Metamaterial impedance prediction method and device based on machine learning and storage medium

Abstract

The embodiment of the invention provides a metamaterial impedance prediction method based on machine learning, and the method comprises the steps: S1, obtaining a group of sample metamaterial information and a group of label sample dielectric constant information, and enabling each piece of label sample dielectric constant information to correspond to one piece of sample metamaterial information; s2, performing iterative training on a to-be-trained initial machine learning regression model according to the group of sample metamaterial information and the group of label sample dielectric constants so as to guide updating of the initial machine learning regression model by utilizing an evaluation function; and obtaining a target machine learning regression model at the end of training, s3, inputting new metamaterial information into the target machine learning regression model to obtain a predicted dielectric constant; and S4, calculating the impedance value of the metamaterial according to the predicted dielectric constant. According to the prediction method, the dielectric constant and the impedance value of the metamaterial can be quickly found, and accurate prediction can be given after certain training iteration.

Description

Technical Field

[0001] The present invention relates to the field of metamaterial technology, and in particular to a metamaterial impedance prediction method based on machine learning, a computer device, and a computer-readable storage medium. Background Art

[0002] Honeycomb materials are crucial in radome design. Their unique geometry provides exceptional strength and rigidity at a low weight, effectively protecting antennas from physical damage caused by wind, frost, scorching sun, rain, snow, and accidental impact, ensuring their proper operation. Furthermore, the honeycomb's relatively low and stable dielectric constant significantly reduces interference and attenuation of electromagnetic waves transmitted and received by the antenna, ensuring the accuracy and efficiency of the antenna's communication and detection functions.

[0003] Currently, metamaterials, for example, consist of honeycombs and microstructured patterns attached to their walls. Methods for calculating the impedance of these metamaterials often derive the dielectric constant of the metamaterial based on specific assumptions and idealized conditions, and then use theoretical calculations to obtain the matching metamaterial impedance value. However, traditional theoretical calculations, which use methods such as grid search and random search to find the optimal solution, consume a large amount of resources and result in excessive computational effort.

[0004] With the rapid development of artificial intelligence technology, machine learning technology has developed rapidly in various fields. By utilizing the inductive and summarizing characteristics of machine learning technology, we can quickly learn the mapping relationship between input features and output results, and improve the efficiency of antenna / radome design while ensuring the accuracy of output data.

[0005] Traditional metamaterial impedance calculation methods mainly use parameter scanning to find the optimal values of the dielectric constant and impedance of the metamaterial. However, there are problems such as excessive calculation time and insignificant optimization effect. In addition, every time new metamaterial impedance data needs to be calculated, the parameters need to be re-scanned, which consumes a lot of resources.

[0006] Therefore, there are the following requirements in the conventional prior art: that is, the need to reduce the difference between the theoretical situation and the actual situation of metamaterials, and the need to reduce the amount of calculation in the impedance design of metamaterials in actual engineering. Summary of the Invention

[0007] The embodiments of the present invention propose a metamaterial impedance prediction method based on machine learning, a computer device, and a computer-readable storage medium, so as to at least solve the technical problem in the related art of obtaining a target machine learning regression model by training an initial machine learning regression model, and deriving a predicted dielectric constant based on the target machine learning regression model, and then calculating the metamaterial impedance value based on the predicted dielectric constant.

[0008] According to one embodiment of the present invention, a method for predicting metamaterial impedance based on machine learning is provided, which includes:

[0009] Step S1: Obtain a set of sample metamaterial information X = {x1, x2, ..., x n} and a set of label sample dielectric constant information Y = {y1,y2,...,y n}, each label sample dielectric constant information corresponds to a sample metamaterial information; the feature set of each sample metamaterial is defined as x i ={feature1,feature2,...,feature w}, where 1≤i≤n, i, n and w are all natural numbers;

[0010] Step S2: iteratively training the initial machine learning regression model to be trained based on the set of sample metamaterial information and the set of labeled sample dielectric constants, so as to guide the update of the initial machine learning regression model using an evaluation function; and obtaining a target machine learning regression model at the end of the training;

[0011] Step S3: inputting the new metamaterial information into the target machine learning regression model to obtain a predicted dielectric constant;

[0012] Step S4: Calculating the metamaterial impedance value based on the predicted dielectric constant.

