Inverse Design Method for Frequency-Selective Surface Microwave Absorbers Based on Machine Learning

Abstract

This invention discloses a machine learning-based inverse design method for frequency-selective surface microwave absorbers, comprising: constructing an absorber structure including a first wide-angle impedance matching layer, a second wide-angle impedance matching layer, a resistive square ring layer, and a metal base plate layer; the absorber structure information including planar topological variables and discrete numerical variables; constructing a training dataset including an input dataset and an output dataset; training a neural network model using the training dataset to obtain a trained neural network model; and, based on the trained neural network model, obtaining the planar topological variables and discrete numerical variables of the absorber for the electromagnetic response target, thus achieving inverse design. This invention designs the absorber through topological modeling and discrete variable combination, providing more degrees of freedom and higher efficiency. Using a neural network model for design achieves reusability of absorber design, and significantly improves the absolute bandwidth, maintaining a wide relative bandwidth for both TE and TM polarizations under oblique incidence.

Description

Technical Field

[0001] This invention relates to the field of microwave absorber technology, and more specifically to a machine learning-based inverse design method for frequency-selective surface microwave absorbers. Background Technology

[0002] A microwave absorber is an electromagnetic device designed to absorb incident electromagnetic waves (EM) at specific frequencies. It has been widely used in electromagnetic compatibility (EMC)[1], electromagnetic interference (EMI) shielding[2], stealth technology and other fields[2-5].

[0003] Generally, absorption bandwidth, total thickness, and reflection reduction are considered to be the three major criteria for evaluating the performance of microwave absorbers. In recent years, the absorption performance under oblique incidence conditions and different polarization conditions has also received increasing attention. Currently, a large number of studies [6-13] have been dedicated to developing absorbers with higher performance. In terms of materials, frequency selective surfaces (FSS) are often used as alternatives to uniform resistive sheets [7-9] because a well-designed FSS can provide both resistance and reactance, thereby effectively improving the bandwidth of the absorber. In terms of design methods, the equivalent circuit method is one of the most widely used methods in microwave absorber design [10-13]. However, the degree of freedom (DoFs) of this method is limited and depends on establishing an accurate equivalent circuit model. When the equivalent circuit model of certain geometries is inaccurate or does not exist, the absorber cannot be designed, which prompts researchers to explore other feasible solutions. In reference

[10] , a single-layer dipole array absorber was designed using the reciprocity principle, with a fractional bandwidth (FBW) of 112% and a total thickness of 0.104λ. L (where λ) L (Wavelength corresponding to the lowest operating frequency), but when the absorption angle exceeds 30°, the absorption rate at the highest frequency is less than 90%. In

[11] , the absorption angle is increased to 45°, but the thickness is larger, at 0.33λ. L In

[12] , a metal square spiral absorber was proposed by combining the least squares method with the equivalent circuit, with an absorption angle increased to 50° and a thickness of 0.071λ. L However, the fractional bandwidth (FBW) is only 54.45%. In

[13] , the optimal absorber structure was obtained by using the equivalent circuit and differential evolution (DE) method and iterating multiple fixed parameters using full-wave simulation. The structure operates in the frequency band of 1.08-5.9 GHz under normal incident conditions and has a fractional bandwidth (FBW) of 137.1%. At the same time, its absorption angle is 45° and its thickness is 0.113λ. LHowever, this method is computationally expensive and still requires significant upfront design work. Furthermore, absorbers designed using this method rarely consider multiple performance aspects such as bandwidth, thinness, and wide angle. Therefore, designing high-performance absorbers simply and quickly remains a challenging task.

[0004] In recent years, machine learning methods have been widely applied to the modeling and design of microwave components [14-17], greatly reducing computational costs. Based on different modeling methods, machine learning-based modeling methods can be divided into parametric modeling and topological modeling. Compared with parametric modeling

[13] , topological modeling [14-15] discretizes the design domain into a binary matrix, allowing for the creation of diverse modeling structures through different pixel combinations. Therefore, topological modeling greatly improves the design freedom.

[0005] References

[0006] [1] R.Amugothu and V.Damera, "A dual-band metamaterial absorber using square split rings for C-band and X-band sensors applications," in Proc.26th Int.Conf.Adv.Commun.Technol.(ICACT), pp.100-103, 2024.

[0007] [2] D.Yi, PRZhao, MCTang, RLZhang, XCWei and EPLi, "Single-layerevanescent wave absorbers in rectangular waveguides based on evanescent modecoupling and attenuation.," IEEE Trans.Antennas Propag., vol.71, no.5, pp.4394-4405, May.2023.

[0008] [3] S.Pandit, A.Mohan and P.Ray, "Single-layer wideband wide-anglemicrowave absorber for stealth applications," in Proc.IEEE MTT-S Int.Microw.RFConf.(IMaRC), pp.1-3, 2018.

