Encoding supercell parameterization modeling method based on physical information representation

Abstract

The application discloses an encoding supercell parameterization modeling method based on physical information representation, realizes accurate prediction of electromagnetic response by constructing a deep neural network of physical information to learn the correspondence between the pole residue of a transfer function and an encoding super surface structure, and simulation results show that the electromagnetic response parameter curve of a random super surface in a test set predicted by using the method is highly fitted with the full-wave simulation result of the super cell, and the trend item sub electromagnetic response curve predicted is highly similar to the shape, thereby verifying the effectiveness and reliability of the method.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of electromagnetic coded metasurface forward prediction, and particularly relates to a parameterized modeling method for coded metasurface based on physical information representation. BACKGROUND

[0002] Metamaterial is a kind of artificial material with unique properties such as negative refractive index and negative Poisson's ratio, which cannot be realized by natural materials. The concept of metamaterials is derived from left-handed materials, that is, the relationship between the wave vector k, the electric field E and the magnetic field H of the metamaterials conforms to the "left-hand rule". After years of research and development, metamaterials play an increasingly important role in the fields of optics, communication and national defense. By arranging metamaterials, functions that natural and traditional materials do not have can be achieved, such as optical invisibility and perfect lens. However, the nanoscale operation of three-dimensional structures required for the preparation and arrangement of metamaterials is extremely difficult, while planar metamaterials can be easily prepared based on existing technologies such as photolithography and nanometer printing, which is the birth of metasurfaces. Traditional metasurfaces are usually characterized by effective medium theory, and a continuous macroscopic medium with effective permittivity and permeability is applied. This kind of metasurface is called "analog metasurface", and its limitation is that once the surface structure is determined, the function will also be fixed after preparation, and it is not convenient to change the arrangement to change the function. In recent years, Academician Cui Tiejun proposed a digital coded metasurface, which can be represented by digital "1" and "0" to represent two out-of-phase response states (phase difference of 180°). The proposal of digital coded metasurface allows real-time large-scale control of metasurfaces, making the programmable function of metasurfaces possible.

[0003] Since metasurfaces have a wide range of applications, how to control their surface structure to obtain the required electromagnetic properties has become one of the important research directions of metasurfaces. However, the traditional method of solving the electromagnetic properties of metasurfaces is to use numerical simulation software tools, which is based on numerical iterative methods such as the method of moments and the finite element method to solve Maxwell's equations. The process is very time-consuming, and every time the surface structure is changed, it needs to be recalculated, which wastes a lot of manpower and resources. The emergence of neural networks provides a new way to solve this problem. Deep neural networks can learn the complex nonlinear function mapping relationship between input and output. Researchers take the parameters representing the geometry of the metasurface as input and the different electromagnetic properties corresponding to different structures as output to train the network, expecting that after inputting new metasurface structure information into the trained network, the corresponding electromagnetic properties can be predicted. This process is forward prediction. However, with the proposal of digital coded metasurfaces, the degree of freedom of metasurface structure is higher, and the corresponding electromagnetic properties are more complex and have higher dimensions. It is difficult to fit using conventional deep neural networks, so it is difficult to learn the mapping relationship between input and output. Therefore, an effective dimension reduction method is needed to solve this problem.

[0004] The study of transfer function provides a new way of thinking for dimension reduction. Researchers find that transfer function can be used to characterize S parameters, which means that high-dimensional electromagnetic characteristics can be converted to low-dimensional transfer function parameters, which facilitates the fitting and learning of neural networks. Therefore, the present application proposes a parameterized modeling method combining transfer function and deep neural network. There are three ways to express transfer function, among which the pole residue transfer function has obvious physical meaning, so the present application proposes an encoding super cell parameterized modeling method based on the physical information representation of pole residue transfer function. SUMMARY

[0005] The purpose of the present application is to combine pole residue transfer function with deep neural network, to represent high-dimensional electromagnetic response curve with low-dimensional parameters, so as to facilitate the learning of neural network. Through research, it is found that the poles in the pole residue transfer function have obvious physical information, so the present application formulates two types of criteria, trend item and residual item, to realize the physical meaning representation of transfer function parameters, and after model training, the electromagnetic response is represented together, improving the accuracy of encoding super surface forward prediction.

[0006] Technical scheme, in order to solve the above technical problems, achieve the above application purpose, the present application proposes an encoding super cell parameterized modeling method based on physical information representation, which comprises the following steps:

[0007] S1, obtaining electromagnetic response S parameters and pole residues;

[0008] S2, constructing data set Wherein, the input is Meta k , which is expressed as a 16x16 encoding matrix centered symmetrically, used to represent the kth encoding super cell, and the output is is the trend item pole vector of the transfer function of the kth encoding super cell, is the trend item residue vector of the transfer function of the kth encoding super cell, is the trend item electromagnetic response S parameter of the kth encoding super cell, is the residual item pole vector of the transfer function of the kth encoding super cell, is the residual item residue vector of the transfer function of the kth encoding super cell, is the residual item electromagnetic response S parameter of the kth encoding super cell;

[0009] S3, constructing trend item pole residue prediction network and residual item pole residue prediction network;

[0010] S4, inputting the training set into the trend item pole residue prediction network and the residual item pole residue prediction network for multi-task joint learning;

[0011] S5, inputting the test set into the trend pole residue prediction network and the residual pole residue prediction network to predict the output electromagnetic response;

[0012] The encoding supercell characterized by the physical information has a metal top layer, a dielectric layer, and a metal bottom layer, wherein the top layer is a metal resonance layer, the encoding pattern area width of the metal top layer is 8 mm, the encoding pattern metal copper patch width is 0.5 mm, the top layer is a center-symmetric 16x16 encoding 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+007 S / m, and the thickness t2 of the metal top layer and the metal bottom layer is 0.017 mm.

