An encoding metasurface inverse design method combining deep learning with CST simulation

Abstract

The application discloses a kind of combined deep learning and CST simulation coding metasurface reverse design method, including the following steps, based on conditional variational autoencoder, using coding metasurface matrix and its corresponding phase response curve are jointly trained, and combined with CTS software automatic simulation, the reverse design model of coding metasurface matrix is constructed.The application overcomes the problem of insufficient model learning ability caused by the discreteness and randomness of coding metasurface matrix, and can obtain a directly usable coding metasurface matrix.Compared with traditional iterative optimization algorithm, the efficiency is further improved, and the time cost of coding metasurface reverse design is effectively reduced.In addition, the method realizes the one-to-many characteristics between the phase response curve and the coding metasurface matrix based on the characteristics of the CVAE model, solving the uniqueness problem of the non-iterative deep learning method solution.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic metamaterial design technology, specifically to a coded metasurface reverse design method that combines deep learning and CST simulation. Background Technology

[0002] Metamaterials are three-dimensional composite materials composed of subwavelength unit structures distributed according to artificial structures with periodic or quasi-periodic patterns. They can possess certain properties not found in naturally occurring materials, such as negative permittivity and negative permeability. Electromagnetic metasurfaces can be considered a two-dimensional manifestation of electromagnetic metamaterials, specifically a layered material. Compared to electromagnetic metamaterials, electromagnetic metasurfaces can utilize the abrupt phase and amplitude changes in electromagnetic waves across the metasurface to control the phase and amplitude distribution of reflected and transmitted fields in space. Electromagnetic metasurfaces allow for flexible control of electromagnetic wave amplitude and phase characteristics, exhibiting superior properties such as low loss and good ductility compared to traditional electromagnetic metamaterials. However, traditional metamaterial and metasurface research relies on analog methods, designing their electromagnetic properties from a continuous-scale perspective. This requires the introduction of numerous and complex physical parameters and equivalent models, hindering further metasurface design. In 2014, Professor Cui Tiejun's team at Southeast University proposed the concept of digitally coded metasurfaces, whose core idea lies in using binary numbers to characterize the physical response of unit cells. Digitally encoded metasurfaces have discrete dimensions and electromagnetic parameters, which makes them flexible and tunable.

[0003] Reverse engineering of digitally coded metasurfaces refers to obtaining the corresponding artificial structure arrangement information based on the desired electromagnetic response curve. Traditional metasurface reverse engineering often relies on analyzing physical models and establishing numerical simulations that correlate the intrinsic unit structure with the electromagnetic wave response. This requires designers to possess extensive electromagnetic theory knowledge and rich design experience, resulting in a high design threshold. Furthermore, in engineering applications, it may involve optimization designs on a scale of millions. Using deep learning algorithms for reverse engineering of coded metasurfaces can reduce the computational scale and accelerate the reverse engineering process. However, due to the discreteness and randomness of the coded metasurface structure and the highly nonlinear relationship between its structure and electromagnetic response, it is difficult to directly obtain the corresponding coded metasurface structure from the electromagnetic response curve simply by relying on the fitting ability of neural networks. Summary of the Invention

[0004] The purpose of this invention is to provide a reverse design method for coded metasurfaces that combines deep learning and CST simulation, in order to solve the problems of insufficient model learning ability caused by the discreteness and randomness of the coded metasurface matrix and the highly nonlinear relationship between its structure and electromagnetic response, as well as the uniqueness problem of the reverse design solution in the prior art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a method for reverse design of coded metasurfaces combining deep learning and CST simulation, comprising the following steps:

[0006] Step 1: Split the dataset into training and testing sets; generate a 16×16 encoded metasurface matrix image. i and its corresponding phase response curve vector y i As network input;

[0007] Step 2: Construct the network model, including building the encoder and decoder networks. The encoder outputs the mean μ and variance ε of the training samples; the decoder outputs the reconstructed encoded hypersurface matrix. The model optimizer is set to Adam with a learning rate of 1e. -3 ;

[0008] Step 3: Transfer the training set samples to images i_train and y i_train Input the data into the model in batches and train it in rounds until convergence.