[0009] [4]Z.Huang et al.,“Partition layout loading of frequency selectivesurface absorbers on the curved surfaces for the significant RCS reduction,”IEEE Trans.Microw.Theory Techn.,vol.70,no.6,pp.2948-2954,June.2022.

[0010] [5]Y.T.Zhao,B.Chen and B.Wu,“Miniaturized periodicity broadbandabsorber with Via-based hybrid metal-graphene structure for large-angle RCSreduction,”IEEE Trans.Antennas Propag.,vol.70,no.4,pp.2832-2840,April.2022.

[0011] [6]T.Shi,L.Jin,L.Han,M.C.Tang,H.X.Xu and C.W.Qiu,“Dispersion-engineered,broadband,wide-angle,polarization-independent microwavemetamaterial absorber,”IEEE Trans.Antennas Propag.,vol.69,no.1,pp.229-238,Jan.2021.

[0012] [7]K.Zhang,W.Jiang and S.Gong,“Design bandpass frequency selectivesurface absorber using LC resonators,”IEEE Antennas Wireless Propa.Lett.,vol.16,pp.2586-2589,Aug.2017.

[0013] [8]S.Sambhav,J.Ghosh and A.K.Singh,“Ultra-wideband polarizationinsensitive thin absorber based on resistive concentric circular rings,”IEEETrans.Electromagn.Compat.,vol.63,no.5,pp.1333-1340,Oct.2021.

[0014] [9]Q.Guo,J.Su,Z.Li,L.Y.Yang and J.Song,“Absorptive / transmissivefrequency selective surface with wide absorption band,”IEEE Access,vol.7,pp.92314-92321,Jul.2019.

[0015]

[10] X.Q.Lin,P.Mei,P.C.Zhang,Z.Z.D.Chen and Y.Fan,“Development of aresistor-loaded ultrawideband absorber with antenna reciprocity,”IEEETrans.Antennas Propag.,vol.64,no.11,pp.4910-4913,Nov.2016.

[0016]

[11] J.Xie et al.,“Truly all-dielectric ultrabroadband metamaterialabsorber:water-based and ground-free,”IEEE Antennas Wireless Propa.Lett.,vol.18,no.3,pp.536-540,Mar.2019.

[0017]

[12] J.B.O.de Araújo,G.L.Siqueira,E.Kemptner,M.Weber,C.Junqueira andM.M.Mosso,“An ultrathin and ultrawideband metamaterial absorber and anequivalent-circuit parameter retrieval method,”IEEE Trans.Antennas Propag.,vol.68,no.5,pp.3739-3746,May.2020.

[0018]

[13] Z.Yao,S.Xiao,Y.Li and B.-Z.Wang,“Wide-angle,ultra-wideband,polarization-independent circuit analog absorbers,”IEEE Trans.AntennasPropag.,vol.70,no.8,pp.7276-7281,Aug.2022.

[0019]

[14] S.Meerabeab,V.Jantarachote and P.Wounchoum,“Design and parametricstudy of a suspended conformal patch antenna,”in Proc.19th int.Con.Electr.Eng.Comput.Telecommun.Inf.Technol.(ECTI-CON),pp.1-4,2022.

[0020]

[15] M.Aziz ul Haq and S.Koziel,“On compact wideband antenna designusing topology modifications,”in Proc.Int.Appl.Comput.Electromagn.Soc.Symp.(ACES),pp.1-2,Mar.2018.

[0021]

[16] E.Hassan, E.Wadbro and M.Berggren, "Topology optimization of metallic antennas," IEEE Trans.Antennas Propag., vol.62, no.5, pp.2488-2500, May.2014.

[0022]

[17] M.Barbuto, M.-A.Miri, A.Alù, F.Bilotti and A.Toscano, "A topological design tool for the synthesis of antenna radiation patterns," IEEETrans.Antennas Propag., vol.68, no.3, pp.1851-1859, Mar.2020. Summary of the Invention

[0023] The purpose of this invention is to address the shortcomings and deficiencies in the existing technology by proposing a machine learning-based inverse design method for frequency-selective surface microwave absorbers. This method achieves high-degree-of-freedom topological inverse design of microwave absorbers and further improves their performance.

[0024] The technical solution of the present invention is as follows.

[0025] A machine learning-based inverse design method for frequency-selective surface microwave absorbers includes:

[0026] The microwave absorber structure is constructed by building an absorber structure comprising a wide-angle impedance matching layer, a resistive square ring layer, and a metal substrate layer. The wide-angle impedance matching layer includes a first wide-angle impedance matching layer and a second wide-angle impedance matching layer. The absorber structure information is divided into planar structure information and spatial structure information. The planar structure information includes the planar topological variables of the ideal metal conductor pattern of the wide-angle impedance matching layer and the discrete numerical variables of the resistive square ring layer. The spatial structure information includes the discrete numerical variables of the thickness of each dielectric substrate and the interlayer spacing of the absorber structure.

