Metasurface optimization design method based on deep learning and differential evolution algorithm

Abstract

The invention discloses a super-surface optimization design method based on deep learning and a differential evolution algorithm, and the method mainly comprises the steps: building a simulation database corresponding to a super-surface structure and a wave transmission coefficient through a joint simulation technology, the simulation database is used for storing a 01 mathematical matrix capable of representing the metasurface structure and simulation values of wave transmission coefficients under all frequency points; constructing a metasurface electromagnetic response prediction model, wherein the metasurface electromagnetic response prediction model outputs a predicted value of a wave transmission coefficient based on the binary image representing the metasurface structure; obtaining a metasurface optimization design target, and randomly initializing a 01 mathematical matrix representing a metasurface structure; obtaining a wave transmission coefficient of the current metasurface based on the trained metasurface electromagnetic response prediction model; and constructing an optimal design fitness function based on a wave transmission coefficient, and iteratively optimizing a 01 mathematical matrix representing the metasurface structure by using a differential evolution algorithm. According to the method, the high-degree-of-freedom metasurface structure meeting the target electromagnetic response can be rapidly and accurately designed.

Description

Technical Field

[0001] The present invention relates to a method for designing a metasurface, and more specifically, to an optimized design method for a metasurface based on deep learning and differential evolution algorithm. Background Art

[0002] A metasurface is a two-dimensional surface or array composed of planar periodic units arranged in a specific order, belonging to artificial periodic materials. By adjusting the microscopic structure of the surface, it can achieve the regulation of the amplitude and phase of electromagnetic waves, and thus has been widely used in fields such as wireless communication and beam control. However, there is a complex non-linear relationship between the metasurface structure and the electromagnetic response, and its structural parameters, patterns, etc. will all affect its electromagnetic response, which makes it challenging to design a metasurface that meets specific requirements.

[0003] Currently, there are mainly two traditional metasurface design methods. One is that designers establish an equivalent circuit that meets the conditions according to the target electromagnetic response characteristics, thereby determining the initial metasurface structure, and then determining the final structure through parameter fine-tuning; the other is to combine an optimization algorithm with a full-wave analysis simulation software, set the target electromagnetic response information as the fitness function, and use structural parameters, material properties, etc. as optimization variables, and determine the optimal structure through continuous iterative optimization. Compared with the former, the latter uses a random optimization method, which can improve the efficiency to a certain extent. In addition, as an important branch in the field of machine learning, deep learning has demonstrated powerful complex data processing capabilities in computer science and engineering-related fields. With the improvement of computer computing power, its application in the electromagnetic field has also received extensive attention. For example, the literature "Optimized design for absorption metasurface based on autoencoder(AE)and BiLSTM-Attention-FCN-Net" realizes the forward prediction from the electromagnetic structure to the electromagnetic response by building a fully connected network, and there is also the literature "Inverse design of electromagnetically induced transparency(EIT)metasurface based on deep convolutional generative adversarial network" that accurately realizes the optimized design of an EIT metasurface with 8 structural parameters using an improved deep convolutional generative adversarial network model.

[0004] Despite certain progress in the existing technologies, there are still some problems. On the one hand, whether it is the traditional design method based on equivalent circuits or the method combining optimization algorithms with simulation software, the determination of the initial structure depends on experienced designers. Moreover, whether it is manual parameter tuning or algorithm optimization iteration, electromagnetic calculations need to be repeatedly performed by simulation software, resulting in low design efficiency. On the other hand, current research mainly focuses on fixed metasurfaces with simple structures and limited adjustable parameters, and relatively little research has been done on metasurfaces with higher degrees of freedom. To achieve diverse performances and meet broader application requirements, it is particularly urgent to conduct research on metasurfaces with higher degrees of freedom. Summary of the Invention

[0005] The present invention provides a metasurface optimization design method based on deep learning and differential evolution algorithm. By combining deep learning with differential evolution algorithm, the problem of low optimization efficiency of complex structures in the design of metasurfaces with high degrees of freedom is solved. A prediction model built using the Resnet-18 framework quickly learns the non-linear relationship between the metasurface structure and electromagnetic response, significantly improving the forward prediction efficiency; at the same time, with the help of the differential evolution algorithm to optimize the metasurface pattern, reverse design is quickly realized. The present invention can efficiently design metasurface structures with high degrees of freedom and meet diverse electromagnetic response requirements.