[0013] Preferably, the metamaterial in each sample metamaterial information includes a honeycomb and a metal microstructure pattern attached to the honeycomb wall; the feature set of each sample metamaterial information is specifically defined as x i =feature1,feature2,feature3,feature 41 ,feature 42 ,...,feature 4p};feature1,feature2,feature3,feature 41 ,feature 42 ,...,feature 4p are the honeycomb thickness, the direction of the incident electromagnetic wave, the operating frequency, the metamaterial at F1, F2, ..., F p p reflectivities are obtained by actual testing or simulation at the frequencies; the operating frequencies are F1, F2, ..., F p Any of the frequencies.

[0014] Preferably, the step S4 specifically includes:

[0015] Step 1: Calculate multiple electromagnetic parameters eps1 according to the following formula 1;

[0016]

[0017] Wherein, Z1 is a plurality of resistance values of a known metamaterial, and the plurality of resistance values of the metamaterial all correspond to the same operating frequency freq, where freq is F1, F2, ..., F p Any one of the frequencies; eps0 is the predicted dielectric constant obtained by the target machine learning regression model, eps0 is a real value; a, b and c are empirical parameters obtained from tests; j is the symbol of the imaginary part;

[0018] Step 2: Obtain multiple electromagnetic parameters S11 based on the multiple electromagnetic parameters eps1; wherein each electromagnetic parameter S11 is an electromagnetic response of the metamaterial obtained by actual testing or simulation under the corresponding electromagnetic parameter eps1, the same honeycomb thickness d, and the same incident angle theta;

[0019] Step 3: Calculate multiple reflectivities ref according to the following formula 2, where the multiple reflectivities ref correspond to multiple electromagnetic parameters S11 respectively;

[0020] ref=10log 10 |S11|..........Formula 2

[0021] Step 4: Obtain a curve graph showing multiple reflectivities ref corresponding to multiple resistance values Z1 of the metamaterial, wherein the abscissa is the resistance value Z1 of the metamaterial and the ordinate is the reflectivity ref; derive from the curve graph at least one resistance value Z1 of the metamaterial corresponding to a desired reflectivity among the multiple reflectivities ref; and determine the at least one resistance value Z1 of the metamaterial as the metamaterial impedance value.

[0022] Preferably, the honeycomb thickness has three categories of thickness values; the direction of the incident electromagnetic wave includes any one of the honeycomb T direction, honeycomb W direction and honeycomb L direction in the TE mode and the honeycomb T direction, honeycomb W direction and honeycomb L direction in the TM mode, wherein the L direction is the direction of the electromagnetic wave parallel to the honeycomb wall, the W direction is the direction of the electromagnetic wave perpendicular to the honeycomb wall, and the T direction is the direction of the electromagnetic wave passing through the honeycomb cells.

[0023] Preferably, the step S2 specifically includes:

[0024] Step S21, obtaining a training set and a validation set divided according to a certain ratio, wherein the training set includes multiple sets of sample metamaterial information and multiple sets of labeled sample dielectric constant information; the validation set includes multiple sets of verified metamaterial information and multiple sets of labeled verified dielectric constant information, and each set of verified metamaterial information corresponds to one set of labeled verified dielectric constant information;

[0025] Step S23: adopting a decision tree training method, using a set of sample metamaterial information X={x1, x2, ..., x n} and a set of label sample dielectric constant information Y=y1,y2,...,y n} as a training data set for training, and establishing a decision tree; looping through this step until all groups of data in the training set are trained, thereby obtaining a plurality of decision trees, each of which constitutes an initial machine learning regression model; wherein each decision tree corresponds to a different set of sample metamaterial information and a different set of labeled sample dielectric constant information;

[0026] In step S25, the plurality of decision trees constituting the initial machine learning regression model all receive a set of verification metamaterial information and a set of label verification dielectric constant information in the validation set, and respectively generate a plurality of first predicted dielectric constant values, and use the mean of the plurality of first predicted dielectric constant values as the second predicted dielectric constant value output by the initial machine learning regression model; this step is looped until all groups of data in the validation set are verified to obtain a plurality of second predicted dielectric constant values; and the plurality of label verification dielectric constant information and the plurality of second predicted dielectric constant values of all groups in the validation set are evaluated using the evaluation function to calculate an evaluation value;

[0027] Step S27, taking step S23 and step S25 as one iteration, and looping through step S23 and step S25 until the current number of iterations reaches the total number of iterations to obtain multiple evaluation values; and when the maximum value among the multiple evaluation values meets the preset conditions, the initial machine learning regression model corresponding to the maximum value among the multiple evaluation values is determined as the trained target machine learning regression model; wherein, the number of multiple decision trees constituting the initial machine learning regression model is different in each iteration.

