A physically-driven machine learning method for metasurface intelligent design

Abstract

The application discloses a physical driven machine learning algorithm for metasurface intelligent design, which is used for accelerating the prediction process of metasurface electromagnetic response, and further realizing efficient metasurface intelligent design. The specific steps are as follows: 1) sampling in the parameter space, performing full-wave electromagnetic simulation on different unit samples containing only one and two resonators, and obtaining the coupled mode (CMT) parameter value through fitting to construct a database; 2) training a neural network to learn the relationship between the geometric parameters and the CMT parameter value; 3) combining the trained neural network with the multi-resonance coupled mode theory equation to accurately predict the electromagnetic response of a multi-resonance system with any number of resonators; and 4) based on the neural network CMT replacement model, using an optimization algorithm to perform rapid optimization design of the metasurface. Compared with a data-driven modeling method, the application significantly reduces the number of training samples by nearly 75%, and shortens the metasurface design optimization time by more than two orders of magnitude, and can be used in microwave scenes such as electromagnetic stealth.

Description

TECHNICAL FIELD

[0001] The present application belongs to the cross field of electronic design automation (EDA), artificial intelligence technology and novel artificial electromagnetic materials, and specifically relates to a physically-driven machine learning method for metasurface intelligent design. BACKGROUND

[0002] In the past decade, metasurfaces have made great progress in many fields. Due to its strong ability to manipulate electromagnetic waves, metasurfaces are considered as one of the most promising technologies in the next generation of communication systems.

[0003] In the design process of metasurfaces, parameter optimization is a key and extremely challenging task. Traditionally, this task is completed by using optimization subroutines on commercial electromagnetic simulation software, in which the geometric parameter values must be repeatedly changed to perform a large number of full-wave electromagnetic simulations, so this direct electromagnetic optimization method is time-consuming and occupies a large amount of memory space. In addition, in order to obtain a good initial design condition as the input of the optimization subroutine, the direct electromagnetic optimization method usually requires engineers to have rich design experience. The final result obtained by the direct electromagnetic optimization method is highly dependent on the input of the initial design condition, and when the size of the metasurface is larger or the structure is more complex, this problem becomes more difficult.

[0004] In order to solve the above problems, machine learning (ML) based design methods have been developed towards fast and intelligent metasurface design. However, most of the existing machine learning based metasurface design methods are data-driven, which requires full-wave electromagnetic simulations to generate a large amount of data. Subsequently, a surrogate model is developed by training through specific machine learning techniques. The machine learning techniques used include deep learning, Kriging interpolation, convolutional neural network (CNN), and Hopfield network, etc. These methods have a common problem: when the structural complexity of the metasurface is improved, the amount of data required by the machine learning model will increase significantly. Thus the computational burden of electromagnetic simulation to generate data will become very heavy, and it is quite difficult to establish an accurate data-driven surrogate model. In order to overcome this difficulty, physically-driven methods can be introduced to introduce prior knowledge into the process of establishing a surrogate model. Due to the introduction of prior knowledge and physical laws in the process of establishing a model, the physically-driven design method can achieve higher design efficiency while having better universality and physical interpretation compared to the data-driven design method.

[0005] The time-domain coupled mode theory is a powerful tool in modeling the multi-resonant response of optical or microwave systems. Recently, the possibility of using the coupled mode theory to guide the efficient inverse design of metasurfaces has been explored. However, the existing optimization design of metasurfaces based on the coupled mode theory all need to construct a coupled mode parameter lookup table as a prerequisite. These optimization design methods of metasurfaces based on the lookup table and the coupled mode theory have a big technical bottleneck and cannot be well applied to large-scale multi-parameter optimization design of metasurfaces. How to use the coupled mode theory to accelerate the design optimization of the coupled multi-resonator system containing metasurfaces still needs further research.

