomly re-divided, and the model weights are calculated and updated using the approximate ideal point model;
[0013] The updated model weights are used to update the multi-model decision-making model, and the performance of the multi-model decision-making model is calculated.
[0014] Furthermore, the performance of the multi-model decision-making model is calculated as follows:
[0015] If the performance of the multi-model decision-making model reaches the stopping condition, the model is output, and the multi-model decision-making model is output;
[0016] If the performance of the multi-model decision-making model does not meet the stopping condition, continue to calculate and search for the region of interest until the stopping condition is met.
[0017] Furthermore, the process of calculating the initial weights of the approximate ideal point weighted model includes: forward processing, standardization processing, score calculation, and normalization processing.
[0018] Furthermore, the forward processing method in the process of calculating the initial weights by the approximate ideal point weighted model is:
[0019]
[0020] Among them, x ij Represents the evaluation score after positive processing; a ij represents the evaluation score of the i-th sample in the original decision matrix under the j-th evaluation index; a best Represents the optimal evaluation score in the original decision matrix.
[0021] Furthermore, the method of standardization in the process of calculating the initial weights by the weighted model approaching the ideal point is:
[0022]
[0023] Among them, z ij represents the standardized evaluation index; x ij Represents the element in the i-th row and j-th column of the forward decision matrix.
[0024] Furthermore, the method for calculating the score in the process of calculating the initial weights by the weighted model approaching the ideal point is:
[0025]
[0026]
[0027]
[0028] Among them, D i + , D i - Respectively represent the distance between the i-th sample and the positive and negative ideal solutions; They represent the optimal solution and the worst solution under the jth evaluation index respectively; z ij represents the standardized evaluation index; w j represents the weight corresponding to the jth evaluation index; S i Represents the calculated score of the i-th sample.
[0029] Furthermore, the method of normalization processing in the process of calculating the initial weights by the weighted model approaching the ideal point is:
[0030]
[0031] Among them, W i represents the weight corresponding to the i-th sample, S i Represents the calculated score of the i-th sample.
[0032] Furthermore, the method of predicting the variance in the process of calculating the prediction error using the initial multi-model decision model and finding the region of interest with the maximum prediction error is as follows:
[0033]
[0034] Where n is the number of proxy models in multi-model decision making; For the jth model in x i The predicted response at For n proxy models in x i The average predicted response.
[0035] Technical effect of the invention: The present invention discloses an adaptive sampling method for multi-model decision-making based on weighted approximation to ideal points. The multi-model decision-making strategy used in the present invention can introduce multiple proxy models as references, and the strategy is not limited by the proxy models. Compared with other methods, this method has better stability and generalization, and is suitable for solving complex engineering optimization design problems. In view of the average weight problem existing in traditional multi-model decision-making, the present invention introduces a weighted model that approximates ideal points, which will give greater weights to models with better performance. Compared with traditional methods, this method can achieve iterative convergence at a faster speed, thereby improving the efficiency of calculations and reducing the cost of calculations. BRIEF DESCRIPTION OF THE DRAWINGS
[0036] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:
[0037] Figure 1 A schematic diagram of a flow chart of a multi-model decision-making adaptive sampling method based on weighted approximation to an ideal point according to an embodiment of the present invention;
[0038] Figure 2 This is a flow chart of the weighted model calculation for approaching an ideal point according to an embodiment of the present invention;
[0039] Figure 3 A schematic diagram of a multi-model decision adaptive sampling method based on weighted approximation to an ideal point according to an embodiment of the present invention;
[0040] Figure 4 This is a graph of experimental data of 200nm wavelength of a multi-model decision adaptive sampling method based on weighted approximation to an ideal point according to an embodiment of the present invention;
[0041] Figure 5 This is a graph of experimental data of a 400nm wavelength using a multi-model decision-making adaptive sampling method based on weighted approximation to an ideal point according to an embodiment of the present invention;
[0042] Figure 6This is a graph of experimental data at a wavelength of 600nm based on a multi-model decision-making adaptive sampling method with weights approaching ideal points according to an embodiment of the present invention. DETAILED DESCRIPTION
[0043] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.
[0044] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.
[0045] like Figure 1 As shown, this embodiment provides a multi-model decision adaptive sampling method based on approximate ideal point weighting, including:
[0046] According to the actual problem requirements, the initial sample set S is built using the parametric simulation modeling method. ini , and use the approximate ideal point weighted model to calculate the initial weight w ini .
[0047] Take the initial sample set S ini Based on, input the initial parameters and combine with the initial weight w ini Build an initial multi-model decision-making model.