[0013] Further, the dielectric layer of the electromagnetic encoding supercell is a dielectric substrate with a material F4B, a relative dielectric constant of 2.65, and a thickness of 2 mm.

[0014] Further, the real part Re and the imaginary part Im of the electromagnetic response of the electromagnetic encoding supercell and the amplitude A and the phase There is a corresponding relationship as follows:

[0015]

[0016]

[0017] Further, the method of step S1 is as follows:

[0018] The encoding supercell structure is imported into a full-wave electromagnetic simulation software, the working frequency of the software is set to 8-12 GHz, the simulation parameters are set, the corresponding electromagnetic response S parameters of the encoding supercell are obtained in batches, and all encoding supercells and the corresponding electromagnetic response data are exported; the electromagnetic response S parameters of the kth encoding supercell sample obtained through the simulation software are H k (s), a group of pole vectors and residue vectors are extracted from the electromagnetic response S parameters using a vector fitting technique, p k and r k represent the pole vector and the residue vector of the transfer function of the kth encoding supercell with an order N k .

[0019] Further, in step S1, the method for extracting a group of pole vectors p k and residue vectors r k from the frequency response parameters S is as follows: the pole residue transfer function H(s) in mixed real form and complex form is obtained using a vector fitting method as follows:

[0020]

[0021] wherein each pair of complex-form pole residue pairs has another pair of pole residue pairs conjugated thereto, s = j x 2pif, j is the imaginary unit, f is the operating frequency band range of the encoding supercell, N real and N com respectively correspond to the order of the real pole residue pair and the complex pole residue pair, p i is the i-th order complex-form pole, r i is the i-th order complex-form residue, p i * is the conjugate of the i-th order complex-form pole, r i * is the conjugate of the i-th order complex-form residue;

[0022] the pole p = a ± j·b, a is the real part of the pole, b is the imaginary part of the pole, b = 0 when the pole is real, b ≠ 0 when the pole is complex, each pole or each pair of poles can be regarded as the root of the following monic quadratic equation:

[0023] s 2 + 2z co c s + co c 2 = 0

[0024] wherein |z| = a / co c is the damping coefficient, and satisfies |z| ≤ 1, is the center angular frequency of the pole, the discriminant A of the monic quadratic equation is:

[0025] the complex pole corresponds to the trend term pole residue pair, the discriminant A of the complex pole is not equal to 0, and the damping coefficient z | < 1;

[0026] the real pole corresponds to the residual term pole residue pair, the discriminant A of the real pole is equal to 0, and the damping coefficient z | = 1.

[0027] Further, the method of step S2 is as follows:

[0028] The initial data set extracted by vector fitting is represented as {Meta k , p k , r k , H k}, wherein Meta k is a 16 x 16 encoding matrix that is centrally symmetric, used to represent the k-th encoding supercell, p k and r k are represented as the pole vector and the residue vector of the transfer function of the k-th encoding supercell with order N k , k = 1, 2,..., n f , n fThe number of supercell samples is the number of samples encoded, for an order of N. k The k-th sample, N min =2 and N max =5 represents the minimum and maximum order among all samples, respectively:

[0029]

[0030] The pole residue data extracted by vector fitting are processed to obtain the final dataset. The dimensions are 4, 4, 3, and 3 respectively. The dimensions are all 2002, which are obtained by concatenating 1001-dimensional real part data and 1001-dimensional imaginary part data;

[0031] n f =40,000 samples, 80% of which are used as training set samples:

[0032]

[0033] 20% are test set samples:

[0034]

[0035] Furthermore, regarding the pole vector p k Residue vector r k Data processing consists of two parts:

[0036] A. Regarding the pole vector p k Residue vector r k Perform data preprocessing;

[0037] B. The pole vector p of the preprocessed trend term and residual term k Residue vector r k Perform homogeneity;

[0038] Among them, for the pole vector p k Residue vector r k The method for data preprocessing is as follows:

[0039] I. Remove the poles with negative imaginary parts and their corresponding residues from each pair of conjugate complex pole-residue pairs to compress redundant data information and obtain the order N of each sample. k Orders 2 to 5;

[0040] II. Extracting trend term pole-residue pairs and residual term pole-residue pairs to represent the physical information of the data. The order N of the processed trend term pole-residue pairs is... Trend For orders 1 to 2, the residual term pole residues are of order N. Residual Orders 1 to 3;

[0041] III, the trend item pole number pair and the pole number pair of the residual item are sorted according to the central angle frequency ω of each pole c ascending order;

[0042] the pre-processed trend item and residual item pole vector p k and the residual vector r k The homogeneous method is:

[0043] I, the trend item 1st order pole number pair is homogeneous to N Trend = 2 order:

[0044]

[0045] The trend item only contains 1st order pole number pair and 2nd order pole number pair, and after all 1st order pole number pairs are split, the trend item pole number pair is uniformly homogeneous to 2nd order;

[0046] II, the 1st-2nd order pole number pair of the residual item is homogeneous to N Residual = 3 order:

[0047] For each sample s1 in the sample set S1 with effective order N min , each sample s2 in the sample set S2 with effective order N min +1, compare the central angle frequency of the trend item pole of the sample s1 in the l1 norm with the trend item pole central angle frequency of all samples in S2 Select one of the nearest neighbor samples as the splitting basis:

[0048]

[0049] After splitting the mth residual item pole number pair, compare the central angle frequency of the residual item pole of the sample s1 in the l1 norm with the central angle frequency of the residual item pole of the nearest neighbor sample s2

[0050]

[0051] Select the pair of poles with the smallest distance D m , that is, split the mth residual item pole p m and the residual r m

[0052]

[0053] ​The split sample s1 is moved from S1 to S2, and the samples in S1 continue to be homogenized to S1, and the 1st order pole residue pair set is homogenized to the 2nd order, and the new 2nd order pole residue pair set is homogenized to the 3rd order, and all the pole residue pairs of the residual term are homogenized to the 3rd order;

[0054] The pole vector p k and the residue vector r k are processed, and the extracted trend term and residual term pole vector p k and the residue vector r k are homogenized, and the 1st order pole residue pair of the trend term is homogenized to the 2nd order, and the 1st-2nd order pole residue pair of the residual term is homogenized to the 3rd order, and after homogenization, each sample k = 1, 2,..., n f , n f is the number of encoding supercell samples, and the electromagnetic response S parameter H k (s), the trend term electromagnetic response S parameter and the residual term electromagnetic response S parameter are characterized as:

[0055]

[0056] The order of the trend term electromagnetic response transfer function corresponding to all encoding super surfaces is The order of the residual term electromagnetic response transfer function is

[0057] Further, the method of step S3 is as follows:

[0058] The network is divided into a trend term pole residue prediction network Net trend and a residual term pole residue prediction network Net residual , both of which use a CGC custom gated network model with parameter sharing, each CGC model has two task outputs, which are to predict the pole and the residue, and the CGC model has a three-layer structure, the bottom layer is composed of two independent expert modules and a shared expert module, each expert module is composed of a plurality of convolution layers and fully connected layers with jump connection, and the output of the n-th task expert module is denoted as S n (x); the middle layer is a gated network with a Softmax activation function, and the output is:

[0059]

[0060] Where x is the input 16x16 encoding matrix flattened into a one-dimensional vector with dimension d = 256, is a single-layer feedforward network with dimension (m n +m s )xd, and m nLet m be the number of independent experts for task n. s S is the number of shared experts for task n. n (x) represents the m-th task n. n +m s The output feature vectors of each expert module, with the top layer being the task tower layer, take the output of the gating network as input for feature extraction;

[0061] Net trend The trend term of the output predicts the poles. and predicted residues The predicted trend term electromagnetic response S-parameters are obtained by feeding them into the constructed trend term transfer function layer. Net residual The predicted poles of the residual terms of the output and predicted residues The predicted electromagnetic response S-parameters of the residual term are obtained by feeding them into the constructed residual term transfer function layer. The electromagnetic responses predicted by the two networks are added together to obtain the total electromagnetic response S-parameters.

[0062]

[0063] The transfer function layer is constructed by using the trend term pole-residue prediction network to calculate the trend term pole-residue electromagnetic response, and using the residual term pole-residue prediction network to calculate the residual term pole-residue electromagnetic response. The two are then added together to calculate the overall spectral response function. Recorded as:

[0064]

[0065] s=j×2πf

[0066] In this context, the slash ^ represents the output of the network prediction, j is the imaginary unit, f is the operating frequency band of the coding superunit, and this transfer function layer does not update its parameters.

[0067] Furthermore, the method for step S4 is as follows:

[0068] Trend term extreme residue prediction network Net trend Enter Meta k The trend term poles predicted by the network output Residue Task and The loss functions are respectively and Net Residue Prediction Network for Residue Term Pole residual Enter Meta k The poles of the residual terms predicted by the network output and the number of residuals task and The loss functions of and are and respectively and

[0069]

[0070] The calculation formula of MSE is:

[0071]

[0072] Where y is the true value, is the predicted value, and N is the dimension;

[0073] Trend item pole and the number of residuals into the trend item transfer function layer, residual item pole and predicted residual number into the residual item transfer function layer to obtain the predicted trend item electromagnetic response and the total electromagnetic response and the true trend item electromagnetic response and the total electromagnetic response H k (s) Calculate MSE to get the task and T Hs The loss functions of and are and respectively and L Hs :

[0074]

[0075] Based on the same variance uncertainty design target function total loss L total , multi-task T Hs joint learning:

[0076]

[0077] Where σ1, σ2, σ3, σ4, σ5, σ6 are trainable learning weight parameters, the initial value is set to 1, and it is self-adaptive learning in back propagation. The parameters of the trend item network and the residual item network are denoted as θ tre and θ res , then the goal of multi-task joint training is:

[0078]

[0079] The training period is set to 150, and the network converges after the parameters are updated by back propagation iteration. The predicted pole residual number pair and electromagnetic response parameters are obtained.

[0080] Further, the method of step S5 is as follows:

[0081] The test data set is input into the network model trained by joint learning to obtain the output predicted electromagnetic response and pole residue, and the mean absolute error MAE, mean square error MSE and regression coefficient R k of the network are used as evaluation indexes to evaluate the effect of the network on the test set. test 2 The input is input into the network model trained by joint learning to obtain the output predicted electromagnetic response and pole residue, and the mean absolute error MAE, mean square error MSE and regression coefficient R 2 of the network are used as evaluation indexes to evaluate the effect of the network on the test set.

