Neural network-based near-zero refractive index metamaterial design method

Abstract

The invention discloses a near-zero refractive index metamaterial design method based on a neural network, and the method comprises the following steps: constructing a Fourier transform neural network, carrying out the fast Fourier transform of a discrete time domain signal sequence through the Fourier transform neural network, obtaining a frequency spectrum sequence of a signal, removing a high-frequency component, and obtaining simplified data, finally, structure parameters are speculated from the simplified data through a neural network, and a result is verified. The discrete S parameter curve data, obtained through simulation, of the metamaterial unit with the near-zero refractive index serves as the discrete time domain signal sequence, and the Fourier transform neural network is trained; and translation of a near-zero refractive index point can be realized by using the trained Fourier transform neural network.

Description

Technical Field

[0001] The present invention belongs to the field of computer or artificial intelligence technology, in particular to the design of antennas in wireless communications, and is a near-zero refractive index metamaterial design method based on a neural network. Background Art

[0002] In wireless communications, high-gain metamaterials have shown important value in many fields such as mobile communications, satellite communications, radar detection, the Internet of Things, and radio and television because they can significantly improve the efficiency and accuracy of signal transmission. For this reason, the current demand for metamaterial design methods is increasing. At the same time, artificial neural networks have shown great potential in solving electromagnetic inverse problems and rapid industrial design. Generally speaking, the application of neural networks in antenna design is to use neural networks to establish a mapping relationship from the complete simulation results of the antenna (such as S curve) to the antenna structure parameters, and then use the expected simulation results to calculate the corresponding target structure parameters to achieve the function of rapid antenna structure parameter design. However, it also leads to a serious problem in the neural network training process. The antenna simulation data used as input is too large, which affects the speed of neural network training and the accuracy of the calculation results. In addition, since the number of frequency points contained in different simulations in different antenna designs is different, the input dimension and network architecture of the neural network need to be modified each time the simulated frequency point is changed.

[0003] Chinese patent CN110245413A discloses a design method for a metamaterial absorbing structure based on a neural network, which uses full-wave simulation software to model the metamaterial structure, establishes a data set of nonlinear relationships between various parameters of the absorbing structure and the corresponding S11 curve; establishes a neural network model, tests the performance of the model, constructs an optimization algorithm based on the neural network, and optimizes the absorbing structure parameters that meet the required goals. However, the disadvantage of this neural network is that the input data is relatively complex, but the key information of the data is not fully mined, resulting in low data processing efficiency.

[0004] In summary, the existing technology has the following two main problems: First, the data processing in the antenna design process is complex, the neural network training speed is slow, and the calculation result accuracy is low. Second, the application of metasurface materials is limited to a single frequency band and lacks frequency band adjustability. Summary of the invention

[0005] In order to overcome the above-mentioned shortcomings of the prior art, the object of the present invention is to provide a near-zero refractive index metamaterial design method based on a neural network to quickly achieve the translation of the near-zero refractive index point of a near-zero refractive index metamaterial unit (Zero-Refractive Index Metamaterial Unit, ZRI-MU).

[0006] In order to achieve the above object, the technical solution adopted by the present invention is:

[0007] A near-zero refractive index metamaterial design method based on a neural network comprises the following steps:

[0008] Step 1, constructing a Fourier transform neural network, wherein the Fourier transform neural network performs fast Fourier transform on a discrete time domain signal sequence to obtain a signal spectrum sequence, removes high frequency components to obtain simplified data, and finally uses the neural network to infer structural parameters from the simplified data and verify the results;

[0009] Step 2, using the discrete S parameter curve data of the near-zero refractive index metamaterial unit obtained by simulation as the discrete time domain signal sequence to train the Fourier transform neural network;

[0010] Step 3: Use the trained Fourier transform neural network to achieve the translation of the near-zero refractive index point.

[0011] In one embodiment, the Fourier transform neural network performs fast Fourier transform on the discrete time domain signal sequence to obtain the spectrum sequence of the signal, and removes the high frequency component to obtain simplified data, and the implementation method is as follows:

[0012] The discrete time domain signal sequence x(n) is subjected to fast Fourier transform to obtain the signal spectrum sequence X(k), namely the Fourier series. The high-frequency components are filtered out by low-frequency filtering, and the low-frequency components are retained to simplify the sampling points.

