Multilayer frequency selective surface filter reverse design method based on machine learning

Abstract

The invention provides a reverse design method for a multi-layer frequency selective surface filter based on machine learning, which combines topology modeling and parameter modeling and comprises the following steps of: constructing a multi-layer frequency selective surface microwave filter structure, namely constructing a filter structure comprising a metal resonance patch and key physical parameters; a training data set construction step: constructing a training data set including an input and output data set; and a machine learning model training and reverse design step: training the data set by using a Res-MLP network, inputting a target electromagnetic response on the trained model, fitting a filter structure through the Res-MLP network, and realizing reverse design. According to the method, hybrid modeling is realized by combining topology modeling and parameter modeling, the FSS filter with a specific layer number and structure is deduced according to requirements, the filter design with higher design freedom and application frequency band is realized, and the FSS filter design outside the training frequency band can be realized based on the frequency band offset of the FSS under the low-dispersion or non-dispersion material.

Description

Technical Field

[0001] The present invention relates to the technical field of microwave filters, and in particular to a method for inverse design of a multi-layer frequency selective surface filter based on machine learning. Background Art

[0002] A frequency selective surface (FSS) is a metasurface composed of periodic units, with a metal layer printed on a substrate, that selectively absorbs or transmits electromagnetic waves within a specific frequency band. Due to its unique ability to suppress out-of-band interference while preserving in-band signals, FSS is widely used in radar and antenna design, among other applications.

[0003] Traditional FSS design relies on forward optimization techniques, which iteratively adjust the structure through full-wave simulation and optimization algorithms. Although this method can produce accurate designs, it is computationally expensive and time-consuming, making it inefficient for rapid electromagnetic design.

[0004] In recent years, machine learning has been widely applied to microwave device design, including FSS design. This process can be categorized into forward and inverse design based on different modeling approaches. In forward design, structural parameters are input and the electromagnetic response is generated as output. A well-trained forward model can replace full-wave simulation in forward optimization techniques, improving efficiency. However, direct inverse design has proven to be a more efficient and accurate approach. It takes the desired electromagnetic response as input and directly generates the target structure, eliminating the need for an iterative process. Furthermore, machine learning-based modeling approaches can be categorized into parametric modeling and topological modeling. Parametric modeling focuses on the physical parameters that influence the electromagnetic response within a fixed initial structure. It provides a simpler mapping, making it easier for the network to learn, but its electromagnetic response is constrained by the initial structure, limiting its performance over a wide frequency range. In contrast, topological modeling represents the geometric variables of the electromagnetic device, such as discretizing the metal patches of an FSS into hundreds of pixels. This provides greater design freedom and flexibility for inverse design. By combining parametric and topological modeling, accurate design of electromagnetic devices across a wider design space can be achieved. Summary of the Invention

[0005] The purpose of the present invention is to address the defects and shortcomings of the existing technology and propose a multi-layer frequency selective surface filter inverse design method based on machine learning. By combining parameter modeling and topology modeling, a high-freedom hybrid inverse design of the frequency selective surface (FSS) is realized, further improving the device design accuracy and design range.

[0006] The technical solutions of the present invention are as follows.

[0007] A machine learning-based inverse design method for multi-layer frequency selective surface filters, including:

[0008] S101, a step of constructing a multi-layer frequency selective surface microwave filter structure, constructing a filter structure including metal resonant patch layers and key physical parameters; the metal resonant patch layers include one to five metal patch layers; the key physical parameters include numerical variables of the dielectric substrate material, thickness, periodic unit size, and interlayer distance of each layer; the filter structure includes a planar structure and a spatial structure; the planar structure is the planar topological variable of the metal resonant patch layer; the spatial structure is the above-mentioned key physical parameters and the number of FSS layers constituting the filter;

[0009] S102, a training data set construction step, constructing a training data set including an input data set and an output data set; the input data set is a square wave signal generated by electromagnetic response preprocessing obtained by full-wave simulation, and the output data set is a filter structure corresponding to the electromagnetic response, and the filter structure includes planar topological variables and discrete numerical variables; data set collection is achieved by constructing an efficient data set collection strategy.