[0027] The training dataset construction steps include constructing a training dataset that includes an input dataset and an output dataset; the input dataset is a square wave signal obtained by preprocessing the electromagnetic response of the absorber, and the output dataset is the absorber structure information corresponding to the electromagnetic response, which includes planar topological variables and discrete numerical variables.

[0028] The machine learning model training and reverse design steps involve using the training dataset to train a multilayer perceptron-based neural network model to obtain a trained neural network model; for the electromagnetic response target, the planar topological variable values ​​and discrete numerical variable values ​​of the absorber structure are obtained based on the trained neural network model to achieve reverse design.

[0029] Preferably, the planar topological variables of the ideal metal conductor pattern are (N×N)×2; where N represents the number of pixels in the rows / columns of the first wide-angle impedance matching layer / second wide-angle impedance matching layer; N×N represents the total number of pixels in the first wide-angle impedance matching layer / second wide-angle impedance matching layer, and ×2 represents the total number of pixels in the first wide-angle impedance matching layer and the second wide-angle impedance matching layer.

[0030] Preferably, the discrete numerical variables of the resistive square ring layer include four, namely [P, l] 21 , l 22 [R]; where P represents the size of the resistive square ring layer, l 21 The outer ring size of the metal pattern on the resistor square ring layer, l 22 R represents the inner ring size of the metal pattern on the resistor ring layer, and R represents the resistance value on the resistor ring layer.

[0031] Preferably, the discrete numerical variables for the thickness of each dielectric substrate and the interlayer spacing include five, namely [h0, h1, h3, h4, h5]; where h0 represents the dielectric substrate thickness of the first wide-angle impedance matching layer / second wide-angle impedance matching layer; h1 represents the spacing between the first wide-angle impedance matching layer and the second wide-angle impedance matching layer; h3 represents the spacing between the second wide-angle impedance matching layer and the resistor ring layer; h4 represents the dielectric substrate thickness of the resistor ring layer; and h5 represents the spacing between the resistor ring layer and the metal base plate layer.

[0032] Preferably, a training dataset is constructed that includes an input dataset and an output dataset, specifically as follows:

[0033] A training dataset, including input and output datasets, was constructed using a classic frequency-selective surface broadband absorber planar metal pattern structure and its random variants, along with simulation results from the electromagnetic simulation software CST.

[0034] Preferably, the Cuckoo Optimization Algorithm is used to optimize the construction process of the training dataset.

[0035] Preferably, the electromagnetic response is preprocessed into a square wave signal, specifically including:

[0036] In electromagnetic response |S 11 When the value range is [-A dB, +∞), the sample point is set to 0 dB; while in the electromagnetic response |S 11When the value range is [-∞, -A dB), the sample point is set to -A dB; where A is a preset value.

[0037] Preferably, the neural network model of the multilayer perceptron is an MLP-Mixer, comprising an input segmentation module, an information mixing module, and a prediction output module connected in sequence; the input segmentation module is connected to the input square wave signal and divides the square wave signal into multiple blocks of a preset size; the information mixing module extracts and integrates feature information from the divided blocks; the prediction output module uses global average pooling to connect the feature information and generates the final prediction output through post-processing; the prediction output includes planar topological variables and discrete numerical variables of the absorber structure.

[0038] Preferably, the total loss function Loss during the training of a neural network model based on a multilayer perceptron includes the topology loss function Loss. topological and spatial variable loss function Loss Spatial The weights for the topology loss function and the spatial variable loss function are both 0.5, as shown below:

[0039]

[0040]

[0041] Loss = Loss topological ×0.5+Loss Spatial ×0.5

[0042] Where k is the amount of training data used in each iteration. Let i be the topological variable of the absorber plane in the i-th prediction. Let i be the topological variable of the i-th target absorber plane. Let i be the absorber space variable for the i-th prediction. Let be the spatial variable of the i-th target absorber.

[0043] Compared with the prior art, the present invention has the following beneficial effects:

[0044] This invention presents a machine learning-based inverse design method for frequency-selective surface microwave absorbers. It combines an efficient training dataset construction method for absorber design. Unlike traditional equivalent circuit methods or parametric modeling, the proposed method utilizes inverse modeling and topology modeling, enhancing the freedom and flexibility of absorber design. Furthermore, it employs an MLP-Mixer computer vision network architecture to map the desired electromagnetic response to the predicted absorber structure, achieving rapid and reusable absorber design. In addition, the effectiveness and accuracy of the design method are verified through design samples, and physical prototypes are fabricated and physically tested in a darkroom. Test results show that under normal incident conditions, the prototype exhibits a significant improvement in absolute bandwidth and performs ideally in other performance indicators of the microwave absorber. Attached Figure Description

[0045] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0046] Figure 1 This is a flowchart of the inverse design method for a frequency-selective surface microwave absorber based on machine learning, according to an embodiment of the present invention.