[0013] In one embodiment, the method of filtering out high-frequency components by low-frequency filtering and retaining low-frequency components to simplify sampling points is implemented as follows:

[0014] Select the cutoff parameter L so that X L (k) is equal to X(k) multiplied by a vector whose first L elements and last L elements are all 1 and the rest are 0, thus obtaining the Fourier series subspace X after low-frequency filtering. L (k);

[0015] By formula Calculate the energy concentration, where a i For X L The modulus of the i-th element in (k), a j is the modulus of the jth element in X(k), and γ is the value of X L The ratio of the energy contained in (k) to the energy contained in X(k), assuming γ>c, indicates that X L (k) can inherit enough information to meet the requirements of neural network modeling, c is the threshold, and for example, c is between 0.9 and 0.99.

[0016] In one embodiment, the method of using a neural network to infer structural parameters from simplified data and reverse verification is as follows:

[0017] Inferring corresponding structural parameters from the simplified data using a complex inverse neural network;

[0018] A complex forward neural network was used to calculate the corresponding simplified data from the inferred structural parameters and verify the results.

[0019] In one embodiment, the complex inverse neural network and the complex forward neural network both have a complex forward propagation process, an optimizer, a CReLU activation function, and a CMSELoss function, but the input and output are opposite.

[0020] In one embodiment, the complex forward propagation process is to perform real-valued two-dimensional convolution on the complex domain, and the formula is:

[0021] W=A+iB

[0022] h=x+iy

[0023] W*h=(A*xB*y)+i(B*x+A*y)

[0024] Where W is the complex convolution kernel, A and B represent the real and imaginary parts of the complex convolution kernel, h is the input complex number, x and y represent the real and imaginary parts of the input complex number, and W*h is the complex convolution process;

[0025] The optimizer adopts the Adam adaptive learning rate optimizer and adds an L2 regularization function to it;

[0026] The CReLU activation function performs activation operations on the real part and the imaginary part, namely:

[0027] CReLU(z)=ReLU(Re(z))+iReLU(Im(z))

[0028] The CMSELoss function has the following formula:

[0029] E loss =(Re(a)-Re(b)) 2 +(Im(a)-Im(b)) 2

[0030] Where a is the predicted value of the structural parameter, b is the true value of the structural parameter, Re() represents the real part, and Im() represents the imaginary part.

[0031] In one embodiment, the verification result is implemented as follows:

[0032] The simplified data obtained by fast Fourier transform and removing high-frequency components and the simplified data obtained using the complex forward neural network are input into the CMSELoss function, and the result is used as the total loss of the Fourier transform neural network. If the total loss is lower than the established threshold, the calculation is considered correct.

[0033] In one embodiment, in step 2, the discrete S parameter curve data is obtained by:

[0034] HFSS full-wave simulation is used to simulate the near-zero refractive index metamaterial unit and generate multiple sets of S-parameter curve data.

[0035] In one embodiment, the step 3 analyzes the key structural parameters that affect the near-zero refractive index characteristics of the near-zero refractive index metamaterial unit, inputs the desired S parameter curve into the trained Fourier transform neural network, obtains its corresponding key structural parameters through inverse design, and realizes the translation of the near-zero refractive index point.

[0036] Compared with the prior art, the present invention has the following beneficial effects:

[0037] By introducing Fourier transform, the input dimension of the neural network is greatly reduced, the number of hidden layers in the neural network is simplified, the number of neurons required is reduced, and the training speed and accuracy of the neural network are improved. At the same time, the reverse and forward cascade network structure is used to effectively improve the accuracy of the neural network calculation results.

[0038] The present invention proposes a fast and universal method for improving the gain of existing antennas. The existing antennas can select the required ZRI-MU refractive index curve by analyzing the working frequency band, and then calculate their structural parameters through FTNN and realize the translation of the near-zero frequency point of ZRI-MU. Through the application of FTNN, key information can be quickly extracted from a large amount of data, thereby accelerating the antenna design process.

