Frequency selective surface performance prediction method and related equipment

Abstract

The invention discloses a frequency selective surface performance prediction method and related equipment. The method comprises the following steps: constructing a pre-training data set; constructing a variational auto-encoder model, and extracting potential common features of a performance curve by using a variational auto-encoder as a generative model; training a variational auto-encoder model by using the pre-training data set; preprocessing the data of the target frequency selective surface scene, extracting resonance characteristics of the performance curve, and obtaining a characteristic data set; constructing a resonance sensing variable-length proxy model; and sampling the characteristic data set to train a resonance sensing variable-length proxy model, and using the trained model to predict the performance of the frequency selective surface. According to the method, physical priori knowledge is embedded in the agent model training process to improve the curve representation capability, a resonance point sensing curve generation mechanism is introduced, the physical consistency modeling and high-quality reconstruction of the performance curve are realized from the resonance point characteristics of the curve, and the expression capability of the model to the complex resonance characteristics is remarkably improved.

Description

Technical Field

[0001] The present invention relates to the field of electromagnetic functional structure performance prediction, and in particular to a frequency selective surface performance prediction method and related equipment. Background Art

[0002] With the continuous advancement of machine learning and deep learning technologies in frequency selective surface structural design, surrogate models are widely used to replace traditional simulation methods to reduce high simulation costs. However, in high-dimensional design spaces, constructing surrogate models with good accuracy and generalization capabilities still faces many difficulties. On the one hand, electromagnetic structure performance evaluation often relies on detailed simulation, which is computationally time-consuming and resource-intensive, resulting in a limited number of high-quality training samples. On the other hand, as the design dimension increases, the entire design space becomes highly sparse, making it difficult to cover key areas of the performance distribution with limited samples.

[0003] Especially for complex frequency-selective surface structures with multiple resonant points, their performance curves are diverse and drastically change, accounting for a relatively low proportion of the sample. Sampling methods struggle to effectively obtain such representative data, and surrogate models, lacking sufficiently complex samples, are prone to overfitting during the training phase, which in turn affects the prediction of unknown structures and limits the model's application value in practical engineering. However, existing methods generally utilize neural networks to directly fit the mapping between the frequency-selective surface and its corresponding complete performance curve, making it difficult to maintain predictive robustness in the face of structural changes and response diversity.

[0004] In summary, how to effectively utilize limited samples under the premise of limited simulation resources and construct a performance prediction model with sensitivity to complex structures and generalization capabilities is still a key issue that needs to be broken through in the current research field of frequency selective surface proxy models. Summary of the Invention

[0005] In order to solve at least one of the technical problems existing in the prior art to a certain extent, the purpose of the present invention is to provide a method and related equipment for predicting the performance of frequency selective surfaces based on physical priors and resonance perception.

[0006] The first technical solution adopted by the present invention is:

[0007] A method for predicting performance of a frequency selective surface comprises the following steps:

[0008] Build a pre-training dataset;

[0009] Construct a variational autoencoder model and use it as a generative model to extract the underlying common features of the performance curve.

[0010] Use the pre-training dataset to train the variational autoencoder model;

[0011] Preprocess the data of the target frequency selective surface scene, extract the resonance characteristics of the performance curve, and obtain a feature data set;

[0012] Construct a resonance-aware variable-length agent model based on a variational autoencoder model;

[0013] The sampled feature dataset is used to train a resonance-aware variable-length proxy model, and the trained model is used to predict the performance of frequency selective surfaces.

[0014] Furthermore, the constructing of the pre-training data set includes:

[0015] For the application scenario of the target frequency-selective surface structure, a class of scenarios with similar performance curve characteristics as the target structure is obtained;

[0016] In the obtained similar scenes, the performance curve is calculated using analytical expressions, and all original performance curves are normalized and preprocessed; the curve data set obtained after normalization is recorded as where t i Represents the normalized performance curve calculated for each structure.

[0017] Furthermore, the variational autoencoder model includes an encoder and a decoder; wherein the encoder is used to extract and compress curve data features into a latent space, and the decoder is used to re-decode the variables in the latent space into a curve of full dimension;

[0018] The forward propagation process of the variational autoencoder model is shown below:

[0019]

[0020] Where, f θ represents the decoder network, θ is its network parameter; μ φ (x) and σ φ (x) are the potential mean and standard deviation of the encoder output, parameterized by φ; ∈ represents random noise sampled from the standard normal distribution N(0,I); is the final reconstructed frequency response curve.

[0021] Furthermore, the use of a pre-training dataset to train a variational autoencoder model includes:

[0022] Using curve data set D pre The constructed variational autoencoder model is trained, where the training loss function L VAE It is calculated by weighting the reconstruction loss, KL divergence and Sobolev smoothing loss:

[0023] L VAE =LMSE +αL KLD +βL Sobolev

[0024] Where α and β are the weights of KL divergence and Sobolev smoothing loss respectively; L MSE is the reconstruction loss, L KLD is the KL divergence, L Sobolev is the Sobolev smoothing loss;

[0025] Among them, the expression of reconstruction loss is:

[0026]

[0027] Where L is the total number of data points of a single sample, and N is the total number of samples in the batch; is the jth data point in the input curve of the nth sample, is the jth data point in the reconstructed frequency response curve of the nth sample;

[0028] The expression of KL divergence is:

[0029]

[0030] Where d is the dimension of the encoder’s latent space; are the mean and standard deviation of the nth sample on the kth latent dimension;

[0031] The expression of Sobolev smoothing loss is:

[0032]

[0033] After training the variational autoencoder model, a pre-trained generative model is obtained. The structure and parameters of the decoder in the model are saved and fixed, and the module is recorded as Decoder.

