Coding super-unit parametric modeling method based on physical information representation

Abstract

The invention discloses a coding super-unit parameterized modeling method based on physical information characterization, and the method achieves the accurate prediction of electromagnetic response through constructing a corresponding relation between the pole residue of a deep neural network learning transfer function of physical information and a coding super-surface structure. Simulation results show that the electromagnetic response parameter curve predicted by using the method for the random metasurface in the test set is highly fitted with a super-unit full-wave simulation result, and the predicted trend term sub-electromagnetic response curve is highly similar to the shape of the electromagnetic response curve, so that the effectiveness and the reliability of the method are verified.

Description

Technical Field

[0001] The present invention belongs to the field of electromagnetic coded supersurface forward prediction, and in particular relates to a coded superunit parameterized modeling method based on physical information representation. Background Art

[0002] Metamaterials are artificial materials with unique properties that natural materials cannot achieve, such as negative refractive index and negative Poisson's ratio. The concept of metamaterials is extended from left-handed materials, that is, the relationship between the wave vector k, electric field E and magnetic field H of metamaterials conforms to the "left-hand rule". After years of research and development, metamaterials have played an increasingly important role in applications such as optics, communications and national defense. By arranging metamaterials, various functions that natural traditional materials do not have can be achieved, such as optical invisibility, perfect lenses, etc. However, the nanoscale operation of the three-dimensional structure required for the preparation and arrangement of metamaterials is extremely difficult, while planar metamaterials can be easily prepared based on existing technologies such as lithography and nanoprinting. This is the birth of metasurfaces. Traditional metasurfaces are usually characterized by effective medium theory, using continuous macroscopic media with effective dielectric constant and magnetic permeability. This kind of metasurface is called "analog metasurface". Its limitation is that once the surface structure is determined, its function will be fixed after preparation, and it is not easy to change the arrangement to change the function. In recent years, Academician Cui Tiejun proposed a digital coding metasurface, which can use the numbers "1" and "0" to represent two out-of-phase response states (phase difference of 180°). The introduction of digitally coded metasurfaces allows real-time and large-scale regulation of metasurfaces, making programmable metasurface functions possible.

[0003] Since metasurfaces have a wide range of applications, how to obtain the required electromagnetic properties by regulating their surface structures has become one of the important research directions for studying metasurfaces. However, the traditional method of solving the electromagnetic properties of metasurfaces is to use numerical simulation software tools. The principle adopted is to solve the Maxwell equations based on numerical iterative methods such as the method of moments and the finite element method. 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 birth of neural networks provides a new idea for solving this problem. Deep neural networks can learn the complex nonlinear function mapping relationship between input and output. Researchers use the parameters that characterize the geometric structure of the metasurface as input and the different electromagnetic properties corresponding to different structures as output to train the network. It is expected that the corresponding electromagnetic properties can be predicted after the new metasurface structure information is input into the trained network. This process is a forward prediction. However, with the introduction of the concept of digitally coded metasurfaces, the degree of freedom of the metasurface structure is higher, and the corresponding electromagnetic properties are more complex and higher in dimension. It is difficult to fit the conventional deep neural network alone, and the mapping relationship between input and output cannot be learned. Therefore, it is necessary to find an effective dimensionality reduction method to solve this problem.

[0004] The study of transfer functions provides a new idea for dimensionality reduction. Researchers have found that transfer functions can be used to characterize S parameters, which means that high-dimensional electromagnetic properties can be converted to low-dimensional transfer function parameters, which facilitates the fitting and learning of neural networks. Therefore, the present invention proposes a parametric modeling method that combines transfer functions with deep neural networks. There are three ways to express transfer functions, among which the pole residue transfer function has obvious physical meaning. Therefore, the present invention proposes a parametric modeling method for encoding super units based on the physical information representation of the pole residue transfer function. Summary of the invention

[0005] Purpose of the invention: The purpose of the present invention is to combine the pole residue transfer function with the deep neural network, and use low-dimensional parameters to characterize the high-dimensional electromagnetic response curve, so as to facilitate the learning of the neural network. Through research, it is found that the poles in the pole residue transfer function have obvious physical information. Therefore, the present invention formulates two types of criteria, trend terms and residual terms, to achieve the physical characterization of the transfer function parameters, and jointly characterize the electromagnetic response after model training, thereby improving the accuracy of the forward prediction of the coded metasurface.

[0006] Technical solution, in order to solve the above technical problems and achieve the above invention objectives, the present invention proposes a coding super unit parameterized modeling method based on physical information representation, the method comprising the following steps:

[0007] S1. Obtain electromagnetic response S parameters and pole residues;

[0008] S2. Build a dataset Among them, the input is Meta k , which is represented as a centrally symmetric 16×16 encoding matrix, used to characterize the kth encoding superunit, and the output is is the trend term pole vector of the transfer function of the kth encoding superunit, is the trend term residue vector of the transfer function of the kth encoding superunit, is the trend term electromagnetic response S parameter of the kth coding superunit, is the residual term pole vector of the transfer function of the kth coding superunit, is the residual vector of the transfer function of the kth coding superunit, is the residual electromagnetic response S parameter of the kth coding super unit;

[0009] S3, constructing a trend term extreme point residue prediction network and a residual term extreme point residue prediction network;

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

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

[0012] The coding super unit represented by physical information has three layers: 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 8 mm, the width of the coding pattern metal copper patch is 0.5 mm, the top layer is a centrally symmetrical 16×16 coding matrix, the conductivity σ of the metal copper patch of the metal top layer and the metal backplane of the bottom layer is 5.8+007S / m, and the thickness t2 of the metal top layer and the metal bottom layer is 0.017 mm.

