Metasurface broadband scattering simulation method based on immittance tensor and neural network

Abstract

The application discloses a metasurface broadband scattering simulation method based on an admittance tensor and a neural network, and belongs to the technical field of computational electromagnetics and artificial intelligence. The method combines a surface admittance tensor sheet model with a neural network method, equivalently regards a to-be-solved metasurface as a sheet model located on a two-dimensional plane, and adopts a surface admittance tensor matrix group to represent a tangential electromagnetic response relationship, thereby avoiding repeated modeling of the metasurface and solving of each frequency point in broadband analysis, and reducing consumption of computing resources. The method adopts a base function to discretize surface equivalent electromagnetic current density, and introduces an admittance residual as a physical constraint in a neural network training process, so that base function coefficient diagrams generated by the network can meet the tangential electromagnetic response relationship represented by the surface admittance tensor model, the physical interpretability and stability of a prediction result of the model can be improved, the neural network can realize high-precision and fast calculation, and the solving efficiency and engineering application feasibility are improved.

Description

Technical Field

[0001] This invention belongs to the field of computational electromagnetics and artificial intelligence technology, specifically relating to a metasurface broadband scattering simulation method based on impedance tensor and neural network. Background Technology

[0002] Metasurfaces are two-dimensional artificial electromagnetic structures formed by the regular arrangement of subwavelength artificial electromagnetic units, capable of controlling the amplitude, phase, polarization, and propagation direction of incident electromagnetic waves. Due to their low profile, ease of fabrication, and high degree of design freedom, metasurfaces have wide applications in antennas, radar stealth, and beamforming. With the increasing size of metasurface structures, the broadening of their operating bandwidth, and the increasing complexity of their applications, the efficient and accurate calculation of the broadband electromagnetic scattering characteristics of finite-period metasurfaces has become a crucial issue in metasurface engineering applications.

[0003] Scattering analysis of finite-periodic metasurface arrays is typically a large-scale electromagnetic problem. The larger the array, the greater the number of unknowns and the higher the storage resource consumption. Existing numerical simulation methods, when performing broadband analysis, often require solving multiple frequency points separately, necessitating repeated calculations and resulting in lengthy overall analysis times. This repeated frequency point solving further increases computational costs, especially during rapid design and parameter optimization.

[0004] Generalized Sheet Transition Conditions (GSTC) are a method for parametric analysis of artificial electromagnetic surfaces. They characterize the metasurface's control over incident electromagnetic waves by establishing the relationship between the electromagnetic fields on both sides of the metasurface. Existing metasurface electromagnetic calculation methods based on GSTC typically require combination with the finite element method, finite difference method, or integral equation method, and mesh generation within the solution domain. For broadband scattering analysis of finite periodic metasurface arrays, calculations at different frequency points still need to be performed separately, making it difficult to directly achieve multi-frequency scattering analysis.

[0005] In recent years, neural network methods have been used in electromagnetic simulation, parameter prediction, and fast computation. Neural networks can establish a mapping relationship between input features and output response through trainable parameters. After training, they can quickly obtain prediction results under target conditions through forward computation, thus providing a new approach for the rapid solution of multi-frequency electromagnetic problems.

[0006] Existing neural network-based electromagnetic scattering simulation methods typically obtain electromagnetic response data under different structural parameters and incident conditions through numerical simulation, and then use this data to train the neural network to establish the relationship between the input conditions and the scattering field. However, these methods usually require a large number of training samples, resulting in high data generation costs, and lack constraints on the electromagnetic response relationship of metasurfaces. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings of the prior art and provide a metasurface broadband scattering simulation method based on impedance tensor and neural network. Through the training process of neural network model constrained by impedance boundary condition residual, it is possible to reduce the computational cost of far-field scattering field of metasurface while ensuring high prediction accuracy, improve the efficiency of broadband scattering analysis, and realize high-precision and fast simulation of broadband scattering characteristics of finite period metasurface arrays.