[0034] Furthermore, the preprocessing of the target frequency selective surface scene data to extract the resonance characteristics of the performance curve includes:

[0035] K samples are randomly sampled on the target frequency selective surface scene. The structure of each sample is represented by a binary matrix x. The simulation software is used to simulate and calculate the corresponding performance curve y to obtain the target frequency selective surface data set.

[0036] After obtaining the data set, the resonance point information in each performance curve is extracted: by performing a first-order difference operation on the performance curve, the derivative sequence Δy(t) is obtained, and the extreme value judgment condition is used to locate all local maximum points to obtain the maximum point set;

[0037] Based on the set of maximum points, an interval segmentation operation is performed: the original data between each two adjacent maximum points is retained, and the data outside the interval is set to zero, thereby generating the corresponding segmented sub-curve, and the x-coordinates corresponding to the two adjacent maximum points are labeled as l and r respectively; this process is repeated in an iterative mechanism until the next pair of adjacent maximum points no longer exists in the set of maximum points;

[0038] After the interval segmentation operation is performed, the performance curve corresponding to the original i-th structure will be transformed into a new curve composed of several segmented sub-curves; each sub-curve is normalized, and the amplitude A required for each sub-curve to be restored to the real sub-curve is recorded. i With bias b i , such sub-curve data is recorded as It is a vector of variable length. Each sub-category stores the corresponding normalized sub-curve. It also needs to save the non-zero left and right endpoints of each sub-curve. i 、r i ; Finally, record each curve y i The number of sub-curves M i .

[0039] Furthermore, the method of locating all local maximum points using the extreme value determination condition to obtain a maximum point set includes:

[0040] The extreme value judgment conditions are:

[0041] Δy(t-1)>0∧Δy(t)<0

[0042] Use extreme value judgment conditions to locate all local maximum points, complete the initial maximum point detection, and obtain candidate maximum points;

[0043] Perform secondary verification on the candidate maximum points, assuming that the candidate maximum point sequence is q:

[0044] Calculate the floating value: based on the starting anchor point q k , calculate its distance from the next adjacent point q k+1 The difference between the maximum and minimum values in the interval is the floating value ΔA of the data in the interval;

[0045] Validity judgment: Set the threshold as θ A , if ΔA≥θ A , then we think q k+1 is a valid extreme point, and the anchor point is updated to q k+1 ;

[0046] Remove invalid points: If ΔA<θ A , then judge q k+1 For invalid noise points, delete them from the extreme value sequence and continue to maintain the current anchor point qk constant;

[0047] Iterate to the end of the sequence in the form of a sliding window, and finally generate The set of maximum points of .

[0048] Furthermore, the resonance-aware variable-length proxy model includes a feature extraction network, an autoregressive module, and a decoding and reconstruction module;

[0049] The feature extraction network is used to encode the input two-dimensional structure matrix into a one-dimensional structure feature vector, thereby extracting high-dimensional feature representations from the original structure information. Where d is the input dimension of the pre-trained decoder, that is, the potential space dimension of the variational autoencoder model;

[0050] The autoregressive module consists of a feedforward neural network and a continuous prediction head composed of a fully connected layer and a sigmoid function cascade; the first round of input of this module is the high-dimensional features extracted from the matrix by the feature extraction network It will be input into the feedforward neural network to predict the next feature feature In addition to being sent to the decoding and reconstruction module, it will also be sent to the continuity prediction head of the autoregressive module and output the probability of continuing to perform autoregression If the probability is greater than the set autoregressive threshold p, the feature Will be re-input into the feedforward neural network and output new features This process will iterate until the output of the continuity prediction head is less than the threshold p or the maximum preset autoregressive number is reached;

[0051] Each set of features will be input into the decoding and reconstruction module and split into z according to the dimensions of d, 1, 1, 1, 1 n 、A n 、b n 、l n 、r n ; Then z n Input into the decoder obtained by pre-training and freezing the weights to decode the corresponding normalized sub-curve Then multiply by the corresponding amplitude and add the bias to calculate and satisfy Finally, based on the interval [l n ,r n ] for the curve Perform bilinear interpolation to obtain the transformed prediction subcurve After decoding and reconstructing each set of features, all predicted sub-curves Sum up and you can get the final complete curve output

[0052] Furthermore, the sampled feature data set is used to train a resonance-aware variable-length proxy model, including:

[0053] Adopt fixed length filling strategy: use the sub-curve number information M of all data i , calculate the maximum number of sub-curves M max ; Expand the sub-curve sequence after all samples are output by autoregression to the maximum number of sub-curves M max , fill the insufficient part with zero; fill the sub-curves in the dataset label to the maximum number of sub-curves M max ;

[0054] During the model training process, multiple loss functions are introduced to collaboratively constrain the generation accuracy, structural consistency of sub-curves, and the reconstruction effect of the overall curve, thereby improving the stability and generalization ability of the generation module.