[0010] S103, the machine learning model training and inverse design step, uses a Res-MLP network to train the aforementioned dataset. The target electromagnetic response is input into the trained model, and the filter structure is fitted to the model to achieve inverse design. For design targets within the training frequency band, the aforementioned inverse design method is used. For design targets outside the training frequency band, the design target is scaled using FSS band offset theory under low-dispersion or dispersion-free conditions. This is then input into the trained Res-MLP network to obtain the basic filter structure. This structure is then inversely transformed by the same scale to obtain the final result.

[0011] Preferably, the planar topological variables of the metal resonant patch layer are composed of (N×N)×5 pixel variables; where N represents the number of pixels in the rows / columns of the metal resonant patch layer; N×N represents the total number of pixels in each layer of the metal resonant patch layer, and 5 represents that a maximum of 5 layers of FSS design can be realized in the total modeling area.

[0012] Preferably, the filter structure has four discrete numerical variables, namely [U,h air ,h sub ,M,n]; where U represents the unit size of FSS, that is, the period of unit arrangement; n represents the number of FSS layers; h air Represents the inter-layer distance matrix, with a size of (n-1)×1; h sub represents the dielectric substrate thickness matrix, which is n×1 in size; M represents the dielectric substrate material matrix, which is n×1 in size.

[0013] Preferably, the dielectric substrate material of each layer is a low-dispersion or non-dispersion material with low loss (tan δ < 0.003).

[0014] Preferably, the calculation frequency band of the full-wave simulation of the training data set is designed to be 2-12 GHz.

[0015] Preferably, an efficient data set collection strategy is constructed, specifically: using the classical frequency selective surface filter metal resonant patch layer pattern structure and its random variants to form a planar topological variable data set; using the electromagnetic simulation software CST for full-wave simulation; proposing a two-level progressive evolutionary algorithm based on the cuckoo optimization algorithm, in which the outer optimization goal is to select the patch topology shape from the initial shape data set based on the equivalent circuit and filtering theory, and the inner optimization shape geometric parameters (l, r) and structural parameters (U, h air ,h sub ,M); save the electromagnetic response and filter structure during the iteration process as a data set.

[0016] Preferably, the electromagnetic response is preprocessed into a square wave signal, specifically: in the electromagnetic response |S 11 When the value range is [-A dB, +∞), the sample point is set to 0dB; in the electromagnetic response |S 11 When the value range is [-∞, -A dB), the sample point is set to -AdB; where A is the preset value.

[0017] Preferably, the machine learning model selects the Res-MLP architecture, including a linear partitioning module, a feature mixture extraction module and an output prediction and post-processing module; the linear partitioning module divides the input square wave signal and layer flag into multiple blocks of preset sizes; the feature mixture extraction module performs feature extraction and mixing of the channel dimension and token dimension (block dimension) on the divided input; the output prediction and post-processing module performs Affine operation (instead of global average pooling) on ​​the information extracted by the feature mixture extraction module, and performs binarization and One-hot decoding operations to obtain planar topological variables and discrete numerical variables.

[0018] Preferably, the Loss function of the machine learning model includes a plane topology variable loss L t and discrete numerical variable loss L p , as follows:

[0019]

[0020] Loss=a*L t +b*L p (3)

[0021] Among them, NS represents the number of calculation samples, Represents the predicted topological shape of the i-th sample, represents the topological shape of the i-th sample target, represents the matrix of discrete numerical variables predicted by the i-th sample, represents the discrete numerical variable matrix of the i-th sample target, a and b represent the weights of the planar topological variable loss and discrete numerical variable loss in the total loss, respectively.

[0022] Preferably, the planar topological variable loss a and the discrete numerical variable loss b are set to 1 and 0.5 respectively.