[0008] The technical problem addressed by this invention is solved as follows:

[0009] A method for simulating broadband scattering of metasurfaces based on impedance tensor and neural networks includes the following steps:

[0010] Step 1: The metasurface to be solved consists of several metasurface units with the same structure arranged periodically; select several uniformly distributed discrete frequency points within a set broadband frequency range; apply infinitely large periodic boundary conditions to the metasurface units and perform electromagnetic simulation to obtain the scattering parameters of the metasurface units at each discrete frequency point; calculate the surface conduction tensor matrix of the metasurface units at each discrete frequency point based on the scattering parameters of the metasurface units.

[0011] Step 2: The metasurface to be solved is equivalent to a thin sheet model of surface resistivity tensor located in a two-dimensional plane, and the surface resistivity tensor matrix is ​​used to characterize the relationship between the surface equivalent electromagnetic current density distribution and the tangential average electromagnetic field; basis functions are constructed on the two-dimensional plane to represent the surface equivalent electromagnetic current density distribution of the metasurface to be solved.

[0012] Step 3: Construct a neural network model; input the initially set basis function coefficient map and the normalized frequency features of the input frequency points into the neural network model, and output the basis function coefficient map corresponding to the basis functions; obtain the surface equivalent electromagnetic current density distribution on the metasurface to be solved based on the output basis function coefficient map and basis functions;

[0013] Step 4: Calculate the tangential average electromagnetic field of the surface impedance tensor thin sheet model based on the surface equivalent electromagnetic current density distribution, and construct the impedance boundary condition residual between the surface equivalent electromagnetic current density distribution and the tangential average electromagnetic field according to the surface impedance tensor matrix set.

[0014] Step 5: Construct a loss function using the residual of the conductive impedance boundary condition. Use each discrete frequency point as the input frequency point of the neural network model. Train the neural network model by minimizing the loss function to obtain a trained neural network model.

[0015] Step 6: Input the target frequency into the trained neural network model to generate the basis function coefficient map of the metasurface at the target frequency, obtain the surface equivalent electromagnetic current density distribution of the metasurface at the target frequency, and calculate the scattering characteristics of the metasurface.

[0016] Furthermore, in step 1, the surface-guided tensor matrix is ​​represented as:

[0017]

[0018] in, For the first Discrete frequency points, Discrete frequency points The metasurface unit surface conductivity tensor matrix set at the location; Discrete frequency points The surface admittance tensor at the point, Discrete frequency points The surface magnetic impedance tensor at that location. Discrete frequency points The magnetoelectric coupling tensor at that point, Discrete frequency points The electromagnetic coupling tensor at that location.

[0019] Furthermore, in step 3, the neural network model includes an input module, a convolutional feature module, and an output module cascaded in sequence. The input module receives the initially set basis function coefficient map and the normalized frequency features of the input frequency points, and combines the two to form an input feature map. The convolutional feature module is composed of multiple layers of two-dimensional convolutional layers connected in sequence, with nonlinear activation functions set between adjacent two-dimensional convolutional layers. The input feature map is passed through the convolutional feature module to obtain an intermediate feature map. The output module is a single two-dimensional convolutional layer. The intermediate feature map is mapped by the two-dimensional convolutional layer to obtain the basis function coefficient map corresponding to the basis functions.

[0020] Furthermore, in step 3, the normalized frequency features Represented as:

[0021]

[0022] in, For the input frequency point, To set the center frequency of the wideband frequency range, It is half the bandwidth of the broadband frequency range.

[0023] Furthermore, in step 3, the two-dimensional convolutional layer uses a 3×3 convolutional kernel.

[0024] Furthermore, in step 3, the convolutional feature module introduces a basis function neighborhood coupling mechanism, specifically: the coefficients corresponding to the basis functions are arranged into a two-dimensional coefficient map according to their positions on the two-dimensional plane; for any basis function coefficient position in the two-dimensional coefficient map, the two-dimensional convolutional layer performs convolution operation based on the features of that position and its neighboring positions, and obtains the output features of that position through a nonlinear activation function, thereby extracting the local spatial correlation features of the surface equivalent electromagnetic current coefficient on the two-dimensional computational plane.