[0009] Step 4: Convert the phase response curve vector y in the test set i_test The data is fed into the decoder of the trained encoded metasurface matrix prediction model to obtain the corresponding reconstructed encoded metasurface matrix. t The encoded metasurface matrix will then be reconstructed. Image of the encoded metasurface matrix in the test set i_test Similarity matching is performed and the results are sorted in descending order to obtain the top n candidate encoded metasurface matrices. i_test Then calculate the image of each candidate encoded metasurface. i_cand The corresponding phase response curve vector y i_cand With phase response curve vector y i_test Curve error loss curve The calculation formula is as follows:

[0010]

[0011] Where M is the dimension of the phase response curve vector;

[0012] Set a curve error threshold (threshold) when the curve error loss... curve The reverse design is considered successful when the error is less than or equal to the threshold. curveThe threshold indicates a failed reverse design, and the design accuracy ACC is obtained. Its value represents the number of coded metasurface matrices that satisfy the conditions found by averaging one phase response curve. The calculation formula is as follows:

[0013]

[0014] Where right_num is the number of correctly designed items; total_num is the number of metasurface matrices encoded in the test set;

[0015] Step 5: In practical applications, the desired phase response curve vector is fed into the decoder of the trained coded metasurface matrix prediction model to obtain the corresponding reconstructed coded metasurface matrix. Then, the reconstructed coded metasurface matrix is ​​matched with the randomly generated set of coded metasurface matrices for similarity and sorted in descending order to obtain a set of candidate coded metasurface matrices. The candidate coded metasurface matrices are then simulated in CST simulation software, and the coded metasurface with the best performance is selected as the final design result.

[0016] Preferably, the encoder includes a convolutional neural network layer, a first concatenative layer, and two fully connected neural network layers with identical network structures: a first fully connected neural network layer and a second fully connected neural network layer.

[0017] Preferably, the decoder includes a second Concatena layer, a fully connected neural network layer, and a deconvolutional neural network layer.

[0018] Preferably, the cyclic training steps are as follows:

[0019] S1. Perform forward computation to calculate the encoded metasurface matrix image. i and its corresponding phase response curve vector y i The encoder obtains the sample mean μ and variance ε, and the decoder outputs the reconstructed encoded metasurface matrix. Calculate the encoding metasurface reconstruction loss Recon The formula for calculating the KL divergence loss is as follows:

[0020]

[0021]

[0022] Where N is the number of samples in the training set;

[0023] S2. Construct a binary constraint loss function based on the reconstructed encoded hypersurface matrix. Binary To ensure the binary nature of the matrix values, the calculation formula is as follows:

[0024]

[0025] The overall loss function of the network is:

[0026] Loss total =loss Recon +loss KL +loss Binary ;

[0027] S3. Update the overall network model parameters through the backpropagation algorithm, calculate the gradient of each variable of each network according to the total network loss function, and feed the obtained gradient of each network variable into the network optimizer, set it as the Adam optimizer, and update the model network parameters through the backpropagation algorithm.

[0028] Compared with existing technologies, the beneficial effects of this invention are as follows: Based on the CVAE model, the encoded metasurface matrix and its corresponding phase response curve are jointly trained, providing prior information based on the intrinsic physical properties for the training of deep neural networks, improving the accuracy of the inverse design of encoded metasurfaces and the generalization performance of the model; and by using the reconstructed encoded metasurface and a series of randomly generated encoded metasurfaces for similarity matching, the problem of low model learning efficiency caused by the randomness of the encoded metasurface matrix is ​​overcome, while realizing the one-to-many characteristic between the phase response curve and the metasurface matrix, that is, multiple encoded metasurfaces that meet the conditions can be obtained by using one phase response curve through one inverse design. Attached Figure Description

[0029] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0030] In the attached diagram:

[0031] Figure 1 This is a flowchart illustrating the structure and training process of the network model of this invention;

[0032] Figure 2 This invention uses the desired phase response curve to obtain the corresponding encoded metasurface flowchart;

[0033] Figure 3 This is a graph showing the decreasing trend of the loss function value during the network training process in this embodiment of the invention.