[0039] The above description is only an overview of the technical solution of the present invention. In order to more clearly understand the technical means of the present invention, it can be implemented in accordance with the contents of the specification. In order to make the above and other purposes, features and advantages of the present invention more obvious and easy to understand, the following specifically cites a preferred embodiment and describes it in detail with the accompanying drawings as follows. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a flow chart of a design method for realizing ZRI-MU near-zero refractive index point translation based on Fourier transform neural network provided by an embodiment of the present invention.

[0041] Figure 2 This is a schematic diagram of the ZRI-MU structure.

[0042] Figure 3It is a schematic diagram of the transmission characteristics and refractive index of ZRI-MU.

[0043] Figure 4 There are two sets of expected S curves. DETAILED DESCRIPTION

[0044] In order to further explain the technical means and effects adopted by the present invention to achieve the predetermined invention purpose, the following is a detailed description of a method for designing near-zero refractive index metamaterials based on Fourier transform neural network proposed in accordance with the present invention, in combination with the accompanying drawings and specific implementation methods.

[0045] The above and other technical contents, features and effects of the present invention are clearly presented in the following detailed description of the specific implementation modes in conjunction with the accompanying drawings. Through the description of the specific implementation modes, the technical means and effects adopted by the present invention to achieve the predetermined purpose can be more deeply and specifically understood. However, the attached drawings are only for reference and explanation purposes and are not used to limit the technical solutions of the present invention.

[0046] The present invention provides a near-zero refractive index metamaterial design method based on a neural network, the goal of which is to achieve near-zero refractive index point translation of a metamaterial unit, referring to Figure 1 As shown, the main steps are as follows:

[0047] Step 1: Build and train a Fourier transform neural network (FTNN).

[0048] Step 2: Use the trained FTNN to achieve the translation of the near-zero refractive index point of the near-zero refractive index metamaterial unit (ZRI-MU).

[0049] Specifically, step 1 includes:

[0050] Step 1.1: Simplify the data using Fourier transform and its subspace method.

[0051] Specifically, in one embodiment of the present invention, the simulation data of the known metasurface are the S11 curve and the S21 curve in the range of 3 to 15 GHz, and the stepping of both is 0.1 GHz, that is, each curve has 121 frequency points. First, the discrete S parameter curve data is converted into the corresponding Fourier series, and the formula of the known fast Fourier transform is as follows:

[0052]

[0053] x(n)=[x1,x2…,x n ],X(k)=[k1,k2…,k n ]

[0054] Where x(n) is the discrete time domain signal sequence, X(k) is the signal spectrum sequence, that is, the Fourier series, N e represents the number of samples in the time domain and frequency domain, is the basis of Fourier transform. The discrete S-curve data obtained by antenna simulation is compared to a discrete time domain signal sequence, and its corresponding Fourier series can be obtained through FFT transform. The FFT transform formula can be transformed into:

[0055] X(k)=D·x(n)

[0056] Consider x(n) and X(k) as two vectors, and D as the FFT transformation matrix:

[0057]

[0058] Since most of the energy is distributed at both ends of the Fourier series, the high-frequency components in the middle can be filtered out by low-frequency filtering, and only the low-frequency components on both sides can be retained to simplify the sampling points without losing too much information. For this reason, the cutoff parameter L is selected. Considering that each S21 curve in the data set has 121 points, L=25 is selected to establish the Fourier transform subspace. After the cutoff parameter L is determined, X L (k) is equal to X(k) multiplied by a vector whose first L elements and last L elements are all 1 and the rest are 0. Thus, the Fourier series subspace X after low-frequency filtering can be obtained. L (k). The specific formula is as follows:

[0059] X L (k)=X(k)·(1,1,1,1…0,0,0,0…1,1,1,1)

[0060] Next, calculate the energy convergence and take:

[0061]

[0062] where a i For X L The modulus of the i-th element in (k), a j is the modulus of the jth element in X(k), and γ is the value of X L The ratio of the energy contained in (k) to the energy contained in X(k) can reflect the amount of Fourier series information inherited by the Fourier series subspace. Taking γ>c, it means that X L(k) can inherit enough information to meet the requirements of neural network modeling, c is the threshold, c∈0.9~0.99. The present invention believes that when γ>0.95, the Fourier series subspace can inherit enough information to meet the requirements of subsequent neural network modeling. In this embodiment, 121 points are compressed to 25 points, and it is calculated that γ is approximately 0.9555, which meets the requirement of being greater than 0.95.