[0006] The technical means adopted by the present invention are as follows:

[0007] A metasurface optimization design method based on deep learning and differential evolution algorithm, comprising the following steps:

[0008] Model the metasurface, where the metasurface includes an upper layer structure and a dielectric substrate, and the upper layer structure is modeled as an n×n grid structure with rotational symmetry;

[0009] Establish a simulation database corresponding to the metasurface structure and transmission coefficient through co-simulation technology, and the simulation database is used to store the 01 mathematical matrix representing the metasurface structure and the simulation values of the transmission coefficient at each frequency point;

[0010] Construct a metasurface electromagnetic response prediction model, where the metasurface electromagnetic response prediction model outputs the predicted value of the transmission coefficient based on the 01 mathematical matrix representing the metasurface structure; train the metasurface electromagnetic response prediction model based on the simulation database;

[0011] Obtain the metasurface optimization design goal, randomly initialize the 01 mathematical matrix representing the metasurface structure; obtain the transmission coefficient of the current metasurface based on the trained metasurface electromagnetic response prediction model;

[0012] Construct an optimization design fitness function based on the transmission coefficient, and use the differential evolution algorithm to iteratively optimize the 0-1 mathematical matrix representing the metasurface structure. When the number of iterations reaches the maximum number of rounds or the fitness value is 0, the optimization ends.

[0013] Further, model the metasurface, including: constructing a grid structure of size n×n through a first simulation system, where the n×n grid structure is generated by rotating and expanding a randomly generated 0-1 matrix of size "0" indicates that there is no metal patch in the corresponding grid, and "1" indicates that there is a metal patch in the corresponding grid. Among them, the rotation and expansion operation is to Rotate the 0-1 matrix by 90°, 180°, and 270° respectively to generate three new matrices, and then splice them with the original matrix to finally form an n×n matrix.

[0014] Further, establish a simulation database corresponding to the metasurface structure and the transmission coefficient through joint simulation technology, including: constructing each metasurface structure through a second simulation system, setting boundary conditions and sweep frequency range, and collecting the transmission coefficients at each frequency point

[0015] Further, the metasurface electromagnetic response prediction model is constructed based on the Resnet-18 model. The Resnet-18 model consists of an initial convolutional layer, a pooling layer, several residual blocks, and a fully connected layer. Each residual block is composed of a convolutional layer, a BN layer, and a ReLU activation function.

[0016] Further, train the metasurface electromagnetic response prediction model based on the simulation database, including training the metasurface electromagnetic response prediction model under the best network hyperparameters, and using the backpropagation algorithm to update the network weights and biases. The network hyperparameters include the learning rate, batch size, and input pixel resolution.

[0017] Further, the best network hyperparameters are set as: the learning rate is 2×10 -3 , the batch size is 64, and the input pixel resolution is 64×64.

[0018] Further, the optimization design fitness function based on the transmission coefficient is:

[0019] L=(S 21 -S min )(S 21 -S max ) T +

[0020] |(S 21 -S min )(S 21 -S max )T |

[0021] Among them, S 21 is the wave transmission coefficient of the metasurface, S min is the lower threshold of the preset wave transmission coefficient in the optimization design objective, and S max is the upper threshold of the preset wave transmission coefficient in the optimization design objective.