[0025] Furthermore, in step 4, the residual of the conduction impedance boundary condition includes the residual of the current boundary condition. and magnetic flux boundary condition residuals , respectively represented as:

[0026]

[0027]

[0028] in, The surface equivalent current density distribution The surface equivalent magnetic flux density distribution For the tangential average electric field, The tangential average magnetic field, These are the surface admittance tensor, magnetoelectric coupling tensor, electromagnetic coupling tensor, and surface magnetic impedance tensor in the surface impedance tensor matrix corresponding to the input frequency point, respectively.

[0029] Furthermore, in step 5, the single-frequency point physical constraint loss function Represented as:

[0030]

[0031] in, Let q be the q-th sampling point on the two-dimensional plane, where 1 ≤ q ≤ N, and N is the number of sampling points. and Let be the residuals of the current boundary condition and the residuals of the magnetic current boundary condition at the q-th sampling point, respectively. Indicates taking the 2-norm;

[0032] The system performs joint training at each discrete frequency point, calculates the physical constraint loss function for each discrete frequency point, and combines them to obtain the total loss function. :

[0033]

[0034] in, , The total number of discrete frequency points. Discrete frequency points The physical constraint loss function at a single frequency point.

[0035] The beneficial effects of this invention are:

[0036] This invention provides a broadband scattering simulation method for metasurfaces based on the surface impedance tensor and neural networks. It creatively combines a surface impedance tensor thin-plate model with a neural network method, treating the metasurface to be solved as an equivalent thin-plate model located on a two-dimensional computational plane. The surface impedance tensor matrix is ​​used to characterize its tangential electromagnetic response, avoiding repetitive modeling and frequency-by-frequency solving of the metasurface in broadband analysis, thus reducing computational resource consumption. Simultaneously, this invention uses basis functions to discretize the equivalent electromagnetic current density of the surface and introduces impedance residuals as physical constraints during neural network training. This ensures that the basis function coefficient diagram generated by the network satisfies the tangential electromagnetic response relationship characterized by the surface impedance tensor model. Compared to methods that directly predict the scattering field or radar cross section, this improves the physical interpretability and stability of the model's prediction results. Furthermore, after training, the neural network can achieve a rapid calculation process from target frequency input and surface electromagnetic current density generation to broadband scattering characteristic output, reducing the number of full-wave simulations while maintaining computational accuracy, thus improving solution efficiency and engineering application feasibility. Attached Figure Description

[0037] Figure 1 This is a flowchart illustrating the method described in this invention;

[0038] Figure 2 This is a schematic diagram of the metasurface unit structure in the method described in the embodiment;

[0039] Figure 3 This is a schematic diagram of the metasurface to be solved in the method described in the embodiment;

[0040] Figure 4 This is a schematic diagram comparing the bistatic RCS of the metasurface array calculated at 3.5 GHz using the method described in the embodiment with the results obtained by electromagnetic simulation software.

[0041] Figure 5 This is a schematic diagram comparing the bistatic RCS of the metasurface array calculated at 5.5 GHz using the method described in the embodiment with the results obtained by electromagnetic simulation software.

[0042] Figure 6 This is a schematic diagram comparing the bistatic RCS of the metasurface array calculated at 7.5 GHz using the method described in the embodiment with the results from electromagnetic simulation software. Detailed Implementation

[0043] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0044] This embodiment provides a metasurface broadband scattering simulation method based on the impedance tensor and neural networks, such as... Figure 1 As shown, it includes the following steps:

[0045] Step 1: The metasurface to be solved consists of several metasurface units with the same structure arranged periodically; select several uniformly distributed discrete frequency points within a set broadband range; apply infinitely large periodic boundary conditions to the metasurface units and perform electromagnetic simulation to obtain the scattering parameters of the metasurface units at each discrete frequency point; calculate the surface conduction tensor matrix of the metasurface units at each discrete frequency point based on the scattering parameters of the metasurface units.

