CN118378521A - An adaptive sampling method for multi-model decision making based on weighted approximation to ideal points - Google Patents

Abstract

The invention discloses a multi-model decision self-adaptive sampling method based on approximation ideal point weighting, which comprises the following steps: constructing an initial sample set by using a parameterized simulation modeling method, and calculating initial weights by using a weighted model approaching ideal points; based on an initial sample set, inputting initial parameters and constructing an initial multi-model decision model by combining initial weights; calculating a prediction error by adopting an initial multi-model decision model, searching an interested region with the maximum prediction error, and sampling in the interested region to obtain a sampling point set; the sampling point set processing specifically comprises the following steps: calculating output response by adopting a sampling point set, adding the sampling point and the response thereof into an initial sample set, and updating the sample set; based on the updated sample set, the training set and the test set are randomly divided again, and model weights are calculated and updated by using the approximate ideal point model. And updating the multi-model decision model by adopting the updated model weight, and calculating the performance of the multi-model decision model.

Description

An adaptive sampling method for multi-model decision making based on weighted approximation to ideal points

Technical Field

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 technique

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.

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.

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 together 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.

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 uses the radial basis function method to build a proxy model. 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.

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

In order to solve the above technical problems, the present invention proposes an adaptive sampling method for multi-model decision-making 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 an adaptive sampling method for multi-model decision-making.

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;

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 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:

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;

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.

Furthermore, 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, continue to calculate and search for the region of interest until the stopping condition is met.

Furthermore, the process of calculating the initial weights by the approximate ideal point weighted model includes: forward processing, standardization processing, score calculation, and normalization processing.

Furthermore, the forward processing method in the process of calculating the initial weights by the weighted model approaching the ideal point 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.

Furthermore, the method of standardization in the process of calculating the initial weights by the weighted model approaching the ideal point is:

Among them, z _ij represents the standardized evaluation index; x _ij represents the element in the i-th row and j-th column in the forward decision matrix.

Furthermore, the method for calculating the score in the process of calculating the initial weights by the weighted model approaching the ideal point is:

Where D _i ⁺ and D _i ^- represent the distance between the i-th sample and the positive and negative ideal solutions, respectively; They represent the optimal solution and the worst solution under the j-th evaluation index respectively; z _ij represents the standardized evaluation index; w _j represents the weight corresponding to the j-th evaluation index; S _i represents the calculated score of the ith sample.

Furthermore, the method of normalization processing in the process of calculating the initial weights by the weighted model approaching the ideal point is:

Among them, _Wi represents the weight corresponding to the i-th sample, and _Si represents the calculated score of the i-th sample.

Furthermore, the method of predicting the variance in the process of using the initial multi-model decision model to calculate the prediction error and find the region of interest with the maximum prediction error is:

Where n is the number of proxy models in multi-model decision making; is the predicted response of the jth model at _xi ; is the predicted response averaged by the n surrogate models at _xi .

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 calculation and reducing the cost of calculation.

BRIEF DESCRIPTION OF THE DRAWINGS

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:

FIG1 is 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;

FIG2 is a flow chart of calculation of a weighted model approaching an ideal point according to an embodiment of the present invention;

3 is 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;

FIG4 is a graph of experimental data of a 200 nm 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;

FIG5 is a graph showing experimental data of a 400 nm wavelength 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;

FIG6 is a graph showing experimental data of a 600 nm wavelength 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.

Detailed ways

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.

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.

As shown in FIG1 , this embodiment provides a multi-model decision adaptive sampling method based on approximate ideal point weighting, including:

According to the actual problem requirements, the parametric simulation modeling method is used to build the initial sample set S _ini , and the approximate ideal point weighted model is used to calculate the initial weights w _ini .

Based on the initial sample set S _ini , the initial parameters are input and combined with the initial weights _wini to build the initial multi-model decision-making model.

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:

Use the sampling point set to calculate its output response, then add the sampling points and their responses to the initial sample set S _ini , update the sample set, and the updated sample set is S;

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.

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 performance of the multi-model decision-making model:

If the model performance reaches the stopping condition, the model is output. At this time, the multi-model decision model is the required model.

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.

Specifically, first, according to the actual problem requirements, the initial sample set S _ini is constructed using a parametric simulation modeling method. For example, the parameters to be measured of the semiconductor nanostructure and the related measurement configuration parameters are marked as an n-dimensional column vector X = (x ₁ , x ₂ , ..., x _n ) ^T as input parameters for constructing the sample set; then, the initial sample set S _ini is constructed using a parametric simulation modeling method such as rigorous coupled wave analysis (RCWA).

Based on the initial sample set, the initial weights w _ini of the weighted calculation model approaching the ideal point are used. The weighted calculation process of the approximate ideal point is shown in Figure 2, and the 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.

In the embodiment of the present invention, the forward processing process adopts an intermediate forward processing, which is expressed as:

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.