[0022] Compared with the prior art, the present invention has the following advantages:

[0023] The present invention is directed to a high-degree-of-freedom metasurface structure, and combines deep learning and differential evolution algorithm to achieve the design under the target electromagnetic response. In terms of forward prediction, a prediction model is built with Resnet-18 as the framework to learn the non-linear relationship between the metasurface structure and the electromagnetic response. The trained model can calculate the electromagnetic response characteristics of a single sample within 2 ms, significantly improving the calculation efficiency, and can be used as a "surrogate model" for full-wave simulation. In terms of inverse design, the differential evolution algorithm is used to traverse and optimize the metasurface pattern, and combined with the "surrogate model", a metasurface structure that meets the design objective can be quickly optimized. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required to be used in the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0025] Figure 1 is a flowchart of a metasurface optimization design method based on deep learning and differential evolution algorithm in an embodiment of the present invention.

[0026] Figure 2 is a schematic diagram of a high-degree-of-freedom metasurface structure in an embodiment of the present invention.

[0027] Figure 3 is a schematic diagram of a forward prediction network in an embodiment of the present invention.

[0028] Figure 4 is a comparison chart of the performance of the forward prediction network under different batch sizes in an embodiment of the present invention.

[0029] Figure 5 is a comparison chart of the performance of the forward prediction network under different learning rates in an embodiment of the present invention.

[0030] Figure 6 is a comparison chart of the true electromagnetic response and the predicted electromagnetic response of the test sample in an embodiment of the present invention.

[0031] Figure 7 This is the flow chart of the differential evolution algorithm for optimizing the design of a high-degree-of-freedom metasurface structure in an embodiment of the present invention.

[0032] Figure 8 This is the convergence curve of the loss of the broadband bandpass metasurface optimization in an embodiment of the present invention.

[0033] Figure 9 This is the comparison chart of the simulation prediction and the prediction curve of the optimized broadband bandpass metasurface in an embodiment of the present invention. Detailed implementation manners

[0034] In order to enable those skilled in the art to better understand the solution of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0035] As Figure 1 shown, the present invention provides a metasurface optimization design method based on deep learning and differential evolution algorithm, including the following steps:

[0036] S1. Model the metasurface. The metasurface includes an upper layer structure and a dielectric substrate, wherein the upper layer structure is modeled as an n×n grid structure with rotational symmetry.

[0037] This step is mainly used for encoding and modeling the high-degree-of-freedom metasurface. In the embodiments of the present application, optionally, the high-degree-of-freedom metasurface is composed of an upper layer structure with a 32×32 grid and a dielectric substrate. In Matlab, a 16×16 01 matrix is randomly generated and expanded to 32×32 by rotation. "0" represents no metal patch, and "1" represents a metal patch, so as to form an upper layer metal grid structure with rotational symmetry and realize polarization insensitivity.

[0038] S2. Establish a simulation database corresponding to the metasurface structure and the transmission coefficient through the co-simulation technology. The simulation database is used to store the 01 mathematical matrix capable of characterizing the metasurface structure and the simulation values of the transmission coefficients at each frequency point.

[0039] This step mainly conducts data acquisition through CST-MATLAB co-simulation technology to establish a database corresponding to the metasurface structure and the transmission coefficient S21. S21 is a key parameter for evaluating and optimizing the performance of the metasurface; each set of samples in the database includes a 01 mathematical matrix that can characterize the metasurface structure and the magnitude of S21 at each frequency point. The CST-MATLAB co-simulation technology realizes the automatic interaction between MATLAB and CST through the COM interface of CST, thereby realizing the full-automatic process from structure design, parameter transfer, simulation calculation to result extraction.

[0040] S3. Construct a metasurface electromagnetic response prediction model, where the metasurface electromagnetic response prediction model outputs the predicted value of the transmission coefficient based on the binary image characterizing the metasurface structure; train the metasurface electromagnetic response prediction model based on the simulation database.