[0046] The surface impedance tensor matrix includes the surface admittance tensor, surface magnetoresistance tensor, magnetoelectric coupling tensor, and electromagnetic coupling tensor, specifically represented as follows:

[0047]

[0048] in, For the first Discrete frequency points, Discrete frequency points The metasurface unit surface conductivity tensor matrix set at the location; Discrete frequency points The surface admittance tensor at the point, Discrete frequency points The surface magnetic impedance tensor at that location. Discrete frequency points The magnetoelectric coupling tensor at that point, Discrete frequency points The electromagnetic coupling tensor at that location.

[0049] Step 2: The metasurface to be solved is equivalent to a thin sheet model of surface resistivity tensor located in a two-dimensional plane, and the surface resistivity tensor matrix is ​​used to characterize the relationship between the surface equivalent electromagnetic current density distribution and the tangential average electromagnetic field; basis functions are constructed on the two-dimensional plane to represent the surface equivalent electromagnetic current density distribution of the metasurface to be solved.

[0050] Step 3: Construct a neural network model; input the initially set basis function coefficient map and the normalized frequency features of the input frequency points into the neural network model, and output the basis function coefficient map corresponding to the basis functions; obtain the surface equivalent electromagnetic current density distribution on the metasurface to be solved based on the output basis function coefficient map and basis functions;

[0051] A neural network model consists of a cascaded input module, a convolutional feature module, and an output module.

[0052] The input module receives the initially set basis function coefficient map and the normalized frequency features of the input frequency points, and combines them to form an input feature map. In this embodiment, the training frequency points are multiple frequency points within a preset frequency band, and the center frequency and bandwidth of the training frequency band are determined according to the target operating frequency band. The target frequency is converted into normalized frequency features. The normalized frequency features are expanded into frequency feature channels with the same spatial size as the trainable initial feature map, and then concatenated with the trainable initial feature map to obtain the input feature map.

[0053] The convolutional feature module is composed of multiple layers of two-dimensional convolutional layers connected in sequence. A non-linear activation function is set between each adjacent two-dimensional convolutional layer. The input feature map is passed through the convolutional feature module to obtain an intermediate feature map. In this embodiment, each convolutional layer uses a 3×3 convolutional kernel, and the spatial size of the feature map is kept unchanged by boundary padding.

[0054] The output module is a single two-dimensional convolutional layer. The intermediate feature maps are mapped by the two-dimensional convolutional layer to obtain a basis function coefficient map corresponding to the basis functions. In this embodiment, the spatial position of the basis function coefficient map corresponds to the position of the basis functions in the two-dimensional computational domain, and is used to represent the expansion coefficients of the equivalent electromagnetic current on the lower surface at the input frequency point.

[0055] In the neural network model described in this embodiment, a basis function neighborhood coupling mechanism is introduced. Specifically, the coefficients corresponding to the basis functions are arranged into a two-dimensional coefficient map according to their positions on the two-dimensional plane. For any basis function coefficient position in the two-dimensional coefficient map, a two-dimensional convolutional layer performs convolution operations based on the features of that position and its neighboring positions, and obtains the output features of that position through a nonlinear activation function, thereby extracting the local spatial correlation features of the surface equivalent electromagnetic current coefficient on the two-dimensional computational plane. The two-dimensional convolutional layer acts on the coefficient grid corresponding to the basis functions, so that the output features at any basis function position are jointly determined by the input features of that position and its neighboring positions, thereby extracting the local spatial correlation features of the surface equivalent electromagnetic current coefficient on the two-dimensional computational plane.