[0013] Furthermore, the dielectric layer of the electromagnetic coding super unit is a dielectric substrate made of F4B with a relative dielectric constant of 2.65 and a thickness of 2 mm.

[0014] Furthermore, the real part Re and the imaginary part Im of the electromagnetic response of the electromagnetic coding metasurface unit are related to the amplitude A and the phase The following corresponding relationship exists:

[0015]

[0016]

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

[0018] The coded metasurface unit structure is imported into the full-wave electromagnetic simulation software. The operating frequency of the software is set to 8-12 GHz, and the simulation parameters are set to batch obtain the electromagnetic response S parameters corresponding to the coded metasurface, and all coded superunits and corresponding electromagnetic response data are exported; the electromagnetic response S parameter obtained by the simulation software for the kth coded superunit sample is H k (s), using vector fitting technology to extract a set of pole vectors and residue vectors from the electromagnetic response S parameters, p k and r k Expressed as order N k The pole vector and residue vector of the transfer function of the kth coded superunit.

[0019] Further, in step S1, a set of pole vectors p is extracted from the frequency response parameter S k and the residue vector r k The method is to use the vector fitting method to obtain the pole residue transfer function H(s) in mixed real and complex form:

[0020]

[0021] Among them, each pair of complex pole residue pairs has another pair of pole residue pairs that are conjugate with it, s = j × 2πf, j is the imaginary unit, f is the working frequency band range of the coding super unit, N real and N com They correspond to the order of the real pole residue pair and the complex pole residue pair respectively. The p in the bracket of the second term i is the ith order complex form pole, r i is the residue of the complex form of order i, p i * is the conjugate of the pole of the ith order complex form, r i * is the conjugate of the residue of the complex form of order i;

[0022] The pole p = α ± j · β, α is the real part of the pole, β is the imaginary part of the pole, the pole is a real number when β = 0, and the pole is a complex number when β ≠ 0. Each pole or each pair of poles can be regarded as the root of the following quadratic equation:

[0023] s 2 +2ζω c s+ω c 2 =0

[0024] Where |ζ|=α / ω c is the damping coefficient and satisfies |ζ|≤1, is the central angular frequency of the pole, and the discriminant Δ of the quadratic equation is:

[0025] The complex poles correspond to the trend term pole residue pairs, the discriminant of the complex poles Δ≠0, and the damping coefficient ζ|<1;

[0026] The real poles correspond to the residual term pole residue pairs, the discriminant of the real poles is Δ=0, and the damping coefficient ζ|=1.

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

[0028] The initial dataset extracted by vector fitting is represented as {Meta k ,p k ,r k ,H k}, where Meta k is a 16×16 coding matrix with central symmetry, used to represent the kth coding super unit, p k and r k Expressed as order N k The pole vector and residue vector of the transfer function of the kth coded superunit, k = 1, 2, ..., n f , n fis the number of coded superunit samples, for order N k The kth sample, N min =2 and N max =5 respectively represent the minimum and maximum order of all samples:

[0029]

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

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

[0032]

[0033] 20% are test set samples:

[0034]

[0035] Furthermore, for the pole vector p k and the residue vector r k Data processing consists of two parts:

[0036] A. Pole vector p k and the residue vector r k Perform data preprocessing;

[0037] B. For the trend term and residual term pole vector p after preprocessing k and the residue vector r k Conduct homogeneous;

[0038] Among them, the pole vector p k and the residue vector r k The method for data preprocessing is:

[0039] Ⅰ. Eliminate the poles with negative imaginary parts and their corresponding residues in each pair of conjugate complex pole residues, compress the redundant information of the data, and obtain the order N of each sample k 2 to 5 levels;

[0040] Ⅱ. Extract the trend term pole residue pairs and the residual term pole residue pairs to realize the physical information representation of the data. After processing, the order of the trend term pole residue pairs is N Trend For 1~2 orders, the residual term pole residue is N Residual It is 1 to 3 levels;

[0041] III. The pole residue pairs of the trend term and the pole residue pairs of the residual term are divided into the following groups according to the central angular frequency ω of their respective poles: c Sort in ascending order;

[0042] For the trend term and residual term pole vector p after preprocessing k and the residue vector r k The homogeneous method is:

[0043] Ⅰ. Homogenize the first-order pole residue pairs of the trend term to N Trend =2nd order:

[0044]

[0045] The trend term only contains 1st-order pole residue pairs and 2nd-order pole residue pairs. After all 1st-order pole residue pairs are split, the pole residue pairs of the trend term are uniformly homogeneous to 2nd order.