[0047] Figure 2 A schematic diagram of the basic three-dimensional geometry of the microwave absorber constructed according to an embodiment of the present invention;

[0048] Figure 3 The present invention relates to a classic FSS empirical pattern structure and a planar topological variable construction method used to construct a training set in an embodiment of the invention; wherein, (a) to (f) are classic FSS empirical pattern structures used to construct a training set, and (g) is a method for discretizing a planar pattern into topological variables;

[0049] Figure 4 This is a schematic diagram of the construction of a discrete numerical variable set according to an embodiment of the present invention; wherein, (a) is the planar structure of the resistive square ring layer; and (b) is a side view of the three-dimensional spatial structure modeling of the absorber.

[0050] Figure 5 This is a schematic diagram of the structure of the MLP-Mixer according to an embodiment of the present invention;

[0051] Figure 6 This is a schematic diagram of two test samples in the verification set of an embodiment of the present invention; wherein, (a) shows the label structure of the test sample; (b) shows the prediction structure designed using the proposed method; and (c) shows the electromagnetic response results of the label and the prediction structure.

[0052] Figure 7 The diagram illustrates the design, manufacturing, and testing of an example of an embodiment of the present invention; wherein, (a) is the predicted absorber sample structure; (b) is a physical three-dimensional view of the sample; (c) is the physical testing environment and equipment; and (d) is the design target and electromagnetic response results under normal and oblique incidence obtained through full-wave simulation and actual measurement. Detailed Implementation

[0053] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0054] like Figure 1 As shown in the figure, this embodiment discloses a machine learning-based inverse design method for frequency-selective surface microwave absorbers, which includes the following steps.

[0055] S101, Microwave absorber structure construction steps: Constructing an absorber structure including a wide-angle impedance matching layer, a resistive square ring layer, and a metal substrate layer; the wide-angle impedance matching layer includes a first wide-angle impedance matching layer and a second wide-angle impedance matching layer; the absorber structure information is divided into planar structure information and spatial structure information; the planar structure information includes the planar topological variables of the ideal metal conductor pattern of the wide-angle impedance matching layer and the discrete numerical variables of the resistive square ring layer; the spatial structure information includes the discrete numerical variables of the thickness of each dielectric substrate and the interlayer spacing of the absorber structure.

[0056] like Figure 2As shown, the basic absorber structure is based on a wide-angle impedance matching (WAIM) layer, a resistive square ring layer, and a metal base plate layer. Unlike previous designs where the WAIM layer uses the same frequency-selective surface (FSS) structure, in this invention, the first and second wide-angle impedance matching layers, as WAIM layers, can employ different ideal metal conductor (PEC) patterns, thus providing more design freedom. Based on the topology modeling method proposed in the prior art (H.Lv, LYXiao, HJHu and QHLiu, “A spatial inverse design method (SIDM) based on machine learning for frequency-selective-surface (FSS) structures,” IEEE Trans. Antennas Propag., vol.72, no.3, pp.2434-2444, Mar.2024.), the absorber structure information is divided into two parts: planar structure information and spatial structure information.

[0057] The planar structure information includes the ideal metallic conductor pattern of the WAIM layer and the resistive square ring layer. For the cells of the WAIM layer, such as... Figure 3 As shown in (g), the design domain of the cell is discretized into N×N pixels and represented by a binary matrix of dimension N×N, where "0" indicates that there is no PEC at the pixel and "1" indicates that there is a PEC. The physical size of each pixel is a×a. When there are two WAIM layers, the corresponding dimension of this binary matrix is ​​(N×N)×2. For the resistor square ring layer, considering the resistance value limitations and common size limitations of impedance devices in the market, the relevant size information and resistance value of the resistor square ring layer are set as discrete numerical variables, and the corresponding variables [P, l 21 , l 22 ,R], such as Figure 4 As shown in (a). Where N represents the number of pixels in the rows / columns of the first wide-angle impedance matching layer / second wide-angle impedance matching layer; P represents the size of the resistor ring layer, i.e., the size information of the absorber structure. Each layer of the absorber is a cube, and the length and width of each layer are the same, so they are represented by a single variable; l 21 Indicates the outer ring size of the metal pattern on the resistor square ring layer; l 22 R represents the inner ring size of the metal pattern on the resistor ring layer; R represents the resistance value on the resistor ring layer.