[0056] The normalized frequency characteristics are determined by the target frequency, the center frequency of the training band, and the half-width of the training band, and are expressed as: ,in, For the target frequency, To train the center frequency of the frequency band, For training half-width, This represents the normalized frequency characteristics.

[0057] Step 4: Calculate the tangential average electromagnetic field of the surface impedance tensor thin sheet model based on the surface equivalent electromagnetic current density distribution, and construct the impedance boundary condition residual between the surface equivalent electromagnetic current density distribution and the tangential average electromagnetic field according to the surface impedance tensor matrix set.

[0058] For a single discrete frequency point, the surface equivalent current density and surface equivalent magnetic flux density are discretized onto a regular grid in a two-dimensional plane, and a two-dimensional Fourier transform is performed to obtain the spectral domain surface equivalent electromagnetic current. For each spectral domain component, based on its spatial spectral variables and corresponding propagation relations, the tangential average electromagnetic field corresponding to that component is calculated using the spectral domain tangential electromagnetic field propagation operator; then, through a two-dimensional inverse Fourier transform, the tangential average electromagnetic field at the surface conductance tensor sheet model in the spatial domain is obtained.

[0059] After obtaining the tangentially averaged electromagnetic field, the tangential field of the incident wave at the location of the two-dimensional thin-film model is superimposed with the tangentially averaged field generated by the surface equivalent electromagnetic current to obtain the total tangentially averaged field used for impedance boundary condition calculation. Based on the surface impedance tensor matrix, the impedance boundary condition residuals between the surface equivalent electromagnetic current and the total tangentially averaged field are constructed, including the current boundary condition residuals. and magnetic flux boundary condition residuals , respectively represented as:

[0060]

[0061]

[0062] in, The surface equivalent current density distribution The surface equivalent magnetic flux density distribution For the tangential average electric field, The tangential average magnetic field, These are the surface admittance tensor, magnetoelectric coupling tensor, electromagnetic coupling tensor, and surface magnetic impedance tensor in the surface impedance tensor matrix corresponding to the input frequency point, respectively.

[0063] Step 5: Construct a loss function using the residual of the conductive impedance boundary condition. Use each discrete frequency point as the input frequency point of the neural network model. Train the neural network model by minimizing the loss function to obtain a trained neural network model.

[0064] In this embodiment, the single-frequency point physical constraint loss function It consists of the residuals of the impedance boundary conditions at each sampling point on the two-dimensional computational plane, and is expressed as:

[0065]

[0066] in, Let q be the q-th sampling point on the two-dimensional plane, where 1 ≤ q ≤ N, and N is the number of sampling points. and Let be the residuals of the current boundary condition and the residuals of the magnetic current boundary condition at the q-th sampling point, respectively. Indicates taking the 2-norm;

[0067] The system performs joint training at each discrete frequency point, calculates the physical constraint loss function for each discrete frequency point, and combines them to obtain the total loss function. :

[0068]

[0069] in, , The total number of discrete frequency points. Discrete frequency points The physical constraint loss function at a single frequency point.

[0070] During training, the Adam + L-BFGS optimization algorithm is used to minimize the total loss function. Backpropagation updates the initially set basis function coefficient map and convolutional neural network model parameters, gradually ensuring that the basis function coefficient map output by the convolutional neural network model satisfies the impedance boundary conditions of the surface impedance tensor sheet model.

[0071] Step 6: Input the target frequency into the trained neural network model to generate the basis function coefficient map of the metasurface at the target frequency, obtain the surface equivalent electromagnetic current density distribution of the metasurface at the target frequency, and calculate the scattering characteristics of the metasurface.

[0072] This embodiment uses the calculation of the scattering characteristics of a metasurface array as an example. A schematic diagram of the metasurface unit structure is shown below. Figure 2 As shown, the metal patch is 1.2 mm wide and 8 mm long, with a dielectric substrate of 8.5 mm in length and width and 1 mm in thickness loaded at the bottom. The relative permittivity is 4.4. It is extended along the x and y directions to form an 8×8 metasurface array, as shown. Figure 3 As shown. The incident wave is set as an x-polarized uniform plane wave, along the angle... Incident, solve xoz noodles Dual-station RCS. and These are the pitch angle and the azimuth angle, respectively.