[0046] Ⅱ. Homogenize the residual term 1st to 2nd order pole residue pairs to N Residual =3rd order:

[0047] For an effective order of N min Each sample s1 in the sample set S1 has an effective order of N min For each sample s2 in the sample set S2 of +1, the central angular frequency of the trend term pole of sample s1 is compared in l1 form The central angular frequency of the trend term pole of all samples in S2 Select one of the nearest neighbor samples as the basis for splitting:

[0048]

[0049] After calculating the residue pair of the splitting mth residual term pole, compare the residual term pole center angular frequency of the s1 sample in l1 norm The residual term pole center angular frequency with the nearest neighbor sample s2

[0050]

[0051] Select distance D m The smallest pair of pole residues is split, that is, the pole p of the mth residual term m and residue r m Perform the following split:

[0052]

[0053] Move the split sample s1 from S1 to S2, and continue to homogenize the samples in S1 until S1 becomes an empty set. After the set of 1st-order pole residue pairs is homogenized to the 2nd order, the new set of 2nd-order pole residue pairs is homogenized to the 3rd order, and all pole residue pairs of the residual term are uniformly homogenized to the 3rd order.

[0054] Pole vector p k and the residue vector r k Perform data processing and extract the trend term and residual term pole vector p k and the residue vector r k When homogenizing, the 1st order pole residue of the trend term is aligned to the 2nd order, and the 1st to 2nd order pole residue of the residual term is aligned to the 3rd order. After homogenization, each sample k=1,2,...,n f , n f is the number of coded superunit samples, and its electromagnetic response S parameter H k (s), trend item electromagnetic response S parameter And the residual electromagnetic response S parameters Characterized by:

[0055]

[0056] The order of the trend term electromagnetic response transfer function corresponding to all coding metasurfaces is The order of the residual electromagnetic response transfer function is

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

[0058] The network is divided into trend term extreme residue prediction network Net trend and residual term pole residue prediction network Net residual , all use the CGC custom gating network model with parameter sharing. Each CGC model has two task outputs, namely predicted extreme points and predicted residues. The CGC model has a three-layer structure. The bottom layer consists of two independent expert modules and a shared expert module. Each expert module consists of several convolutional layers and fully connected layers with skip connections. The output of the expert module of the nth task is recorded as S n (x); the middle layer is a gated network with Softmax as the activation function, and the output is:

[0059]

[0060] Where x is the input 16×16 encoding matrix flattened into a one-dimensional vector with dimension d=256, Dimension (m n +m s )×d single-layer feedforward network, m nis the number of independent experts for task n, m s is the number of shared experts for task n, S n (x) is m of task n n +m s The output feature vector of the expert module, the top layer is the task tower layer, and the output of the gated network is used as input for feature extraction;

[0061] Net trend Output trend term prediction extremes and predicted residue The constructed trend term transfer function layer is sent to obtain the predicted trend term electromagnetic response S parameters Net residual The residual term of the output predicts the extreme point and predicted residue The residual term transfer function layer is sent to obtain the predicted residual term electromagnetic response S parameters. The electromagnetic responses predicted by the two networks are added together to obtain the total electromagnetic response S parameters.

[0062]

[0063] The construction of the transfer function layer uses the trend term pole residue obtained by the trend term pole residue prediction network to calculate the trend term pole residue electromagnetic response, and uses the residual term pole residue obtained by the residual term pole residue prediction network to calculate the residual term pole residue electromagnetic response. The two are added to calculate the overall spectrum response function Denoted as:

[0064]

[0065] s=j×2πf

[0066] Among them, the pointed mark ^ represents the output result of the network prediction, j is the imaginary unit, f is the working frequency band of the coding super unit, and the transfer function layer does not update the parameters.

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

[0068] Trend term extreme residue prediction network Net trend Enter Meta k , the trend term extreme point predicted by the network output and residue Task and The loss functions are and Towards the residual term extreme residue prediction network Net residual Enter Meta k , the residual term pole of the network output prediction and residue Task and The loss functions are and

[0069]

[0070] The calculation formula of MSE is:

[0071]

[0072] Among them, y is the true value, is the predicted value, N is the dimension;

[0073] Trend Term Extreme and residue Send to the trend term transfer function layer, the residual term pole and predicted residue Send it to the residual term transfer function layer to get the predicted trend term electromagnetic response and total electromagnetic response The trend of the electromagnetic response and the total electromagnetic response H k (s) Calculate MSE to get the task and T Hs The loss functions are and L Hs :

[0074]

[0075] The total loss L of the objective function based on homoscedastic uncertainty design total , multi-tasking T Hs Federated Learning:

[0076]

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

[0078]

[0079] The training cycle is set to 150, and the network converges after back-propagation iteratively updates the parameters, and the predicted pole residue pairs and electromagnetic response parameters are obtained.

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

[0081] The test data set {Meta k} test The input is fed into the network model trained by joint learning to obtain the output predicted electromagnetic response and pole residue, using the mean absolute error MAE, mean square error MSE, and regression coefficient R 2 The evaluation index evaluates the network effect on the test set.

[0082] Beneficial effects: Compared with the prior art, the technical solution of the present invention has the following beneficial technical effects:

[0083] (1) Based on the underlying physical meaning of the poles, the present invention specifies two types of criteria for the pole residues of the trend term and the residual term, thereby achieving the physical characterization of the transfer function. At the same time, two independent sub-models are designed to be learned separately to achieve the construction of an interpretable model.

[0084] (2) The present invention addresses the problem of inconsistent pole orders by selecting the nearest neighbor samples to provide a physically meaningful reference basis for pole splitting.