[0023] Compared with the prior art, the present invention has the following beneficial effects:

[0024] The present invention is a method for inverse design of multi-layer frequency selective surface filters based on machine learning. It combines an efficient training data set construction method for filter design, uses optimization algorithms and equivalent circuit guidance to collect high-quality data for the design of FSS passive bandpass, low-pass, and high-pass filters with different numbers of layers. Unlike existing machine learning methods that only focus on topological modeling or parameter modeling, this method combines topological modeling and parameter modeling to achieve hybrid modeling. It can derive FSS filters with a specific number of layers and structures according to requirements, achieving filter design with higher design freedom and application frequency bands. In addition, the effectiveness and accuracy of the design method were verified by design samples. Under vertical incidence, the method can design a variety of filters within the training frequency band, including low-pass, high-pass, and bandpass filters. At the same time, the use of low-loss substrate materials (tanδ<0.003) supports FSS design with a wider frequency range, expanding the application scenarios of the method. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0026] Figure 1 This is a flow chart of a method for inverse design of a multi-layer frequency selective surface filter based on machine learning according to an embodiment of the present invention;

[0027] Figure 2 A schematic diagram showing the basic three-dimensional geometric shape and discrete variable annotation of a microwave filter modeling domain constructed according to an embodiment of the present invention;

[0028] Figure 3 The classical FSS empirical pattern structure and planar topology variable construction method used in constructing the training set in the embodiment of the present invention;

[0029] Figure 4 Schematic diagram of the basic planar topological discretization structure of an embodiment of the present invention; wherein, (1) is the planar structure of a single-layer FSS filter; (2) is a side view of the three-dimensional spatial structure modeling of the filter;

[0030] Figure 5 A schematic diagram of a two-stage progressive evolutionary algorithm based on the cuckoo optimization algorithm according to an embodiment of the present invention is provided;

[0031] Figure 6 This is a machine learning network framework diagram of an embodiment of the present invention;

[0032] Figure 7-Figure 9 A schematic diagram of a design example of an embodiment of the present invention;

[0033] in, Figure 7 Schematic diagram of the design example of a 0.2-2.5GHz bandpass filter within the design frequency band. (1) Comparison between the single-layer FSS filter structure designed for the model and the full-wave simulation results and the input design target; (2) Comparison between the double-layer FSS filter structure designed for the model and the full-wave simulation results and the input design target; (3) Comparison between the three-layer FSS filter structure designed for the model and the full-wave simulation results and the input design target;

[0034] Figure 8 Schematic diagram of the design example of a 2-5 GHz ultra-wideband high-pass filter within the design frequency band. (1) The four-layer FSS filter structure designed for the model and the comparison of the full-wave simulation results with the input design target; (2) The five-layer FSS filter structure designed for the model and the comparison of the full-wave simulation results with the input design target;

[0035] Figure 9 Schematic diagram of a design example for a bandpass filter outside the design frequency band (12-22 GHz). (1) The three-layer FSS filter structure designed for the model; (2) The full-wave simulation results before the filter size change are compared with the input target; (3) The full-wave simulation results after the filter size change are compared with the design target. DETAILED DESCRIPTION

[0036] To make the objectives, technical solutions, and advantages of the present invention more apparent, the present invention will be further described in detail below with reference to the accompanying drawings. It is apparent that the embodiments described are only some, not all, of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort are intended to fall within the scope of protection of the present invention.

[0037] like Figure 1 As shown, this example discloses a method for inverse design of a multi-layer frequency selective surface filter based on machine learning. The specific steps are introduced as follows with reference to a design example.

[0038] S101, multi-layer frequency selective surface microwave filter structure construction step. The overall modeling area of ​​the multi-layer frequency selective surface (FSS) microwave filter is as follows: Figure 2 As shown. The multilayer frequency selective surface used in the example of the present invention is formed by stacking multiple single-layer FSS units. The interlayer coupling will produce complex and diverse electromagnetic properties. In this example, the number of layers of the FSS design can vary between 1 and 5 layers according to the design goals. Within the modeling area, each layer of FSS has the same unit size U, ranging from 12mm to 30mm, with a step size of 6mm, and is divided into a 1mm grid, as shown in the figure. Figure 4 As shown. The dielectric substrate thickness matrix h of each layer sub The interlayer space is filled with air, and the interlayer distance matrix h air The thicknesses are 4mm, 6mm, 8mm, and 12mm respectively. The dielectric substrate material was selected from 30 materials in the CSTStudio Suite material library, including Rogers RT5880LZ (lossy) and Taconic TLY-5A (lossy). Its relative dielectric constant ranges from 2.0 to 4.3, and its loss tangent is less than 0.003 (tanδ<0.003). The simulation frequency range is 2 to 12 GHz, and the simulation is saved through full-wave simulation. 11 |Serves as input data for the model. Figure 1 The entire modeling area shown is processed as the output data of the model, including the planar topological shape of the metal resonant patch, whose dimensions are 30×30×n, where n represents the number of layers of FSS. In addition, the unit size U, the inter-layer distance matrix h air , dielectric substrate thickness matrix h sub The structural parameter matrix composed of the dielectric substrate material matrix M is also part of the output data, and its dimensions are 1×1, 1×(n-1), 1×n and 1×n respectively.

