A coded supercell parameterization modeling method based on polynomial transfer function

Abstract

The application discloses a parameterized modeling method of coded supercell electromagnetic response combining a polynomial transfer function and deep neural network incremental learning, and realizes accurate prediction of electromagnetic response by constructing a deep neural network that fuses self-adaptive homogeneous processing to learn the corresponding relationship between polynomial transfer function coefficients and coded supercell structures. Simulation results show that the electromagnetic response parameter curve of the supercell in the test set predicted by using the parameterized modeling method highly fits the full-wave simulation result of the supercell, and the accuracy is better than that of other traditional methods.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of electromagnetic supercell design, and particularly relates to a coding supercell parameterization modeling method based on a polynomial transfer function and deep neural network incremental learning. BACKGROUND

[0002] Metamaterial is a kind of artificial material realized by artificially arranging micro units, and the size of the structural unit is much smaller than the wavelength of the processed wave. Compared with natural materials, metamaterials can have a negative refractive index, and their unique electromagnetic properties mainly come from their microstructure rather than the constituent material itself. Accordingly, researchers have designed novel metamaterial structures such as invisibility cloaks and superlenses. However, traditional metamaterials are three-dimensional structures that usually need to be arranged and processed in three-dimensional space, which can cause problems such as difficulty in processing and large volume in actual engineering applications. Therefore, metasurfaces have emerged. We regard metasurfaces as two-dimensional structures of metamaterials, which are usually subwavelength thick and composed of subwavelength structures with specific electromagnetic responses. Not only do they overcome the above problems, but they also have the advantages of low cost, low loss, and easy processing. In 2014, the digital coding metasurface proposed by Academician Cui Tiejun allows real-time large-scale control of metasurfaces, making the programmability of metasurface functions possible. Currently, electromagnetic simulation of metasurfaces usually requires the use of numerical simulation software and traditional numerical analysis methods to iteratively solve Maxwell's equations, which consumes a lot of manpower and resources.

[0003] In order to more efficiently design and optimize the structure of electromagnetic metamaterials, it is necessary to propose efficient electromagnetic optimization techniques. Deep neural networks can learn complex function mapping relationships, and researchers have applied them to the field of metamaterial design by inputting parameters that can represent the geometric information of metamaterials into the network, allowing the network to output the corresponding electromagnetic response. This process is called forward prediction. Although the emergence of deep neural networks has efficiently solved the problem of complex and time-consuming iterative solution of Maxwell's equations, with the introduction of coding metamaterials, the degrees of freedom of their surface structures are higher, and simple deep neural networks are no longer able to accurately predict the electromagnetic response of coding metasurfaces, making it urgent to develop more accurate and efficient design methods.

[0004] With a deep understanding of transfer functions and S parameters, researchers have found that transfer functions have the ability to use low-dimensional vectors to represent high-dimensional electromagnetic responses, so combining transfer functions with deep neural networks has become a new research direction. Traditional neural networks sample electromagnetic response S parameters at equal intervals, which has a large dimension and a complex network that is difficult to fit. However, the parameter dimension of the transfer function is greatly reduced, and it can accurately represent the electromagnetic response. Therefore, using the transfer function for parameter modeling has a natural advantage in data dimension reduction.

[0005] However, unlike the parameters representing the coding metamaterial geometric structure, the effective order of the transfer function parameters used to represent the electromagnetic response is not fixed, which requires the parameters of the transfer function to be homogenized to make the order of each sample consistent and facilitate the training of the neural network. However, how to change the parameters during homogenization and how to ensure the consistency and accuracy of the results is a major problem. The present application proposes a new modeling method for this difficult problem. SUMMARY

[0006] The purpose of the present application is to combine the transfer function with the deep neural network to provide a new parameterized modeling method, design a polynomial transfer function coding supercell parameterized modeling method, effectively solve the coefficient discontinuity problem between data with large geometric / coding pattern changes, and improve the accuracy of the forward prediction of the coding supercell.

[0007] Technical scheme: In order to solve the above technical problems and achieve the above application purposes, the present application proposes an electromagnetic coding super surface unit structure with a metal top layer, a dielectric layer, and a metal bottom layer, wherein the top layer is a metal resonance layer; the coding pattern area width of the metal top layer is 8mm, the coding pattern metal copper patch width is 0.5mm, the metal top layer is a center-symmetric 16x16 coding matrix, the metal copper patch of the metal top layer and the metal back plate of the bottom layer have an electrical conductivity σ of 5.8+007S / m, and the thickness t2 of the metal top layer and the metal bottom layer is 0.017mm.

[0008] Further, the dielectric layer of the electromagnetic coding supercell is a dielectric substrate with a material F4B, a relative dielectric constant of 2.65, and a thickness of 2mm.

[0009] Further, the real part Re and the imaginary part Im of the electromagnetic response of the electromagnetic coding super surface unit and the amplitude A and the phase There is a corresponding relationship as follows:

[0010]

[0011]

[0012] In addition, the present application proposes a coding supercell parameterized modeling method based on incremental learning and polynomial transfer function based on any one of the above, which includes the following steps:

[0013] S1, obtaining electromagnetic response S parameters and polynomial transfer function coefficients;

[0014] S2, constructing a data set, the data set is represented as {Meta k ,a k ,b k ,Hs k}, wherein Meta k is a 16x16 encoding matrix which is centrosymmetric, used to represent the kth encoding hypercell, a k and b k represent the polynomial transfer function coefficient vector of the kth encoding hypercell, Hs k represents the response of the kth encoding hypercell;

[0015] S3, construct a coefficient prediction network model fused with adaptive secondary processing:

[0016] S4, input the training set {Meta k} train into the numerator coefficient prediction network, the denominator coefficient prediction network and the homogeneous vector prediction network for multi-task incremental learning;

[0017] S5, input the test set {Meta k} test into the trained three networks to obtain the electromagnetic response within the error allowable range.