[0058] Spatial structure information includes the thickness of each dielectric substrate and the interlayer spacing, which are important factors affecting absorber performance. For example... Figure 4As shown in (b), the physical information of each spatial modeling domain is represented by the vector [h0, h1, h2, h3, h4, h5], including the thickness of each dielectric substrate and the thickness of the air gap. Since the two WAIM layers have the same thickness, i.e., h0 = h2, they can be represented by a single numerical variable. In summary, the entire structure of the absorber can be represented by a three-dimensional binary matrix of dimension (N×N)×2 and a numerical vector of dimension 1×9. The three-dimensional binary matrix represents the planar pattern information of the WAIM layer, while the numerical vector contains the mode parameters (i.e., resistance values) and the spatial structure information of the resistance ring layer, represented as [P, l 21 , l 22 h0, h1, h3, h4, h5, R]. Where h0 represents the dielectric substrate thickness of the first wide-angle impedance matching layer / second wide-angle impedance matching layer; h1 represents the spacing between the first wide-angle impedance matching layer and the second wide-angle impedance matching layer; h3 represents the spacing between the second wide-angle impedance matching layer and the resistor ring layer; h4 represents the dielectric substrate thickness of the resistor ring layer; and h5 represents the spacing between the resistor ring layer and the metal base plate layer.

[0059] S102, Training dataset construction step: Construct a training dataset including an input dataset and an output dataset; the input dataset is a square wave signal obtained by preprocessing the electromagnetic response of the absorber, and the output dataset is the absorber structure information corresponding to the electromagnetic response, the absorber structure information including planar topological variables and discrete numerical variables.

[0060] Generally, random datasets are commonly used in parametric modeling. However, topological modeling involves a large number of binary variables, resulting in a massive amount of data with possible combinations. Therefore, to ensure the quality of the training dataset, some classic FSS empirical pattern structures and their variants (such as...) are used. Figure 3 The training dataset is constructed using simulation results from the electromagnetic simulation software CST (shown in (a)-(f)) and other methods. It should be noted that, for ease of description using three-dimensional binary matrices, Figure 3The variables marked in (a)-(f) change in units of pixel decomposition step size, i.e., the size 'a' of the decomposed pixels. Meanwhile, to improve data acquisition efficiency, the Cuckoo Search (CS) algorithm is used to optimize and accelerate the dataset acquisition process (XS Yang and Suash Deb. "Cuckoo search via lévy flights," in Proc. WorldCongr. Nat. Biol. Inspir. Comput. (NaBIC), pp. 210-214, 2009.). By setting an appropriate fitness function, the Cuckoo Search algorithm can iteratively guide the search process through full-wave simulation to converge to the target performance objective, such as broadband absorption performance. Therefore, through this iterative process, samples with broader absorption characteristics can be obtained, thereby enhancing the learning value of the dataset and significantly improving the efficiency of dataset construction.

[0061] In this invention, the input to the reverse topology design method is the electromagnetic response of the absorber, i.e., |S 11 |, and the output is the corresponding absorber structure information. However, in the reverse engineering process, accurately describing |S 11 The curve is relatively difficult to predict. Therefore, the original |S 11 The curve is preprocessed into a square wave signal, where |S 11 When the value range is [-AdB, +oo), the sample point is set to 0dB; while in |S 11 When the value range is [-∞, -A dB), the sample point is set to -A dB. When the reflection loss is -10 dB, it indicates that the absorber can absorb 90% of the electromagnetic waves. Therefore, it is generally believed that when the reflection loss is below -10 dB, the absorber has good absorption of electromagnetic waves of that frequency. Thus, in this embodiment, A is set to 10. After this preprocessing, the characteristic information of the original curve is still retained in the converted square wave.

[0062] S103, Machine learning model training and reverse design steps: The training dataset is used to train the neural network model based on the multilayer perceptron to obtain the trained neural network model; For the electromagnetic response target, the planar topological variable values ​​and discrete numerical variable values ​​of the absorber structure are obtained based on the trained neural network model to realize the reverse design.

[0063] In this invention, MLP-Mixer is used to complete the predictive learning task from the desired electromagnetic response to the corresponding feasible absorber structure. MLP-Mixer is a neural network architecture based on multilayer perceptrons (MLPs). Compared to traditional convolutional neural networks (CNNs), MLP-Mixer adopts the Transformer concept, converting image data into sequential data and processing the sequence through multilayer perceptrons. It has fewer parameters and a simpler structure, and has been used for image prediction tasks with good results. Figure 5 As shown, the MLP-Mixer architecture consists of three main parts.

[0064] Input Patch Embedding Module: This module divides the input square wave signal into multiple smaller patches for further processing in subsequent hybrid networks.