[0006] To make up for this research gap, the present application proposes a physical driving machine learning method combined with the coupled mode theory and applies it to the efficient intelligent design of metasurfaces. SUMMARY

[0007] Technical problem: The purpose of the present application is to provide a physical driving machine learning method for intelligent design of metasurfaces, which combines machine learning (neural network technology) with the coupled mode theory to construct a surrogate model, realizes the fast prediction of the electromagnetic response of the coupled multi-resonant system containing metasurfaces, and further realizes the fast optimization design of metasurfaces based on the surrogate model using optimization algorithms.

[0008] Technical solution: The physical driving machine learning method for intelligent design of metasurfaces of the present application includes the following steps:

[0009] Step 1). For single-resonant and multi-resonant coupled systems, grid sampling is performed in the geometric parameter space. For samples of different geometric sizes, full-wave electromagnetic simulation is performed on the unit structures containing one and two resonators to obtain the electromagnetic response of the corresponding metasurfaces.

[0010] Step 2). According to the coupled mode theory equation, the electromagnetic response of the unit containing one and two resonators is fitted to obtain the corresponding coupled mode parameter values by the Nelder-Mead simplex direct search algorithm or local optimization algorithm, and the coupled mode parameter database of single-resonant and double-resonant is constructed.

[0011] Step 3). Based on the constructed coupled mode parameter database of single-resonant, the relationship between single-resonant coupled mode parameters and geometric parameters is learned using a multilayer perceptron neural network MLP.

[0012] Step 4). Based on the constructed coupled mode parameter database of double-resonant, the relationship between double-resonant coupled mode parameters and geometric parameters is learned using a multilayer perceptron neural network MLP.

[0013] Step 5). Combine the trained single-resonance and double-resonance neural networks with the multi-resonance coupled-mode formulas to build an overall physics-driven machine learning model, making it an efficient tool that can accurately predict the electromagnetic response of any coupled multi-resonance system.

[0014] Step 6). Based on the trained physics-driven machine learning model, determine the super surface design indicators, and use the gradient-based quasi-Newton optimization algorithm to solve the constrained optimization problem, thereby obtaining the optimal design of the super surface unit structure.

[0015] wherein,

[0016] Step 1) For the single-resonator system, let L represent the length of the metal strip along the transverse x-axis. Perform equidistant grid sampling of L in one-dimensional parameter space. Perform full-wave electromagnetic simulation on the unit corresponding to each geometric parameter L sample to obtain the electromagnetic response of the corresponding super surface. For the double-resonator system, let z represent the parameter vector containing the lengths of the two metal strips along the transverse x-axis and the spacing. Perform equidistant grid sampling of z in three-dimensional parameter space, and perform full-wave electromagnetic simulation on the unit containing two resonators corresponding to each geometric parameter sample to obtain the electromagnetic response of the corresponding super surface.

[0017] Step 2) Based on the electromagnetic response data of the single-resonator system, use the Nelder-Mead simplex direct search algorithm to solve the binary nonlinear minimization problem, and construct a database that maps the geometric parameter L and the coupled-mode parameters of the single-resonator system between the resonant frequency and the decay rate. Based on the electromagnetic response data of the double-resonator system, use the Nelder-Mead simplex direct search algorithm to solve the binary nonlinear minimization problem, and construct a database that maps the three geometric parameter vectors x and the coupling coefficients of the double-resonator system.

[0018] Step 3) After obtaining the training data set of all geometric parameter values by learning the relationship between the single-resonance coupled-mode parameters and the geometric parameters, use a multi-layer perceptron neural network MLP to learn the relationship between the coupled-mode parameters and the geometric parameter L. Let the vector represent the output vector of the single-resonance neural network, wherein, corresponding to the resonant frequency of the neural network output, and corresponding to the decay rate of the neural network output; let w sr represent the weight parameter vector of the single-resonance neural network, and the training process can be expressed as the following optimization problem:

[0019]

[0020] wherein E1(w sr) is a single-resonator neural network training error function, arg min is a minimization operator, represents the optimal solution of the optimization problem. sr represents the optimal solution of the optimization problem.