[0055] Furthermore, the multiple loss functions are specifically as follows:

[0056] 1) Normalized sub-curve reconstruction error L norm , which is calculated as follows:

[0057]

[0058] Where B is the index of the sample in the current training batch, and index m represents the mth sub-curve in the sample; represents the mth true normalized sub-curve label in the Bth sample, The prediction result of the mth normalized sub-curve obtained after the model predicts and decodes the Bth sample;

[0059] 2) Continuity prediction head loss L cont , which is calculated as follows:

[0060]

[0061] Where, Whether the output of the continuity prediction head during the mth autoregression needs to continue to generate the true label of the next sub-curve, which has only two cases: 0 or 1, where 1 means "should continue" and 0 means "should terminate"; is the predicted probability of the mth autoregressive output of the continuity prediction head, indicating the confidence level of "should continue to generate";

[0062] 3) Amplitude, bias, left endpoint, right endpoint loss L A , L b , L l , L r, which is calculated as follows:

[0063]

[0064] Where k (B,m) is the true label of the amplitude A, bias b, left endpoint l, and right endpoint r of the mth true normalized subcurve in the Bth sample, is the model's predicted value of the amplitude A, bias b, left endpoint l, and right endpoint r of the m-th sub-curve in the B-th sample;

[0065] 4) Combined curve regularization term L comb , which is calculated as follows:

[0066]

[0067] Where y B is the true complete performance curve label of the Bth sample, is the complete performance curve of the Bth sample finally predicted by the model;

[0068] The overall loss of the model is:

[0069] L total =L norm +λ 1n L cont +λ2L A +λ3L b +λ4L l +λ5L r +λ6L comb

[0070] Where λ1, λ2, λ3, λ4, λ5, and λ6 are weight coefficients.

[0071] The second technical solution adopted by the present invention is:

[0072] An electronic device includes a processor and a memory, wherein the memory stores at least one instruction, at least one program, a code set, or an instruction set, and the at least one instruction, at least one program, the code set, or the instruction set is loaded and executed by the processor to implement a frequency selective surface performance prediction method as described above.

[0073] The third technical solution adopted by the present invention is:

[0074] A computer-readable storage medium stores at least one instruction, at least one program, a code set, or an instruction set, wherein the at least one instruction, at least one program, a code set, or an instruction set is loaded and executed by a processor to implement a frequency selective surface performance prediction method as described above.

[0075] The fourth technical solution adopted by the present invention is:

[0076] A computer program product or computer program includes computer instructions stored in a computer-readable storage medium. A processor of a computer device can read the computer instructions from the computer-readable storage medium and execute the computer instructions, causing the computer device to perform the above-mentioned method for predicting performance of a frequency selective surface.

[0077] The beneficial effects of the present invention are as follows: the present invention introduces a similar scenario performance curve dataset with extremely high computational efficiency in the pre-training stage, and uses a variational autoencoder to extract the potential features of the performance curve, thereby integrating physical priors into the model training process and improving the model's adaptability to new structures; in addition, an autoregressive module based on the distribution characteristics of resonance points is proposed, which can model and generate variable-length sub-curves segment by segment, thereby enhancing the model's perception and expression capabilities of resonance changes, so that it can still have good performance prediction capabilities in complex, high-dimensional, and small-sample scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following introduction is made to the drawings of the embodiments of the present invention or the related technical solutions in the prior art. It should be understood that the drawings introduced below are only for the convenience of clearly describing some embodiments of the technical solutions of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative work.

[0079] Figure 1 This is a flowchart of the steps of a method for predicting performance of a frequency selective surface in an embodiment of the present invention;

[0080] Figure 2 3 is a schematic diagram of the workflow of the frequency selective surface performance prediction method based on physical priors and resonance perception in an embodiment of the present invention. DETAILED DESCRIPTION

[0081] The embodiments of the present application are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present application and are not to be construed as limiting the present application. For the step numbers in the following embodiments, they are provided only for the convenience of explanation and are not intended to limit the order of the steps. The order of execution of the steps in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.

[0082] The terms used in the embodiments of the present application are only for the purpose of describing specific embodiments and are not intended to limit the embodiments of the present application. The singular forms of "a", "said", and "the" used in the embodiments of the present application and the appended claims are also intended to include the plural forms, unless the context clearly indicates otherwise. In addition, unless otherwise clearly defined, words such as setting, installing, and connecting should be understood in a broad sense, and those skilled in the art can reasonably determine the specific meanings of the above words in the present invention in combination with the specific content of the technical solution.

[0083] In the description of this application, it should be understood that descriptions involving orientations, such as up, down, front, back, left, right, etc., indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings. They are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, they cannot be understood as limitations on this application.

[0084] In the description of this application, "several" means one or more, "many" means more than two, "greater than," "less than," and "exceed" are understood to exclude the number itself, while "above," "below," and "within" are understood to include the number itself. The terms "first" and "second" are used solely to distinguish technical features and are not to be construed as indicating or implying relative importance, or as implicitly specifying the number or order of the technical features indicated.

[0085] In the description of this application, "and / or" describes the relationship between associated objects, indicating that three possible relationships exist. For example, "A and / or B" can represent: A exists alone, A and B exist simultaneously, and B exists alone. The character " / " generally indicates that the associated objects are in an "or" relationship.

[0086] With the convergence of artificial intelligence and electromagnetic simulation technology, data-driven modeling methods have been widely used in performance prediction tasks for electromagnetic functional structures such as frequency selective surfaces (FSSs). In this context, achieving high-precision modeling in a high-dimensional design space and with limited samples has become a key technical challenge in the field of automated design and performance analysis of FSSs. While traditional modeling methods can replace costly simulation processes with surrogate models, in real-world scenarios with sparse samples and complex response curves, insufficient model generalization often leads to a significant decrease in prediction accuracy. This makes it particularly difficult to accurately fit complex response curves with multiple resonant points.