[0073] To verify the fast solution capability of the method described in this embodiment within a certain broadband frequency range, a simulation and training frequency range of 3GHz to 8GHz was selected. Specifically, 3GHz, 4GHz, 5GHz, 6GHz, 7GHz, and 8GHz are the discrete training frequency points for the convolutional neural network model, used to construct the loss function and optimize the network parameters.

[0074] After training, to verify the predictive capability of the convolutional neural network model in the method described in this embodiment within a wide frequency range, 3.5 GHz, 5.5 GHz, and 7.5 GHz were selected as verification frequency points, i.e., target frequencies. For any target frequency, its normalized frequency features were input into the trained convolutional neural network model. Only one forward computation was needed to obtain the basis function coefficient map at the target frequency, thereby obtaining the surface equivalent electromagnetic current density on the metasurface array to be solved at the corresponding target frequency. Furthermore, the far-field scattering field and radar cross section at the corresponding target frequency were calculated.

[0075] To verify the computational accuracy and acceleration effect of the method described in this embodiment, the bistatic RCS obtained by the method described in this embodiment is compared with the results of electromagnetic simulation software. Under the same computational conditions, the time required to train the convolutional neural network model using the method described in this embodiment is 1261s, while the time required to complete a full-wave simulation solution in the 3GHz to 8GHz frequency band using electromagnetic simulation software is 16813s.

[0076] After training, for the three verification frequencies of 3.5 GHz, 5.5 GHz, and 7.5 GHz, the method described in this embodiment only requires one forward computation of the convolutional neural network and one electromagnetic field propagation computation to obtain the corresponding bistatic RCS, with a computation time of approximately 1 second for a single frequency. Simulation results are compared below. Figure 4 , Figure 5 and Figure 6 As shown, the bistatic RCS curve obtained by the method described in this embodiment is highly consistent with the full-wave simulation results of the electromagnetic simulation software. This demonstrates that the method described in this embodiment can significantly reduce the computation time for broadband metasurface array scattering while maintaining computational accuracy.

Claims

1. A metasurface broadband scattering simulation method based on impedance tensor and neural network, characterized in that, Includes the following steps: Step 1: The metasurface to be solved consists of several metasurface units with the same structure arranged periodically; select several uniformly distributed discrete frequency points within a set broadband frequency range; apply infinitely large periodic boundary conditions to the metasurface units and perform electromagnetic simulation to obtain the scattering parameters of the metasurface units at each discrete frequency point; calculate the surface conduction tensor matrix of the metasurface units at each discrete frequency point based on the scattering parameters of the metasurface units. Step 2: The metasurface to be solved is equivalent to a thin sheet model of surface resistivity tensor located in a two-dimensional plane, and the surface resistivity tensor matrix is ​​used to characterize the relationship between the surface equivalent electromagnetic current density distribution and the tangential average electromagnetic field; basis functions are constructed on the two-dimensional plane to represent the surface equivalent electromagnetic current density distribution of the metasurface to be solved. Step 3: Construct a neural network model; input the initially set basis function coefficient map and the normalized frequency features of the input frequency points into the neural network model, and output the basis function coefficient map corresponding to the basis functions; obtain the surface equivalent electromagnetic current density distribution on the metasurface to be solved based on the output basis function coefficient map and basis functions; Step 4: Calculate the tangential average electromagnetic field of the surface impedance tensor thin sheet model based on the surface equivalent electromagnetic current density distribution, and construct the impedance boundary condition residual between the surface equivalent electromagnetic current density distribution and the tangential average electromagnetic field according to the surface impedance tensor matrix set. Step 5: Construct a loss function using the residual of the conductive impedance boundary condition. Use each discrete frequency point as the input frequency point of the neural network model. Train the neural network model by minimizing the loss function to obtain a trained neural network model. In step 5, the single-frequency point physical constraint loss function Represented as: in, Let q be the q-th sampling point on the two-dimensional plane, where 1 ≤ q ≤ N, and N is the number of sampling points. and Let be the residuals of the current boundary condition and the residuals of the magnetic current boundary condition at the q-th sampling point, respectively. Indicates taking the 2-norm; The system performs joint training at each discrete frequency point, calculates the physical constraint loss function for each discrete frequency point, and combines them to obtain the total loss function. : in, , The total number of discrete frequency points. Discrete frequency points The physical constraint loss function at a single frequency point; Step 6: Input the target frequency into the trained neural network model to generate the basis function coefficient map of the metasurface at the target frequency, obtain the surface equivalent electromagnetic current density distribution of the metasurface at the target frequency, and calculate the scattering characteristics of the metasurface.