[0021] Step 4) The relationship between the coupled-mode parameters and the three geometric parameters in z is learned using a multi-layer perceptron neural network; let the vector represents the output vector of the dual-resonance neural network, where, and represent the real and imaginary parts of the coupling coefficient of the dual-resonance system, respectively; let w dr represent the weight parameter vector of the dual-resonance neural network, the training process can be expressed as the following optimization problem:

[0022]

[0023] where E2(w dr ) is a dual-resonator neural network training error function, arg min is a minimization operator, represents the optimal solution of the optimization problem. dr represents the optimal solution of the optimization problem.

[0024] Step 5) The trained single-resonance and dual-resonance neural networks are combined with the multi-resonance coupled-mode formula to build an overall physics-driven machine learning model, and w * is defined as the optimized weight vector of the two neural networks, i.e. The overall output of the neural network coupled-mode model obtained by combining the trained single-resonance and dual-resonance neural networks with the multi-resonance coupled-mode formula is:

[0025] y(x,ω,w * ) = 1 - |1 + D(x,w * ) T γ -1 (x,w * )D(x,w * )| 2

[0026] where y(x,ω,w * ) represents the output of the neural network coupled-mode model, ω represents the frequency variable, x represents the geometric size vector of the metasurface, and the symbol D(x,w * ) is a complex N-by-1 vector that allows the metasurface system to be coupled with incoming and outgoing plane waves, γ -1 (x,w * ) is an N-by-N complex matrix, defined as:

[0027] γ-1 (x,w*) = [j(ωI N -Ω(x,w * ))+Γ(x,w * )] -1

[0028] The above formula can be used to efficiently and accurately predict the electromagnetic response of a multi-resonant system corresponding to any geometric parameters, wherein the symbol Ω(x,w * ) is an N×N complex matrix containing resonance frequencies and coupling constants, I N represents an N×N identity matrix, and Γ(x,w * ) represents an N×N real matrix containing the decay rate of the resonator.

[0029] Step 6) Optimal design of the super surface unit structure, using the constructed neural network CMT model to realize the rapid optimization design of the super surface, defining the geometric parameters x as the optimization variables, and describing the design of the super surface unit as the following constrained optimization problem:

[0030]

[0031]

[0032]

[0033]

[0034] wherein a represents the length of the super surface unit along the x-axis direction; U(x) represents the minimum maximum value or the generalized error function; x * represents the optimal design of the super surface unit structure obtained by solving the optimization algorithm; L min and L max respectively represent the minimum and maximum values of L when the geometric parameters of the single resonator are sampled; d min and d max respectively represent the minimum and maximum values of the distance between the two resonators when the geometric parameters of the double resonator are sampled; N represents the number of resonators in the super surface structure; x k represents the kth element of x, which is also the kth optimization variable; K represents the number of elements in the vector x, which is also the total number of optimization variables. A quasi-Newton algorithm based on gradient is used to solve the above optimization problem, thereby obtaining the optimal design x * of the super surface unit structure.

[0035] Advantages: Compared with the prior art, the present application has the following advantages

[0036] 1. Compared with the existing full-wave electromagnetic simulation-based electromagnetic response calculation and optimization, the intelligent algorithm provided by the present application can shorten the time of the metasurface design optimization process by more than two orders of magnitude, thereby realizing efficient microwave device design and optimization.

[0037] 2. Compared with the existing data-driven modeling method, the physical-driven intelligent modeling method provided by the present application fuses the prior knowledge of the physical coupling between units (i.e., coupled mode theory), so that the number of samples required for training the neural network can be significantly reduced, and the physical interpretability and calculation accuracy of intelligent calculation can be improved. BRIEF DESCRIPTION OF DRAWINGS

[0038] Figure 1 is the physical-driven metasurface parameterization model structure proposed by the present application.