[0082] Compared with the prior art, the technical scheme of the present application has the following beneficial technical effects:

[0083] (1) The present application is based on the underlying physical meaning of the pole, and specifies two types of criteria for the pole residue of the trend item and the residual item, thereby realizing the representation of the physical meaning of the transfer function, and designing two independent sub-models for learning, respectively, to realize the construction of a model with explainability.

[0084] (2) The present application is aimed at the problem of inconsistent pole order, and provides a reference with physical meaning for pole splitting by selecting the nearest neighbor sample.

[0085] (3) The present application adopts parameter sharing technology, which allows the pole prediction model and the residue prediction model in the trend item and the residual item to use the same parameters, reduces the parameter amount of the model, reduces the complexity of the model, and improves the performance and generalization ability of the model.

[0086] (4) The present application introduces a joint learning strategy to predict multiple targets, and the trend item prediction and the residual item prediction are two independent sub-models. i ,r i ) as the model optimization task, and also introduces the trend item electromagnetic response H trend and the residual item electromagnetic response H residual as another optimization task, respectively, to realize end-to-end training of the model and make the network training more efficient.

[0087] (5) The present application introduces an adaptive loss weight of homoscedastic uncertainty, takes the prediction of the trend item pole, residue, residual item pole and residue, and trend item electromagnetic response as an auxiliary task, balances the loss order of magnitude using the homoscedastic uncertainty, and realizes the weight adaptation. DETAILED DESCRIPTION

[0088] Figure 1 is the flowchart of the method of the present application;

[0089] Figure 2A schematic diagram of an encoding metasurface unit geometry for the present application. DETAILED DESCRIPTION

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

[0091] Embodiment: An electromagnetic encoding metasurface unit structure has three layers of a metal top layer, a dielectric layer, and a metal bottom layer. The top layer is a metal resonance layer; characterized in that the encoding pattern area width of the top layer is 8 mm, the encoding pattern metal patch width is 0.5 mm, the metal resonance layer is a center-symmetric 16x16 encoding matrix, each unit is a metal patch, the conductivity σ of the metal copper patch and the metal backplate layer of the bottom layer is 5.8+007 S / m, the thickness t2 of the metal top layer and the bottom layer is 0.017 mm. The middle layer is a dielectric substrate with a material of F4B and a relative permittivity of 2.65, and a thickness of 2 mm. The real part Re and the imaginary part Im of the electromagnetic response, the amplitude A and the phase of the electromagnetic response There is a corresponding relationship as follows:

[0092]

[0093]

[0094] As Figure 1 shown, the present application proposes an encoding super unit parameterized modeling method based on physical information representation, which includes the following steps:

[0095] S1, obtaining electromagnetic response S parameters and pole residues;

[0096] S2, constructing a data set Wherein, the input is Meta k , which is expressed as a center-symmetric 16x16 encoding matrix, used to represent the kth encoding super unit, and the output is is the trend item pole vector of the transfer function of the kth encoding super unit, is the trend item residue vector of the transfer function of the kth encoding super unit, is the trend item electromagnetic response S parameter of the kth encoding super unit, is the residual item pole vector of the transfer function of the kth encoding super unit, is the residual item residue vector of the transfer function of the kth encoding super unit, is the residual item electromagnetic response S parameter of the kth encoding super unit;

[0097] S3, constructing a trend item pole residue prediction network and a residual item pole residue prediction network;

[0098] S4, input the training set into the trend item pole residue prediction network and the residual item pole residue prediction network for multi-task joint learning;

[0099] S5, input the test set into the trend item pole residue prediction network and the residual item pole residue prediction network for prediction output of the electromagnetic response;

[0100] The encoding supercell represented by the physical information has a metal top layer, a dielectric layer, and a metal bottom layer, wherein the top layer is a metal resonance layer, the encoding pattern area width of the metal top layer is 8 mm, the encoding pattern metal copper patch width is 0.5 mm, the top layer is a center-symmetric 16x16 encoding 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+007 S / m, and the thickness t2 of the metal top layer and the metal bottom layer is 0.017 mm.

[0101] Further, the dielectric layer of the electromagnetic encoding supercell is a dielectric substrate with a material F4B, a relative dielectric constant of 2.65, and a thickness of 2 mm.

[0102] Further, the real part Re and the imaginary part Im of the electromagnetic response of the electromagnetic encoding supercell and the amplitude A and the phase There is a corresponding relationship as follows:

[0103]

[0104]

[0105] Further, the method of step S1 is as follows:

[0106] The encoding supercell structure is imported into a full-wave electromagnetic simulation software, the working frequency of the software is set to 8-12 GHz, the simulation parameters are set, the corresponding electromagnetic response S parameters of the encoding supercell are obtained in batches, and all encoding supercells and corresponding electromagnetic response data are exported; the electromagnetic response S parameters of the kth encoding supercell sample obtained through the simulation software are H k (s), a set of pole vectors and residue vectors p k and r k are extracted from the electromagnetic response S parameters using vector fitting technology. k The pole vector and the residue vector of the transfer function of the kth encoding supercell with order N

[0107] Further, in step S1, the method for extracting a set of pole vectors p k and residue vectors r k from the frequency response parameters S is as follows: the pole residue transfer function H(s) in mixed real form and complex form is obtained by using vector fitting method.