[0063] Step 1.2: Use a complex inverse neural network to infer the corresponding structural parameters from the simplified data.

[0064] Specifically, in one embodiment of the present invention, pytorch is used as the basic framework of the neural network. Since it is a complex neural network, it is necessary to make certain modifications based on the original framework. The original framework needs to perform a one-dimensional linear operation on the real number domain each time it propagates forward:

[0065] Y=AX+B

[0066] Where X and Y are input and output respectively, which are the simplified data and predicted structural parameters in step 1.1 in the present invention, A represents the weight matrix, and B represents the bias vector. After modification, each forward propagation needs to perform a traditional real-valued two-dimensional convolution in the complex domain. The formula is:

[0067] W=A+iB

[0068] h=x+iy

[0069] W*h=(A*xB*y)+i(B*x+A*y)

[0070] Where W is the complex convolution kernel, A and B represent the real and imaginary parts of the complex convolution kernel respectively, h is the input complex number, x and y represent the real and imaginary parts of the input complex number respectively, and W*h is the complex convolution process.

[0071] After the linear convolution operation, an activation operation is required. The complex inverse neural network uses the CReLU activation function. The CReLU activation function needs to be activated on the real part and the imaginary part respectively, that is:

[0072] CReLU(z)=ReLU(Re(z))+iReLU(Im(z))

[0073] In order to speed up the training, the inverse neural network is initially set to 3 layers. The number of neurons in the input layer and the output layer is determined by the dimensions of the input and output data respectively. In order to maintain good calculation accuracy and speed, the number of neurons in the hidden layer is kept decreasing layer by layer. The calculation formula is:

[0074]

[0075] Where I is the number of neurons in this layer, L and LS represent the current layer and the total number of layers respectively, and B' is the dimension of the input data. When the training effect is not good, gradually increase the number of layers of the inverse neural network to improve the training ability.

[0076] The optimizer of the complex inverse neural network uses the Adam adaptive learning rate optimizer, which speeds up the training process without manually searching for the optimal learning rate, and adds the L2 regularization function to avoid overfitting.

[0077] The loss function of the model adopts the CMSELoss function, which is a modified MSELoss function. Specifically, it calculates the average of the sum of the squares of the real and imaginary parts of the difference between the predicted value and the true value of a set of structural parameters and adds them up as E loss . Where a is the predicted value of the structural parameter, b is the true value of the structural parameter, Re() represents the real part, and Im() represents the imaginary part. The specific formula is as follows:

[0078] E loss =loss(a,b)=(Re(a)-Re(b)) 2 +(Im(a)-Im(b)) 2

[0079] Step 1.3: Use a complex forward neural network to calculate the corresponding simplified data from the inferred structural parameters and verify the results.

[0080] Specifically, in one embodiment of the present invention, the complex forward neural network used is similar to the complex inverse neural network and also has a complex forward propagation process, Adam adaptive learning rate optimizer, L2 regularization, CReLU activation function, and CMSELoss function, but the number of neurons in its hidden layer increases layer by layer, and the input and output are opposite. The structural parameters predicted in step 1.2 are input, and the simplified data obtained by the prediction is output.

[0081] The simplified data calculated in step 1.1 and the simplified data predicted in step 1.3 are input into the CMSELoss function, and the result is used as the total loss of the Fourier transform neural network. If the total loss is lower than the set threshold, the calculation is considered correct.

[0082] Step 1.4: Input data to train the network until the network loss meets expectations.

[0083] Specifically, in one embodiment of the present invention, HFSS full-wave simulation of near-zero refractive index metamaterial units is used to generate a total of 444 sets of S21 curve data as discrete time domain signal sequences, and Fourier transform neural networks are trained. Among these 444 sets of S21 curve data, 400 sets of data are selected as training sets, and the remaining 44 sets of data are used as validation sets. Considering that each S21 curve in the data set has 121 points, L=25 is selected to establish the Fourier transform subspace, and the 121 points are compressed into 25 points. It is calculated that γ is about 0.9555, which meets the requirement of being greater than 0.95. After training, the training time of the model is 1.145 minutes, the training set loss is 0.029, and the validation set loss is 0.0407. It has good speed and accuracy. The full-wave simulation S11 curves corresponding to a set of data X1 = [2.6, 0.85] within the training range but excluded from the training and a set of data X2 = [3.2, 3.2] outside the training range are input below, and the calculation results are Y1 = [2.5452, 0.8142], Y2 = [3.1229, 3.1795]. It can be seen that the model has a relatively accurate prediction ability.