[0034] Figure 4 This is a specific numerical diagram of the loss function during network training in this embodiment of the invention;

[0035] Figure 5This is a comparison diagram of the phase response curves of multiple solutions obtained by reverse design of a certain desired phase response curve in an embodiment of the present invention: the upper right corner of the figure is the coded metasurface matrix obtained by reverse design;

[0036] Figure 6 This is a comparison chart of four random examples of the present invention and the metasurfaces and their phase response curves obtained by reverse design: the upper right corner of the figure is the coded metasurface matrix obtained by reverse design. Detailed Implementation

[0037] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0038] Example: Figures 1-6 As shown, a method for reverse design of coded metasurfaces combining deep learning and CST simulation includes the following steps:

[0039] Step 1: Split the dataset into training and testing sets; generate a 16×16 encoded metasurface matrix image. i and its corresponding phase response curve vector y i As network input;

[0040] 40,000 sets of 16×16 encoded metasurface matrices were randomly generated and fed into the electromagnetic simulation software CST for numerical simulation. The frequency range was set to 8-12 GHz. A dataset containing 40,000 (encoded metasurface matrix, phase response curve) label pairs was constructed. The dataset was then divided into a training set of size 39,000 and a test set of size 1,000 according to the specific implementation step one.

[0041] Step 2: Construct the network model, including building the encoder and decoder networks. The encoder includes a convolutional neural network layer, a first concatenative layer, and two fully connected neural network layers with identical structures (first and second fully connected neural network layers). The decoder includes a second concatenative layer, a fully connected neural network layer, and a deconvolutional neural network layer. The encoder outputs the mean μ and variance ε of the training samples; the decoder outputs the reconstructed encoded hypersurface matrix. The model optimizer is set to Adam, with an initial learning rate of 1e. -3 The training period is set to 100, the curve error threshold is set to 4, and the selection range select_num is set to 60.

[0042] Step 3: Transfer the training set samples to images i_trainand y i_train Input the data into the model in batches and train it in rounds until convergence.

[0043] The cyclical training steps are as follows:

[0044] S1. Perform forward computation to calculate the encoded metasurface matrix image. i and its corresponding phase response curve vector y i The encoder obtains the sample mean μ and variance ε, and the decoder outputs the reconstructed encoded metasurface matrix. Calculate the encoding metasurface reconstruction loss Recon The formula for calculating the KL divergence loss is as follows:

[0045]

[0046]

[0047] Where N is the number of samples in the training set;

[0048] S2. Construct a binary constraint loss function based on the reconstructed encoded hypersurface matrix. Binary To ensure the binary nature of the matrix values, the calculation formula is as follows:

[0049]

[0050] The overall loss function of the network is:

[0051] Loss total =loss Recon +loss KL +loss Binary ;

[0052] S3. Update the overall network model parameters through the backpropagation algorithm, calculate the gradient of each variable of each network according to the total network loss function, and feed the obtained gradient of each network variable into the network optimizer, set it as the Adam optimizer, and update the model network parameters through the backpropagation algorithm.

[0053] Step 4: Convert the phase response curve vector y in the test set i_test The data is fed into the decoder of the trained encoded metasurface matrix prediction model to obtain the corresponding reconstructed encoded metasurface matrix. The encoding metasurface matrix will then be reconstructed. Image of the encoded metasurface matrix in the test set i_test Similarity matching is performed and the results are sorted in descending order to obtain the top n candidate encoded metasurface matrices. i_test Then calculate the image of each candidate encoded metasurface. i_candThe corresponding phase response curve vector y i_cand With phase response curve vector y i_test Curve error loss curve The calculation formula is as follows:

[0054]

[0055] Where M is the dimension of the phase response curve vector;

[0056] Set a curve error threshold (threshold) when the curve error loss... curve The reverse design is considered successful when the error is less than or equal to the threshold. curve The threshold indicates a failed reverse design, and the design accuracy ACC is obtained. Its value represents the number of coded metasurface matrices that satisfy the conditions found by averaging one phase response curve. The calculation formula is as follows:

[0057]

[0058] Where right_num is the number of correctly designed items; total_num is the number of metasurface matrices encoded in the test set;

[0059] Step 5: In practical applications, the desired phase response curve vector is fed into the decoder of the trained coded metasurface matrix prediction model to obtain the corresponding reconstructed coded metasurface matrix. Then, the reconstructed coded metasurface matrix is ​​matched with the randomly generated set of coded metasurface matrices for similarity and sorted in descending order to obtain a set of candidate coded metasurface matrices. The candidate coded metasurface matrices are then simulated in CST simulation software, and the coded metasurface with the best performance is selected as the final design result.