[0108]

[0109] wherein each pair of complex-form pole residue pairs has another pair of pole residue pairs conjugate to it, s = j x 2pif, j is the imaginary unit, f is the operating frequency band range of the encoding hypercell, N real and N com respectively correspond to the order of the real pole residue pair and the complex pole residue pair, p i is the i-th order complex-form pole, r i is the i-th order complex-form residue, p i * is the conjugate of the i-th order complex-form pole, r i * is the conjugate of the i-th order complex-form residue;

[0110] a pole p = a ± j·b, a is the real part of the pole, b is the imaginary part of the pole, b = 0 when the pole is real, b ≠ 0 when the pole is complex, each pole or each pair of poles can be regarded as the root of the following monic quadratic equation:

[0111] s 2 + 2z co c s + co c 2 = 0

[0112] wherein |z| = a / co c is the damping coefficient, and satisfies |z| ≤ 1, is the center angular frequency of the pole, the discriminant A of the monic quadratic equation is:

[0113] the complex pole corresponds to a trend term pole residue pair, the discriminant A of the complex pole is not equal to 0, and the damping coefficient z | < 1;

[0114] the real pole corresponds to a residual term pole residue pair, the discriminant A of the real pole is equal to 0, and the damping coefficient z | = 1.

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

[0116] The initial data set extracted by vector fitting is represented as {Meta k , p k , r k , H k}, wherein Meta k is a 16 x 16 encoding matrix that is center-symmetric, used to represent the k-th encoding hypercell, p k and r k are represented as order N kThe pole vector and residue vector of the transfer function of the k-th coding superunit, k = 1, 2, ..., n f n f The number of supercell samples is the number of samples encoded, for an order of N. k The k-th sample, N min =2 and N max =5 represents the minimum and maximum order among all samples, respectively:

[0117]

[0118] The pole residue data extracted by vector fitting are processed to obtain the final dataset. The dimensions are 4, 4, 3, and 3 respectively. The dimensions are all 2002, which are obtained by concatenating 1001-dimensional real part data and 1001-dimensional imaginary part data;

[0119] n f =40,000 samples, 80% of which are used as training set samples:

[0120]

[0121] 20% are test set samples:

[0122]

[0123] Furthermore, regarding the pole vector p k Residue vector r k Data processing consists of two parts:

[0124] A. Regarding the pole vector p k Residue vector r k Perform data preprocessing;

[0125] B. The pole vector p of the preprocessed trend term and residual term k Residue vector r k Perform homogeneity;

[0126] Among them, for the pole vector p k Residue vector r k The method for data preprocessing is as follows:

[0127] I. Remove the poles with negative imaginary parts and their corresponding residues from each pair of conjugate complex pole-residue pairs to compress redundant data information and obtain the order N of each sample. k Orders 2 to 5;

[0128] II. Extracting trend term pole-residue pairs and residual term pole-residue pairs to represent the physical information of the data. The order N of the processed trend term pole-residue pairs is...Trend is 1~2 order, the residual pole pair is left to the order N Residual is 1~3 order;

[0129] III, the trend pole pair and the residual pole pair are sorted in ascending order according to the center angular frequency ω c of the respective poles;

[0130] The pre-processed trend and residual pole vectors p k and the residual vectors r k are sorted in ascending order according to the center angular frequency ω Trend of the respective poles, and the homogeneous method is as follows:

[0131] I. The trend 1st order pole pair is homogenized to N Residual = 2 order:

[0132]

[0133] The trend only contains 1st order pole pairs and 2nd order pole pairs, and all 1st order pole pairs are split, and the trend pole pairs are homogenized to 2nd order;

[0134] II. The residual 1~2 order pole pair is homogenized to N Residual = 3 order:

[0135] For each sample s1 in the sample set S1 with effective order N min , each sample s2 in the sample set S2 with effective order N min +1, the center angular frequency ω of the trend pole of the sample s1 is compared with the center angular frequency ω of the trend pole of all samples in S2 in the l1 norm:

[0136]

[0137] After splitting the mth residual pole pair, the center angular frequency ω of the residual pole of the sample s1 is compared with the center angular frequency ω of the residual pole of the nearest neighbor sample s2 in the l1 norm:

[0138]

[0139] The pair of poles with the smallest distance D m is selected for splitting, i.e. the mth residual pole p m and the residual r m are split as follows:

[0140]

[0141] The split sample s1 is moved from S1 to S2, and the samples in S1 continue to be homogenized to S1, and the 1st order pole residue pair set is homogenized to 2nd order, and the new 2nd order pole residue pair set is homogenized to 3rd order, and all the pole residue pairs of the residual term are homogenized to 3rd order;

[0142] The pole vector p k and the residue vector r k are processed, and the extracted trend term and residual term pole vector p k and the residue vector r k are homogenized, and the 1st order pole residue pair of the trend term is homogenized to 2nd order, and the 1st-2nd order pole residue pair of the residual term is homogenized to 3rd order, and each sample k = 1, 2,..., n f , n f is the number of encoding super unit samples, and the electromagnetic response S parameter H k (s), the trend term electromagnetic response S parameter and the residual term electromagnetic response S parameter are characterized as:

[0143]

[0144] The order of the trend term electromagnetic response transfer function corresponding to all encoding super surfaces is The order of the residual term electromagnetic response transfer function is

[0145] Further, the method of step S3 is as follows:

[0146] The network is divided into a trend term pole residue prediction network Net trend and a residual term pole residue prediction network Net residual , both of which use a CGC custom gated network model with parameter sharing, each CGC model has two task outputs, which are to predict the pole and the residue, and the CGC model has a three-layer structure, the bottom layer is composed of two independent expert modules and a shared expert module, each expert module is composed of a plurality of convolution layers and fully connected layers with jump connection, and the output of the nth task expert module is denoted as S n (x); the middle layer is a gated network with Softmax as the activation function, and the output is:

[0147]

[0148] Wherein, x is the input 16x16 encoding matrix, which is flattened into a one-dimensional vector with dimension d = 256, is a single-layer feedforward network with dimension (m n +m s )xd, m nThe number of independent experts for task n, m s The number of shared experts for task n, S n (x) The output feature vector of m n + m s expert modules for task n, the top layer is the task tower layer, and the output of the gated network is taken as the input for feature extraction;

[0149] The trend item prediction pole trend output by Net and the prediction residue are sent to the constructed trend item transfer function layer to obtain the predicted trend item electromagnetic response S parameter The residual item prediction pole residual output by Net and the prediction residue are sent to the constructed residual item transfer function layer to obtain the predicted residual item electromagnetic response S parameter The electromagnetic responses predicted by the two networks are added to obtain the total electromagnetic response S parameter

[0150]

[0151] The construction of the transfer function layer uses the trend item pole residue prediction network to obtain the trend item pole residue, uses the residual item pole residue prediction network to obtain the residual item pole residue, and adds the two to calculate the overall spectral response function denoted as:

[0152]

[0153] s = j * 2 * pi * f

[0154] Where, the superscript ^ indicates the output result predicted by the network, j is the imaginary unit, and f is the working frequency band of the encoding super unit. The transfer function layer does not update parameters.

[0155] Further, the method of step S4 is as follows:

[0156] Meta trend is input into the trend item pole residue prediction network Net k , the network outputs the predicted trend item pole and the residue The loss functions of tasks and are and Meta k is input into the residual item pole residue prediction network Net residual , and the network outputs the predicted residual item pole and the number of residuals task and The loss functions of and are and respectively and

[0157]

[0158] The calculation formula of MSE is:

[0159]

[0160] Where y is the true value, is the predicted value, and N is the dimension.

[0161] Trend item pole and the number of residuals into the trend item transfer function layer, residual item pole and predicted residual number into the residual item transfer function layer to obtain the predicted trend item electromagnetic response and the total electromagnetic response and the true trend item electromagnetic response and the total electromagnetic response H k (s) Calculate MSE to get the task and T Hs The loss functions of and are and respectively and L Hs :

[0162]

[0163] Based on the same variance uncertainty design target function total loss L total , multi-task T Hs joint learning:

[0164]

[0165] Where σ1, σ2, σ3, σ4, σ5, σ6 are trainable learning weight parameters, the initial value is set to 1, and it is self-adaptively learned in back propagation. The parameters of the trend item network and the residual item network are denoted as θ tre and θ res , then the goal of multi-task joint training is:

[0166]

[0167] The training period is set to 150, and the network converges after the parameters are updated by back propagation. The predicted pole residual number pair and electromagnetic response parameters are obtained. ​

[0168] Furthermore, the method for step S5 is as follows:

[0169] Test dataset {Meta k} test The input is fed into a network model trained through joint learning to obtain the predicted electromagnetic response and pole residues. The mean absolute error (MAE), mean squared error (MSE), and regression coefficient R are then used. 2 The evaluation metrics assess the network performance on the test set.

[0170] When performing parametric modeling of the electromagnetic response of the electromagnetically coded metasurface unit in this embodiment according to the above method, 40,000 0-1 coded matrices are randomly generated in the embodiment, where 0 represents air and 1 represents a copper patch, with a size of 8×8. The matrices are converted to matrices of 0.9 and -0.1 by subtracting 0.1, and then extended to a 16×16 centrally symmetric matrix to characterize the coded meta-unit Meta. k The electromagnetic response Hs with a dimension of 2002 was obtained using full-wave electromagnetic simulation software. k The pole residue vector p of the transfer function is extracted using a vector fitting method. k and r k。

[0171] The dataset required to construct the deep neural network model according to the method in step S2 is divided into a training set of 32,000 samples. and a test set of 8,000 samples For Meta k The corresponding tags.

[0172] Construct the trend term pole residue prediction network Net according to step S3. trend Residual term pole residue prediction network Net residual The parameters are shared with the CGC custom gated network model, the optimizer uses Adam, and the network input is the encoding matrix Meta. k Net trend Output the 4-dimensional trend term and predict the poles. And 4-dimensional predicted residues The predicted 2002-dimensional trend term electromagnetic response is obtained by feeding the constructed trend term transfer function layer. Net residual The output 3D residual term predicts the poles. And 3D predicted residues The predicted 2002-dimensional electromagnetic response of the residual term is obtained by feeding it into the constructed residual term transfer function layer. The electromagnetic responses predicted by the two networks are added together to obtain the total predicted electromagnetic response in 2002 dimensions. According to the homoscedasticity uncertainty setting, the trainable parameters are obtained to obtain the joint optimization objective function L total The data batch size is set to 64, the network training period is set to 150, and the learning rate is set to 0.01. After updating the network parameters by back propagation, the network converges.

[0173] As shown in Table 1, the mean absolute error MAE, mean square error MSE, regression coefficient R 2 The evaluation index is used to evaluate the network effect on the test set The predicted frequency response and the frequency response calculated by the full-wave simulation software are compared, and it can be seen that the difference between the two is very small. The fitting performance of the real part of the frequency response is 99.280%, the fitting performance of the imaginary part of the frequency response is 99.306%, the fitting performance of the phase of the frequency response is 90.830%, and the fitting performance of the amplitude of the frequency response is negative. Because the constructed metal metasurface unit structure is with metal as the bottom backboard, almost all the incident electromagnetic signals are reflected, and the amplitude-frequency response characteristics are almost 1, so it is very sensitive to wave.