[0039] Figure 2 is a modeling accuracy comparison diagram of the parameterization model and the data-driven parameterization model when modeling a three-resonator system.

[0040] Figure 3 is a modeling accuracy comparison diagram of the parameterization model and the data-driven parameterization model when modeling a four-resonator system.

[0041] Figure 4 is the electromagnetic response corresponding to the initial design when the present application is applied to the rapid design of a metasurface.

[0042] Figure 5 is the electromagnetic response corresponding to the optimal design when the present application is applied to the rapid design of a broadband microwave absorber.

[0043] Figure 6 is a flowchart of the present application. DETAILED DESCRIPTION

[0044] The neural network-CMT model proposed by the present application is a mathematical model capable of rapidly predicting the electromagnetic response of a periodic multi-resonator system. The neural network-CMT model structure proposed by the present application mainly comprises three parts, a neural network of single-resonator CMT parameters, a neural network of double-resonator CMT parameters, and a multi-resonator coupled mode parameter equation. The input parameters of the model are the design variables (i.e., geometric parameters) of the multi-resonator system (i.e., metasurface) and the frequency. The output of the model is the electromagnetic response (i.e., absorption rate) of the metasurface, denoted by y. The vector composed of the design variables of the metasurface is denoted by x. In a one-dimensional metasurface electromagnetic structure, the design variables x include the lengths of all strips and the distances between adjacent two strips.

[0045] As the geometric parameter x changes, the CMT parameters change accordingly. To quickly and accurately predict the CMT parameters when the geometric parameters change, this invention trains two neural networks (one for a single resonator system and the other for a dual resonator system) to learn the relationship between the CMT parameters and the geometric parameters. Taking a one-dimensional metasurface as an example, assume the resonator is an infinitely long metal strip along the longitudinal direction (y-axis), and let L represent the length of the strip along the transverse direction (x-axis). Define ω0, γ a and γ r These are the coupled-mode parameters corresponding to a single-resonant system. As L changes, the CMT parameters ω0 and γ... a and γ r The situation will change accordingly.

[0046] Establishing a neural network model for predicting CMT parameters of a single resonator mainly involves the following two steps:

[0047] 1) First, full-wave electromagnetic simulations are performed on units containing a single resonator with different L values. Let M1 represent the training sample size of the single-resonator neural network model. Let... This represents the training sample index set under different L values, i.e. L (n) Indicates the first in the training data A geometric sample. For each geometric parameter value The electromagnetic response of the corresponding metasurface's absorbance was obtained through full-wave electromagnetic simulation. Let ω f Let α represent the f-th frequency sample. (n) (ω f ) represents a frequency of ω f The geometric sample is L (n) The electromagnetic response at time. Find the peak value of the electromagnetic response curve to extract L. (n) The corresponding resonant frequency At the same time, L (n) The corresponding attenuation rate and The following result is obtained by solving the bivariate nonlinear minimization problem:

[0048]

[0049] Wherein, the symbol |·| represents taking the absolute value, and formula (1) is a nonlinear unconstrained optimization problem solved by the classic Nelder-Mead simplex direct search algorithm.

[0050] 2) Then, train the neural network corresponding to the single-resonant system. The above process generates a training sample {L}. (n) ,d (n)},in symbol Let L represent the geometric sample.(n) resonant frequency, and denotes the geometric sample L (n) The decay rate at time. After obtaining the training dataset of all geometric parameter values, a three-layer multilayer perceptron neural network is used to learn the relationship between the CMT parameters and the geometric parameter L. Let the output vector of the single-resonator neural network be denoted as and the weight parameter vector of the single-resonator neural network be denoted as w sr The training process can be formulated as the following optimization problem:

[0051]

[0052] where E1(w sr ) is the single-resonator neural network training error function, defined as follows:

[0053]

[0054] where the notation ||·||2 2 denotes the second-order norm of a vector. The purpose of the above training step is to minimize the difference between the neural network output and the three CMT parameters extracted from the electromagnetic response. This allows the trained neural network to give fast and accurate single-strip CMT parameter predictions for a new L value.