[0028] Preferably, when the maximum value among the multiple evaluation values does not meet the preset conditions, the hyperparameters of the initial machine learning regression model are adjusted, and steps S23, S25 and S27 are repeated; the hyperparameters of the initial machine learning regression model include the number of multiple decision trees constituting the initial machine learning regression model and / or the depth of each decision tree.

[0029] Preferably, the number of decision trees constituting the initial machine learning regression model is equal to the current number of iterations; the training set includes 1,500 sets of sample metamaterial information and corresponding 1,500 sets of labeled sample dielectric constant information, and the verification set includes 200 sets of verified metamaterial information and corresponding 200 sets of labeled verified dielectric constant information.

[0030] Preferably, the evaluation function includes at least one of mse, rmse, mae and r2, where mse stands for mean square error, rmse stands for root mean square error, mae stands for mean absolute error, and r2 stands for correlation coefficient; their calculation formulas are as follows:

[0031]

[0032]

[0033] Among them, n is the number of multiple label verification dielectric constant information of all groups in the verification set, y i Verify the dielectric constant information for the actual tag, y′ i is the second dielectric constant value predicted by the model, and y_mean is the mean of the actual dielectric constant information verified by multiple labels.

[0034] Preferably, the training process of each decision tree of the initial machine learning regression model is as follows:

[0035] The training data set D for each decision tree is: D = {(x1, y1), (x2, y2), ... (x n ,y n )};

[0036] The dataset at a leaf node m of the current decision tree is defined as Q, where Q is the sub-dataset after multiple divisions of the original training dataset D. If feature j in the feature set is selected to divide the dataset Q into K categories, the probability that each sample in the dataset Q belongs to the i-th category is p i , then the Gini index calculation method for feature j of data set Q is:

[0037]

[0038] Assuming that the value t of feature j of dataset Q is selected as the threshold, the dataset Q can be divided into two subsets Q left and Q right , the division method is:

[0039] Q left ={(x,y)|x j ≤t};

[0040] Q right =QQ left ;

[0041] x j feature1, feature2, ..., feature w Multiple features in

[0042] At this time, the calculation method of the Gini index of the data set Q is:

[0043]

[0044] Traverse all features and possible values of features in the data set Q, select the feature that minimizes the Gini index and use it as the threshold value to divide the data set Q;

[0045] Recursively divide the dataset Q until it can no longer be divided, and obtain the final decision tree;

[0046] After each decision tree performs the training process, the trained decision trees constitute an initial machine learning regression model.

[0047] According to another embodiment of the present invention, a computer device is provided, comprising a memory and a processor, wherein the memory stores a computer program; wherein the processor implements the steps of the above method when executing the computer program.

[0048] According to yet another embodiment of the present invention, a computer-readable storage medium storing a computer program is provided, wherein the computer program implements the steps of the above method when executed by a processor.

[0049] The beneficial effects of the present invention are:

[0050] The machine learning-based metamaterial impedance prediction method described in the embodiments of the present invention can quickly determine the dielectric constant and impedance values of metamaterials. After a certain number of training iterations, it can provide relatively accurate predictions and is more suitable for practical scenarios. Furthermore, as the number of metamaterial samples and metamaterial test data increases, the predicted metamaterial dielectric constant and impedance values deviate less from the theoretical values. This invention has broad application in aviation, aerospace, military, and other fields involving metamaterials including honeycombs and metal microstructure patterns attached to the honeycomb walls. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0052] Figure 1 This is a flow chart of a metamaterial impedance prediction method based on machine learning according to an embodiment of the present invention.

[0053] Figure 2A specific training flowchart for training the initial machine learning regression model to obtain the target machine learning regression model.

[0054] Figure 3 Comparison of the difference between the model's predicted dielectric constant and the true dielectric constant after training iterations 0 to 350. DETAILED DESCRIPTION

[0055] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention are within the scope of protection of the present invention.

[0056] To reduce the discrepancy between theoretical and practical metamaterials and reduce the computational complexity involved in metamaterial impedance design in practical engineering applications, the present invention proposes a machine learning-based metamaterial impedance prediction method. As a non-limiting explanation, the metamaterial comprises a honeycomb and a metal microstructure pattern attached to the honeycomb walls.