[0060] After 100 training cycles, the training set = 3.29e -1 =2.48e -1 =2.44e -2 =5.66e -2 Test set ACC = 3.0725; Reference Figure 5 These are multiple solutions obtained by reverse designing a certain phase response curve in an embodiment of the present invention.

[0061] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for inverse design of coding metasurfaces combining deep learning with CST simulation, characterized in that, The method comprises the following steps: Step one: Split the dataset into training and test sets; encode the metasurface matrix image i and its corresponding phase response curve vector y i as network input; Step two: constructing a network model, including constructing an encoder Encoder and a decoder Decoder, respectively, and the encoder Encoder outputs the mean value mu and the variance epsilon of the training sample; Decoder outputs a reconstructed encoding metasurface matrix The model optimizer is set to Adam with a learning rate of 1e -3 ; Step three: input the training set samples image i_train and y i_train into the model in batches, and train in rounds until convergence; Step four: the phase response curve vector y in the test set i_test is input into the decoder of the trained encoding metasurface matrix prediction model to obtain the corresponding reconstructed encoding metasurface matrix Subsequently, the reconstructed encoding metasurface matrix is compared with the encoding metasurface matrix image in the test set i_test for similarity matching and descending sorting to obtain the top n candidate encoding metasurface matrices image i_test Then, the phase response curve vector y corresponding to each candidate encoding metasurface matrix image i_cand is calculated i_cand The curve error loss between the phase response curve vector y corresponding to each candidate encoding metasurface matrix image i_test is calculated curve , and the calculation formula is as follows: Wherein M is the dimension of the phase response curve vector; A curve error threshold threshold is set, and when the curve error loss curve is less than the threshold, it is determined that the inverse design is successful, when the curve error loss curve is greater than the threshold, it is determined that the inverse design fails, and a design accuracy ACC is obtained, the value of which represents that ACC code metasurface matrices meeting the conditions can be found for an average phase response curve, and the calculation formula is as follows: Wherein right_num is the number of correct designs; total_num is the number of test set coding metasurface matrixes; Step five: in practical application, the expected phase response curve vector is input into the decoder of the trained coding metasurface matrix prediction model to obtain the corresponding reconstructed coding metasurface matrix, then the reconstructed coding metasurface matrix is matched with the randomly generated coding metasurface matrix set in similarity and is sorted in descending order to obtain a candidate coding metasurface matrix set, and then the candidate coding metasurface matrix is simulated in CST simulation software, and the coding metasurface with the optimal performance is selected as the final design result.

2. The method of claim 1, wherein the method is characterized by: The encoder Encoder comprises a convolutional neural network layer, a first Concatena layer, and two first fully connected neural network layers and second fully connected neural network layers with the same network structure.

3. The method of claim 1, wherein the method further comprises: determining a CST simulation of the designed coding metasurface based on the determined CST parameters. The decoder Decoder comprises a second Concatena layer, a fully connected neural network layer, and an inverse convolutional neural network layer.

4. The method of claim 1, wherein the method further comprises: The round-robin training step is as follows: S1, perform forward calculation, calculate the encoding metasurface matrix image i and its corresponding phase response curve vector y i After the encoder, the sample mean μ and the variance ε are obtained, and the reconstructed encoding metasurface matrix output after the decoder Calculate the encoding metasurface reconstruction loss loss Recon And the KL divergence loss calculation formula is as follows: Wherein N is the number of training set samples; S2, according to the reconstruction of the encoding metasurface matrix, construct the binary constraint loss loss Binary , ensure the binary of the matrix value, the calculation formula is as follows: The total loss function of the network is: Loss total = loss Recon + loss KL + loss Binary ; S3, updating the overall network model parameters through a back propagation algorithm, calculating the gradient of each variable of each network according to the total loss function of the network, inputting the obtained gradient of each variable of each network into a network optimizer, setting the optimizer as an Adam optimizer, and updating the model network parameters through a back propagation algorithm.

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