[0039] S102, a training data set construction step, constructing a training data set including an input data set and an output data set. The input data set is a square wave after electromagnetic response preprocessing, specifically: 11 When the value range is [-A dB, +∞), the sample point is set to 0dB; in the electromagnetic response |S 11 When the value range is [-∞, -A dB), the sample point is set to -A dB; where A is a preset value. In this example, A is set to -10. The output dataset is the microwave filter structure dataset described in S101, which includes planar topological variables and discrete numerical variables.

[0040] In order to generate high-quality data, equivalent circuit theory is used in the present invention. According to traditional filter theory, the frequency characteristics of FSS can be divided into four categories: low-pass, band-pass, band-stop and high-pass. The FSS structure is divided into patch type and aperture type units. The patch type unit (usually band-stop type) is modeled as a series resonant circuit, while the aperture type unit (usually band-pass type) is modeled as a parallel resonant circuit. Classic FSS units include solid patch type, ring type, gate type and combination type. To ensure the diversity of the data set, the present invention uses several classic FSS structures and their combinations such as Figure 3 By adjusting the parameters of these structures, precise control of the electromagnetic properties can be achieved.

[0041] In order to efficiently collect sufficient training data sets, a two-level progressive evolutionary algorithm based on the cuckoo optimization algorithm was proposed, such as Figure 5 The outer layer optimization goal is to select the patch shape from the initial shape data set based on the equivalent circuit and filtering theory, while the inner layer optimizes the geometric parameters (l, r) and structural parameters (such as unit size P, dielectric substrate thickness h sub , interlayer distance h air A full-wave simulation is performed on each generation of the population, and the electromagnetic response is used to calculate the fitness function. The algorithm has two optimization objectives: a single passband within the design frequency range, and a passband width exceeding 0.2 GHz. If the number of inner-layer iterations does not reach the maximum value T1, the geometric parameters are adjusted. Once T1 is reached, the patch shape is readjusted and the next inner-layer iteration begins, until the number of outer-layer iterations reaches the upper limit T2. The electromagnetic response and the corresponding structure are saved to form the inverse design dataset.

[0042] S103, machine learning model training and reverse design steps, please refer to Figure 6 , use the Res-MLP network to train the above data set, input the target electromagnetic response into the trained model, and implement the reverse design by fitting the filter structure through the model. In the present invention, Res-MLP is used to complete the mapping learning from the required electromagnetic response to the corresponding filter structure. Res-MLP is a deep neural network architecture that combines residual connections (Residual Connections) and multilayer perceptrons (Multilayer Perceptron, MLP). Unlike traditional convolutional neural networks (CNN) or self-attention networks (such as Transformer), Res-MLP is completely based on the MLP structure, removing the convolution and self-attention layers, which not only maintains the expressive power of the deep network, but also reduces the computational complexity to a certain extent, showing good performance. Figure 6 As shown, the Res-MLP framework consists of three main parts.

[0043] Linear division module: This module divides the input square wave signal and layer mark into multiple blocks of preset size to facilitate subsequent feature analysis.

[0044] Feature mixing extraction module: This module extracts and mixes features of the channel dimension and token dimension (block dimension) of the divided input through a preset N-layer Res-MLP layer;

[0045] Prediction and post-processing module: This module performs Affine operation (instead of global average pooling) on ​​the information extracted by the feature mixture extraction module, and then performs binarization and one-hot decoding operations to obtain planar topological variables and discrete numerical variables as the final prediction output.