[0087] To address these issues, the present invention proposes a method for predicting the performance of frequency-selective surfaces based on physical priors and resonance perception. This method improves curve representation capabilities by embedding physical prior knowledge in the surrogate model training process. It also introduces a curve generation mechanism based on resonance point perception. This method achieves physically consistent modeling and high-quality reconstruction of performance curves based on the curve's resonance point characteristics. Compared to traditional methods, this method significantly improves the model's ability to express complex resonance characteristics and generalizes to new samples without relying on large-scale simulation samples.

[0088] Specifically, the present invention first constructs a data set of electromagnetic structure performance curves in similar scenarios with similar frequency response characteristics and extremely high computational efficiency, and uses it to train a variational autoencoder to extract the common features of the frequency selective surface performance curve, thereby obtaining a pre-trained model infused with physical prior knowledge. The pre-trained model is then embedded in the prediction framework to enhance the generalization ability of the proxy model. On this basis, the distribution characteristics of the resonance points in the performance curve are utilized to design an autoregressive prediction module to generate sub-curve representations with variable-length structures segment by segment. The sub-curves are spliced together and combined with the decoding module to reconstruct the complete performance curve, thereby achieving high-precision performance prediction of the frequency selective surface structure in high-dimensional and small-sample scenarios. The present invention effectively solves the problems of low precision and weak fitting ability of existing proxy models when processing complex frequency response curves, significantly improves the modeling accuracy and prediction stability of complex structural performance under limited simulation data conditions, and has broad engineering application value.

[0089] Example 1

[0090] See also Figure 1 and Figure 2 This embodiment provides a method for predicting the performance of a frequency selective surface based on physical priors and resonance perception, comprising the following steps:

[0091] S1: Build a pre-training dataset.

[0092] As an optional implementation, step S1 specifically includes the following steps:

[0093] S1-1: First, we select the application scenario of the surface structure for the target frequency and search for a class of scenarios with similar performance curve characteristics to the target structure. Specifically, the candidate structure set we are looking for should have high performance diversity and a performance curve computation efficiency much higher than the target scenario, such as the Butterworth filter structure scenario.

[0094] S1-2: Use analytical expressions to calculate the performance curves in the similar scenes found. At the same time, in order to unify the scales and features between different curves, all original performance curves need to be normalized and preprocessed to make them comparable and feasible to learn within a unified numerical range. The curve dataset obtained after normalization is recorded as where yi Represents the normalized performance curve calculated for each structure.

[0095] S2: Build a variational autoencoder model.

[0096] Step S2 will complete the construction of the curve characterization module driven by physical prior. The generative model is mainly used to learn the potential distribution of the performance curve to inject physical prior knowledge into the model. Specifically, this embodiment uses a variational autoencoder as a generative model to extract the potential common features of the performance curve. Its core module includes a variational autoencoder model consisting of a set of encoders and decoders. Among them, the encoder is used to extract and compress the curve data features into the latent space, and the decoder is used to re-decode the latent space variables into a curve of full dimension. Both are neural network structures composed of multi-layer one-dimensional convolutional neural networks and fully connected layers.

[0097] In some embodiments, based on the above framework, the forward propagation process of the network is further designed. The forward propagation process of the variational autoencoder model proposed in this embodiment is shown as follows:

[0098]

[0099] Among them, f θ represents the decoder network, θ is its network parameter; μ φ (x) and σ φ (x) are the potential mean and standard deviation of the encoder output, parameterized by φ; ∈ represents random noise sampled from the standard normal distribution N(0,I); is the final reconstructed frequency response curve.

[0100] S3: Train the variational autoencoder model.

[0101] Specifically, based on the data set D obtained in step S1 pre The variational autoencoder model framework constructed in step S2 completes the training of the variational autoencoder, and its output is the data set D pre The performance curve y in the final decoder is the reconstructed performance curve

[0102] In order to achieve comprehensive constraints on model performance, this embodiment designs a training loss function L of the variational autoencoder model consisting of three parts: VAE , which is calculated by the weighted values of reconstruction loss, KL divergence and Sobolev smoothing loss. The specific calculation method is as follows:

[0103] L VAE =L MSE +αL KLD +βL Sobolev

[0104] Among them, α and β are the weights of KL divergence and Sobolev smoothing loss respectively, in order to balance the influence of each loss during training. The specific meaning and calculation method of each loss are as follows:

[0105] 1) Reconstruction loss L MSE : Used to measure the input curve y and the reconstructed curve The mean square error between , which is defined as:

[0106]

[0107] Where L is the total number of data points for a single sample, and N is the total number of samples in the batch.

[0108] 2) KL divergence L KLD : The latent space distribution q(z|x)=N(μ,σ 2 ) and the standard normal prior p(z) = N(0,I), which is expressed as:

[0109]

[0110] Where d is the dimension of the encoder’s latent space; are the mean and standard deviation of the nth sample on the kth latent dimension, respectively.

[0111] 3) Sobolev smoothing loss L Sobolev : It is used to improve the local smoothness of the reconstructed curve and suppress high-frequency oscillations. It generates violent oscillations of the curve through the second-order difference penalty. The specific calculation method is:

[0112]

[0113] Among them, the specific meaning of each symbol is consistent with that in the reconstruction loss.