[0055] For a double-resonator system, define β ij as the coupling coefficient corresponding to resonator i and resonator j. As the geometric parameter x changes, the double-resonator system CMT parameter β ij correspondingly changes. Building a neural network model to predict double-resonator CMT parameters involves the following two steps:

[0056] 1) For a double-resonator system, define L1 and L2 to represent the lengths of the two metal strips along the x-axis, and define d to represent the distance between the two strips. As the three geometric parameters L1, L2, and d change, the coupling coefficient β 12 correspondingly changes. Define the geometric parameter vector as z = [L1 L2 d] T , then the input of the neural network model is z, and the output is the real and imaginary parts of β 12 .

[0057] First, full-wave electromagnetic simulations are performed on units containing two resonators with different geometric parameter values. Let M2 represent the training sample size of the double-resonator neural network model. Let denote the training sample index set under different geometric parameters, for example Let z (m) denote the k th geometric sample in the training data, where

[0058] For each geometry sample z (m) , the electromagnetic response (absorptivity) of the corresponding metasurface is obtained through full-wave electromagnetic simulation. Let α (m) (ω f ) denote the absorptivity electromagnetic response of the metasurface at frequency ω f with geometry sample z (m) . Meanwhile, the real and imaginary parts of the coupling mode coefficient corresponding to z (m) can be obtained by solving the following binary nonlinear minimization problem:

[0059]

[0060] where the explicit expression of α(β 12 , ω f ) is derived from the coupling mode formula of a two-resonator system, denotes the index set of all the frequency points of interest, denotes the optimal value of the coupling coefficient β 12 obtained through fitting. In the above minimization problem, the single-resonator CMT parameters are available for the double-strip structure, which makes the coupling mode coefficient β 12 the only free variable. After extracting the single-resonator CMT parameters corresponding to L1 and L2, the nonlinear unconstrained optimization problem in (4) is solved using the Nelder-Mead simplex direct search algorithm.

[0061] 2) Then, the neural network corresponding to the two-resonator system is trained. The above step generates a training sample {z (m) , c (m)}, where c (m) = [Re(β 12 ) (m) Im(β 12 ) (m) ] T , where Re(β 12 ) (m) and Im(β 12 ) (m) denote the real and imaginary parts of the coupling coefficient corresponding to geometry sample z (m) . After obtaining the training dataset of all the geometry parameter values, a three-layer multilayer perception neural network is used to learn the relationship between the CMT parameters and the three geometry parameters in z . Let the output vector of the two-resonator neural network be denoted by w dr , and let the weight parameter vector of the two-resonator neural network be denoted by w

[0062]

[0063] where E2(w dr ) represents the double-resonator neural network training error function, defined as follows:

[0064]

[0065] After the training process of the double-resonator neural network is completed, the trained neural network can quickly and accurately predict the coupling mode coefficients of samples with any new geometric parameters {L1, L2, d}.

[0066] Let w * be the optimization weight vector of the two neural networks, for example Thus, the output of the neural network CMT model can be given by the following equation:

[0067] y(x,ω,w * )=1-|1+D(x,w * ) T γ -1 (x,w * )D(x,w * )| 2 (7)

[0068] where γ -1 (x,w * ) is an N x N complex-valued matrix, defined as:

[0069] Υ -1 (x,w * )=[j(ωI N -Ω(x,w * ))+Γ(x,w * )] -1 (8)

[0070] Equation (8) can be used to efficiently and accurately predict the electromagnetic response of a coupled multi-resonator system under any geometric parameters x.