[0065] Information-Mixing Module: This module extracts and integrates feature information from these processed input data fragments (blocks).

[0066] Prediction Module: This module uses global average pooling to fully concatenate the input feature information and generates the final prediction output through post-processing techniques (such as binarization or thresholding).

[0067] The parameters of the MLP-Mixer are updated by minimizing the loss between the predicted absorber structure and the target absorber structure. The loss function Loss consists of two parts: the topology loss function Loss. topological and spatial variable loss function Loss Spatial Both parts of the loss function have a weight of 0.5, and the specific expressions are as follows:

[0068]

[0069] Loss = Loss topological ×0.5+Loss Spatial ×0.5 (3)

[0070] in, Let i be the topological variable of the absorber plane in the i-th prediction. Let i be the topological variable of the i-th target absorber plane. Let i be the absorber space variable for the i-th prediction. Let be the spatial variables of the i-th target absorber. The planar structure contains (N×N)×2 variables, while the spatial structure contains 9 variables. In each iteration, the MLP-Mixer predicts the information of the training sample structure in the training set. To prevent the machine learning model from focusing only on the more numerous planar variables and ignoring the less numerous spatial structure information, the loss of the planar variables and spatial information of each predicted sample relative to the original label is calculated, resulting in the Loss in formulas (1) and (2). topological and Loss Spatial Then, take the loss. topological and Loss Spatial The average value Loss is used as the error loss between the predicted FSS absorber structure and the original FSS absorber structure in this iteration, thereby allowing MLP-Mixer to update the network parameters based on this error loss.

[0071] The following will illustrate this through a design application example.

[0072] Specifically, based on the basic absorber structure, 3400 training data samples were generated as the training set within the frequency range of 1 GHz to 8 GHz. Rogers 4003 with a relative permittivity of 3.55 was used as the dielectric substrate material for the WAIM layer and the resistive square ring layer. The modeling domain was defined as the maximum size of the absorber element, i.e., 30 mm × 30 mm (i.e., the maximum value of variable P is 30 mm, while l...). 21 The value of l does not exceed P. 22 The value does not exceed l 21 The planar structure is divided into 60×60 discrete binary pixels (i.e., N is 60), so the size of each pixel is 0.5mm×0.5mm (i.e., the value of variable a is 0.5mm). The number of topological variables for the planar structure is (60×60)×2, or 7200. Considering that the metal pattern in the Frequency Selective Surface (FSS) absorber structure design is assumed to be centrally symmetric, further simplification can be made in practical applications. Therefore, the number of topological variables for the planar structure is ((60 / 2)×(60 / 2))×2, or 1800. The number of discrete numerical variables for the spatial structure is 9, and the total number of variables for the absorber structure is 1800+1×9, or 1809. For the numerical variables of the designed absorber, the resistance value and the thickness of the spatial modeling area are considered. The physical value of the resistance value (i.e., variable R) is randomly selected from a 1×25 numerical vector set composed of commonly used resistance values ​​in the market. The physical values ​​of the thickness of each spatial modeling region (i.e., the variables [h0, h1, h2, h3, h4, h5]) are randomly selected from a uniformly distributed 1×8 set of numerical vectors.

[0073] The initial learning rate, layer depth, and patch size of the MLP-Mixer neural network model were set to 5×10⁻⁶. -4 24 and 4. PyTorch is used as a training framework for machine learning-based methods and imports additional libraries such as H5py, NumPy, SciPy, and Einops to support various functions during the training process.

[0074] The calculations in this real-time example were performed on an Intel Gold 6226R 2.90GHz computer equipped with 512GB of memory and an NVIDIA A6000 GPU. Full-wave simulation was performed using CST software. For performance comparison, the following formula (4) was used as the metric for mismatch.

[0075]

[0076] Among them, S i |S represents the initial absorber structure 11 |Square wave vector after curve processing |S represents the predicted absorber structure obtained from the full-wave simulation. 11 |Square wave vector after curve processing.

[0077] After 300 iterations, the MLP-Mixer has been fully trained. To evaluate its performance, 100 design set test samples were used. According to formula (4), the |S| of the design set test samples can be calculated. 11 The average error is 3.884%. Figure 6 Table 1 shows two randomly selected test samples, from which the |S| obtained from the predicted structure can be seen. 11 |The curve can be related to the label structure|S 11 |Curve matching. However, some differences still exist between the label structure and the predicted structure, due to the inherent non-uniqueness problem of reverse engineering methods.

[0078] Table 1. Labels and predicted values ​​of discrete numerical variables.

[0079]

[0080] The following is a description of the actual performance verification.