[0114] After training is complete, a pre-trained generative model is generated, and its decoder model structure and parameters are saved and fixed. This module is denoted as Decoder. This model effectively learns the common characteristics of this type of performance curve, enabling it to maintain a certain degree of curve representation in new scenarios with sparse data.

[0115] S4: Extract the resonance characteristics of the performance curve.

[0116] As an implementation method, step S4 pre-processes the data of the target frequency selective surface scene to meet the training requirements of the method proposed in this embodiment. First, through random sampling, K samples are obtained. Each structure is represented by a binary matrix x. The simulation software is used to simulate and calculate the corresponding performance curve y, and the frequency selective surface dataset can be obtained.

[0117] After obtaining the data set, it is necessary to further extract the resonance point information in each performance curve. By calculating the first-order difference of the performance curve The derivative sequence Δy(t) can be obtained. Then, the extreme value judgment condition can be further used to locate all local maximum points. The specific extreme value judgment condition is:

[0118] Δy(t-1)>0∧Δy(t)<0

[0119] To address the problem of pseudo-extreme interference caused by high-frequency noise in the performance curve, this embodiment proposes an extreme value correction mechanism based on dynamic threshold screening. Specifically, after completing the initial maximum point detection, the candidate maximum point needs to be verified twice. Let the candidate maximum point sequence be q:

[0120] 1) Calculate the floating value: based on the starting anchor point q k , calculate its distance from the next adjacent point q k+1 The difference between the maximum and minimum values in the interval is the floating value ΔA of the data in the interval.

[0121] 2) Validity judgment: Set the threshold as θ A , if ΔA≥θ A , then we think q k+1 is a valid extreme point, and the anchor point is updated to q k+1 .

[0122] 3) Remove invalid points: If ΔA<θ A , then judge q k+1 For invalid noise points, delete them from the extreme value sequence and continue to maintain the current anchor point q k constant.

[0123] The process is iterated in the form of a sliding window to the end of the sequence, and finally generates The set of maximum points of .

[0124] Using the maximum point set obtained above, we perform an interval segmentation operation: retaining the original data between each pair of adjacent maximum points while setting the data outside the interval to zero. This generates the corresponding segmented sub-curves, and labels the x-coordinates of the two adjacent maximum points as l and r, respectively. This process is repeated iteratively until the next pair of adjacent maximum points no longer exists in the maximum point set.

[0125] At this point, the performance curve corresponding to the original i-th structure will be transformed into a new curve composed of several segmented sub-curves. In order to facilitate model training and match the decoder output mode obtained by training in step S3, it is necessary to further complete the normalization operation on each sub-curve, and in this process record the amplitude A required for each sub-curve to be restored to the real sub-curve. i With bias b i Such sub-curve data is recorded as It is a vector of variable length. Each sub-category stores the corresponding normalized sub-curve. At the same time, it is necessary to further save the non-zero left endpoint and right point l of each sub-curve. i 、r i ; Finally, record each curve y i The number of sub-curves M i .

[0126] S5: Construct a resonance-aware variable-length agent model.

[0127] Step S5 mainly completes the construction of the proposed resonance-aware variable-length proxy model. In some embodiments, the resonance-aware variable-length proxy model consists of three parts: a feature extraction network, an autoregressive module, and a decoding and reconstruction module.

[0128] 1) First, we need to build a feature extraction network, which is used to encode the input two-dimensional structure matrix into a one-dimensional structure feature vector, thereby extracting the high-dimensional feature representation in the original structure information Wherein, d is the input dimension of the decoder obtained by pre-training, that is, the potential space dimension of the variational autoencoder model. Optionally, this embodiment uses a convolutional residual neural network based on ResNet50 as the feature extraction network.

[0129] 2) After the feature extraction network is built, it is necessary to further build an autoregressive module. The autoregressive module consists of a feedforward neural network and a continuous prediction head composed of a fully connected layer and a sigmoid function cascade. The first round of input to this module is the high-dimensional features extracted from the matrix by the feature extraction network. It will be input into the feedforward neural network to predict the next feature feature In addition to being sent to the decoding and reconstruction module, it will also be sent to the continuity prediction head of the autoregressive module and output the probability of continuing to perform autoregression If the probability is greater than the set autoregressive threshold p, the feature Will be re-input into the feedforward neural network and output new features This process will iterate until the output of the continuity prediction head is less than the threshold p or reaches the maximum preset autoregressive number Rmax .

[0130] 3) Each set of features will be input into the decoding and reconstruction module and split into z according to the dimensions of d, 1, 1, 1, 1 n 、A n 、b n 、l n 、r n ; Then z n Input into the decoder obtained by pre-training and freezing the weights to decode the corresponding normalized sub-curve Then multiply by the corresponding amplitude and add the bias to calculate and satisfy Finally, based on the interval [l n ,r n ] for the curve Perform bilinear interpolation to obtain the transformed prediction subcurve After decoding and reconstructing each set of features, all predicted sub-curves Sum up and you can get the final complete curve output

[0131] S6: Training resonance-aware variable-length proxy models.

[0132] Step S6 completes the training of the resonance-aware variable-length proxy model based on the data set processed in S4. Since the number of sub-curves generated by different structures is inconsistent, in order to achieve unified batch training, this embodiment adopts a fixed-length filling strategy: using the sub-curve number information M of all data i , calculate the maximum number of sub-curves M max Expand the sub-curve sequence after all samples are output by autoregression to the maximum number of sub-curves M max , the insufficient part is filled with zero. Similarly, the sub-curves in the dataset label are filled in the same way to the maximum number of sub-curves M max .