[0071] The neural network-CMT parameterization model construction process proposed by the present application can be summarized by the following step-by-step algorithm:

[0072] Step 1) Set the sample range for a single strip unit, with the geometric parameter L ranging from [L min ,L max ];

[0073] Step 2) Use the grid sampling method to generate M1 geometric samples in the training range [L min ,L max ], denoted as

[0074] Step 3) For each geometric parameter value Calculate geometric sample L using full-wave electromagnetic simulation (n) Corresponding absorptivity electromagnetic response;

[0075] Step 4) Solve optimization problem (1) using Nelder-Mead simplex direct search algorithm to extract single-resonance CMT parameters;

[0076] Step 5) Train neural network to learn the relationship between single-resonance CMT parameters and geometric parameters L based on (2) and (3);

[0077] Step 6) Define three parameter ranges as [L min ,L max ], [L min ,L max ] and [d min ,d max ] respectively. Generate M2 geometric samples in three-parameter space using grid sampling method, denoted as

[0078] Step 7) For each geometric sample Calculate geometric sample z using full-wave electromagnetic simulation (m) Corresponding absorptivity electromagnetic response;

[0079] Step 8) Solve optimization problem (4) using Nelder-Mead simplex direct search algorithm to extract double-resonance CMT parameters;

[0080] Step 9) Train neural network to learn the relationship between double-resonance CMT parameters and three geometric parameters {L1, L2, d} based on (5) and (6);

[0081] Step 10) Obtain the output of neural network-CMT model according to formulas (7) and (8).

[0082] Next, the neural network-CMT model constructed in the above is further used to realize the fast optimization design of metasurfaces. In the optimization process, the geometric parameter x is defined as the optimization variable. The design of metasurface unit can be described by the following constrained optimization problem:

[0083]

[0084] where symbol a represents the length of the metasurface unit along the x-axis direction; U(·) represents the minimum maximum or generalized error function. For example, for frequency selective or broadband microwave absorber, the error function has the following form:

[0085]

[0086] wherein denotes the set of indices of all frequency samples where the design metric is present; e(x, ω f is calculated with the following formula:

[0087]

[0088] where S(ω f ) denotes the corresponding design metric at frequency ω f . and denote the set of all upper design metric samples and lower design metric samples containing the absorber, respectively. The optimization problem (9) is solved using a gradient-based quasi-Newton algorithm to obtain the optimal design x * of the metasurface unit structure.

[0089] Table 1 gives the comparison of the training data amount and the model accuracy of the present application and the data-driven technique when parameterizing the modeling of the frequency selective absorber. From the table, it can be seen that when the range of variation of the geometric parameters is small (scenario one), both methods can achieve high modeling accuracy. However, the number of training samples (i.e. the number of electromagnetic simulations) required by the present application is nearly one third less than that of the pure data-driven technique. This greatly improves the modeling efficiency. When the range of variation of the geometric parameters is large (scenario two), under the premise of the same number of training samples, only the present application can still achieve high modeling accuracy.

[0090] Table 2 gives the comparison of the time of the present application and the traditional optimization design method based on full-wave electromagnetic simulation. From the table, it can be seen that the optimization efficiency realized by the present application is at least two orders of magnitude higher than that of the traditional optimization method. Under different design metrics, the present application has achieved very good design results.

[0091] Figure 1 The structure of the physically driven metasurface parameterization model proposed by the present application is given.

[0092] Figure 2 The modeling accuracy comparison diagram of the parameterization model proposed by the present application and the data-driven parameterization model when modeling the three-resonator system is given. It can be seen that the parameterization model proposed by the present application realizes a more accurate prediction result than the data-driven model.

[0093] Figure 3 The modeling accuracy comparison diagram of the parameterization model proposed by the present application and the data-driven parameterization model when modeling the four-resonator system is given. It can be seen that the output of the parameterization model proposed by the present application is highly consistent with the full-wave electromagnetic simulation result.

[0094] Figure 4The electromagnetic response corresponding to the initial design when the application is applied to the rapid design of metasurfaces.