2. The metasurface broadband scattering simulation method based on impedance tensor and neural network according to claim 1, characterized in that, In step 1, the surface-guided tensor matrix is ​​represented as follows: in, For the first Discrete frequency points, Discrete frequency points The metasurface unit surface conductivity tensor matrix set at the location; Discrete frequency points The surface admittance tensor at the point, Discrete frequency points The surface magnetic impedance tensor at that location. Discrete frequency points The magnetoelectric coupling tensor at that point, Discrete frequency points The electromagnetic coupling tensor at that location.

3. The metasurface broadband scattering simulation method based on impedance tensor and neural network according to claim 1, characterized in that, In step 3, the neural network model includes an input module, a convolutional feature module, and an output module cascaded in sequence. The input module receives the initially set basis function coefficient map and the normalized frequency features of the input frequency points, and combines the two to form an input feature map. The convolutional feature module is composed of multiple layers of two-dimensional convolutional layers connected in sequence. A non-linear activation function is set between each adjacent two-dimensional convolutional layer. The input feature map is passed through the convolutional feature module to obtain an intermediate feature map. The output module is a single two-dimensional convolutional layer. The intermediate feature map is mapped by the two-dimensional convolutional layer to obtain the basis function coefficient map corresponding to the basis function.

4. The metasurface broadband scattering simulation method based on impedance tensor and neural network according to claim 1, characterized in that, In step 3, normalized frequency features Represented as: in, For the input frequency point, To set the center frequency of the wideband frequency range, It is half the bandwidth of the broadband frequency range.

5. The metasurface broadband scattering simulation method based on impedance tensor and neural network according to claim 3, characterized in that, In step 3, the two-dimensional convolutional layer uses a 3×3 convolutional kernel.

6. The metasurface broadband scattering simulation method based on impedance tensor and neural network according to claim 5, characterized in that, In step 3, the convolutional feature module introduces a basis function neighborhood coupling mechanism, specifically: the coefficients corresponding to the basis functions are arranged into a two-dimensional coefficient map according to their positions on the two-dimensional plane; for any basis function coefficient position in the two-dimensional coefficient map, the two-dimensional convolutional layer performs convolution operation based on the features of that position and its neighboring positions, and obtains the output features of that position through a nonlinear activation function, thereby extracting the local spatial correlation features of the surface equivalent electromagnetic current coefficient on the two-dimensional computational plane.

7. The metasurface broadband scattering simulation method based on impedance tensor and neural network according to claim 1, characterized in that, In step 4, the residual of the conduction reactance boundary condition includes the residual of the current boundary condition. and magnetic flux boundary condition residuals , respectively represented as: in, The surface equivalent current density distribution The surface equivalent magnetic flux density distribution For the tangential average electric field, The tangential average magnetic field, These are the surface admittance tensor, magnetoelectric coupling tensor, electromagnetic coupling tensor, and surface magnetic impedance tensor in the surface impedance tensor matrix corresponding to the input frequency point, respectively.

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