[0133] As an implementation method, this embodiment introduces multiple loss functions during model training to collaboratively constrain the generation accuracy, structural consistency, and overall curve reconstruction of the sub-curves, thereby improving the stability and generalization ability of the generation module. Let B be the index of the sample in the batch, and m refers to the mth sub-curve in the sample. The specific loss is composed of the following:

[0134] 1) Normalized sub-curve reconstruction error L norm This loss is used to measure the normalized sub-curves generated in each batch The corresponding real sub-curve The calculation formula is as follows:

[0135]

[0136] 2) Continuity prediction head loss L cont In order to correctly complete the training of the continuity prediction head and enable it to accurately judge the input structure, the autoregression should be terminated after generating several groups of sub-curves. This embodiment introduces a supervisory signal. For sample i, the number of true sub-curves it contains should be M. i , then in front of M i -1 step sets the label 1 (instructing to continue generating), and the label of the subsequent step is set to 0 (instructing to terminate generating). The label is recorded as After that, the output probability can be constrained based on the cross entropy loss BCE, which is calculated as follows:

[0137]

[0138] 3) Amplitude, bias, left endpoint, right endpoint loss L A , L b , L l , L r It constrains the amplitude, bias, left endpoint, and right endpoint predicted by the autoregressive model, all of which are calculated using the mean square error loss. The formula can be abstracted as follows:

[0139]

[0140] 4) Combined curve regularization term L comb It is still calculated based on the mean square error loss, and uses the final restored complete curve to complete the regularization constraint of the overall model. The specific loss is as follows:

[0141]

[0142] Finally, the overall loss of the model is:

[0143] L total＝ L norm +λ1L cont +λ2L A +λ3L b +λ4L l +λ5L r +λ6L comb

[0144] Among them, λ1, λ2, λ3, λ4, λ5, and λ6 are the loss weight coefficients of each sub-item, respectively, to effectively balance the local and global generation quality during the training process.

[0145] In summary, most existing frequency-selective surface performance prediction methods directly use deep neural networks to perform regression modeling on simulation data. Although this can reduce simulation evaluation overhead to a certain extent, under the conditions of high-dimensional parameter space and extremely scarce samples, the model often finds it difficult to strike a balance between prediction accuracy and generalization ability, especially when faced with complex response curves containing multiple resonant points. In contrast, this embodiment provides a frequency-selective surface performance prediction method based on physical priors and resonance perception, which fully integrates the physical characteristics of the frequency response curve with the representation ability of the neural network, and can still achieve high-precision modeling when structural design data is scarce. Specifically, this embodiment introduces a highly computationally efficient similar scenario performance curve dataset in the pre-training stage, and uses a variational autoencoder to extract the potential features of the performance curve, thereby incorporating physical priors into the model training process and improving the model's adaptability to new structures. In addition, an autoregressive prediction module based on the distribution characteristics of the resonant points is proposed, which can model and generate variable-length sub-curves segment by segment, enhancing the model's perception and expression capabilities of resonance changes, enabling it to still have good performance prediction capabilities in complex, high-dimensional, and small-sample scenarios.

[0146] By introducing physical priors and resonance perception mechanisms, this paper effectively improves the modeling capability of the frequency selective surface performance prediction model under high-dimensional and small-sample conditions, and has the following significant advantages:

[0147] 1) The present invention uses similar structural scenarios to construct a pre-training dataset, combines a variational autoencoder to extract the potential common features of the performance curve, and embeds physical priors into the model training process, significantly enhancing the model's ability to express structural response patterns and effectively alleviating the problem of decreased generalization performance caused by data sparsity in high-dimensional design space.

[0148] 2) In response to the common multi-resonance point response characteristics of frequency selective surfaces, the present invention designs a resonance-aware variable-length proxy model module, which can model the performance curve in segments, gradually generate sub-curves, and then splice them into a complete response curve through a reconstruction mechanism, thereby greatly improving the fitting accuracy of complex performance changes.

[0149] 3) Unlike traditional methods that rely on large numbers of simulation samples, this method can achieve high-precision predictions with less simulation data, significantly reducing reliance on simulation resources and achieving superior modeling efficiency and resource adaptability. By rationally utilizing low-computational cost similar domain knowledge and dividing the expression units in the performance curve, this method can achieve high-quality predictions for complex performance curves without incurring additional simulation costs.

[0150] 4) The method of the present invention has good model scalability and application adaptability. It can be used to quickly screen and evaluate the performance of multiple types of frequency-selective structures, and can also be extended to other complex response curve modeling tasks with multi-resonance characteristics, such as metasurface response design and microwave device modeling. It has broad practical application value and promotion potential in the field of electromagnetic functional structure performance prediction.

[0151] Example 2

[0152] An embodiment of the present invention further provides an electronic device, comprising a processor and a memory, wherein the memory stores at least one instruction, at least one program, a code set, or an instruction set, and the at least one instruction, the at least one program, the code set, or the instruction set is loaded and executed by the processor to implement the following Figure 1 A method for predicting the performance of frequency selective surfaces is shown.