[0084] Specifically, step 2 includes:

[0085] Step 2.1: Design the ZRI-MU and analyze the key structural parameters affecting it.

[0086] The ZRI-MU used in the present invention is composed of a substrate and a metal pattern printed on the front and back surfaces of the substrate. The metal pattern is a complementary double-layer symmetrical resonant ring structure. The ZRI-MU can be periodically arranged in the X-axis direction and the Y-axis direction to form a single-layer coating. Figure 2 As shown, in this embodiment, the metal pattern includes a rectangular patch with a length of l1 and a width of l2, and an elliptical groove is opened in the center. The outer ring major axis of the elliptical groove is r o , the outer ring minor axis is r i There are two intersecting strip grooves along the diagonal of the rectangular patch, and the strip grooves cross the elliptical groove to connect the diagonals. The width of the strip groove outside the elliptical groove is w o , the width of the part inside the elliptical groove is w i The centers of the two long sides of the rectangular patch are respectively provided with strip short grooves, which connect the elliptical groove to the outside of the rectangular patch along the short axis direction of the elliptical groove. The two strip short grooves are symmetrically arranged, and their width is w.

[0087] Refer to the attached Figure 3 , the transmission characteristics of the ZRI-MU of this embodiment and the influence of the refractive index on the antenna gain are analyzed, and it can be found that the near-zero refractive index point of the ZRI-MU is related to the structural parameter w o and w i Related. Figure 3It can be seen that there is a mapping relationship between the near-zero frequency band of its zero refractive index and the S21 curve. The two troughs of the S21 curve correspond to two strong negative electric resonance points and strong negative magnetic resonance points, respectively, forming a transmission stopband, and the near-zero refractive index point is the peak point of the transmission stopband; the high-frequency trough of the S11 curve corresponds to the electric near-zero refractive index point.

[0088] Step 2.2: Input the desired S-parameter curve or refractive index curve into FTNN, and obtain the corresponding key structural parameters through reverse design.

[0089] Refer to the attached Figure 4 , the present invention selects two sets of expected S parameter curves as units 1 and 2, and then finds their corresponding structural parameters. The structural parameters obtained by FTNN calculation are

[0090]

[0091]

[0092] Through the above design, two sets of key structural parameters that affect the near-zero refractive index characteristics of the near-zero refractive index metamaterial unit are obtained, and thus two different sets of S curves with different near-zero frequency points can be obtained, which means that translation is achieved.

[0093] In summary, the present invention constructs FTNN and can realize the translation of the near-zero refractive index point of ZRI-MU for application scenarios such as satellite communication, radar, radio direction finding, and aviation communication. FTNN uses a preprocessing algorithm based on Fourier transform to simplify a large amount of raw data into a small amount of complex data, and then uses an inverse forward tandem neural network (I-FTNN) to quickly inversely design the corresponding structural parameters of ZRI-MU using a simplified expected response curve, thereby realizing the near-zero frequency point translation of ZRI-MU.

[0094] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, replacements and improvements made within the present invention should be included in the protection scope of the present invention.

Claims

1. A method for designing near-zero refractive index metamaterials based on neural networks, characterized in that: The steps include: Step 1, constructing a Fourier transform neural network, wherein the Fourier transform neural network performs fast Fourier transform on a discrete time domain signal sequence to obtain a signal spectrum sequence, removes high frequency components to obtain simplified data, and finally uses the neural network to infer structural parameters from the simplified data and verify the results; Step 2, using the discrete S parameter curve data of the near-zero refractive index metamaterial unit obtained by simulation as the discrete time domain signal sequence to train the Fourier transform neural network; Step 3: Use the trained Fourier transform neural network to achieve the translation of the near-zero refractive index point.