[0085] (3) The present invention adopts parameter sharing technology, which allows the extreme point prediction model and the residue prediction model in the trend term and the residual term to use the same parameters, thereby reducing the number of parameters of the model, reducing the complexity of the model, and improving the performance and generalization ability of the model.

[0086] (4) The present invention introduces a joint learning strategy to predict multiple targets. The trend term prediction and the residual term prediction are two independent sub-models. In the two sub-models, in addition to the transfer function coefficient (p i ,r i ) as the model optimization task, the trend term electromagnetic response H trend and the residual electromagnetic response H residual For another optimization task, end-to-end training of the model is implemented, making network training more efficient.

[0087] (5) The present invention introduces adaptive loss weights of homoscedastic uncertainty, takes the prediction of trend term poles, residues, residual term poles, residues and trend term electromagnetic response as auxiliary tasks, adopts homoscedastic uncertainty to balance the difference in loss orders of magnitude, and realizes weight adaptation. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] Figure 1 is a flow chart of the method of the present invention;

[0089] Figure 2Schematic diagram of the geometric structure of the coding super surface unit of the present invention. DETAILED DESCRIPTION

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

[0091] Embodiment: An electromagnetic coding metasurface unit structure has three layers: a metal top layer, a dielectric layer, and a metal bottom layer. The top layer is a metal resonance layer; it is characterized in that the width of the coding pattern area of ​​the top layer is 8mm, the width of the coding pattern metal patch is 0.5mm, the metal resonance layer is a centrosymmetric 16×16 coding matrix, each unit is a metal patch, the conductivity σ of the metal copper patch and the bottom metal backplane layer is 5.8+007S / m, and the thickness of the metal top layer and the bottom layer is t2=0.017mm. The middle layer is a dielectric substrate made of F4B with a relative dielectric constant of 2.65 and a thickness of 2mm. The real part Re and the imaginary part Im of the electromagnetic response are related to the amplitude A and phase of the electromagnetic response The following corresponding relationship exists:

[0092]

[0093]

[0094] like Figure 1 As shown, the present invention proposes a coding super unit parameterized modeling method based on physical information representation, the method comprising the following steps:

[0095] S1. Obtain electromagnetic response S parameters and pole residues;

[0096] S2. Build a dataset Among them, the input is Meta k , which is represented as a centrally symmetric 16×16 encoding matrix, used to characterize the kth encoding superunit, and the output is is the trend term pole vector of the transfer function of the kth encoding superunit, is the trend term residue vector of the transfer function of the kth encoding superunit, is the trend term electromagnetic response S parameter of the kth coding superunit, is the residual term pole vector of the transfer function of the kth coding superunit, is the residual vector of the transfer function of the kth coding superunit, is the residual electromagnetic response S parameter of the kth coding super unit;

[0097] S3, constructing a trend term extreme point residue prediction network and a residual term extreme point residue prediction network;

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

[0099] S5, inputting the test set into the trend term pole residue prediction network and the residual term pole residue prediction network to predict the output electromagnetic response;

[0100] The coding super unit represented by physical information has three layers: 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 8 mm, the width of the coding pattern metal copper patch is 0.5 mm, the top layer is a centrally symmetrical 16×16 coding matrix, the conductivity σ of the metal copper patch of the metal top layer and the metal backplane of the bottom layer is 5.8+007S / m, and the thickness t2 of the metal top layer and the metal bottom layer is 0.017 mm.

[0101] Furthermore, the dielectric layer of the electromagnetic coding super unit is a dielectric substrate made of F4B with a relative dielectric constant of 2.65 and a thickness of 2 mm.

[0102] Furthermore, the real part Re and the imaginary part Im of the electromagnetic response of the electromagnetic coding metasurface unit are related to the amplitude A and the phase The following corresponding relationship exists:

[0103]

[0104]

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

[0106] The coded metasurface unit structure is imported into the full-wave electromagnetic simulation software. The operating frequency of the software is set to 8-12 GHz, and the simulation parameters are set to batch obtain the electromagnetic response S parameters corresponding to the coded metasurface, and all coded superunits and corresponding electromagnetic response data are exported; the electromagnetic response S parameter obtained by the simulation software for the kth coded superunit sample is H k (s), using vector fitting technology to extract a set of pole vectors and residue vectors from the electromagnetic response S parameters, p k and r k Expressed as order N k The pole vector and residue vector of the transfer function of the kth coded superunit.

[0107] Further, in step S1, a set of pole vectors p is extracted from the frequency response parameter S k and the residue vector r k The method is to use the vector fitting method to obtain the pole residue transfer function H(s) in mixed real and complex form:

[0108]

[0109] Among them, each pair of complex pole residue pairs has another pair of pole residue pairs that are conjugate with it, s = j × 2πf, j is the imaginary unit, f is the working frequency band range of the coding super unit, N real and N com They correspond to the order of the real pole residue pair and the complex pole residue pair respectively. The p in the bracket of the second term i is the ith order complex form pole, r i is the residue of the complex form of order i, p i * is the conjugate of the pole of the ith order complex form, r i * is the conjugate of the residue of the complex form of order i;

[0110] The pole p = α ± j · β, α is the real part of the pole, β is the imaginary part of the pole, the pole is a real number when β = 0, and the pole is a complex number when β ≠ 0. Each pole or each pair of poles can be regarded as the root of the following quadratic equation:

[0111] s 2 +2ζω c s+ω c 2 =0

[0112] Where |ζ|=α / ω c is the damping coefficient and satisfies |ζ|≤1, is the central angular frequency of the pole, and the discriminant Δ of the quadratic equation is:

[0113] The complex poles correspond to the trend term pole residue pairs, the discriminant of the complex poles Δ≠0, and the damping coefficient ζ|<1;

[0114] The real poles correspond to the residual term pole residue pairs, the discriminant of the real poles is Δ=0, and the damping coefficient ζ|=1.