[0174]

[0175] Table 1 Performance evaluation of model predicted electromagnetic response curve

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

Claims

1. An encoding supercell parameterization modeling method based on physical information characterization, characterized in that, It comprises the following steps: S1, obtaining electromagnetic response S parameters and pole residues; S2, constructing dataset wherein the input is Meta k which is represented as a 16x16 encoding matrix centered symmetrically, is used to represent the kth encoding hypercell, and the output is is the trend term pole vector of the transfer function of the kth encoding hypercell, is the trend term residue vector of the transfer function of the kth encoding hypercell, is the trend term electromagnetic response S parameter of the kth encoding hypercell, is the residual term pole vector of the transfer function of the kth encoding hypercell, is the residual term residue vector of the transfer function of the kth encoding hypercell, is the residual term electromagnetic response S parameter of the kth encoding hypercell; S3, constructing a trend item pole residue prediction network and a residual item pole residue prediction network; S4, inputting the training set into the trend item pole residue prediction network and the residual item pole residue prediction network for multi-task joint learning; S5, inputting the test set into the trend item pole residue prediction network and the residual item pole residue prediction network to output the predicted electromagnetic response. The encoding super unit represented by the physical information has a metal top layer, a dielectric layer and a metal bottom layer, wherein the top layer is a metal resonance layer, the encoding pattern area width of the metal top layer is 8 mm, the encoding pattern metal copper patch width is 0.5 mm, the top layer is a center-symmetric 16x16 encoding 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+007 S / m, and the thickness t2 of the metal top layer and the metal bottom layer is 0.017 mm; The method of step S1 is as follows: The coding metasurface unit structure is introduced into a full-wave electromagnetic simulation software, a working frequency of the software is set to 8-12 GHz, simulation parameters are set, 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 electromagnetic response S parameters of the kth coding metasurface unit sample obtained through the simulation software are H k (s), a set of pole vectors and residue vectors are extracted from the electromagnetic response S parameters by using a vector fitting technology, p k and r k represent the pole vector and the residue vector of the transfer function of the kth coding metasurface with an order N k . In step S1, a set of pole vectors p is extracted from the frequency response parameter S k and residue vectors r k The method for obtaining the pole-residue transfer function H(s) in mixed real and complex forms by using vector fitting method is as follows: where each pair of complex pole residue pairs has another pair of pole residue pairs conjugate to it, s = j x 2pif, j is the imaginary unit, f is the operating frequency band range of the encoding supercell, N real and N com correspond to the order of the real pole residue pair and the complex pole residue pair, respectively, p i is the i-th order complex-form pole, r i is the i-th order complex-form residue, p i * is the conjugate of the i-th order complex-form pole, r i * is the conjugate of the i-th order complex-form residue; The pole p = α ± j·β, α is the real part of the pole, β is the imaginary part of the pole, β = 0 when the pole is a real number, and β ≠ 0 when the pole is a complex number, each pole or each pair of poles can be regarded as the root of the following quadratic equation: s 2 +2ζω c s+ω c 2 =0 wherein |ζ| = a / ω c is a damping coefficient and satisfies |ζ| ≤ 1, is the center angular frequency of the pole, and the discriminant Δ of the monomial quadratic equation is Δ = 4ω c 2 (ζ 2 -1) The complex pole corresponds to a trend item pole residue pair, the discriminant of the complex pole is Δ ≠ 0, and the damping coefficient |ζ| < 1; The real pole corresponds to a residual item pole residue pair, the discriminant of the real pole is Δ = 0, and the damping coefficient |ζ| = 1; The method of step S3 is as follows: The network is divided into a trend item pole number prediction network Net trend and a residual item pole number prediction network Net residual , both of which use a CGC self-defined gating network model with parameter sharing, each CGC model has the outputs of two tasks, which are respectively predicting a pole and predicting a number, the CGC model has a three-layer structure, the bottom layer is composed of two independent expert modules and one shared expert module, each expert module is composed of a plurality of convolutional layers with jump connection and a fully connected layer, and the output of the expert module of the nth task is denoted as S n (x); the intermediate layer is a gating network with a Softmax activation function, and the output is: where x is the input 16x16 coding matrix flattened into a one-dimensional vector of dimension d = 256, is a single-layer feedforward network of dimension (m n + m s ) x d, m n is the number of independent experts for task n, m s is the number of shared experts for task n, S n (x) is the output feature vector of the m n + m s expert modules for task n, and the top layer is a task tower layer that takes the output of the gating network as input for feature extraction; Net trend The trend term of the output predicts the poles. and predicted residues The predicted trend term electromagnetic response S-parameters are obtained by feeding them into the constructed trend term transfer function layer. Net residual The predicted poles of the residual terms of the output and predicted residues The predicted electromagnetic response S-parameters of the residual term are obtained by feeding them into the constructed residual term transfer function layer. The electromagnetic responses predicted by the two networks are added together to obtain the total electromagnetic response S-parameters. The trend pole residue prediction network is used to calculate the trend pole residue electromagnetic response, the residual pole residue prediction network is used to calculate the residual pole residue electromagnetic response, and the overall spectral response function is calculated by adding the two together Noted that: s = j x 2πf Wherein, the caret ^ indicates the output result of the network prediction, j is the imaginary unit, f is the working frequency band of the encoding super unit, and the transfer function layer does not update the parameters.