2. The method for designing near-zero refractive index metamaterials based on neural networks according to claim 1, characterized in that: The Fourier transform neural network performs fast Fourier transform on the discrete time domain signal sequence to obtain the signal spectrum sequence, and removes the high-frequency components to obtain simplified data. The implementation method is as follows: The discrete time domain signal sequence x(n) is subjected to fast Fourier transform to obtain the signal spectrum sequence X(k), namely the Fourier series. The high-frequency components are filtered out by low-frequency filtering, and the low-frequency components are retained to simplify the sampling points.

3. The method for designing near-zero refractive index metamaterials based on neural networks according to claim 2, characterized in that: The method of filtering out high-frequency components by low-frequency filtering and retaining low-frequency components to simplify sampling points is as follows: Select the cutoff parameter L so that X L (k) is equal to X(k) multiplied by a vector whose first L elements and last L elements are all 1 and the rest are 0, thus obtaining the Fourier series subspace X after low-frequency filtering. L (k); By formula Calculate the energy concentration, where a i For X L The modulus of the i-th element in (k), a j is the modulus of the jth element in X(k), and γ is the value of X L The ratio of the energy contained in (k) to the energy contained in X(k), assuming γ>c, indicates that X L (k) can inherit enough information to meet the requirements of neural network modeling, and c is the threshold.

4. The method for designing near-zero refractive index metamaterials based on neural networks according to claim 3, characterized in that: The value of c is 0.9~0.

99.

5. The method for designing near-zero refractive index metamaterials based on neural networks according to claim 1, characterized in that: The method of using a neural network to infer structural parameters from simplified data and reverse verification is as follows: Inferring corresponding structural parameters from the simplified data using a complex inverse neural network; A complex forward neural network was used to calculate the corresponding simplified data from the inferred structural parameters and verify the results.

6. The method for designing near-zero refractive index metamaterials based on neural networks according to claim 5, characterized in that: The complex inverse neural network and the complex forward neural network both have a complex forward propagation process, an optimizer, a CReLU activation function and a CMSELoss function, but the input and output are opposite.

7. The method for designing near-zero refractive index metamaterials based on neural networks according to claim 6, characterized in that: The complex forward propagation process is to perform real-valued two-dimensional convolution on the complex domain, and the formula is: W=A+iB h=x+iy W*h=(A*xB*y)+i(B*x+A*y) Where W is the complex convolution kernel, A and B represent the real and imaginary parts of the complex convolution kernel, h is the input complex number, x and y represent the real and imaginary parts of the input complex number, and W*h is the complex convolution process; The optimizer adopts the Adam adaptive learning rate optimizer and adds an L2 regularization function to it; The CReLU activation function performs activation operations on the real part and the imaginary part, namely: CReLU(z)=ReLU(Re(z))+iReLU(Im(z)) The CMSELoss function has the following formula: E loss =(Re(a)-Re(b)) 2 +(Im(a)-Im(b)) 2 Where a is the predicted value of the structural parameter, b is the true value of the structural parameter, Re() represents the real part, and Im() represents the imaginary part.

8. The method for designing near-zero refractive index metamaterials based on neural networks according to claim 5, characterized in that: The verification result is implemented as follows: The simplified data obtained by fast Fourier transform and removing high-frequency components and the simplified data obtained using the complex forward neural network are input into the CMSELoss function, and the result is used as the total loss of the Fourier transform neural network. If the total loss is lower than the established threshold, the calculation is considered correct.

9. The method for designing near-zero refractive index metamaterials based on neural networks according to claim 1, characterized in that: In step 2, the discrete S parameter curve data is obtained by: HFSS full-wave simulation is used to simulate the near-zero refractive index metamaterial unit and generate multiple sets of S-parameter curve data.

10. The method for designing near-zero refractive index metamaterials based on neural networks according to claim 1, characterized in that: The step 3 is to analyze the key structural parameters that affect the near-zero refractive index characteristics of the near-zero refractive index metamaterial unit, input the desired S parameter curve into the trained Fourier transform neural network, obtain the corresponding key structural parameters through inverse design, and realize the translation of the near-zero refractive index point.

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