[0081] In this embodiment, to verify the performance of the absorber designed by the proposed method, the following will be performed: Figure 7 The design goals shown are input into the trained neural network model. The resulting predicted absorber structure is as follows: Figure 7 As shown in (a), the predicted values ​​of the discrete numerical variables are as follows: P = 19 mm, l 21 =18mm,l 22=14mm, h0=1.6mm, h1=4.5mm, h3=1.6mm, h4=1.3mm, h5=15mm, R=261Ω. The simulation results of the predicted structure are as follows: Figure 7 As shown. Simultaneously, the predicted absorber was physically fabricated using 13×13 units (total dimensions: 247mm×247mm), as shown... Figure 7 As shown in (b). To prevent structural collapse, each layer of the absorber is connected by four plastic screws. Some polymethyl methacrylate (PMI) foam is filled in the air layers to support them. The dielectric constant of the PMI foam is similar to that of air, so its impact on the absorber's performance is negligible. The measuring equipment used in the microwave anechoic chamber for testing is as follows... Figure 7 As shown in (c), the waveguide antenna and the horn antenna are located on the same side, used to transmit and receive electromagnetic waves, thereby testing the absorber's |S 11 |Performance. Reflectance coefficients under normal and oblique incidence conditions are as follows: Figure 7 As shown in (d), during the measurement process, under normal incidence, the operating frequency band with a reflection reduction of at least 10 dB is 1.33–7.31 GHz, achieving a relative bandwidth of 138.2%. Under 45° oblique incidence, the TE polarization operates from 1.42 GHz to 6.13 GHz with a relative bandwidth of 123.0%, while the TM polarization operates from 2.1 GHz to 6.95 GHz with a relative bandwidth of 107.2%. From Figure 7 As can be clearly seen in (c), the measured results are in good agreement with the full-wave simulation results.

[0082] Finally, the performance of the designed and fabricated absorber is compared with that of previous work in Table 2. Compared with “Development of a resistor-loaded ultrawideband absorber with antenna reciprocity

[10] ”, the designed absorber has a significantly larger absorption angle. Compared with “Truly all-dielectric ultrabroadband metamaterial absorber: water-based and ground-free

[11] ” and “An ultrathin and ultrawideband metamaterial absorber and an equivalent-circuit parameter retrieval method

[12] ”, although the absorption angles are similar, the designed absorber has a significant increase in operating bandwidth and a significant reduction in thickness. Compared with “Wide-angle, ultra-wideband, polarization-independent circuit analog absorbers

[13] ”, while maintaining similar relative bandwidth, absorption angle and thickness, the operating absolute bandwidth of the designed absorber has increased by 1.16 GHz, further improving its performance. Overall, the absorber designed using the proposed machine learning-based method shows satisfactory results in multiple performance metrics, including absorption bandwidth, angle and polarization insensitivity, and thickness.

[0083] Table 2 Performance Comparison

[0084]

[0085] As shown above, to more efficiently design multi-degree-of-freedom frequency-selective absorbers and further improve the performance of microwave absorbers, this invention proposes a machine learning-based structural inverse design method for frequency-selective surface absorbers. This method achieves high-degree-of-freedom topological inverse design of microwave absorbers while ensuring the superior performance of the designed absorber, including wide bandwidth, multiple angles, and thinness. In the proposed method, the input is a set of required electromagnetic response curves, and the output is a predicted frequency-selective surface absorber structure composed of the image topology and discrete numerical variable values. This invention combines several classic FSS structures and the Cuckoo Optimization algorithm to propose a training dataset construction strategy for faster and more efficient dataset collection. A design set consisting of 100 electromagnetic response curves verifies the feasibility of the proposed design method. One example was fabricated and measured, and the results show that the design sample operates in the frequency range of 1.33-7.31 GHz, with a significant improvement in absolute bandwidth; the relative bandwidth is 138.2%, and the thickness is 0.114 mm. At an incident angle of 45°, both TE and TM polarization modes maintain a wide relative bandwidth. Comparison with previous work verifies the performance improvement of the method presented in this invention. The results show that the design method of this invention has strong practical significance in the design of microwave absorbers.

[0086] The principles and operation of this invention are illustrated through the specific implementation examples described above. These examples aim to provide readers with a clear framework for understanding the core ideas and key operational points of this invention. However, it should be clarified that these examples are not intended to limit the scope of application of this invention. For those skilled in the art, various improvements and innovations based on the core ideas of this invention should be included within the scope of protection of this invention.