[0095] Figure 5 The electromagnetic response corresponding to the optimal design when the application is applied to the rapid design of broadband microwave absorbers. It can be seen that the application realizes efficient and intelligent metasurface design under different design indicators.

[0096] It should be noted that the above is only the preferred embodiment of the application. Due to the unique use of the prior knowledge of physical coupling between units (i.e. coupling mode theory) for metasurface parameterization modeling, the number of samples required for training the neural network can be significantly reduced, and the physical interpretability and calculation accuracy of intelligent calculation can be improved. It should be pointed out that for ordinary skilled persons in the art, without departing from the principles of the application, a number of improvements and refinements can be made, which should also be considered within the scope of protection of the application.

[0097] Table 1

[0098]

[0099]

[0100] Table 2

[0101]

Claims

1. A physically-driven machine learning method for metasurface intelligent design, characterized in that, The method comprises the following steps: Step 1) For a single resonator system, let L represent the length of the metal strip along the transverse x-axis, and perform equidistant grid sampling on L in a one-dimensional parameter space; perform full-wave electromagnetic simulation on the single resonator unit corresponding to each geometric parameter L sample to obtain the electromagnetic response of the corresponding metasurface; for a double resonator system, let z represent the parameter vector containing the lengths of the two metal strips along the transverse x-axis and the spacing; perform equidistant grid sampling on z in a three-dimensional parameter space, and perform full-wave electromagnetic simulation on the unit containing two resonators corresponding to each geometric parameter sample to obtain the electromagnetic response of the corresponding metasurface. Step 2) According to the coupled mode theory equation, based on the electromagnetic response data of the single resonator system, the Nelder-Mead simplex direct search algorithm is used to solve the binary nonlinear minimization problem to construct a database covering the mapping relationship between the geometric parameter L and the resonant frequency and attenuation rate of the single resonator system coupling mode parameters; based on the electromagnetic response data of the double resonator system, the Nelder-Mead simplex direct search algorithm is used to solve the binary nonlinear minimization problem to construct a database covering the mapping relationship between the three-dimensional vector z and the coupling coefficient of the double resonator system. Step 3) After obtaining the training data set of all geometric parameter values, the relationship between the coupling mode parameters and the geometric parameter L is learned using a multi-layer perceptron neural network MLP; Step 4) The relationship between the coupling mode parameters and the geometric parameters is learned using a multi-layer perceptron neural network to learn the relationship between the coupling mode parameters and the three geometric parameters in z; Step 1) The single resonator system is represented by L, which represents the length of the metal strip along the transverse x-axis. Equidistant grid sampling is performed on L in a one-dimensional parameter space. Full-wave electromagnetic simulation is performed on the single resonator unit corresponding to each geometric parameter L sample to obtain the electromagnetic response of the corresponding metasurface. For the double resonator system, z represents the parameter vector containing the lengths of the two metal strips along the transverse x-axis and the spacing. Equidistant grid sampling is performed on z in a three-dimensional parameter space. Full-wave electromagnetic simulation is performed on the unit containing two resonators corresponding to each geometric parameter sample to obtain the electromagnetic response of the corresponding metasurface. Step 2) According to the coupled mode theory equation, based on the electromagnetic response data of the single resonator system, the Nelder-Mead simplex direct search algorithm is used to solve the binary nonlinear minimization problem to construct a database covering the mapping relationship between the geometric parameter L and the resonant frequency and attenuation rate of the single resonator system coupling mode parameters; based on the electromagnetic response data of the double resonator system, the Nelder-Mead simplex direct search algorithm is used to solve the binary nonlinear minimization problem to construct a database covering the mapping relationship between the three-dimensional vector z and the coupling coefficient of the double resonator system.