[0046] The model parameters of the Res-MLP architecture are updated by minimizing the loss between the predicted filter structure and the target filter structure. The total loss function includes the planar topology shape loss L t and discrete numerical variable loss L p , as follows:

[0047]

[0048] Loss=a*L t +b*L p (3)

[0049] Among them, NS represents the number of calculation samples, Represents the predicted topological shape of the i-th sample, represents the topological shape of the i-th sample target, represents the matrix of discrete numerical variables predicted by the i-th sample, represents the discrete numerical variable matrix of the i-th sample target, a and b represent the weights of the plane topology variable loss and the discrete numerical variable loss in the total loss respectively. The plane topology variable includes (30×30)×5 variables, and the discrete numerical variable represents [U,h air ,h sub ,M,n], with sizes of 1×1, 1×(n-1), 1×n, and 1×n, respectively. In this example, n=5, allowing the design of a maximum of five FSS layers. Because the loss is calculated using relative error, to balance the different impacts of planar topological variables and discrete numerical variables on the model, they are calculated separately and assigned different weights. In this example, weights a=1 and b=0.5 are assigned. The overall loss is then calculated and the model parameters are updated.

[0050] The optimizer, initial learning rate, layer depth and patch size of the Res-MLP neural network model are set to Adam, 5×10 -4, 9, and (1, 10). An early stopping method was used to terminate training when the validation set loss did not decrease for 15 consecutive epochs. PyTorch was used as the training framework for the machine learning-based methods, and additional libraries such as H5py, NumPy, SciPy, and Einops were imported to support various functions during the training process.

[0051] The calculations in this example were performed on a machine equipped with an Intel Gold 6226R 2.90GHz processor, 512GB of memory, and an NVIDIA RTX 4090 GPU. Full-wave simulations were performed using CST software. After training was complete, the accuracy of the model was evaluated using a validation dataset. Full-wave simulations were performed on the predicted structures on the validation dataset and the results were compared with the labeled |S 11 | value, use the mismatch function calculation formula to evaluate the model performance, the mismatch function calculation formula is as follows:

[0052]

[0053] Among them, NS represents the number of calculation samples, S i |S represents the i-th initial FSS structure 11 |Square wave vector after curve processing, represents the predicted FSS structure |S obtained from the full-wave simulation 11 |Square wave vector after curve processing.

[0054] In actual application scenarios, by inputting square wave |S 11 | and layer markings. A fully trained model can design a device structure that meets the target requirements. The designed structure is then subjected to full-wave simulation, and the mismatch between the simulation results and the input target can be calculated using the mismatch function formula. It is worth noting that the dielectric substrates in the dataset constructed in this study are all made of low-dispersion or non-dispersion materials, with tanδ < 0.003. In this case, the resonant frequency band of the FSS and its physical structure in the microwave band have the following relationship:

[0055] (1) The central resonance frequency is inversely proportional to the unit size U and the overall thickness of the filter;

[0056] (2) The resonance bandwidth also has the same relationship.

[0057] Based on this, the proposed machine learning-based inverse design method for multilayer frequency selective surface filters not only performs well within the frequency range of the training dataset, but also can perform design tasks beyond this range. This is achieved by adjusting the size of the design results using a scaling factor, thereby significantly extending the applicable frequency range of the model.

[0058] 15,000 samples are randomly selected from the dataset as the training set and 2,000 samples are randomly selected as the test set. After 375 epochs, the test set loss drops to 1.558%, and the model training stops. In this example, to verify the accuracy of the model under different design goals, three random design goals are proposed, namely:

[0059] Goal 1: Bandpass design goal - within 4.6-5.2GHz |S 11 |<-10dB; requires 1 to 3 layers of FSS to be implemented separately;

[0060] Goal 2: Qualcomm design goal - within 7.5-12GHz | S 11 |<-10dB; requires 4th to 5th layer FSS to be implemented separately;

[0061] Goal 3: Design out-of-band design goal - within 17.4-20.4GHz |S 11 |<-10dB; 3-layer FSS implementation.