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

[0116] The initial dataset extracted by vector fitting is represented as {Meta k ,p k ,r k ,H k}, where Meta k is a 16×16 coding matrix with central symmetry, used to represent the kth coding super unit, p k and r k Expressed as order N kThe pole vector and residue vector of the transfer function of the kth coded superunit, k = 1, 2, ..., n f , n f is the number of coded superunit samples, for order N k The kth sample, N min =2 and N max =5 respectively represent the minimum and maximum order of all samples:

[0117]

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

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

[0120]

[0121] 20% are test set samples:

[0122]

[0123] Furthermore, for the pole vector p k and the residue vector r k Data processing consists of two parts:

[0124] A. Pole vector p k and the residue vector r k Perform data preprocessing;

[0125] B. For the trend term and residual term pole vector p after preprocessing k and the residue vector r k Conduct homogeneous;

[0126] Among them, the pole vector p k and the residue vector r k The method for data preprocessing is:

[0127] Ⅰ. Eliminate the poles with negative imaginary parts and their corresponding residues in each pair of conjugate complex pole residues, compress the redundant information of the data, and obtain the order N of each sample k 2 to 5 levels;

[0128] Ⅱ. Extract the trend term pole residue pairs and the residual term pole residue pairs to realize the physical information representation of the data. After processing, the order of the trend term pole residue pairs is NTrend For 1~2 orders, the residual term pole residue is N Residual It is 1 to 3 levels;

[0129] III. The pole residue pairs of the trend term and the pole residue pairs of the residual term are divided into the following groups according to the central angular frequency ω of their respective poles: c Sort in ascending order;

[0130] For the trend term and residual term pole vector p after preprocessing k and the residue vector r k The homogeneous method is:

[0131] Ⅰ. Homogenize the first-order pole residue pairs of the trend term to N Trend =2nd order:

[0132]

[0133] The trend term only contains 1st-order pole residue pairs and 2nd-order pole residue pairs. After all 1st-order pole residue pairs are split, the pole residue pairs of the trend term are uniformly homogeneous to 2nd order.

[0134] Ⅱ. Homogenize the residual term 1st to 2nd order pole residue pairs to N Residual =3rd order:

[0135] For an effective order of N min Each sample s1 in the sample set S1 has an effective order of N min For each sample s2 in the sample set S2 of +1, the central angular frequency of the trend term pole of sample s1 is compared in l1 form The central angular frequency of the trend term pole of all samples in S2 Select one of the nearest neighbor samples as the basis for splitting:

[0136]

[0137] After calculating the residue pair of the splitting mth residual term pole, compare the residual term pole center angular frequency of the s1 sample in l1 norm The residual term pole center angular frequency with the nearest neighbor sample s2

[0138]

[0139] Select distance D m The smallest pair of pole residues is split, that is, the pole p of the mth residual term m and residue r m Perform the following split:

[0140]

[0141] Move the split sample s1 from S1 to S2, and continue to homogenize the samples in S1 until S1 becomes an empty set. After the set of 1st-order pole residue pairs is homogenized to the 2nd order, the new set of 2nd-order pole residue pairs is homogenized to the 3rd order, and all pole residue pairs of the residual term are uniformly homogenized to the 3rd order.

[0142] Pole vector p k and the residue vector r k Perform data processing and extract the trend term and residual term pole vector p k and the residue vector r k When homogenizing, the 1st order pole residue of the trend term is aligned to the 2nd order, and the 1st to 2nd order pole residue of the residual term is aligned to the 3rd order. After homogenization, each sample k=1,2,...,n f , n f is the number of coded superunit samples, and its electromagnetic response S parameter H k (s), trend item electromagnetic response S parameter And the residual electromagnetic response S parameters Characterized by:

[0143]

[0144] The order of the trend term electromagnetic response transfer function corresponding to all coding metasurfaces is The order of the residual electromagnetic response transfer function is

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

[0146] The network is divided into trend term extreme point residue prediction network Net trend and residual term extreme point residue prediction network Net residual , all use the CGC custom gating network model with parameter sharing. Each CGC model has two task outputs, namely predicted extreme points and predicted residues. The CGC model has a three-layer structure. The bottom layer consists of two independent expert modules and a shared expert module. Each expert module consists of several convolutional layers and fully connected layers with skip connections. The output of the expert module of the nth task is recorded as S n (x); the middle layer is a gated network with Softmax as the activation function, and the output is:

[0147]

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

[0149] Net trend Output trend term prediction extremes and predicted residue The constructed trend term transfer function layer is sent to obtain the predicted trend term electromagnetic response S parameters Net residual The residual term of the output predicts the extreme point and predicted residue The residual term transfer function layer is sent to obtain the predicted residual term electromagnetic response S parameters. The electromagnetic responses predicted by the two networks are added together to obtain the total electromagnetic response S parameters.