[0057] like Figure 1 As shown, the metamaterial impedance prediction method 100 based on machine learning includes the following steps:

[0058] Step S1: Obtain a set of sample metamaterial information X = {x1, x2, ..., x n} and a set of label sample dielectric constant information Y = {y1,y2,...,y n}, each label sample dielectric constant information corresponds to a sample metamaterial information; the feature set of each sample metamaterial is defined as x i ={feature1,feature2,...,feature w}, where 1≤i≤n, i, n and w are all natural numbers;

[0059] Step S2: iteratively training the initial machine learning regression model to be trained based on the set of sample metamaterial information and the set of labeled sample dielectric constants, so as to guide the update of the initial machine learning regression model using an evaluation function; and obtaining a target machine learning regression model at the end of the training;

[0060] Step S3: inputting the new metamaterial information into the target machine learning regression model to obtain a predicted dielectric constant;

[0061] Step S4: Calculating the metamaterial impedance value based on the predicted dielectric constant.

[0062] In an embodiment of the present invention, the initial machine learning regression model may be a variety of regression models such as CNN (convolutional neural network), LSTM (long short-term memory network), SVM (support vector machine), RF (random forest), etc.; preferably, the initial machine learning regression model is an RF (random forest) model.

[0063] In the embodiment of the present invention, the metamaterial in each sample metamaterial information includes a honeycomb and a metal microstructure pattern attached to the honeycomb wall. Specifically, the metal microstructure pattern can be attached to the honeycomb wall by, for example, photolithography. The feature set of each sample metamaterial information is specifically defined as x i ={feature1,feature2,feature3,feature 41 ,feature 42 ,...,feature 4p};feature1,feature2,feature3,feature 41 ,feature 42 ,...,feature 4p are the honeycomb thickness, the direction of the incident electromagnetic wave, the operating frequency, the metamaterial at F1, F2, ..., F p p reflectivities are obtained by actual testing or simulation at the frequencies; the operating frequencies are F1, F2, ..., F p Any of the frequencies.

[0064] Specifically, the honeycomb thickness has three categories of thickness values; the direction of the incident electromagnetic wave includes any one of the honeycomb T direction, honeycomb W direction and honeycomb L direction in the TE mode and the honeycomb T direction, honeycomb W direction and honeycomb L direction in the TM mode, wherein the L direction is the electromagnetic wave direction parallel to the honeycomb wall, the W direction is the electromagnetic wave direction perpendicular to the honeycomb wall, and the T direction is the electromagnetic wave direction passing through the honeycomb cells.

[0065] In this embodiment, Figure 1 The step S4 specifically includes:

[0066] Step 1: Calculate multiple electromagnetic parameters eps1 according to the following formula 1;

[0067]

[0068] Wherein, Z1 is a plurality of resistance values of a known metamaterial, and the plurality of resistance values of the metamaterial all correspond to the same operating frequency freq, where freq is F1, F2, ..., F pAny one of the frequencies; eps0 is the predicted dielectric constant obtained by the target machine learning regression model, eps0 is a real value; a, b and c are empirical parameters obtained from tests; j is the symbol of the imaginary part;

[0069] Step 2: Obtain multiple electromagnetic parameters S11 based on the multiple electromagnetic parameters eps1; wherein each electromagnetic parameter S11 is an electromagnetic response of the metamaterial obtained by actual testing or simulation under the corresponding electromagnetic parameter eps1, the same honeycomb thickness d, and the same incident angle theta;

[0070] Step 3: Calculate multiple reflectivities ref according to the following formula 2, where the multiple reflectivities ref correspond to multiple electromagnetic parameters S11 respectively;

[0071] ref=10log 10 |S11|..........Formula 2

[0072] Step 4: Obtain a curve graph showing multiple reflectivities ref corresponding to multiple resistance values Z1 of the metamaterial, wherein the abscissa is the resistance value Z1 of the metamaterial and the ordinate is the reflectivity ref; derive from the curve graph at least one resistance value Z1 of the metamaterial corresponding to a desired reflectivity among the multiple reflectivities ref; and determine the at least one resistance value Z1 of the metamaterial as the metamaterial impedance value.

[0073] As a non-limiting explanation, in the left or right portion of the graph, a desired reflectivity among the multiple reflectivities ref corresponds to a single resistance value Z1 of the metamaterial, and the single resistance value Z1 of the metamaterial is then determined as the metamaterial impedance value. In the middle portion of the graph, a desired reflectivity among the multiple reflectivities ref corresponds to two or three resistance values Z1 of the metamaterial, and the two or three resistance values Z1 of the metamaterial are then determined as the metamaterial impedance value.