[0041] In the embodiment of the present application, the metasurface electromagnetic response prediction model is constructed based on the Resnet-18 model. This step mainly uses Resnet-18 to establish a forward prediction network and adjusts the network hyperparameter settings to achieve the rapid prediction of the metasurface electromagnetic response; among them, Resnet-18 consists of an initial convolutional layer, a pooling layer, several residual blocks and a fully connected layer; each residual block is composed of a convolutional layer, a BN layer and a ReLU activation function; the network input is a binary image characterizing the metasurface structure, and the output is the S 21 magnitude; the adjusted network hyperparameters include the learning rate, batch size, input pixel resolution, etc.; after the model is trained, the network parameters are fixed, the model is saved, and used as the "surrogate model" for full-wave analysis.

[0042] S4. Obtain the metasurface optimization design goal, and randomly initialize the 01 mathematical matrix characterizing the metasurface structure; obtain the transmission coefficient of the current metasurface based on the trained metasurface electromagnetic response prediction model.

[0043] S5. Construct an optimization design fitness function based on the transmission coefficient, and use the differential evolution algorithm to iteratively optimize the 01 mathematical matrix characterizing the metasurface structure. When the number of iterations reaches the maximum number of rounds or the fitness value is 0, the optimization ends. The optimization design fitness function based on the transmission coefficient is:

[0044] L=(S 21 -S min )(S 21 -S max ) T +

[0045] |(S 21 -S min )(S 21 -S max ) T |

[0046] Among them, S 21 is the wave transmission coefficient of the metasurface, and S min is the lower threshold of the preset wave transmission coefficient in the optimization design goal, and S max is the upper threshold of the preset wave transmission coefficient in the optimization design goal.

[0047] This step uses the differential evolution algorithm to optimize the mathematical matrix that can characterize the metasurface structure, and realizes the design of the metasurface structure under the target electromagnetic response. Among them, the differential evolution algorithm obtains the optimal solution by simulating mutation, crossover and selection in the natural evolution process; the individuals in the population calculate the S 21 value by using the "surrogate model", and then calculates the fitness value; when the number of iterations reaches the maximum number of rounds or the fitness value is 0, the optimization ends.

[0048] Next, through specific application examples, the solutions and effects of the present invention will be further described.

[0049] As Figure 2 shown, in this embodiment, the high-degree-of-freedom metasurface unit structure is composed of an upper-layer structure and a dielectric substrate. Among them, the upper-layer structure is a 32×32 metal grid, which is obtained by rotating a randomly generated 16×16 01 matrix, where 0 represents no metal patch and 1 represents a metal patch, and this rotationally symmetric structure has polarization insensitivity. The dielectric substrate uses F4B-2 board with a dielectric constant of 2.65, a loss tangent value of 0.005, and a thickness value of 1 mm. The period of each unit structure is 8 mm, the metal grid is arranged in a square grid area of 8 mm×8 mm, and the length of each metal grid is 0.25 mm.

[0050] Use CST-MATLAB co-simulation technology to establish a database. The unit structure is simulated in CST software, and the boundary conditions and the frequency sweep range are set, where the frequency sweep range is 1-20 GHz, and a total of 1001 points are scanned. Since S 21 is the key parameter for evaluating and optimizing the performance of the metasurface, the S 21 amplitude at each frequency point is collected as the electromagnetic response parameter. Each group of samples consists of a 01 mathematical matrix that can characterize the structure and the S 21 amplitude at 1001 frequency points, and a total of 180,000 groups of samples are collected. Among them, the training set, validation set and test set are divided according to the ratio of 0.95:0.25:0.25.

[0051] Use Resnet-18 to build a forward prediction network, input the binary image representing the metasurface structure, and output the wave transmission coefficient S 21 , as Figure 3As shown in the figure. Among them, this network model consists of an initial convolutional layer, a pooling layer, 4 residual blocks, and a fully connected layer. In order to more effectively capture the local features of the input image and retain more detailed information, a 3×3 convolutional kernel is used for the initial convolution operation. In addition, each residual block is composed of a convolutional layer, a BN layer, and a ReLU activation function, and the learning ability of the model is enhanced through the identity mapping method.