[0048] The prediction error is calculated using the initial multi-model decision model, and the region of interest with the largest prediction error is found. Then, sampling is performed in the region of interest to obtain a sampling point set. The sampling point set processing specifically includes:
[0049] Use the sample point set to calculate its output response, and then add the sample points and their responses to the initial sample set S ini , update the sample set, the updated sample set is S;
[0050] Based on the sample set S, the training set and test set are randomly re-divided, and the model weight W is calculated and updated using the approximate ideal point model.
[0051] Use the updated model weights W to update the multi-model decision-making model and calculate its performance. Perform the following steps based on the multi-model decision-making model performance:
[0052] If the model performance reaches the stopping condition, the model is output. At this time, the multi-model decision model is the required model.
[0053] If the model performance does not meet the stopping condition, continue to calculate and search for the area of interest until the stopping condition is met. It should be noted that a global search variable G is introduced here to discard some sample points that are close to each other in order to jump out of the current local optimum.
[0054] Specifically, we first build an initial sample set S using a parametric simulation modeling method based on actual problem requirements. ini For example, the measured parameters of the semiconductor nanostructure and the related measurement configuration parameters are marked as an n-dimensional column vector X = (x1, x2, ..., x n ) T As the input parameter for constructing the sample set; then, the initial sample set S is constructed using parametric simulation modeling methods such as rigorous coupled wave analysis (RCWA) ini .
[0055] The initial weight w of the model is calculated based on the initial sample set using the weighted calculation method close to the ideal point. ini , the weighted calculation process of approaching the ideal point is as follows Figure 2 As shown, an initial multi-model decision model is built in combination with the initial parameters. In the embodiment of the present invention, the calculation process of the weighted model approaching the ideal point mainly includes: forward processing, standardization processing, score calculation, and normalization processing.
[0056] In the embodiment of the present invention, the forward processing process adopts an intermediate forward processing, which is expressed as:
[0057]
[0058] Among them, x ij Represents the evaluation score after positive processing; a ij represents the evaluation score of the i-th sample in the original decision matrix under the j-th evaluation index; a best Represents the optimal evaluation score in the original decision matrix.
[0059] In the embodiment of the present invention, the standardization process adopts the Z-score standardization method, which is expressed as:
[0060]
[0061] Among them, z ij represents the standardized evaluation index; x ij Represents the element in the i-th row and j-th column of the forward decision matrix.
[0062] The method for calculating the score in the process of calculating the initial weights of the weighted model approaching the ideal point is:
[0063]
[0064]
[0065]
[0066] Among them, D i + , D i - Respectively represent the distance between the i-th sample and the positive and negative ideal solutions; They represent the optimal solution and the worst solution under the jth evaluation index respectively; z ij represents the standardized evaluation index; w j represents the weight corresponding to the jth evaluation index; S i Represents the calculated score of the i-th sample.
[0067] The method of normalization in the process of calculating the initial weights of the weighted model approaching the ideal point is:
[0068]
[0069] Among them, W i represents the weight corresponding to the i-th sample, S i Represents the calculated score of the i-th sample.
[0070] Based on the initial multi-model decision model, the prediction error is calculated, and the region of interest with the largest prediction error is found. Then, sampling is performed in the region of interest to obtain a set of sampling points. In the embodiment of the present invention, the selected prediction error type is prediction variance, and the region with the largest prediction variance is designated as the region of interest. The prediction variance is defined as follows:
[0071]
[0072] Where n is the number of proxy models in multi-model decision making; For the jth model in x i The predicted response at Represents n proxy models in x i The average predicted response.
[0073] Based on the sampling point set, the training set and the test set are randomly re-divided, and the approximate ideal point model is used to calculate and update the model weight W, and then the multi-model decision model is updated. For example, in an embodiment of the present invention, the training set and the test set are randomly divided according to a ratio of 7:3.
[0074] Based on the updated multi-model decision-making model, the following performance tests are performed:
[0075] If the model performance reaches the stopping condition, the model is output. At this time, the multi-model decision model is the desired model. For example, the stopping condition selected in the embodiment of the present invention is the correlation coefficient R 2 >0.98.
[0076] If the model performance does not meet the stopping condition, the calculation continues and the region of interest is searched until the stopping condition is met. In addition, a global search variable G needs to be introduced here to discard some sample points that are close to each other to jump out of the current local optimum. For example, in the embodiment of the present invention, the Euclidean space distance is selected as the global search variable G to discard sample points that are close to each other.