[0074] Figure 1 The step S2 shown specifically includes the following steps:

[0075] Step S21, obtaining a training set and a validation set divided according to a certain ratio, wherein the training set includes multiple sets of sample metamaterial information and multiple sets of labeled sample dielectric constant information; the validation set includes multiple sets of verified metamaterial information and multiple sets of labeled verified dielectric constant information, and each set of verified metamaterial information corresponds to one set of labeled verified dielectric constant information;

[0076] Step S23: adopting a decision tree training method, using a set of sample metamaterial information X={x1, x2, ..., x n} and a set of label sample dielectric constant information Y=y1,y2,...,y n} as a training data set for training, and establishing a decision tree; looping through this step until all groups of data in the training set are trained, thereby obtaining a plurality of decision trees, each of which constitutes an initial machine learning regression model; wherein each decision tree corresponds to a different set of sample metamaterial information and a different set of labeled sample dielectric constant information;

[0077] In step S25, the plurality of decision trees constituting the initial machine learning regression model all receive a set of verification metamaterial information and a set of label verification dielectric constant information in the validation set, and respectively generate a plurality of first predicted dielectric constant values, and use the mean of the plurality of first predicted dielectric constant values as the second predicted dielectric constant value output by the initial machine learning regression model; this step is looped until all groups of data in the validation set are verified to obtain a plurality of second predicted dielectric constant values; and the plurality of label verification dielectric constant information and the plurality of second predicted dielectric constant values of all groups in the validation set are evaluated using the evaluation function to calculate an evaluation value;

[0078] Step S27, taking step S23 and step S25 as one iteration, and looping through step S23 and step S25 until the current number of iterations reaches the total number of iterations to obtain multiple evaluation values; and when the maximum value among the multiple evaluation values meets the preset conditions, the initial machine learning regression model corresponding to the maximum value among the multiple evaluation values is determined as the trained target machine learning regression model; wherein, the number of multiple decision trees constituting the initial machine learning regression model is different in each iteration.

[0079] When the maximum value among the multiple evaluation values does not meet the preset conditions, the hyperparameters of the initial machine learning regression model are adjusted, and steps S23, S25 and S27 are repeated; the hyperparameters of the initial machine learning regression model include the number of multiple decision trees constituting the initial machine learning regression model and / or the depth of each decision tree.

[0080] The number of decision trees that make up the initial machine learning regression model is equal to the current number of iterations.

[0081] The training set includes 1500 sets of sample metamaterial information and corresponding 1500 sets of labeled sample dielectric constant information, and the validation set includes 200 sets of verified metamaterial information and corresponding 200 sets of labeled verified dielectric constant information.

[0082] The evaluation function includes at least one of mse, rmse, mae and r2, where mse stands for mean square error, rmse stands for root mean square error, mae stands for mean absolute error, and r2 stands for correlation coefficient; their calculation formulas are as follows:

[0083]

[0084] Among them, n is the number of multiple label verification dielectric constant information of all groups in the verification set, y i Verify the dielectric constant information for the actual tag, y′ i is the second dielectric constant value predicted by the model, and y_mean is the mean of the actual dielectric constant information verified by multiple labels.

[0085] Specifically, in this embodiment of the present invention, the MSE value of the final model is 0.009, the RMSE value is 0.004, the MAE value is 0.049, and the R2 value is 0.744. As a non-limiting explanation, when the evaluation value is the R2 value, whether the maximum value among the multiple evaluation values meets the preset condition refers to whether the maximum value among the multiple R2 values is close to 0.744. If the maximum value among the multiple R2 values deviates significantly from 0.744 (for example, the maximum value among the multiple R2 values is 0.5), then it is obvious that the maximum value among the multiple evaluation values does not meet the preset condition.

[0086] As a non-limiting illustration, specifically, Figure 2 A specific training flowchart for training the initial machine learning regression model to obtain the target machine learning regression model includes steps 201 to S215.

[0087] Step 201: Obtain a training set and a validation set divided according to a certain ratio (for example, a training set and a validation set accounting for 80% and 20% respectively, or a training set and a validation set accounting for 85% and 25% respectively, etc.), wherein the training set includes multiple groups of sample metamaterial information and multiple groups of labeled sample dielectric constant information; the validation set includes multiple groups of verified metamaterial information and multiple groups of labeled verified dielectric constant information, and each verified metamaterial information corresponds to a piece of labeled verified dielectric constant information.

[0088] Step 203: Using a decision tree training method, a set of sample metamaterial information X = {x1, x2, ..., x n} and a set of label sample dielectric constant information Y=y1,y2,...,y n} is used as a training data set for training and a decision tree is built.

[0089] Step 205: Determine whether all the group data in the training set have been trained. If not, return to step 203. If yes, execute step 207.