[0018] Further, the method of step S1 is as follows:

[0019] The pole residue transfer function form is set as:

[0020]

[0021] wherein H(s) represents the electromagnetic response, p i represents the ith pole, r i represents the ith residue, and N represents the number of pole residue pairs;

[0022] The factor transfer function form is:

[0023]

[0024] wherein p i represents the ith pole, and there are N poles, z i represents the ith zero point, and there are M zero points;

[0025] The numerator and denominator polynomial transfer function is represented as:

[0026]

[0027] wherein a i represents the ith numerator coefficient, and the vector a is composed of M a coefficients, b i represents the ith denominator coefficient, and the vector b is composed of N b coefficients;

[0028] The coding metasurface unit structure is introduced into a full-wave electromagnetic simulation software, and the electromagnetic response S parameters corresponding to the coding metasurface are obtained in batches. The S parameters of the coding metasurface unit sample obtained by the simulation software are H(s), and a set of pole vectors p and residue vectors r are extracted from the S parameters by using the vector fitting technology. The pole vectors and the residue vectors are converted into polynomial transfer function coefficient vectors a and b by using the MATLAB built-in functions zpk and zp2tf.

[0029] The method for extracting a set of numerator polynomial transfer function coefficients from the frequency response parameter S is as follows: the pole vectors p and the residue vectors r in the pole residue transfer function are obtained by using the vector fitting method; the pole vectors and the zero point vectors in the factor transfer function are converted by using the zpk function; and the coefficient vectors a and the coefficient vectors b in the numerator denominator polynomial transfer function are converted by using the zp2tf function.

[0030] The frequency response parameter s is associated with the coefficient vectors a and b by using the numerator denominator polynomial transfer function, where s = j * 2 * pi * f, j is the imaginary unit, and f is the working frequency band of the coding metasurface unit.

[0031] Further, the method of step S2 is as follows:

[0032] The data set is represented as {Meta k ,a k ,b k ,Hs k}, where Meta k is a 16 * 16 coding matrix that is central symmetric and is used to represent the kth coding metasurface unit, a k and b k represent the polynomial transfer function coefficient vectors of the kth coding metasurface unit with an order of N k , and are specifically represented as:

[0033]

[0034] wherein, represents the numerator coefficient of the ith order in the kth coding metasurface unit, represents the denominator coefficient of the ith order in the kth coding metasurface unit, k = 1, 2,..., n f , and n f is the number of coding metasurface unit samples. For the kth sample with an order of N k , N min = 4 and N max = 12 represent the minimum order and the maximum order in all samples, respectively:

[0035]

[0036] and a k and b k are N max polynomial transfer function vectors with effective dimension N k , Hs k is the spectral response data of the k-th sample with dimension 2002, which is obtained by splicing 1001 real part data and 1001 imaginary part data;

[0037] n f = 40000 samples are divided into 80% training set samples {Meta k} train and 20% test set samples {Meta k} test Each sample input is a 16x16 encoding matrix, and the corresponding label is a 12-dimensional numerator polynomial coefficient vector a k , a 12-dimensional denominator polynomial coefficient vector b k , and a 2002-dimensional spectral response vector.

[0038] Further, the method of step S3 is as follows:

[0039] S31, predict the same order numerator denominator coefficient vector A (k) , B (k) and homogeneous vector q (k) :

[0040] The input of the numerator coefficient prediction network A-Predictor, the denominator coefficient prediction network B-Predictor, and the homogeneous vector prediction network Q-Predictor is the encoding matrix Meta k of the encoding super cell, the three network structures all use the ResNet18 structure using a residual network, the optimizer is Adam, A-Predictor outputs N max order numerator coefficient vector A (k) , B-Predictor outputs N max order denominator coefficient vector B (k) , and Q-Predictor outputs N max x N k order homogeneous coefficient vector q (k) ;

[0041] S32, convert different order coefficient prediction vectors and

[0042] Homogeneous coefficient vector q (k) Expand the different order numerator denominator coefficient prediction vectors to the same order numerator denominator coefficient prediction vectors, the order is N max :

[0043]

[0044] in, This represents the i-th numerator coefficient of the k-th coding superunit. This represents the denominator coefficient of the k-th coding superunit. This represents the i-th homogeneous coefficient of the k-th coding superunit. This represents the numerator coefficient of the i-th homogeneous superunit of the k-th coding superunit. M is the denominator coefficient of the i-th homogeneous division of the k-th coding superunit. k =N max -N k M k It is homogeneous as N max The order required for the time step;

[0045] The homogeneous coefficient vector q (k) Construct an N along the diagonal max ×N k matrix Q (k) The homogeneous numerator coefficient vector A of the same order (k) Prediction vectors of molecular coefficients of different orders There is a corresponding relationship:

[0046] A (k) =Q (k) ·a (k)

[0047] Detailed Explanation

[0048]

[0049] The predicted values ​​A of the three sub-models are obtained by using matrix inversion and matrix multiplication. (k) B (k) and q (k) Convert to the corresponding coefficient prediction vector and

[0050]

[0051] S33. Construct a transfer function layer to predict frequency response parameters:

[0052] The homogeneous coefficient vector A is obtained using the numerator coefficient prediction network A-Predictor and the denominator coefficient prediction network B-Predictor. (k) and B (k) Meta is obtained indirectly through the polynomial transfer function. k The corresponding electromagnetic response H k(s), i.e. the transfer function layer, is constructed as a 2002-dimensional spectral response vector by concatenating the real and imaginary parts of the response.