In the embodiment of the present invention, the standardization process adopts the Z-score standardization method, which is expressed as:

Among them, z _ij represents the standardized evaluation index; x _ij represents the element in the i-th row and j-th column in the forward decision matrix.

The method for calculating the score in the process of calculating the initial weights of the weighted model approaching the ideal point is:

Where D _i ⁺ and D _i ^- represent the distance between the i-th sample and the positive and negative ideal solutions, respectively; They represent the optimal solution and the worst solution under the j-th evaluation index respectively; z _ij represents the standardized evaluation index; w _j represents the weight corresponding to the j-th evaluation index; S _i represents the calculated score of the ith sample.

The normalization method in the process of calculating the initial weights of the weighted model approaching the ideal point is:

Among them, _Wi represents the weight corresponding to the i-th sample, and _Si represents the calculated score of the i-th sample.

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:

Where n is the number of proxy models in multi-model decision making; is the predicted response of the jth model at _xi ; represents the predicted response averaged over the n surrogate models at _xi .

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.

Based on the updated multi-model decision-making model, the following performance tests are performed:

If the model performance reaches the stopping condition, the model is outputted, and 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.

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.

As shown in FIG3 , the method proposed in the present invention can replace the parametric simulation modeling process from the input space to the output space, thereby accelerating the simulation modeling, improving its computational efficiency, and reducing the high computational cost.

Figures 4 to 6 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, and achieves the purpose of using fewer sample points to build a more accurate proxy model.

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 any technician familiar with the technical field 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 (8)

1.A multi-model decision self-adaptive sampling method based on approximation ideal point weighting is characterized by comprising the following steps: according to the actual problem demand, an initial sample set is built by using a parameterized simulation modeling method, and initial weights are calculated by using an approximate ideal point weighting model;

based on the initial sample set, inputting initial parameters and constructing an initial multi-model decision model by combining the initial weights;

Calculating a prediction error by adopting the initial multi-model decision model, and searching an interested region with the maximum prediction error, sampling in the interested region, and obtaining a sampling point set; the sampling point set processing specifically comprises the following steps:

calculating output response by adopting the sampling point set, adding the sampling points and the response thereof into an initial sample set, and updating the sample set;

Based on the updated sample set, randomly dividing the training set and the test set again, and calculating and updating model weights by using the model approaching ideal points;

And updating the multi-model decision model by adopting the updated model weight, and calculating the performance of the multi-model decision model.

2. The multi-model decision adaptive sampling method based on the approximate ideal point weighting according to claim 1, wherein the performance expression method for calculating the multi-model decision model is as follows:

outputting a model if the performance of the multi-model decision model reaches a stop condition, and outputting the multi-model decision model;

and if the performance of the multi-model decision model does not meet the stopping condition, continuing to calculate and search the region of interest until the stopping condition is met.

3. The multi-model decision adaptive sampling method based on approximate ideal point weighting according to claim 1, wherein the process of calculating initial weights by the approximate ideal point weighting model comprises: forward normalization processing, score calculation and normalization processing.

4. The multi-model decision adaptive sampling method based on the approximate ideal point weighting according to claim 3, wherein the forward processing method in the process of calculating the initial weight by the approximate ideal point weighting model is as follows:

wherein x _ij represents the evaluation value after forward treatment; a _ij represents the evaluation score of the ith sample in the original decision matrix under the jth evaluation index; a _best represents the optimal evaluation score in the original decision matrix.

5. The multi-model decision adaptive sampling method based on the approximate ideal point weighting according to claim 3, wherein the method for standardization processing in the process of calculating the initial weight by the approximate ideal point weighting model is as follows:

Wherein z _ij represents the normalized evaluation index; x _ij represents an element of the ith row and jth column of the forward decision matrix.

6. The multi-model decision adaptive sampling method based on the approximate ideal point weighting according to claim 3, wherein the method for calculating the score in the process of calculating the initial weight by the approximate ideal point weighting model is as follows:

Wherein D _i ⁺、D_i ^- represents the distances between the ith sample and the positive and negative ideal solutions, respectively; z _j ⁺、z_j ^- represents the optimal solution and the worst solution under the j-th evaluation index respectively; z _ij represents a normalized evaluation index; w _j represents the weight corresponding to the j-th evaluation index; s _i represents the calculated score for the i-th sample.

7. The multi-model decision adaptive sampling method based on the approximate ideal point weighting according to claim 3, wherein the normalization processing method in the process of calculating the initial weight of the approximate ideal point weighting model is as follows:

Wherein W _i represents the weight corresponding to the i-th sample, and S _i represents the calculated score of the i-th sample.

8. The multi-model decision adaptive sampling method based on approximate ideal point weighting according to claim 1, wherein the method for calculating prediction errors by using the initial multi-model decision model and searching the prediction variance in the process of the region of interest with the largest prediction errors is as follows:

Wherein n is the number of agent models in the multi-model decision; predicted response at x _i for the j-th model; Predicted responses averaged at x _i for the n proxy models.