[0052] Adjust the hyperparameter settings of the prediction network to determine the optimal parameters. Among them, network parameters such as the learning rate and batch size are adjusted in detail. As Figure 4 shown, the batch size and the convergence speed generally show a negative correlation. When the batch size is set to 32 or 64, the convergence speed is the fastest and the loss is the lowest. Considering the factor of computational efficiency, 64 is finally selected as the optimal batch size; as Figure 5 shown, when the learning rate is 2×10-3, the training loss is the lowest, and it is used as the optimal learning rate of the network.

[0053] To improve the model's ability to capture the details of the electromagnetic response and the spatial information of the unit structure, and extract richer features, the pixel resolution of the input image is adjusted. Each pixel unit is divided into 4 sub-units through the upsampling technique, and the structure is improved from a 32×32 pixel resolution to 64×64. As shown in Table 1, using the improved metasurface structure as the network input, the training loss, validation loss, and test loss all decrease, which indicates that increasing the input pixel resolution helps the model better capture the detailed features and thus improve the model accuracy.

[0054] Table 1

[0055]

[0056] Train the forward prediction network under the optimal hyperparameters, use the backpropagation algorithm to update the network weights and biases, save the model and use it as the "proxy model" for electromagnetic response calculation. After training is completed, test on the test set. As Figure 6 shown, the black solid line represents the S 21 value obtained by simulation, and the red dashed line represents the predicted S 21 value. The curve characteristics of different samples are different, which strongly proves the diversity of the electromagnetic characteristics of the high-degree-of-freedom metasurface structure. In addition, the two curves coincide highly, effectively verifying the superiority of the proposed network in terms of prediction accuracy. In terms of prediction efficiency, after the network is trained, it can complete the electromagnetic response calculation of a single metasurface structure within 2 ms, significantly breaking through the problem of slow traditional simulation calculation.

[0057] Use the differential evolution algorithm to optimize the mathematical matrix representing the metasurface, and determine the high-degree-of-freedom metasurface structure under the target electromagnetic response. The process is as Figure 7As shown in the figure. Since the design goal of the metasurface is usually to meet the band-pass or band-stop characteristics in a certain frequency band, the fitness function is defined as follows:

[0058]

[0059] where S 21 is the transmission coefficient of the metasurface, which is calculated by the "surrogate model"; S min is the lower threshold of the required transmission coefficient; S max is the upper threshold of the required transmission coefficient. When the S 21 of the optimized structure is between S min and S max , the fitness value L is 0. Set the number of iterations to 1000. When the maximum number of iterations is reached or the fitness value is 0, the optimization ends.

[0060] Taking the broadband band-pass metasurface as an example, the design goal is that the transmission coefficient is greater than -1 dB within 5 - 10 GHz. The differential optimization algorithm process is used to optimize its design. Among them, to meet the design goal, 2 - 13 GHz and 5 - 10 GHz are set as the upper threshold and the lower threshold, as Figure 9 shown. The red solid line represents the upper threshold line, and the green solid line represents the lower threshold line. As Figure 8 shown, after 1000 rounds of iteration, the fitness value converges to 0.2. To verify the accuracy of the designed structure, a simulation is carried out in CST. As Figure 9 shown, the optimized structure can meet the design requirements with high precision, achieving a -1 dB bandwidth within 5.1 GHz - 9.65 GHz, and the relative bandwidth fraction is 61.7%. In addition, the simulated electromagnetic response curve is basically consistent with the predicted curve, further verifying the accuracy of the forward prediction network.

[0061] The present invention takes a 32×32 high-degree-of-freedom metasurface as the object, uses Resnet-18 to design a forward prediction network, effectively learns the non-linear relationship between the metasurface structure and the electromagnetic response, and can complete the electromagnetic response calculation of a single sample in a very short time, which can be used as a "surrogate model" of the simulation software. Based on this model, the differential evolution algorithm is used to optimize the metasurface structure, set the maximum and minimum threshold lines, and quickly optimize the high-degree-of-freedom metasurface structure under the target electromagnetic response.