[0053] Further, the construction of the transfer function layer in step S33 is to calculate the spectral response function H k (s) is denoted as:

[0054]

[0055] s = j x 2pf

[0056] where j is the imaginary unit, f is the working frequency band of the encoding hypercell, and the transfer function layer does not update the parameters.

[0057] Further, the specific method of step S4 is as follows:

[0058] S41, the training phase of the numerator coefficient prediction network A-Predictor, the denominator coefficient prediction network B-Predictor, and the homogeneous vector prediction network Q-Predictor is a task T ab :

[0059] Input {Meta k ,a k ,b k} train into the three sub-network models, where {a k ,b k} train is the network training label, and the network output is the predicted numerator and denominator coefficient vector Denoted as task T ab ;

[0060] Input the encoding hypercell matrix Meta k into A-Predictor, B-Predictor, and Q-Predictor, k = 1, 2, …, n f , n f is the number of encoding hypercell samples, the same order homogeneous numerator prediction vector A (k) is output through the numerator coefficient network, the same order homogeneous denominator prediction vector B (k) is output through the denominator coefficient network, and the homogeneous prediction vector q (k) is output through the homogeneous coefficient network, and the numerator and denominator coefficient prediction vector is output after matrix operation. The loss function L ab of the first phase task T old is:

[0061]

[0062] The calculation formula of MAE is:

[0063]

[0064] Wherein, y is the true value, is the predicted value, N is the dimension, and the weight parameters of the three sub-network models are represented as θ A , θ B , θ Q , the task T ab Training target is:

[0065]

[0066] According to the loss function of the task, the gradients of the variables of the three sub-networks are calculated by back propagation, and the parameters of the three sub-networks are updated by the optimizer. The training period epoch is set to 50, and the network weight is updated as θ A ', θ B ', θ Q ';

[0067] S42, obtain the pseudo-label data generated by the first-stage network:

[0068] The output value {a′ k ,b k ′} of the input data Meta k predicted by the source model trained in the first stage is used as a pseudo-label for the training of the second-stage model.

[0069] S43, train the molecular coefficient prediction network A-Predictor, the denominator coefficient prediction network B-Predictor, and the homogeneous vector prediction network Q-Predictor in the second-stage task T Hs :

[0070] Input {Meta k ,a′ k ,b k ′,Hs k} train to the three sub-network models, wherein

[0071] {a′ k ,b k ′,Hs k} train is the network training label, a′ k represents the molecular coefficient pseudo-label of the kth encoding hypercell, and b krepresents the denominator coefficient pseudo label of the kth encoding super unit, and the network output predicts the numerator denominator coefficient vector denoted as old task T ab and the frequency response prediction vector denoted as new task T Hs ;

[0072] In the second stage, two tasks, old task T ab and new task T old are trained simultaneously.

[0073]

[0074] The loss function L Hs of new task T new is as follows:

[0075]

[0076] The calculation formula of MSE is as follows:

[0077]

[0078] Wherein, y is the true value, is the predicted value, N is the dimension, and the weight parameters of the three sub-network models are represented as θ A , θ B and θ Q The training targets of the whole task T ab and T Hs are as follows:

[0079]

[0080] Wherein, λ is a weight coefficient.

[0081] On the basis of the source model trained in the first stage, incremental learning is carried out, the gradients of the variables of the three sub-networks are calculated according to the loss function of the task, the parameter variables of the three sub-networks are updated through the optimizer, the training period epoch is set to 150, and the network weight is updated as θ A ", θ B " and θ Q ".

[0082] After a certain training period in the two stages, the three sub-networks will converge, and after convergence, the network outputs the predicted numerator coefficient predicted denominator coefficient predicted electromagnetic response

[0083] Beneficial effects, compared with the prior art, the technical scheme of the present application has the following beneficial technical effects:

[0084] (1) This invention is based on a coefficient prediction model that integrates adaptive homogeneous processing built upon a polynomial transfer function. This model aims to learn the mapping relationship between the geometry of the superunit and the numerator and denominator coefficients of the polynomial transfer function using a neural network. The model includes two independent, structurally consistent symmetric sub-networks, A-Predictor and B-Predictor, as well as a homogeneous vector prediction model network, Q-Predictor. This enables parametric modeling and homogeneous processing of the superunit, ensuring that the deep neural network can accurately represent the high-dimensional electromagnetic response in a low-dimensional environment.

[0085] (2) This invention introduces the transfer function coefficient a (k) b (k) The prediction error and the prediction error of the electromagnetic response H(s) are optimized simultaneously. A multi-stage fine-tuning training strategy is designed and non-forgetting learning is introduced to design loss functions for different stages, so as to realize incremental learning of the model task.