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

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

4. The method of claim 1, wherein, The method of step S2 is as follows: The initial data set extracted by vector fitting is denoted as {Meta k ,p k ,r k ,H k}, where Meta k is a 16x16 encoding matrix with central symmetry, used to represent the kth encoding hypercell, p k and r k are the pole vector and residue vector of the transfer function of the kth encoding hypercell with order N k , k = 1, 2,..., n f , n f is the number of encoding hypercell samples, and N k is the order of the kth sample, N min = 2 and N max = 5 represent the minimum order and the maximum order in all samples, respectively: The extracted pole data of the vector fitting is processed to obtain a final data set The dimension sizes are 4, 4, 3, 3, The dimension size of the data is 2002, which is obtained by splicing 1001-dimensional real part data and 1001-dimensional imaginary part data; n f = 40000 samples are divided 80% into training set samples: 20% are test set samples:

5. The method of claim 4, wherein, The pole vector p k and the residual vector r k The data processing includes two parts, which are respectively: A. The pole vector p k and the residual vector r k Data pre-processing; B. The trend and residual pole vectors p and r after pre-processing k and the residual vector r k Homogenize; where the pole vector p k and the residual vector r k are pre-processed by the method: Ⅰ, the imaginary part of the pole in the number pair of each pair of conjugate complex poles is negative, and the pole and the corresponding number are removed, so as to compress the data redundancy information and obtain the order N of each sample k is 2-5 II, the trend item pole residue pair and the residual item pole residue pair realize the physical information representation of data, the order N of the trend item pole residue pair after processing Trend is 1-2 order, the order N of the residual item pole residue pair Residual is 1-3 order; III. The pole number pairs of the trend term and the pole number pairs of the residual term are sorted in ascending order according to the central angular frequency ω of each pole c are sorted in ascending order; The pre-processed trend and residual pole vectors p k and the residual vector r k The homogeneous method is performed as follows: I. Homogenize the coefficients of the 1st order poles of the trend term 1 to N Trend = 2nd order: The trend item only contains 1st order pole residue pairs and 2nd order pole residue pairs, after splitting all 1st order pole residue pairs, the trend item pole residue pairs are uniformly homogeneous to 2nd order; II. Homogenize the residue term 1-2 pole fraction to N Residual = 3rd order: For each sample s1 in a sample set S1 of effective order N min For each sample s2 in a sample set S2 of effective order N min Compare the center angular frequency of the trend term pole of sample s1 to the center angular frequency of the trend term pole of each sample s2 in S2 in the l1 norm Compare the center angular frequency of the trend term pole of sample s1 to the center angular frequency of the trend term pole of each sample s2 in S2 in the l1 norm Select one of the nearest neighbor samples as the split criterion: The mth split residual pole pair is calculated to compare the s1 sample residual pole center angular frequency with the l1 norm The residual pole center angular frequency of the nearest neighbor sample s2 Selecting a distance D m The pair of poles with the smallest residue r m and the mth residual term pole p m is split as follows: Move the split sample s1 from S1 to S2, continue to make the samples in S1 homogeneous to S1, and the 1st order pole residue pair set is homogeneous to 2nd order, the new 2nd order pole residue pair set is homogeneous to 3rd order, and all the pole residue pairs of the residual item are uniformly homogeneous to 3rd order; polar vector p k and residue vector r k Data processing is performed on the extracted trend term and residual term polar vectors p k and residue vectors r k After homogenization, the trend term 1st order polar residue is 2nd order, and the residual term 1st-2nd order polar residue is 3rd order, and after homogenization, each sample k = 1, 2,..., n f , n f is the number of encoding supercell samples, and the electromagnetic response S parameter H k (s), the trend term electromagnetic response S parameter and the residual term electromagnetic response S parameter are characterized as: The order of the trend term electromagnetic response transfer function corresponding to all the coded metasurfaces is The order of the residual term electromagnetic response transfer function is 6. The method of claim 1, wherein, The method of step S4 is as follows: to the trend term pole trend Meta k , the network outputs the predicted trend term pole and the residue task and loss functions are and to the residual term pole residual Meta k , the network outputs the predicted residual term pole and the residue task and loss functions are and The calculation formula of MSE is: where y is the true value, is the predicted value, and N is the dimensionality. trend term pole and residual into the trend term transfer function layer, residual term pole and predicted residual into the residual term transfer function layer to get the predicted trend term electromagnetic response and total electromagnetic response with the true trend term electromagnetic response and total electromagnetic response H k (s) compute the MSE to get the task and T Hs loss function is and L Hs : Based on homoscedastic uncertainty design objective function total loss L total , performing multitask T Hs joint learning: Wherein, σ1, σ2, σ3, σ4, σ5, σ6 are trainable weight parameters, the initial value is set to 1, and self-adaptive learning is performed in back propagation. The parameters of the trend item network and the residual item network are denoted as θ tre and θ res The target of the multi-task joint training is: The training period is set to 150, the network converges after the parameters are updated by back propagation iteration, and the predicted pole residue pairs and electromagnetic response parameters are obtained.

7. The method of claim 6, wherein, The method of step S5 is as follows: The test data set in {Meta k} test is input into the network model trained by joint learning to obtain output predicted electromagnetic response and pole residue, and mean absolute error MAE, mean square error MSE, regression coefficient R 2 evaluation indexes are used to evaluate the network effect on the test set.

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