[0153] It is understood that the memory may include random access memory (RAM) or read-only memory (ROM). Optionally, the memory includes a non-transitory computer-readable storage medium. The memory may be used to store instructions, programs, codes, code sets, or instruction sets. The memory may include a program storage area and a data storage area, wherein the program storage area may store instructions for implementing an operating system, instructions for at least one function, instructions for implementing the various method embodiments described above, etc.; the data storage area may store data created based on the use of the server, etc.

[0154] The processor may include one or more processing cores. The processor utilizes various interfaces and circuits to connect various components within the server. It executes various server functions and processes data by running or executing instructions, programs, code sets, or instruction sets stored in memory, as well as accessing data stored in memory. Optionally, the processor may be implemented using at least one of the following hardware forms: digital signal processing (DSP), field-programmable gate array (FPGA), and programmable logic array (PLA). The processor may integrate one or a combination of a central processing unit (CPU) and a modem. The CPU primarily processes the operating system and application programs, while the modem handles wireless communications. It is understood that the modem may not be integrated into the processor and may be implemented separately via a single chip.

[0155] Since the electronic device is an electronic device corresponding to a frequency selective surface performance prediction method of an embodiment of the present invention, and the principle of solving the problem by the electronic device is similar to that of the method, the implementation of the electronic device can refer to the implementation process of the above-mentioned method embodiment, and the repeated parts will not be repeated.

[0156] Example 3

[0157] An embodiment of the present invention further provides a computer-readable storage medium, wherein the storage medium stores at least one instruction, at least one program, code set or instruction set, and the at least one instruction, the at least one program, the code set or instruction set is loaded and executed by a processor to implement the following Figure 1 A method for predicting the performance of frequency selective surfaces is shown.

[0158] Those skilled in the art will appreciate that all or part of the steps in the various methods of the above embodiments can be completed by instructing related hardware through a program. The program can be stored in a computer-readable storage medium, and the storage medium includes a read-only memory (ROM), a random access memory (RAM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), a one-time programmable read-only memory (OTPROM), an electronically erasable programmable read-only memory (EEPROM), a compact disc read-only memory (CD-ROM) or other optical disc storage, magnetic disk storage, magnetic tape storage, or any other computer-readable medium capable of carrying or storing data.

[0159] Since the storage medium is a storage medium corresponding to a frequency selective surface performance prediction method of an embodiment of the present invention, and the principle of solving the problem by the storage medium is similar to that of the method, the implementation of the storage medium can refer to the implementation process of the above-mentioned method embodiment, and the repeated parts will not be repeated.

[0160] Example 4

[0161] In some possible implementations, various aspects of the methods of the embodiments of the present invention may also be implemented in the form of a program product, which includes program code. When the program product is executed on a computer device, the program code is used to cause the computer device to perform the steps of a method for predicting the performance of a frequency selective surface according to various exemplary embodiments of the present application as described above in this specification. The executable computer program code or "code" for performing the various embodiments may be written in a high-level programming language such as C, C++, Python, Smalltalk, Java, JavaScript, Visual Basic, Structured Query Language (e.g., Transact-SQL), Perl, or in various other programming languages.

[0162] It should be understood that various parts of the present invention can be implemented using hardware, software, firmware, or a combination thereof. In the above-described embodiments, multiple steps or methods can be implemented using software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented using hardware, as in another embodiment, any one of the following technologies known in the art or a combination thereof can be used: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application-specific integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0163] In the description of this specification, the reference terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" mean that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine different embodiments or examples described in this specification and features of different embodiments or examples without contradiction.

[0164] The above embodiments are intended only to illustrate the technical concepts and features of the present invention. Their purpose is to enable those skilled in the art to understand the contents of the present invention and implement them accordingly. They are not intended to limit the scope of protection of the present invention. Any equivalent changes or modifications made based on the essence of the present invention are intended to be covered by the scope of protection of the present invention.

Claims

1. A method for predicting the performance of a frequency selective surface, characterized in that: The following steps are involved: Build a pre-training dataset; Construct a variational autoencoder model and use it as a generative model to extract the underlying common features of the performance curve. Use the pre-training dataset to train the variational autoencoder model; Preprocess the data of the target frequency selective surface scene, extract the resonance characteristics of the performance curve, and obtain a feature data set; Construct a resonance-aware variable-length agent model based on a variational autoencoder model; The sampled feature dataset is used to train a resonance-aware variable-length proxy model, and the trained model is used to predict the performance of frequency selective surfaces.

2. A method for predicting performance of a frequency selective surface according to claim 1, characterized in that: The constructing of the pre-training dataset includes: For the application scenario of the target frequency-selective surface structure, a class of scenarios with similar performance curve characteristics as the target structure is obtained; In the obtained similar scenes, the performance curve is calculated using analytical expressions, and all original performance curves are normalized and preprocessed; the curve data set obtained after normalization is recorded as where y i Represents the normalized performance curve calculated for each structure.

3. The method for predicting performance of a frequency selective surface according to claim 1, wherein: The variational autoencoder model includes an encoder and a decoder; wherein the encoder is used to extract and compress the curve data features into a latent space, and the decoder is used to re-decode the variables in the latent space into a curve of full dimension; The forward propagation process of the variational autoencoder model is shown below: Where, f θ represents the decoder network, θ is its network parameter; μ φ (x) and σ φ (x) are the potential mean and standard deviation of the encoder output, parameterized by φ; ∈ represents random noise sampled from a standard normal distribution; is the final reconstructed frequency response curve.