[0086] (3) In this invention, the transfer function coefficient a (k) b (k) Prediction of electromagnetic response H(s) and prediction of electromagnetic response H(s) are used as two tasks in model learning, and the model is trained incrementally based on these tasks, which greatly improves the model's predictive performance.

[0087] (4) In order to better quantify the model performance, the present invention evaluates the model performance using MSE and regression coefficients respectively. At the same time, in order to verify the performance improvement of the incremental learning strategy of non-forgetting learning in the present invention, it is also compared with the traditional fine-tuning strategy, further illustrating that the method mentioned in the present invention has great significance for network optimization. Attached Figure Description

[0088] Figure 1 This is a diagram of the network model structure and training mechanism of the present invention;

[0089] Figure 2 This is a schematic diagram of the geometric structure of the coding superunit of this invention. Detailed Implementation

[0090] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings, but the scope of protection of the present invention is not limited to the embodiments described.

[0091] Example:

[0092] like Figure 2As shown, the application proposes an electromagnetic coding super surface unit structure, which has a metal top layer, a dielectric layer and a metal bottom layer, wherein the top layer is a metal resonance layer; the coding pattern area width of the metal top layer is 8mm, the coding pattern metal copper patch width is 0.5mm, the metal top layer is a center-symmetric 16x16 coding matrix, the metal copper patch of the metal top layer and the metal back plate of the bottom layer have an electrical conductivity σ of 5.8+007S / m, and the thickness t2 of the metal top layer and the metal bottom layer is 0.017mm.

[0093] Further, the dielectric layer of the electromagnetic coding super unit is a dielectric substrate with a material of F4B, a relative dielectric constant of 2.65 and a thickness of 2mm.

[0094] Further, different coding matrixes correspond to different electromagnetic responses, a simulation frequency range of 8-12GHz is set, and a full-wave simulation software is used to obtain corresponding high-dimensional electromagnetic responses, the real part Re and the imaginary part Im of the electromagnetic response of the electromagnetic coding super surface unit, and the amplitude A and the phase of the electromagnetic response There is a corresponding relationship as follows:

[0095]

[0096] In addition, the application proposes an encoding super unit parameterization modeling method based on incremental learning and polynomial transfer function based on any one of the above, which includes the following steps:

[0097] S1, obtaining electromagnetic response S parameters and polynomial transfer function coefficients;

[0098] S2, constructing a data set, which is represented as {Meta k ,a k ,b k ,Hs k}, wherein Meta k is a center-symmetric 16x16 coding matrix, which is used to represent the kth coding super unit, a k and b k represent the polynomial transfer function coefficient vector of the kth coding super unit, and Hs k represents the response of the kth coding super unit;

[0099] S3, constructing a coefficient prediction network model fused with adaptive secondary processing:

[0100] S4, inputting the training set {Meta k} train into the numerator coefficient prediction network, the denominator coefficient prediction network and the homogeneous vector prediction network for multi-task incremental learning;

[0101] S5, inputting the test set {Meta k}test The input is the electromagnetic response within the error range obtained from the three trained networks.

[0102] Further, the method of step S1 is as follows:

[0103] The pole residue transfer function is set as:

[0104]

[0105] wherein H(s) represents the electromagnetic response, p i represents the ith pole, r i represents the ith residue, and N represents the number of pole residue pairs;

[0106] The factor transfer function is as follows:

[0107]

[0108] wherein p i represents the ith pole, and there are N poles, z i represents the ith zero point, and there are M zero points;

[0109] The numerator denominator polynomial transfer function is as follows:

[0110]

[0111] wherein a i represents the ith numerator coefficient, and the vector a is composed of M a coefficients, b i represents the ith denominator coefficient, and the vector b is composed of N b coefficients;

[0112] The coded metasurface unit structure is imported into a full-wave electromagnetic simulation software, and the electromagnetic response S parameter corresponding to the coded metasurface is obtained in batches. All coded metasurface units and corresponding electromagnetic response data are exported. The S parameter of the coded metasurface unit sample obtained through the simulation software is H(s). A set of pole vector p and residue vector r are extracted from the S parameter using vector fitting technology, and the polynomial transfer function coefficient vector a and vector b are converted through the MATLAB built-in function zpk and function zp2tf.

[0113] A set of numerator denominator polynomial transfer function coefficients is extracted from the frequency response parameter S. The method for obtaining a and vector b is as follows: the pole vector p and residue vector r in the pole residue transfer function are obtained using the vector fitting method; the pole vector and zero point vector in the factor transfer function are converted using the zpk function; and the coefficient vector a and coefficient vector b in the numerator denominator polynomial transfer function are converted using the zp2tf function.

[0114] The frequency response parameter s is associated with the coefficient vectors a and b by a molecular denominator polynomial transfer function, where s = j x 2pif, j is the imaginary unit, and f is the operating frequency band of the coding supercell.