Claims

1. A machine learning-based inverse design method for frequency-selective surface microwave absorbers, characterized in that, include: The microwave absorber structure is constructed by building an absorber structure including a wide-angle impedance matching layer, a resistive square ring layer, and a metal base plate layer. The wide-angle impedance matching layer includes a first wide-angle impedance matching layer and a second wide-angle impedance matching layer; the information of the absorber structure is divided into planar structure information and spatial structure information; the planar structure information includes the planar topological variables of the ideal metal conductor pattern of the wide-angle impedance matching layer and the discrete numerical variables of the resistive square ring layer; the spatial structure information includes the discrete numerical variables of the thickness of each dielectric substrate and the interlayer spacing of the absorber structure. The training dataset construction steps include constructing a training dataset that includes an input dataset and an output dataset; the input dataset is a square wave signal obtained by preprocessing the electromagnetic response of the absorber, and the output dataset is the absorber structure information corresponding to the electromagnetic response, which includes planar topological variables and discrete numerical variables. The machine learning model training and reverse design steps involve using the training dataset to train a multilayer perceptron-based neural network model to obtain a trained neural network model; for the electromagnetic response target, the planar topological variable values ​​and discrete numerical variable values ​​of the absorber structure are obtained based on the trained neural network model to achieve reverse design.

2. The inverse design method for frequency-selective surface microwave absorbers based on machine learning according to claim 1, characterized in that, The planar topological variables of the ideal metallic conductor pattern are (N×N)×2; where N represents the number of pixels in the first wide-angle impedance matching layer / second wide-angle impedance matching layer; N×N represents the total number of pixels in the first wide-angle impedance matching layer / second wide-angle impedance matching layer; and ×2 represents the total number of pixels in the first wide-angle impedance matching layer and the second wide-angle impedance matching layer.

3. The inverse design method for frequency-selective surface microwave absorbers based on machine learning according to claim 1, characterized in that, The discrete numerical variables of the resistive square ring layer include four, namely [P, l] 21 , l 22 [R]; where P represents the size of the resistive square ring layer, l 21 The outer ring size of the metal pattern on the resistor square ring layer, l 22 R represents the inner ring size of the metal pattern on the resistor ring layer, and R represents the resistance value on the resistor ring layer.

4. The inverse design method for frequency-selective surface microwave absorbers based on machine learning according to claim 1, characterized in that, The discrete numerical variables for the thickness of each dielectric substrate and the interlayer spacing include five, namely [h0, h1, h3, h4, h5]; where h0 represents the dielectric substrate thickness of the first wide-angle impedance matching layer / second wide-angle impedance matching layer; h1 represents the spacing between the first wide-angle impedance matching layer and the second wide-angle impedance matching layer; h3 represents the spacing between the second wide-angle impedance matching layer and the resistor ring layer; h4 represents the dielectric substrate thickness of the resistor ring layer; and h5 represents the spacing between the resistor ring layer and the metal base plate layer.

5. The inverse design method for frequency-selective surface microwave absorbers based on machine learning according to claim 1, characterized in that, Construct a training dataset that includes both the input and output datasets, specifically as follows: A training dataset, including input and output datasets, was constructed using a classic frequency-selective surface broadband absorber planar metal pattern structure and its random variants, along with simulation results from the electromagnetic simulation software CST.

6. The inverse design method for frequency-selective surface microwave absorbers based on machine learning according to claim 1, characterized in that, The Cuckoo Optimization Algorithm is used to optimize the construction process of the training dataset.

7. The inverse design method for frequency-selective surface microwave absorbers based on machine learning according to claim 1, characterized in that, The electromagnetic response is preprocessed into a square wave signal, specifically including: In electromagnetic response |S 11 When the value range is [-A dB, +∞), the sample point is set to 0 dB; while in the electromagnetic response |S 11 When the value range is [-∞, -AdB), the sample point is set to -AdB; where A is a preset value.

8. The inverse design method for frequency-selective surface microwave absorbers based on machine learning according to claim 1, characterized in that, The neural network model of the multilayer perceptron is an MLP-Mixer, which includes an input segmentation module, an information mixing module, and a prediction output module connected in sequence. The input segmentation module is connected to the input square wave signal and divides the square wave signal into multiple blocks of a preset size. The information mixing module extracts and integrates feature information from the divided blocks. The prediction output module uses global average pooling to connect the feature information and generates the final prediction output through post-processing; the prediction output includes planar topological variables and discrete numerical variables of the absorber structure.

9. The inverse design method for frequency-selective surface microwave absorbers based on machine learning according to claim 1, characterized in that, The total loss function Loss during the training of a neural network model based on a multilayer perceptron includes the topology loss function Loss. topological and spatial variable loss function Loss Spatial The weights for the topology loss function and the spatial variable loss function are both 0.5, as shown below: Loss=Loss topological ×0.5+Loss Spatial ×0.5 Where k is the amount of training data used in each iteration. Let i be the topological variable of the absorber plane in the i-th prediction. Let i be the topological variable of the i-th target absorber plane. Let i be the absorber space variable for the i-th prediction. Let be the spatial variable of the i-th target absorber.

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