[0062] Objectives 1 and 2 are to demonstrate the model's design capabilities within the training frequency band. Figure 7 As shown, by taking the same bandpass design target and different layer number flags as input, the model predicts the FSS filter structure with 1 to 3 layers, and the full-wave simulation obtains |S 11 |The mismatch loss with the design target is calculated to be 0.6%, 0.6% and 0.4% respectively. 4 and 5-layer FSS use the same or similar units cascaded to achieve ultra-wideband design, such as Figure 8 As shown in the figure, by inputting the ultra-wideband high-pass design target and the number of layers, the model can design 4 to 5-layer high-pass filters. The errors between the electromagnetic response obtained by the full-wave simulation of the predicted structure and the input target are 0.102% and 0.122%, respectively. Goals 1 and 2 confirm the proposed model's ability to design high-degree-of-freedom filters within the training frequency band. Goal 3 is used to demonstrate the proposed model's design capability outside the design frequency band under low dispersion or non-dispersion conditions. Figure 9 As shown. The scale factor between the original design target and the training frequency band is determined by frequency band offset. The original design target is scaled by this factor to obtain the intermediate design target within the training frequency band. The intermediate prediction result is obtained by inputting it into the trained model. Finally, the device structure size is inversely transformed according to the same scale factor to obtain the final design structure. The intermediate design structure and the final design structure are subjected to electromagnetic full-wave simulation respectively, and the obtained |S 11 The mismatch loss calculated with the intermediate design target and the initial design target is 0.521% and 0.413%, respectively.

[0063] In summary, the present invention proposes a machine learning-based inverse design method for multi-layer frequency selective surface filters, which combines topological modeling and parameter modeling to design frequency selective filter structures with more degrees of freedom. In addition, based on the band offset theory of frequency selective dispersion-free or low-dispersion materials, the proposed model can obtain design targets that exceed the frequency range of the training data set. The effectiveness of the method is demonstrated through three design examples. The first two targets are both within the training frequency band and are used to demonstrate the design performance of the proposed model for different filters within the training frequency band. The last design target exceeds the training frequency band and is used to demonstrate the effectiveness of the proposed method for extended frequency band design under low-dispersion or dispersion-free material conditions. It can be concluded that the present invention can efficiently and accurately design FSS structures with more degrees of freedom in a wide range of design fields.

[0064] The principles and operation of the present invention are illustrated through the above-mentioned specific implementation examples. These examples are intended to provide readers with a clear understanding framework to grasp the core ideas and key operational points of the present invention. However, it should be made clear that these examples are not intended to limit the scope of application of the present invention. For professionals in this field, various forms of improvements and innovations based on the core ideas of the present invention should be included in the scope of protection of the present invention.

Claims

1. A machine learning-based inverse design method for multi-layer frequency selective surface filters, characterized in that: The following steps are involved: S101, a step of constructing a multi-layer frequency selective surface microwave filter structure: constructing a filter structure including a metal resonant patch layer and key physical parameters; the metal resonant patch layer includes 1 to 5 metal patch layers; the key physical parameters include the material, thickness, periodic unit size, and interlayer spacing of each dielectric substrate layer; the filter structure includes a planar structure and a spatial structure, wherein the planar structure is a planar topological variable of the metal resonant patch layer, and the spatial structure is a discrete numerical variable of the key physical parameters and the number of frequency selective surface layers; S102, a training data set construction step: constructing a training data set comprising an input data set and an output data set; the input data set is a square wave signal generated by electromagnetic response preprocessing obtained by full-wave simulation, and the output data set is a filter structure corresponding to the electromagnetic response, wherein the filter structure includes key physical parameters represented by planar topological variables and discrete numerical variables and the number of frequency selective surface layers; S103, machine learning model training and reverse design steps: use the Res-MLP network to train the training data set, and fit the filter structure by inputting the target electromagnetic response into the trained Res-MLP network to achieve reverse design; wherein, for the design target within the training frequency band, the filter structure that can meet the design target is directly generated through the Res-MLP network. For the design target outside the training frequency band, the design target is proportionally transformed based on the frequency band offset theory of low-dispersion or dispersion-free materials, and the basic filter structure is generated and then inversely transformed to obtain the final result that can meet the design target.

2. The inverse design method of a multi-layer frequency selective surface filter based on machine learning according to claim 1 is characterized in that: In step S101: The planar topology variables of the metal resonant patch are composed of (N×N)×5 discrete pixel variables, where N is the number of row / column pixels of a single metal patch layer, N×N is the total number of pixels of a single layer, and 5 indicates that a maximum of 5 layers of FSS design are supported. The discrete numerical variables include [U,h air ,h sub ,M,n], where U represents the unit size of the frequency selective surface, that is, the period of the unit arrangement; n represents the number of frequency selective surface layers; h air Represents the inter-layer distance matrix, with a size of (n-1)×1; h sub represents the dielectric substrate thickness matrix, with a size of n×1; M is the dielectric substrate material matrix, with a size of n×1.