[0115] Further, the method of step S2 is as follows:

[0116] The data set is represented as {Meta k ,a k ,b k ,Hs k}, where Meta k is a 16 x 16 coding matrix that is centrosymmetric, used to represent the kth coding supercell, a k and b k represent the polynomial transfer function coefficient vectors of the kth coding supercell with order N k , and are specifically represented as:

[0117]

[0118] wherein, represents the numerator coefficient of the ith order in the kth coding supercell, represents the denominator coefficient of the ith order in the kth coding supercell, k = 1, 2,..., n f , n f is the number of coding supercell samples, and for the kth sample with order N k , N min = 4 and N max = 12 represent the minimum order and the maximum order in all samples, respectively:

[0119]

[0120] And a k and b k are both N max dimensional polynomial transfer function vectors, with effective dimension N k , Hs k is the spectral response data of the kth sample with dimension 2002, obtained by splicing 1001-dimensional real part data and 1001-dimensional imaginary part data;

[0121] The n f = 40000 samples are divided into 80% training set samples {Meta k} train and 20% test set samples {Meta k} test , and each sample input is a 16 x 16 coding matrix, and the corresponding label is a 12-dimensional numerator polynomial coefficient vector a k, 12-dimensional denominator polynomial coefficient vector b k , 2002-dimensional spectral response vector.

[0122] Further, the method of step S3 is as follows:

[0123] S31, predict the same order numerator denominator coefficient vector A (k) , B (k) and homogeneous vector q (k) :

[0124] The input of the numerator coefficient prediction network A-Predictor, the denominator coefficient prediction network B-Predictor, and the homogeneous vector prediction network Q-Predictor is the encoding matrix Meta of the encoding super cell k The three network structures all use the ResNet18 structure using the residual network, and the optimizer is Adam, A-Predictor outputs N max order numerator coefficient vector A (k) , B-Predictor outputs N max order denominator coefficient vector B (k) , Q-Predictor outputs N max ×N k order homogeneous coefficient vector q (k) ;

[0125] S32, convert different order coefficient prediction vectors and

[0126] Homogeneous coefficient vector q (k) The different order numerator denominator coefficient prediction vectors are expanded into the same order numerator denominator coefficient prediction vectors, and the order is N max :

[0127]

[0128] Wherein, represents the i-th numerator coefficient of the k-th encoding super cell, represents the i-th denominator coefficient of the k-th encoding super cell, represents the i-th homogeneous coefficient of the k-th encoding super cell, represents the i-th homogeneous numerator coefficient of the k-th encoding super cell, is the i-th homogeneous denominator coefficient of the k-th encoding super cell, M k =N max -N k , M k is the order required when the homogeneous is N max order;

[0129] The homogeneous coefficient vector q (k) An N max ×N k matrix Q (k) is constructed along the diagonal, the same order homogeneous numerator coefficient vector A (k) and different order numerator coefficient prediction vector have a corresponding relationship:

[0130] A (k) = Q (k) ·a (k)

[0131] Detailed expansion is

[0132]

[0133] The prediction values A (k) , B (k) and q (k) of the three sub-models are converted into corresponding coefficient prediction vectors and

[0134]

[0135] S33, construct a transfer function layer for frequency response parameter prediction:

[0136] The homogeneous coefficient vectors A (k) and B (k) are obtained by using the numerator coefficient prediction network A-Predictor and the denominator coefficient prediction network B-Predictor, and the corresponding electromagnetic response H k (s) of Meta k is indirectly obtained through the polynomial transfer function, that is, the transfer function layer, and the response real part and imaginary part are spliced to construct a 2002-dimensional spectral response vector.

[0137] Further, the construction of the transfer function layer in step S33 is to calculate the spectral response function H k (s) using the homogeneous numerator coefficient vector generated by the numerator coefficient prediction network A-Predictor and the homogeneous denominator coefficient vector generated by the denominator coefficient prediction network B-Predictor, denoted as:

[0138]

[0139] s = j × 2πf

[0140] Where j is the imaginary unit, and f is the working frequency band of the encoding supercell. The transfer function layer does not update the parameters.

[0141] Further, the specific method of step S4 is as follows:

[0142] S41, the molecular coefficient prediction network A-Predictor, the denominator coefficient prediction network B-Predictor, and the homogeneous vector prediction network Q-Predictor training stage one task T ab :

[0143] Input {Meta k ,a k ,b k} train training data set, wherein {a k ,b k} train is the network training label, and the network output is the predicted numerator denominator coefficient vector denoted as task T ab ;

[0144] Input the encoding hypercell matrix Meta k into A-Predictor, B-Predictor, and Q-Predictor, k=1, 2,..., n f , n f is the number of encoding hypercell samples, the same order homogeneous numerator prediction vector A (k) is output through the molecular coefficient network, the same order homogeneous denominator prediction vector B (k) is output through the denominator coefficient network, and the homogeneous prediction vector q (k) is output through the homogeneous coefficient network, and the numerator denominator coefficient prediction vector is output after matrix operation ab The loss function L old of stage one task T A is:

[0145]

[0146] The calculation formula of MAE is:

[0147]

[0148] Wherein, y is the true value, is the predicted value, N is the dimension, and the weight parameters of the three sub-network models are represented as θ A , θ B , θ Q , the training target of task T ab is:

[0149]

[0150] The gradients of the variables of the three sub-networks are calculated by back propagation according to the loss function of the task, and the parameters of the three sub-networks are updated by the optimizer, the training period epoch is set to 50, and the network weight is updated as θ A ′,θ B ′,θ Q ′;

[0151] S42, obtain the pseudo-label data generated by the first-stage network:

[0152] predict the input data Meta k by the source model trained in the first stage, and output the values {a′ k ,b k ′} on the old task, which are used as pseudo-labels for the training of the second-stage model;