[0090] Step 207: All groups of data in the training set are trained, and multiple decision trees are obtained respectively. The multiple decision trees constitute an initial machine learning regression model; wherein, the group of sample metamaterial information and the group of label sample dielectric constant information corresponding to each decision tree are different. The multiple decision trees constituting the initial machine learning regression model receive a group of verification metamaterial information and a group of label verification dielectric constant information in the validation set, and respectively generate multiple first predicted dielectric constant values, and use the mean of the multiple first predicted dielectric constant values as the second predicted dielectric constant value output by the initial machine learning regression model. This step is executed cyclically until all groups of data in the validation set are verified, so as to obtain multiple second predicted dielectric constant values respectively; the multiple label verification dielectric constant information of all groups in the validation set and the multiple second predicted dielectric constant values are calculated through the evaluation function to obtain evaluation values.

[0091] Step 209: Considering steps S203, S205, and S207 as one iteration, the process loops through steps S203, S205, and S207 to determine whether the current number of iterations has reached the total number of iterations. If not, the process returns to step S203. If so, the process proceeds to step 211.

[0092] Step 211: The current number of iterations has reached the total number of iterations, resulting in multiple evaluation values. The number of evaluation values is equal to the total number of iterations, that is, one evaluation value is obtained for each iteration. Determine whether the maximum value of the multiple evaluation values meets a preset condition. (That is, determine whether the maximum value of the multiple evaluation values (such as the MSE value, the RMSE value, or the MAE value) is close to 0? Or determine whether the maximum value of the multiple evaluation values (such as the R2 value) is close to 1?) If so, execute step 213. If not, execute step 215.

[0093] Step 213: Adjust the hyperparameters of the initial machine learning regression model and repeat steps S203, S205, S207, and S209 (i.e., perform the next iteration) to determine the optimal initial machine learning regression model as the trained target machine learning regression model. As a non-limiting example, the hyperparameters of the initial machine learning regression model include the number of decision trees that constitute the initial machine learning regression model and / or the depth of each decision tree.

[0094] Step 215: Determine the initial machine learning regression model corresponding to the maximum value among the multiple evaluation values as the trained target machine learning regression model.

[0095] In the embodiment of the invention, as a non-limiting explanation, specifically, the training process of each decision tree of the initial machine learning regression model is as follows:

[0096] The training data set D for each decision tree is: D = {(x1, y1), (x2, y2), ... (x n ,y n )};

[0097] The dataset at a leaf node m of the current decision tree is defined as Q, where Q is the sub-dataset after multiple divisions of the original training dataset D. If feature j in the feature set is selected to divide the dataset Q into K categories, the probability that each sample in the dataset Q belongs to the i-th category is p i , then the Gini index calculation method for feature j of data set Q is:

[0098]

[0099] Assuming that the value t of feature j of dataset Q is selected as the threshold, the dataset Q can be divided into two subsets Q left and Q right , the division method is:

[0100] Q left ={(x,y)|x j ≤t};

[0101] Q right =QQ left ;

[0102] x j feature1, feature2, ..., feature w Multiple features in

[0103] At this time, the calculation method of the Gini index of the data set Q is:

[0104]

[0105] Traverse all features and possible values of features in the data set Q, select the feature that minimizes the Gini index and use it as the threshold value to divide the data set Q;

[0106] Recursively divide the dataset Q until it cannot be divided any further (as a non-limiting example, the dataset Q cannot be divided any further, including but not limited to the following situations: the depth of the decision tree reaches the maximum depth value or the preset depth value set when adjusting the hyperparameters of the decision tree, or the decision tree is divided until only one column of features remains (such as only one column of honeycomb thickness features or one column of emitted electromagnetic wave direction features).), and obtain the final decision tree;

[0107] After each decision tree executes the training process, the multiple decision trees after training constitute the initial machine learning regression model. As a non-limiting explanation, since the dielectric constant predicted by the present invention is a continuous value, each decision tree is a regression decision tree; by selecting the best feature for dividing the data set each time, the data set is recursively divided into smaller subsets, so that the disordered data set becomes ordered; the decision tree continues to grow until the data set can no longer be divided (for example, the selection is divided until only one column of features remains (only one column of honeycomb thickness features or one column of incident electromagnetic wave direction features, etc.) or for example, the depth of the decision tree reaches the maximum depth value, etc.), and the final decision tree is obtained; the multiple decision trees finally obtained by executing this method constitute the initial machine learning regression model. In the embodiment of the present invention, the training set includes 1500 groups of sample metamaterial information and corresponding 1500 groups of labeled sample dielectric constant information, and the verification set includes 200 groups of verified metamaterial information and corresponding 200 groups of labeled verified dielectric constant information; wherein, 1500 groups of data are 1500 rows of data; 200 groups of data are 200 rows of data.