[0077] like Figure 3 As shown, the method proposed in the present invention can replace the parametric simulation modeling process from input space to output space, thereby accelerating the simulation modeling, improving its calculation efficiency, and reducing the high calculation cost.
[0078] Figures 4 to 6 They are respectively experimental data diagrams of a multi-model decision-making adaptive sampling method based on weighted approximation to ideal points proposed in accordance with the present invention at wavelengths of 200nm, 400nm, and 600nm. As shown in the figure, the problem in the embodiment of the present invention is a five-dimensional optimization problem, and n in the sample size is the dimension of the problem, that is, n=5. The red dotted line in the figure is the performance of the multi-model decision-making adaptive sampling method based on weighted approximation to ideal points under the same experimental conditions. In this embodiment, the method adds 10 sample points each iteration; therefore, the method uses at least 160 sample points (200nm), 110 sample points (400nm), and 130 sample points (600nm) to reach the stopping condition. The above experimental data fully proves that the method of the present invention realizes the rapid and efficient construction of the proxy model, so as to achieve the purpose of building a more accurate proxy model using fewer sample points.
[0079] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.
Claims
1. A multi-model decision adaptive sampling method based on approximate ideal point weighting, characterized in that: include: According to the actual problem requirements, the initial sample set is built using the parametric simulation modeling method, and the initial weights are calculated using the ideal point weighted model; Specifically, building the initial sample set includes: marking the parameters to be measured of the semiconductor nanostructure and the related measurement configuration parameters as an n-dimensional column vector X = (x1, x2, ..., x n ) T As input parameters for constructing sample sets; using parametric simulation modeling methods to build initial sample sets; Based on the initial sample set, initial parameters are input and an initial multi-model decision model is built in combination with the initial weights; The prediction error is calculated using the initial multi-model decision model, and the region of interest with the maximum prediction error is found. Sampling is performed in the region of interest to obtain a sampling point set. The sampling point set processing specifically includes: The sampling point set is used to calculate the output response, and then the sampling points and their responses are added to the initial sample set to update the sample set; Based on the updated sample set, the training set and test set are randomly re-divided, and the model weights are calculated and updated using the approximate ideal point model; Updating the multi-model decision-making model using the updated model weights, and calculating the performance of the multi-model decision-making model; The process of calculating the initial weights by the weighted model approaching the ideal point includes: forward processing, standardization processing, score calculation and normalization processing; The method for calculating the score in the process of calculating the initial weights in the weighted model approaching the ideal point is: Among them, D i + , D i - Respectively represent the distance between the i-th sample and the positive and negative ideal solutions; z j + 、z j - They represent the optimal solution and the worst solution under the jth evaluation index respectively; z ij represents the standardized evaluation index; w j represents the weight corresponding to the jth evaluation index; S i represents the calculated score of the i-th sample; The method of calculating the prediction error using the initial multi-model decision model and finding the prediction variance in the process of the region of interest with the maximum prediction error is: Where n is the number of proxy models in multi-model decision making; For the jth model in x i The predicted response at For n proxy models in x i The average predicted response.
2. The multi-model decision adaptive sampling method based on approximate ideal point weighting according to claim 1, characterized in that: The performance of the multi-model decision-making model is calculated as follows: If the performance of the multi-model decision-making model reaches the stopping condition, the model is output, and the multi-model decision-making model is output; If the performance of the multi-model decision-making model does not meet the stopping condition, the calculation continues and the region of interest is searched until the stopping condition is met.
3. The multi-model decision adaptive sampling method based on approximate ideal point weighting according to claim 1, characterized in that: The forward processing method in the process of calculating the initial weights of the approximate ideal point weighted model is: Among them, x ij Represents the evaluation score after positive processing; a ij represents the evaluation score of the i-th sample in the original decision matrix under the j-th evaluation index; a best Represents the optimal evaluation score in the original decision matrix.
4. The multi-model decision adaptive sampling method based on approximate ideal point weighting according to claim 1, characterized in that: The method of standardization in the process of calculating the initial weights in the approximate ideal point weighted model is: Among them, z ij represents the standardized evaluation index; x ij Represents the element in the i-th row and j-th column of the forward decision matrix.
5. The multi-model decision adaptive sampling method based on approximate ideal point weighting as claimed in claim 1, characterized in that: The method of normalization in the process of calculating the initial weights by the weighted model approaching the ideal point is: Among them, W i represents the weight corresponding to the i-th sample, S i Represents the calculated score of the i-th sample.