[0153] S43, train the molecular coefficient prediction network A-Predictor, the denominator coefficient prediction network B-Predictor, and the homogeneous vector prediction network Q-Predictor on the second-stage task T Hs :

[0154] input {Meta k ,a′ k ,b k ′,Hs k} train to the three sub-network models, where

[0155] {a′ k ,b k ′,Hs k} train are the training labels of the network, a′ k represents the pseudo-label of the molecular coefficient of the kth encoding hypercell, b k ′ represents the pseudo-label of the denominator coefficient of the kth encoding hypercell, and the network output predicts the molecular and denominator coefficient vector denoted as the old task T ab and the frequency response prediction vector denoted as the new task T Hs ;

[0156] The second stage simultaneously trains two tasks, the loss function L ab of the old task T old is:

[0157]

[0158] the loss function L Hs of the new task T new is:

[0159]

[0160] The calculation formula of MSE is:

[0161]

[0162] wherein y is the real value, is the predicted value, N is the dimension, and the weight parameters of the three sub-network models are represented as θ A , θ B , and θ Q , the overall task T ab , and T Hs The training target is recorded as:

[0163]

[0164] wherein λ is the weight coefficient;

[0165] Based on the source model after the first stage of training, the gradients of the variables of the three sub-networks are calculated by back propagation according to the loss function of the task, and the parameters of the three sub-networks are updated by the optimizer, the training period epoch is set to 150, and the network weight is updated as θ A , θ B , and θ Q .

[0166] After a certain training period in the two stages, the three sub-networks will converge, and the network output prediction numerator coefficients prediction denominator coefficients predicted electromagnetic response

[0167] When the electromagnetic behavior of the electromagnetic coding supercell in the embodiment is parameterized modeled according to the above method, 40,000 8x8 0-1 coding matrices are randomly generated in the embodiment, 0 represents that the position is air, 1 represents that the position is a metal copper patch, and the phase difference between the two is π. The matrix value is reduced by 0.1 to obtain a matrix of 0.9 and -0.1, and is extended to a 16x16 matrix through central symmetry to represent the coding supercell Meta k , and the corresponding electromagnetic response Hs k is obtained through electromagnetic simulation software, and the electromagnetic response vector Hs k has a dimension of 2002, and the corresponding polynomial transfer function coefficient vectors a k and b k are extracted through vector fitting according to steps S1 and S2.

[0168] The data set of the first stage is composed of {Meta k , a k , and b k}, which is divided into a training dataset of size 32,000 {Meta k ,a k ,b k} train and a test dataset of size 8,000 {Meta k ,a k ,b k} test . Among them, the input Meta k has a dimension of 16x16, the dimensions of vectors a k and b k are both 12, the effective minimum dimension is 8, and the maximum dimension is 12, and {a k ,b k} is labeled as the label data of matrix Meta k .

[0169] According to step S3, the numerator coefficient prediction network B-Predictor and the homogeneous vector prediction network Q-Predictor are constructed. The structures of the three networks are all ResNet18 structures using residual networks, the optimizer is Adam, and the input is the encoding matrix Meta k of the encoding hypercell. The numerator coefficient network generates a 12-dimensional high-order homogeneous vector The denominator coefficient network generates a 12-dimensional high-order homogeneous vector The homogeneous vector prediction network generates an 8-dimensional vector which is converted into a 12x12 Q matrix. Then, the predicted values and of the three sub-models are converted into corresponding 12-dimensional coefficient prediction vectors and , of which the effective dimension is at least 4 and at most 12. In phase one, the training period is set to 50, and the learning rate is 0.01.

[0170] In phase two, the pseudo data labels {a′ k ,b k ′} are obtained using the pre-trained network in phase one, and the dataset is constructed as {Meta k ,a′ k ,b k ′,Hs k}. The dataset is divided into a training dataset of size 32,000 {Meta k ,a′ k ,b k ′,Hs k} train and a test dataset of size 8,000 {Meta k ,a′k ,b k ′,Hs k} test 。

[0171] The predicted high-order homogeneous denominator coefficient vector input transfer function layer obtains the predicted value of the electromagnetic response The dimension is 2002. In the second stage, the training period is set to 150, and the learning rate is 0.001. After training for a certain period of time in two stages, the three sub-networks will converge.

[0172] As shown in Table 1, the incremental learning strategy based on the test set verifies that the performance of the non-forgetting learning is improved compared with the traditional fine-tuning strategy. The traditional fine-tuning model and the incremental learning model are trained based on the same source model pre-trained in stage one in the second stage. The mean square error (MSE) and the regression coefficient (R 2 The evaluation index compares the effects of the two models. It can be seen that the MSE of the polynomial transfer function coefficients a and b and the real part, imaginary part, amplitude and phase of the frequency response obtained by the model based on the incremental learning strategy is smaller than that of the model based on the traditional fine-tuning strategy, and the regression coefficient is larger. Among them, the fitting performance of the real part, imaginary part and phase reaches 98.928%, 98.973% and 85.346%, which proves that the fitting accuracy of the incremental learning in the polynomial transfer function coefficients and the frequency response is better than that of the traditional fine-tuning strategy.

[0173] Table 1 Comparison of performance of incremental learning and traditional fine-tuning strategy

[0174]

[0175] The simulation results show that the polynomial transfer function based on the coding hypercell parameterization modeling method constructed according to the method is highly fitted with the polynomial transfer function coefficients and the electromagnetic response real part, imaginary part, amplitude and phase parameter curves of the hypercell in the test set. The full-wave simulation results verify the effectiveness and reliability of the proposed method.