[0108] Technical solution attached Figure 3 The figure shows the difference between the predicted values of the model dielectric constant and the true values of the dielectric constant after training iterations 0 to 350. Figure 3 It can be seen that the machine learning regression model can give a relatively accurate prediction after a certain number of training iterations (that is, the difference between the model dielectric constant prediction value and the actual dielectric constant value is small, and the two are relatively close). Specifically, Figure 3 As shown in the figure, after training iterations 0 to 150, the predicted dielectric constant of the machine learning regression model differed significantly from the actual dielectric constant value, making the model's predictions inaccurate. However, as the number of iterations increased, for example, after training iterations 250 to 350, the predicted dielectric constant of the machine learning regression model and the actual dielectric constant value became closer, and the model was able to provide more accurate predictions.

[0109] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A metamaterial impedance prediction method based on machine learning, characterized in that: include: Step S1: Obtain a set of sample metamaterial information X = {x1, x2, ..., x n } and a set of label sample dielectric constant information Y = {y1,y2,...,y n }, each label sample dielectric constant information corresponds to a sample metamaterial information; the feature set of each sample metamaterial is defined as x i ={feature1,feature2,...,feature w }, where 1≤i≤n, i, n and w are all natural numbers; Step S2: iteratively training the initial machine learning regression model to be trained based on the set of sample metamaterial information and the set of labeled sample dielectric constants, so as to guide the update of the initial machine learning regression model using an evaluation function; and obtaining a target machine learning regression model at the end of the training; Step S3: inputting the new metamaterial information into the target machine learning regression model to obtain a predicted dielectric constant; Step S4: Calculating the metamaterial impedance value based on the predicted dielectric constant.

2. The method according to claim 1, wherein: The metamaterial in each sample metamaterial information includes a honeycomb and a metal microstructure pattern attached to the honeycomb wall; the feature set of each sample metamaterial information is specifically defined as x i =feature1,feature2,feature3,feature 41 ,feature 42 ,...,feature 4p };feature1,feature2,feature3,feature 41 ,feature 42 ,...,feature 4p are the honeycomb thickness, the direction of the incident electromagnetic wave, the operating frequency, the metamaterial at F1, F2, ..., F p p reflectivities are obtained by actual testing or simulation at the frequencies; the operating frequencies are F1, F2, ..., F p Any of the frequencies.

3. The method according to claim 2, characterized in that The step S4 specifically includes: Step 1: Calculate multiple electromagnetic parameters eps1 according to the following formula 1; Wherein, Z1 is a plurality of resistance values of a known metamaterial, and the plurality of resistance values of the metamaterial all correspond to the same operating frequency freq, where freq is F1, F2, ..., F p Any one of the frequencies; eps0 is the predicted dielectric constant obtained by the target machine learning regression model, eps0 is a real value; a, b and c are empirical parameters obtained from tests; j is the symbol of the imaginary part; Step 2: Obtain multiple electromagnetic parameters S11 based on the multiple electromagnetic parameters eps1; wherein each electromagnetic parameter S11 is an electromagnetic response of the metamaterial obtained by actual testing or simulation under the corresponding electromagnetic parameter eps1, the same honeycomb thickness d, and the same incident angle theta; Step 3: Calculate multiple reflectivities ref according to the following formula 2, where the multiple reflectivities ref correspond to multiple electromagnetic parameters S11 respectively; ref=10log 10 |S11|..........Official 2 Step 4: Obtain a curve graph showing multiple reflectivities ref corresponding to multiple resistance values Z1 of the metamaterial, wherein the abscissa is the resistance value Z1 of the metamaterial and the ordinate is the reflectivity ref; derive from the curve graph at least one resistance value Z1 of the metamaterial corresponding to a desired reflectivity among the multiple reflectivities ref; and determine the at least one resistance value Z1 of the metamaterial as the metamaterial impedance value.

4. The method according to claim 2, wherein: The honeycomb thickness has three categories of thickness values; the direction of the incident electromagnetic wave includes any one of the honeycomb T direction, honeycomb W direction and honeycomb L direction in the TE mode and the honeycomb T direction, honeycomb W direction and honeycomb L direction in the TM mode, wherein the L direction is the electromagnetic wave direction parallel to the honeycomb wall, the W direction is the electromagnetic wave direction perpendicular to the honeycomb wall, and the T direction is the electromagnetic wave direction passing through the honeycomb cells.