[0062] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for optimizing the design of a metasurface based on deep learning and differential evolution algorithm, characterized in that, Including the following steps: Model the metasurface, where the metasurface includes an upper structure and a dielectric substrate, and the upper structure is modeled as an n×n grid structure with rotational symmetry; Establish a simulation database corresponding to the metasurface structure and the transmission coefficient through joint simulation technology. The simulation database is used to store the 01 mathematical matrix characterizing the metasurface structure and the simulation values of the transmission coefficient at each frequency point; Construct a metasurface electromagnetic response prediction model, which outputs the predicted value of the transmission coefficient based on the 01 mathematical matrix characterizing the metasurface structure; Train the metasurface electromagnetic response prediction model based on the simulation database; Obtain the optimization design objective of the metasurface and randomly initialize the 01 mathematical matrix characterizing the metasurface structure; Obtain the transmission coefficient of the current metasurface based on the trained metasurface electromagnetic response prediction model; Construct an optimization design fitness function based on the transmission coefficient, and use the differential evolution algorithm to iteratively optimize the 01 mathematical matrix characterizing the metasurface structure. When the number of iterations reaches the maximum number of rounds or the fitness value is 0, the optimization ends.

2. The super-surface optimization design method based on deep learning and differential evolution algorithm according to claim 1, wherein Modeling the metasurface includes: constructing a grid structure of size n×n through a first simulation system, where the n×n grid structure is generated by rotating and expanding a randomly generated 01 matrix of size . "0" indicates that there is no metal patch in the corresponding grid, and "1" indicates that there is a metal patch in the corresponding grid. Among them, the rotation and expansion operation is to rotate the 01 matrix of by 90°, 180°, and 270° respectively to generate three new matrices, and then splice them with the original matrix to finally form an n×n matrix.

3. The method for optimizing the design of a metasurface based on deep learning and differential evolution algorithm according to claim 2, characterized in that Establish a simulation database corresponding to the metasurface structure and the transmission coefficient through joint simulation technology, including: constructing each metasurface structure through a second simulation system, setting boundary conditions and sweep frequency range, and collecting the transmission coefficient at each frequency point.

4. A method for optimizing the design of a metasurface based on deep learning and differential evolution algorithm according to claim 1, characterized in that, The metasurface electromagnetic response prediction model is constructed based on the Resnet-18 model, and the Resnet-18 model includes an initial convolutional layer, a pooling layer, several residual blocks and a fully connected layer. Each residual block is composed of a convolutional layer, a BN layer and a ReLU activation function.

5. A method for optimizing the design of a metasurface based on deep learning and differential evolution algorithm according to claim 4, characterized in that, Train the metasurface electromagnetic response prediction model based on the simulation database, including training the metasurface electromagnetic response prediction model under the best network hyperparameters, and updating the network weights and biases using the backpropagation algorithm. The network hyperparameters include the learning rate, batch size, and input pixel resolution.

6. The super-surface optimization design method based on deep learning and differential evolution algorithm according to claim 4, characterized in that, The optimal network hyperparameters are set as follows: the learning rate is 2×10 -3 , the batch size is 64, and the input pixel resolution is 64×64.

7. A method for optimizing the design of a metasurface based on deep learning and differential evolution algorithm according to claim 1, characterized in that, The optimization design fitness function based on the transmission coefficient is: L = (S 21 - S min )(S 21 - S max ) T + |(S 21 - S min )(S 21 - S max ) T | Among them, S 21 is the wave transmission coefficient of the metasurface, and S min is the lower threshold of the preset wave transmission coefficient in the optimization design goal, and S max is the upper threshold of the preset wave transmission coefficient in the optimization design goal.

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