[0150]

[0151] The construction of the transfer function layer uses the trend term pole residue obtained by the trend term pole residue prediction network to calculate the trend term pole residue electromagnetic response, and uses the residual term pole residue obtained by the residual term pole residue prediction network to calculate the residual term pole residue electromagnetic response. The two are added to calculate the overall spectrum response function Denoted as:

[0152]

[0153] s=j×2πf

[0154] Among them, the pointed mark ^ represents the output result of the network prediction, j is the imaginary unit, f is the working frequency band of the coding super unit, and the transfer function layer does not update the parameters.

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

[0156] Trend term extreme residue prediction network Net trend Enter Meta k , the trend term extreme point predicted by the network output and residue Task and The loss functions are and Towards the residual term extreme residue prediction network Net residual Enter Meta k , the residual term pole of the network output prediction and residue Task and The loss functions are and

[0157]

[0158] The calculation formula of MSE is:

[0159]

[0160] Among them, y is the true value, is the predicted value, N is the dimension;

[0161] Trend Term Extreme and residue Send to the trend term transfer function layer, the residual term pole and predicted residue Send it to the residual term transfer function layer to get the predicted trend term electromagnetic response and total electromagnetic response The trend of the electromagnetic response and the total electromagnetic response H k (s) Calculate MSE to get the task and T Hs The loss functions are and L Hs :

[0162]

[0163] The total loss L of the objective function based on homoscedastic uncertainty design total , multi-tasking T Hs Federated Learning:

[0164]

[0165] Among them, σ1, σ2, σ3, σ4, σ5, σ6 are trainable weight parameters, the initial value is set to 1, and adaptive learning is performed in back propagation. The parameters of the trend term network and the residual term network are denoted by θ tre and θ res , then the goal of multi-task joint training is:

[0166]

[0167] The training cycle is set to 150, and the network converges after back-propagation iteratively updates the parameters, and the predicted pole residue pairs and electromagnetic response parameters are obtained.

[0168] Further, the method of step S5 is as follows:

[0169] The test data set {Meta k} test The input is fed into the network model trained by joint learning to obtain the output predicted electromagnetic response and pole residue, using the mean absolute error MAE, mean square error MSE, and regression coefficient R 2 The evaluation index evaluates the network effect on the test set.

[0170] When the electromagnetic response of the electromagnetic coding metasurface unit in this embodiment is parametrically modeled according to the above method, 40,000 0-1 coding matrices are randomly generated in the embodiment, where 0 represents air and 1 represents a metal copper patch, with a size of 8×8. The matrix is ​​converted into a matrix of 0.9 and -0.1 by subtracting 0.1, and then extended to a 16×16 centrosymmetric matrix to represent the coding super unit Meta k , using full-wave electromagnetic simulation software to obtain the electromagnetic response Hs with a dimension of 2002 k , extract the pole residue vector p of the transfer function by vector fitting method k and r k。

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

[0172] According to step S3, construct the trend term extreme point residue prediction network Net trend and residual term extreme point residue prediction network Net residual The parameter sharing CGC custom gating network model uses Adam as the optimizer, and the input of the network is the encoding matrix Meta k , Net trend Output 4-dimensional trend term prediction extreme point and the 4-dimensional prediction residue The constructed trend term transfer function layer is sent to obtain the predicted 2002-dimensional trend term electromagnetic response. Net residual The 3D residual term of the output predicts the pole and the 3D prediction residue The constructed residual term transfer function layer is sent to obtain the predicted 2002-dimensional residual term electromagnetic response. The electromagnetic responses predicted by the two networks are added together to obtain the total predicted 2002-dimensional electromagnetic response. According to the uncertainty of homoscedasticity, the trainable parameters are set to obtain the joint optimization objective function L total , the data batch size is set to 64, the network training cycle is set to 150, the learning rate is set to 0.01, and the network converges after updating the network parameters through back propagation.

[0173] As shown in Table 1, the mean absolute error MAE, mean square error MSE, and regression coefficient R 2 Evaluation indicators in the test set The network effect is evaluated above, and the predicted frequency response is compared with the frequency response calculated by the full-wave simulation software. It can be seen that the gap 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%, and the fitting performance of the phase of the frequency response is 90.830%. The fitting performance of the frequency response amplitude is negative because the constructed metal metasurface unit structure is based on metal as the underlying backplane, which reflects almost all incident electromagnetic signals, and the amplitude-frequency response characteristic is almost 1, so it is very sensitive to fluctuations.