5. The method according to claim 1, wherein The step S2 specifically includes: Step S21, obtaining a training set and a validation set divided according to a certain ratio, wherein the training set includes multiple sets of sample metamaterial information and multiple sets of labeled sample dielectric constant information; the validation set includes multiple sets of verified metamaterial information and multiple sets of labeled verified dielectric constant information, and each set of verified metamaterial information corresponds to one set of labeled verified dielectric constant information; Step S23: adopting a decision tree training method, using a set of sample metamaterial information X={x1, x2, ..., x n } and a set of label sample dielectric constant information Y=y1,y2,...,y n } as a training data set for training, and establishing a decision tree; looping through this step until all groups of data in the training set are trained, thereby obtaining a plurality of decision trees, each of which constitutes an initial machine learning regression model; wherein each decision tree corresponds to a different set of sample metamaterial information and a different set of labeled sample dielectric constant information; In step S25, the plurality of decision trees constituting the initial machine learning regression model all receive a set of verification metamaterial information and a set of label verification dielectric constant information in the validation set, and respectively generate a plurality of first predicted dielectric constant values, and use the mean of the plurality of first predicted dielectric constant values as the second predicted dielectric constant value output by the initial machine learning regression model; this step is looped until all groups of data in the validation set are verified to obtain a plurality of second predicted dielectric constant values; and the plurality of label verification dielectric constant information and the plurality of second predicted dielectric constant values of all groups in the validation set are evaluated using the evaluation function to calculate an evaluation value; Step S27, taking step S23 and step S25 as one iteration, and looping through step S23 and step S25 until the current number of iterations reaches the total number of iterations to obtain multiple evaluation values; and when the maximum value among the multiple evaluation values meets the preset conditions, the initial machine learning regression model corresponding to the maximum value among the multiple evaluation values is determined as the trained target machine learning regression model; wherein, the number of multiple decision trees constituting the initial machine learning regression model is different in each iteration.

6. The method according to claim 5, characterized in that: When the maximum value among the multiple evaluation values does not meet the preset conditions, the hyperparameters of the initial machine learning regression model are adjusted, and steps S23, S25 and S27 are repeated; the hyperparameters of the initial machine learning regression model include the number of multiple decision trees constituting the initial machine learning regression model and / or the depth of each decision tree.

7. The method according to claim 5, characterized in that: The number of decision trees constituting the initial machine learning regression model is equal to the current number of iterations; the training set includes 1,500 sets of sample metamaterial information and corresponding 1,500 sets of labeled sample dielectric constant information, and the validation set includes 200 sets of verified metamaterial information and corresponding 200 sets of labeled verified dielectric constant information.

8. The method according to claim 5, characterized in that: The evaluation function includes at least one of mse, rmse, mae and r2, where mse stands for mean square error, rmse stands for root mean square error, mae stands for mean absolute error, and r2 stands for correlation coefficient; their calculation formulas are as follows: Among them, n is the number of multiple label verification dielectric constant information of all groups in the verification set, y i Verify the dielectric constant information for the actual tag, y′ i is the second dielectric constant value predicted by the model, and y_mean is the mean of the actual dielectric constant information verified by multiple labels.

9. The method according to claim 5, characterized in that: The training process of each decision tree of the initial machine learning regression model is as follows: The training data set D for each decision tree is: D = {(x1, y1), (x2, y2), ... (x n ,y n )}; The dataset at a leaf node m of the current decision tree is defined as Q, where Q is the sub-dataset after multiple divisions of the original training dataset D. If feature j in the feature set is selected to divide the dataset Q into K categories, the probability that each sample in the dataset Q belongs to the i-th category is p i , then the Gini index calculation method for feature j of data set Q is: Assuming that the value t of feature j of dataset Q is selected as the threshold, the dataset Q can be divided into two subsets Q left and Q right , the division method is: Q left ={(x,y)|x j ≤t}; Q right =Q-Q left ; x j feature1, feature2, ..., feature w Multiple features in At this time, the calculation method of the Gini index of the data set Q is: Traverse all features and possible values of features in the data set Q, select the feature that minimizes the Gini index and use it as the threshold value to divide the data set Q; Recursively divide the dataset Q until it can no longer be divided, and obtain the final decision tree; After each decision tree performs the training process, the trained decision trees constitute an initial machine learning regression model.

10. A computer device comprising a memory and a processor, wherein the memory stores a computer program; When the processor executes the computer program, the steps of the method according to any one of claims 1 to 9 are implemented.

11. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, wherein when the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 9 are implemented.

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