[0176] As described above, although the present application has been represented and described with reference to specific preferred embodiments, it is not to be construed as a limitation on the present application itself. Various changes in form and details can be made therein without departing from the spirit and scope of the present application defined in the appended claims.

Claims

1. A method for parameterized modeling of electromagnetic coded metasurface unit structures based on incremental learning and polynomial transfer functions, characterized in that, Comprise the following steps: S1, obtain electromagnetic response S parameter and polynomial transfer function coefficient; S2, construct a dataset, the dataset is represented as {Meta k ,a k ,b k ,Hs k}, wherein, Meta k is a 16x16 encoding matrix of central symmetry, used to represent the kth encoding metasurface unit, a k and b k represent the polynomial transfer function coefficient vector of the kth encoding metasurface unit, Hs k represents the response of the kth encoding metasurface unit; S3, construct a coefficient prediction network model fused with adaptive homogeneous processing; S4, training set {Meta k} train The input molecule coefficient prediction network, the denominator coefficient prediction network, and the homogeneous vector prediction network are subjected to multi-task incremental learning. S5, the test set {Meta k} test Input the electromagnetic response within the error tolerance range obtained from the three trained networks; The method of step S2 is as follows: The dataset is represented as {Meta k ,a k ,b k ,Hs k}, wherein Meta k is a 16x16 encoding matrix of central symmetry, used to represent the kth encoding metasurface unit, a k and b k represent the polynomial transfer function coefficient vectors of the kth encoding metasurface unit with order N k , and are specifically represented as: wherein, represents the numerator coefficient of the i-th order in the k-th EUS element, represents the denominator coefficient of the i-th order in the k-th EUS element, k = 1, 2,..., n f , n f is the number of EUS element samples, for the k-th sample with order N k , N min = 4 and N max = 12 represent the minimum and maximum order among all samples, respectively: and a k and b k are N max polynomial transfer function vectors of dimension N k , Hs k is the electromagnetic response data of the kth sample of dimension 2002, obtained by concatenating the 1001 real part data and the 1001 imaginary part data. n f = 40000 samples are divided into 80% training set samples {Meta k} train , 20% test set samples {Meta k} test , and each sample input is a 16x16 encoding matrix, and the corresponding label is a 12-dimensional molecular polynomial coefficient vector a k , a 12-dimensional denominator polynomial coefficient vector b k , and a 2002-dimensional electromagnetic response vector; The method of step S3 is as follows: S31, predict the same order molecular denominator coefficient vector A (k) , B (k) and homogeneous vector q (k) : The inputs of the numerator coefficient prediction network A-Predictor, the denominator coefficient prediction network B-Predictor, and the homogeneous vector prediction network Q-Predictor are all the encoding matrix Meta of the encoding metasurface unit k The three network structures all use the ResNet18 structure using a residual network, the optimizer is Adam, the A-Predictor outputs an N max order numerator coefficient vector A (k) The B-Predictor outputs an N max order denominator coefficient vector B (k) The Q-Predictor outputs an N max ×N k order homogeneous coefficient vector q (k) ; S32, convert different order coefficient prediction vector and Homogeneous coefficient vector q (k) Extending different order numerator denominator coefficient prediction vectors to the same order numerator denominator coefficient prediction vectors, the order being N max : wherein, represents the i-th numerator coefficient of the k-th coded metasurface unit, represents the i-th denominator coefficient of the k-th coded metasurface unit, represents the i-th homogeneous coefficient of the k-th coded metasurface unit, represents the i-th homogenized numerator coefficient of the k-th coded metasurface unit, represents the i-th homogenized denominator coefficient of the k-th coded metasurface unit, M k = N max -N k , M k is the order required when the homogeneity is N max order. The homogeneous coefficient vector q (k) is constructed along the diagonal of an N max × N k matrix Q (k) , the homogeneous coefficient vector A (k) of the same order and the coefficient prediction vector of different orders have corresponding relations: In detail: The predicted values A (k) , B (k) and q (k) of the three sub-networks are converted into corresponding coefficient prediction vectors and S33, construct a transfer function layer to predict electromagnetic response parameters: A-Predictor, denominator coefficient prediction network B-Predictor to obtain the homogeneous coefficient vector A (k) and B (k) , indirectly obtained by the polynomial transfer function Meta k corresponding electromagnetic response H k (s), that is, the transfer function layer, is constructed into a 2002-dimensional electromagnetic response vector by splicing the real and imaginary parts of the response; The construction of the transfer function layer in step S33 is calculated using the homogeneous numerator coefficient vector produced by the numerator coefficient prediction network A-Predictor and the homogeneous denominator coefficient vector produced by the denominator coefficient prediction network B-Predictor to produce the electromagnetic response function H k (s), denoted as: s=j×2πf Wherein, j is the imaginary unit, f is the working frequency band of the coding metasurface unit, and the transfer function layer does not update the parameters; The electromagnetic coding metasurface unit structure has a metal top layer, a dielectric layer and a metal bottom layer, wherein the top layer is a metal resonance layer, the coding pattern area width of the metal top layer is 8mm, the coding pattern metal copper patch width is 0.5mm, the metal top layer is a center-symmetric 16×16 coding matrix, and the metal copper patch of the metal top layer and the metal back plate of the bottom layer have an electrical conductivity σ of 5.8+007 S / m, and the thickness t2 of the metal top layer and the metal bottom layer is 0.017mm.