[0174]

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

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

Claims

1. A method for parameterized modeling of coded supercells based on physical information representation, characterized in that: The steps include: S1. Obtain electromagnetic response S parameters and pole residues; S2. Build a dataset Among them, the input is Meta k , which is represented as a centrally symmetric 16×16 encoding matrix, used to characterize the kth encoding superunit, and the output is is the trend term pole vector of the transfer function of the kth encoding superunit, is the trend term residue vector of the transfer function of the kth encoding superunit, is the trend term electromagnetic response S parameter of the kth coding superunit, is the residual term pole vector of the transfer function of the kth coding superunit, is the residual vector of the transfer function of the kth coding superunit, is the residual electromagnetic response S parameter of the kth coding super unit; S3, constructing a trend term extreme point residue prediction network and a residual term extreme point residue prediction network; S4, inputting the training set into the trend term pole residue prediction network and the residual term pole residue prediction network for multi-task joint learning; S5, inputting the test set into the trend term pole residue prediction network and the residual term pole residue prediction network to predict the output electromagnetic response; The coding super unit represented by physical information has three layers: 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 8 mm, the width of the coding pattern metal copper patch is 0.5 mm, the top layer is a centrally symmetrical 16×16 coding matrix, the conductivity σ of the metal copper patch of the metal top layer and the metal backplane of the bottom layer is 5.8+007S / m, and the thickness t2 of the metal top layer and the metal bottom layer is 0.017 mm.

2. The method according to claim 1, characterized in that: The dielectric layer of the electromagnetic encoding super unit is a dielectric substrate made of F4B with a relative dielectric constant of 2.65 and a thickness of 2 mm.

3. The method according to claim 1, characterized in that: The real part Re and imaginary part Im of the electromagnetic response of the electromagnetic coding metasurface unit and the amplitude A and phase of the electromagnetic response The following corresponding relationship exists:

4. The method according to claim 1, characterized in that The method of step S1 is as follows: The coded metasurface unit structure is imported into the full-wave electromagnetic simulation software. The operating frequency of the software is set to 8-12 GHz, and the simulation parameters are set to batch obtain the electromagnetic response S parameters corresponding to the coded metasurface, and all coded superunits and corresponding electromagnetic response data are exported; the electromagnetic response S parameter obtained by the simulation software for the kth coded superunit sample is H k (s), using vector fitting technology to extract a set of pole vectors and residue vectors from the electromagnetic response S parameters, p k and r k Expressed as order N k The pole vector and residue vector of the transfer function of the kth coded superunit.

5. The method according to claim 4, characterized in that In step S1, a set of pole vectors p is extracted from the frequency response parameters S k and the residue vector r k The method is to use the vector fitting method to obtain the pole residue transfer function H(s) in mixed real and complex form: Among them, each pair of complex pole residue pairs has another pair of pole residue pairs that are conjugate with it, s = j × 2πf, j is the imaginary unit, f is the working frequency band range of the coding super unit, N real and N com They correspond to the order of the real pole residue pair and the complex pole residue pair respectively. The p in the bracket of the second term i is the ith order complex form pole, r i is the residue of the complex form of order i, is the conjugate of the pole of the ith order complex form, is the conjugate of the residue of the complex form of order i; The pole p = α ± j · β, α is the real part of the pole, β is the imaginary part of the pole, the pole is a real number when β = 0, and the pole is a complex number when β ≠ 0. Each pole or each pair of poles can be regarded as the root of the following quadratic equation: Where |ζ|=α / ω c is the damping coefficient and satisfies |ζ|≤1, is the central angular frequency of the pole, and the discriminant Δ of the quadratic equation is: The complex poles correspond to the trend term pole residue pairs, the discriminant of the complex poles Δ≠0, and the damping coefficient ζ|<1; The real poles correspond to the residual term pole residue pairs, the discriminant of the real poles is Δ=0, and the damping coefficient ζ|=1.

6. The method according to claim 5, characterized in that The method of step S2 is as follows: The initial dataset extracted by vector fitting is represented as {Meta k ,p k ,r k ,H k }, where Meta k is a 16×16 coding matrix with central symmetry, used to represent the kth coding super unit, p k and r k Expressed as order N k The pole vector and residue vector of the transfer function of the kth coded superunit, k = 1, 2, ..., n f , n f is the number of coded superunit samples, for order N k The kth sample, N min =2 and N max =5 respectively represent the minimum and maximum order of all samples: The pole residue data extracted by vector fitting is processed to obtain the final data set The dimensions are 4, 4, 3, 3 respectively. The dimension size of is 2002, which is obtained by concatenating 1001-dimensional real data and 1001-dimensional imaginary data; n f = 40,000 samples, 80% of which are divided into training set samples: 20% are test set samples:

7. The method according to claim 6, characterized in that Pole vector p k and the residue vector r k Data processing consists of two parts: A. Pole vector p k and the residue vector r k Perform data preprocessing; B. For the trend term and residual term pole vector p after preprocessing k and the residue vector r k Conduct homogeneous; Among them, the pole vector p k and the residue vector r k The method for data preprocessing is: Ⅰ. Eliminate the poles with negative imaginary parts and their corresponding residues in each pair of conjugate complex pole residues, compress the redundant information of the data, and obtain the order N of each sample k 2 to 5 levels; Ⅱ. Extract the trend term pole residue pairs and the residual term pole residue pairs to realize the physical information representation of the data. After processing, the order of the trend term pole residue pairs is N Trend For 1~2 orders, the residual term pole residue is N Residual It is 1 to 3 levels; III. The pole residue pairs of the trend term and the pole residue pairs of the residual term are divided into the following groups according to the central angular frequency ω of their respective poles: c Sort in ascending order; For the trend term and residual term pole vector p after preprocessing k and the residue vector r k The homogeneous method is: Ⅰ. Homogenize the first-order pole residue pairs of the trend term to N Trend =2nd order: The trend term only contains 1st-order pole residue pairs and 2nd-order pole residue pairs. After all 1st-order pole residue pairs are split, the pole residue pairs of the trend term are uniformly homogeneous to 2nd order. Ⅱ. Homogenize the residual term 1st to 2nd order pole residue pairs to N Residual =3rd order: For an effective order of N min Each sample s1 in the sample set S1 has an effective order of N min For each sample s2 in the sample set S2 of +1, the central angular frequency of the trend term pole of sample s1 is compared in l1 form The central angular frequency of the trend term pole of all samples in S2 Select one of the nearest neighbor samples as the basis for splitting: After calculating the residue pair of the splitting mth residual term pole, compare the residual term pole center angular frequency of the s1 sample in l1 norm The residual term pole center angular frequency with the nearest neighbor sample s2 Select distance D m The smallest pair of pole residues is split, that is, the pole p of the mth residual term m and residue r m Perform the following split: Move the split sample s1 from S1 to S2, and continue to homogenize the samples in S1 until S1 becomes an empty set. After the set of 1st-order pole residue pairs is homogenized to the 2nd order, the new set of 2nd-order pole residue pairs is homogenized to the 3rd order, and all pole residue pairs of the residual term are uniformly homogenized to the 3rd order. Pole vector p k and the residue vector r k Perform data processing and extract the trend term and residual term pole vector p k and the residue vector r k When homogenizing, the 1st order pole residue of the trend term is aligned to the 2nd order, and the 1st to 2nd order pole residue of the residual term is aligned to the 3rd order. After homogenization, each sample k=1,2,...,n f , n f is the number of coded superunit samples, and its electromagnetic response S parameter H k (s), trend item electromagnetic response S parameter And the residual electromagnetic response S parameters Characterized by: The order of the trend term electromagnetic response transfer function corresponding to all coding metasurfaces is The order of the residual electromagnetic response transfer function is 8. The method according to claim 7, characterized in that The method of step S3 is as follows: The network is divided into trend term extreme residue prediction network Net trend and residual term extreme point residue prediction network Net residual , all use the CGC custom gating network model with parameter sharing. Each CGC model has two task outputs, namely predicted extreme points and predicted residues. The CGC model has a three-layer structure. The bottom layer consists of two independent expert modules and a shared expert module. Each expert module consists of several convolutional layers and fully connected layers with skip connections. The output of the expert module of the nth task is recorded as S n (x); the middle layer is a gated network with Softmax as the activation function, and the output is: Where x is the input 16×16 encoding matrix flattened into a one-dimensional vector with dimension d=256, Dimension (m n +m s )×d single-layer feedforward network, 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 m of task n n +m s The output feature vector of the expert module, the top layer is the task tower layer, and the output of the gated network is used as input for feature extraction; Net trend Output trend term prediction extremes and predicted residue The constructed trend term transfer function layer is sent to obtain the predicted trend term electromagnetic response S parameters Net residual The residual term of the output predicts the extreme point and predicted residue The residual term transfer function layer is sent to obtain the predicted residual term electromagnetic response S parameters. The electromagnetic responses predicted by the two networks are added together to obtain the total electromagnetic response S parameters. The construction of the transfer function layer uses the trend term pole residue obtained by the trend term pole residue prediction network to calculate the trend term pole residue electromagnetic response, and uses the residual term pole residue obtained by the residual term pole residue prediction network to calculate the residual term pole residue electromagnetic response. The two are added to calculate the overall spectrum response function Denoted as: s=j×2πf Among them, the pointed mark ^ represents the output result of the network prediction, j is the imaginary unit, f is the working frequency band of the coding super unit, and the transfer function layer does not update the parameters.

9. The method according to claim 8, characterized in that The method of step S4 is as follows: Trend term extreme residue prediction network Net trend Enter Meta k , the trend term extreme point predicted by the network output and residue Task and The loss functions are and Towards the residual term extreme residue prediction network Net residual Enter Meta k , the residual term pole of the network output prediction and residue Task and The loss functions are and The calculation formula of MSE is: Among them, y is the true value, is the predicted value, N is the dimension; Trend Term Extreme and residue Send to the trend term transfer function layer, the residual term pole and predicted residue Send it to the residual term transfer function layer to get the predicted trend term electromagnetic response and total electromagnetic response The trend of the electromagnetic response and the total electromagnetic response H k (s) Calculate MSE to get the task and T Hs The loss functions are and L Hs : The total loss L of the objective function based on homoscedastic uncertainty design total , multi-tasking T Hs Federated Learning: Among them, σ1, σ2, σ3, σ4, σ5, σ6 are trainable weight parameters, the initial value is set to 1, and adaptive learning is performed in back propagation. The parameters of the trend term network and the residual term network are denoted by θ tre and θ res , then the goal of multi-task joint training is: The training cycle is set to 150, and the network converges after back-propagation iteratively updates the parameters, and the predicted pole residue pairs and electromagnetic response parameters are obtained.

10. The method according to claim 9, characterized in that The method of step S5 is as follows: The test data set {Meta k } test The input is fed into the network model trained by joint learning to obtain the output predicted electromagnetic response and pole residue, using the mean absolute error MAE, mean square error MSE, and regression coefficient R 2 The evaluation index evaluates the network effect on the test set.

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