2. The physically-driven machine learning method for metasurface intelligent design of claim 1, wherein, Step 3) After obtaining the training data set of all geometric parameter values, the relationship between the coupling mode parameters and the geometric parameter L is learned using a multi-layer perceptron neural network MLP; 3. The physically-driven machine learning method for metasurface intelligent design of claim 1, wherein, Step 4) The relationship between the coupling mode parameters and the geometric parameters is learned using a multi-layer perceptron neural network to learn the relationship between the coupling mode parameters and the three geometric parameters in z; 4. The physically-driven machine learning method for metasurface intelligent design of claim 1, wherein, ​ Let denote the output vector of a single-resonance neural network, where corresponds to the resonance frequency of the neural network output, and corresponds to the decay rate of the neural network output; let sr denote the weight parameter vector of a single-resonance neural network, the training process is formulated as an optimization problem as follows: where E1(w sr ) is a single-resonator neural network training error function, arg min is a minimization operator, denotes the optimal solution of w sr after solving the optimization problem.

5. The physically-driven machine learning method for metasurface intelligent design of claim 1, wherein, ​ Let the vector denote the output vector of the dual-resonance neural network, where and denote the real and imaginary parts of the coupling coefficient of the dual-resonance system, respectively; let w dr denote the weight parameter vector of the dual-resonance neural network, and the training process is formulated as the following optimization problem: where E2(w dr ) is a double-resonator neural network training error function, arg min is a minimization operator, w dr represents the optimal solution of the optimization problem.

6. The physically-driven machine learning method for metasurface intelligent design of claim 1, wherein, Step 5) The single resonance and double resonance neural networks combined with the multi-resonance coupled-mode formula are trained to build an overall physical-driven machine learning model, and w is defined * The optimization weight vector of the two neural networks, i.e. The overall output of the neural network coupled-mode model is obtained by combining the trained single resonance and double resonance neural networks with the multi-resonance coupled-mode formula: y(x, ω, w) = 1 - |1 + D(x, w * ) * ) T γ -1 (x, w * )D(x, w * )| 2 where y(x, ω, w * ) represents the output of the neural network coupled mode model, ω represents a frequency variable, x represents a geometry vector of the metasurface, and the symbol D(x, w * ) is a complex-valued N x 1 vector, where the symbol N represents the number of resonators that make up the metasurface; the symbol D(x, w * ) allows the metasurface system to couple with incoming and outgoing plane waves, γ -1 (x, w * ) is an N x N complex-valued matrix, defined as: gamma -1 (x, w*) = [j(ωI N - Ω(x, w * ))+ Γ(x, w * )] -1 where j represents the complex multiplier; the above equation can be used to efficiently and accurately predict the electromagnetic response of a multi-resonant system corresponding to any geometry, where Ω(x, w * ) is an NxN complex matrix containing the resonant frequencies and coupling constants, I N represents the NxN identity matrix, and Γ(x, w * ) represents an NxN real matrix containing the decay rates of the resonators.

7. The physically-driven machine learning method for metasurface intelligent design of claim 1, wherein, Step 6) Optimal design of the metasurface unit structure, using the constructed neural network CMT model to realize the rapid optimal design of the metasurface, defining the geometric parameter x as the optimization variable, and describing the design of the metasurface unit as the following constrained optimization problem: where a represents the length of the metasurface unit along the x-axis direction; U(x) represents the minimax or the generalized error function; x * represents the optimal design of the metasurface unit structure obtained by solving the optimization algorithm; L min and L max respectively represent the minimum and maximum values of L when sampling the geometry parameters of a single resonator; d min and d max respectively represent the minimum and maximum values of the distance between two resonators when sampling the geometry parameters of a double resonator; N represents the number of resonators in the metasurface structure; x k represents the kth element of x, which is also the kth optimization variable; K represents the number of elements in the vector x, which is also the total number of optimization variables; a gradient-based quasi-Newton algorithm is used to solve the above optimization problem, thereby obtaining the optimal design x * of the metasurface unit structure.

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