3. The inverse design method of a multi-layer frequency selective surface filter based on machine learning according to claim 1 is characterized in that: In step S102: The electromagnetic response preprocessing is to convert |S 11 | value is converted into a square wave signal, and the electromagnetic response |S 11 When the value range is [-A dB, +∞), the sample point is set to 0dB; in the electromagnetic response |S 11 When the value range is [-∞, -A dB), the sample point is set to -AdB; where A is a preset value, and the preset threshold A is -10dB. The training data set is generated by a two-stage progressive evolutionary algorithm, including: Outer layer optimization: Screening topological shapes from the initial shape library based on equivalent circuit and filtering theory; Inner layer optimization: adjust geometric parameters (l,r) and structural parameters (U,h air ,h sub ,M), and save the electromagnetic response and corresponding structure data through full-wave simulation.

4. The inverse design method of a multi-layer frequency selective surface filter based on machine learning according to claim 1, characterized in that: In step S103: The machine learning model adopts the Res-MLP architecture, including: Linear division module: divides the input square wave signal and layer mark into blocks of preset size; Feature hybrid extraction module: extracts channel and block dimension features from the divided input; Output prediction and post-processing module: Generates planar topological variables and discrete numerical variables through affine transformation, binarization and one-hot decoding; The Res-MLP architecture adopts relative loss calculation, including the planar topology shape loss L t and discrete numerical variable loss L p , the calculation formula is: Loss=a*L t +b*L p (3) Among them, NS represents the number of calculation samples, Represents the predicted topological shape of the i-th sample, represents the topological shape of the i-th sample target, represents the matrix of discrete numerical variables predicted by the i-th sample, represents the discrete numerical variable matrix of the i-th sample target, a and b represent the weights of the plane topology shape loss and discrete numerical variable loss in the total loss, which are set to 1 and 0.5 respectively.

5. The method for inverse design of a multi-layer frequency selective surface filter based on machine learning according to claim 2, wherein: The dielectric substrate material is selected from low-dispersion or non-dispersion materials, and its loss tangent satisfies tanδ<0.003; The unit size U of the frequency selective surface ranges from 12 mm to 30 mm, with a step length of 6 mm; The calculation frequency band of the full-wave simulation is 2-12 GHz, and the inter-layer distance matrix h air Selected from [4mm, 6mm, 8mm, 12mm], the dielectric substrate thickness matrix h sub Selected from [0.7mm,1.0mm,1.3mm,1.6mm].

6. The method for inverse design of a multi-layer frequency selective surface filter based on machine learning according to claim 3, wherein: In the two-stage progressive evolutionary algorithm, the outer optimization goal is to generate a single passband with a passband width of ≥ 0.2 GHz, and the inner optimization is to adjust the geometric parameters (I, r) and structural parameters (U, h) by using the cuckoo algorithm. air ,h sub ,M), the maximum number of iterations is T2 for the outer layer and T1 for the inner layer.

7. The inverse design method of a multi-layer frequency selective surface filter based on machine learning according to claim 1, characterized in that: The steps of achieving the design goal outside the training frequency band include: Determine the scaling factor k based on the frequency band offset theory, scale the target frequency band to the training frequency band by k, and input it into the Res-MLP network to generate the intermediate structure; The unit size U of the frequency selective surface of the intermediate structure and the interlayer distance matrix h air and the dielectric substrate thickness matrix h sub Perform inverse transformation according to 1 / k to obtain the final design structure.

8. The method for inverse design of a multi-layer frequency selective surface filter based on machine learning according to any one of claims 1 to 7, characterized in that: The planar topological variables of the metal resonant patch layer are selected from classical frequency selective surface patterns and their variants, including solid patch type, ring type, grid type and combination type; the multi-layer frequency selective surface filter inverse design method based on machine learning supports the design of low-pass, band-pass and high-pass filters, and supports up to 5 layers of frequency selective surface cascade structures.

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