2. The method of claim 1, wherein, The dielectric layer of the electromagnetic coding metasurface unit is a dielectric substrate with F4B material and a relative dielectric constant of 2.65, and the thickness is 2mm.

3. The method of claim 1, wherein, Real part Re and imaginary part Im of the electromagnetic response of the electromagnetic coded metasurface unit and the amplitude A and phase of the electromagnetic response There is a correspondence:

4. The method of claim 1, wherein, The method of step S1 is as follows: The form of the pole residue transfer function is set as: where H(s) represents the electromagnetic response, p i represents the ith pole, r i represents the ith residue, and N represents the number of pole-residue pairs. The form of the factor transfer function is: where p i represents the ith pole, with N poles, z i represents the ith zero, with M zeros; The numerator and denominator polynomial transfer function is expressed as: where a i represents the ith numerator coefficient, and vector a consists of M a coefficients, b i represents the ith denominator coefficient, and vector b consists of N b coefficients; The coding metasurface unit structure is imported into the full-wave electromagnetic simulation software, and the electromagnetic response S parameters corresponding to the coding metasurface are obtained in batches, and all coding metasurface units and corresponding electromagnetic response data are exported; the S parameters obtained by the simulation software are H(s), a set of pole vectors p and residue vectors r are extracted from the S parameters using vector fitting technology, and the polynomial transfer function coefficient vectors a and vectors b are converted by using the MATLAB built-in function zpk and the function zp2tf; A set of numerator and denominator polynomial transfer function coefficients are extracted from the S parameters, that is, the method for obtaining a and vector b is to obtain the pole vector p and the residue vector r in the pole residue transfer function by using the vector fitting method; the pole vector and the zero point vector in the factor transfer function are converted by using the zpk function, and the coefficient vector a and the coefficient vector b in the numerator and denominator polynomial transfer function are converted by using the zp2tf function; The electromagnetic response S parameters are associated with the coefficient vectors a and b through the numerator and denominator polynomial transfer function, wherein s=j×2πf, j is the imaginary unit, and f is the working frequency band of the coding metasurface unit.

5. The method of claim 1, wherein, The specific method of step S4 is as follows: S41, the molecular coefficient prediction network A-Predictor, the denominator coefficient prediction network B-Predictor, and the homogeneous vector prediction network Q-Predictor training phase one task T ab : Input {Meta k ,a k ,b k} train training data set, wherein {a k ,b k} train is the network training label, and the network output predicts the molecular denominator coefficient vector is denoted as task T ab ; Input the encoded metasurface unit matrix Meta into A-Predictor, B-Predictor, and Q-Predictor k k = 1, 2, ..., n f n f To encode the number of metasurface unit samples, a homogeneous molecular prediction vector A is output through a molecular coefficient prediction network. (k) The denominator coefficient prediction network outputs a homogeneous denominator prediction vector B of the same order. (k) The homogeneous vector prediction network outputs a homogeneous prediction vector q. (k) After matrix operations, the predicted vectors of numerator and denominator coefficients are output. Phase 1 Task T ab loss function L old for: The calculation formula of MAE is: wherein y is a true value, is a predicted value, N is a dimension, and the weight parameters of the three sub-network models are represented as θ A , θ B , θ Q , and the task T ab The training target is denoted as: The gradients of the variables of the three sub-networks are calculated by back propagation according to the loss function of the task, and the parameter variables of the three sub-networks are updated by an optimizer, the training period epoch is set to 50, and the network weight is updated as θ A ′,θ B ′,θ Q ′; S42, obtain the pseudo-label data generated by the first network: Predicting input data Meta by the source model trained in phase one k Output values {a ab ′,b k ′} on the old task T k ′} are used as pseudo labels for the training of the model in phase two. S43, the molecular coefficient prediction network A-Predictor, the denominator coefficient prediction network B-Predictor, and the homogeneous vector prediction network Q-Predictor training phase two tasks T Hs : Input {Meta k ,a k ′,b k ′,Hs k} train training dataset, where {a k ′,b k ′,Hs k} train are network training labels, a′ k represents the numerator coefficient pseudo-label of the kth coded metasurface unit, b k ′ represents the denominator coefficient pseudo-label of the kth coded metasurface unit, and the network output predicts the numerator denominator coefficient vector denoted as old task T ab and the electromagnetic response prediction vector denoted as new task T Hs ; Phase two trains two tasks simultaneously, the old task T ab loss function L old is: New task T Hs Loss function L new is: The calculation formula of MSE is: where y is the true value, is the predicted value, N is the dimension, and the weight parameters of the three sub-network models are denoted as θ A , θ B , θ Q , the overall task T ab and T Hs The training target is denoted as: Wherein, λ is the weight coefficient; On the basis of the source model trained in stage one, incremental learning is performed, the gradients of the variables of the three sub-networks are calculated by back propagation according to the loss function of the task, and the parameters of the three sub-networks are updated by the optimizer, the training period epoch is set to 150, and the network weight is updated as θ A ",θ B ",θ Q "; After a certain training period of two stages, the three sub-networks will converge, and after convergence, the network outputs the predicted numerator coefficients predicted denominator coefficients predicted electromagnetic response

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