4. A method for predicting performance of a frequency selective surface according to claim 1, characterized in that: The method of using a pre-training dataset to train a variational autoencoder model includes: Using curve data set D pre The constructed variational autoencoder model is trained, where the training loss function L VAE It is calculated by weighting the reconstruction loss, KL divergence and Sobolev smoothing loss: L VAE =L MSE +αL KLD +βL Sobolev Where α and β are the weights of KL divergence and Sobolev smoothing loss respectively; L MSE is the reconstruction loss, L KLD is the KL divergence, L Sobolev is the Sobolev smoothing loss; Among them, the expression of reconstruction loss is: Where L is the total number of data points of a single sample, and N is the total number of samples in the batch; is the jth data point in the input curve of the nth sample, is the jth data point in the reconstructed frequency response curve of the nth sample; The expression of KL divergence is: Where d is the dimension of the encoder’s latent space; are the mean and standard deviation of the nth sample on the kth latent dimension respectively; The expression of Sobolev smoothing loss is: After training the variational autoencoder model, a pre-trained generative model is obtained. The structure and parameters of the decoder in the model are saved and fixed, and the module is recorded as Decoder.

5. The method for predicting performance of a frequency selective surface according to claim 1, wherein: The preprocessing of the data of the target frequency selective surface scene to extract the resonance characteristics of the performance curve includes: K samples are randomly sampled on the target frequency selective surface scene. The structure of each sample is represented by a binary matrix x. The simulation software is used to simulate and calculate the corresponding performance curve y to obtain the target frequency selective surface data set. After obtaining the data set, the resonance point information in each performance curve is extracted: by performing a first-order difference operation on the performance curve, the derivative sequence Δy(t) is obtained, and the extreme value judgment condition is used to locate all local maximum points to obtain the maximum point set; Based on the set of maximum points, perform interval segmentation: retain the original data between every two adjacent maximum points, and set the data outside the interval to zero, thereby generating the corresponding segmented sub-curve, and mark the x-coordinates of the two adjacent maximum points as l and r respectively; After the interval segmentation operation is performed, the performance curve corresponding to the original i-th structure will be transformed into a new curve composed of several segmented sub-curves; each sub-curve is normalized, and the amplitude A required for each sub-curve to be restored to the real sub-curve is recorded. i With bias b i , such sub-curve data is recorded as It is a vector of variable length. Each sub-category stores the corresponding normalized sub-curve. It is also necessary to save the non-zero left and right endpoints of each sub-curve. i 、r i ; Finally, record each curve y i The number of sub-curves M i .

6. A method for predicting performance of a frequency selective surface according to claim 5, characterized in that: The method of locating all local maximum points using the extreme value determination condition to obtain a maximum point set includes: The extreme value judgment conditions are: Δy(t-1)>0∧Δy(t)<0 Use extreme value judgment conditions to locate all local maximum points, complete the initial maximum point detection, and obtain candidate maximum points; Perform secondary verification on the candidate maximum points, assuming that the candidate maximum point sequence is q: Calculate the floating value: based on the starting anchor point q k , calculate its distance from the next adjacent point q k+1 The difference between the maximum and minimum values in the interval is the floating value ΔA of the data in the interval; Validity judgment: Set the threshold as θ A , if ΔA≥θ A , then we think q k+1 is a valid extreme point, and the anchor point is updated to q k+1 ; Remove invalid points: If ΔA<θ A , then judge q k+1 For invalid noise points, delete them from the extreme value sequence and continue to maintain the current anchor point q k constant; Iterate to the end of the sequence in the form of a sliding window, and finally generate The set of maximum points of .

7. A method for predicting performance of a frequency selective surface according to claim 1, characterized in that: The resonance perception variable-length proxy model includes a feature extraction network, an autoregressive module, and a decoding and reconstruction module; The feature extraction network is used to encode the input two-dimensional structure matrix into a one-dimensional structure feature vector, thereby extracting high-dimensional feature representations from the original structure information. Where d is the input dimension of the decoder obtained by pre-training; The autoregressive module consists of a feedforward neural network and a continuous prediction head composed of a fully connected layer and a sigmoid function cascade; the first round of input of this module is the high-dimensional features extracted from the matrix by the feature extraction network Predict the next feature feature In addition to being sent to the decoding and reconstruction module, it will also be sent to the continuity prediction head of the autoregressive module and output the probability of continuing to perform autoregression If the probability is greater than the set autoregressive threshold p, the feature Will be re-input into the feedforward neural network and output new features This process will iterate until the output of the continuity prediction head is less than the threshold p or the maximum preset autoregressive number is reached; Each set of features will be input into the decoding and reconstruction module and split into z according to the dimensions of d, 1, 1, 1, 1 n 、A n 、b n 、l n 、r n ; Then z n Input into the decoder obtained by pre-training and freezing the weights to decode the corresponding normalized sub-curve Then multiply by the corresponding amplitude and add the bias to calculate and satisfy Finally, based on the interval [l n ,r n ] for the curve Perform bilinear interpolation to obtain the transformed prediction subcurve After decoding and reconstructing each set of features, all predicted sub-curves Sum up and you can get the final complete curve output 8. The method for predicting performance of a frequency selective surface according to claim 1, wherein: The sampled feature data set is used to train a resonance-aware variable-length proxy model, including: Adopt fixed length filling strategy: use the sub-curve number information M of all data i , calculate the maximum number of sub-curves M max ; Expand the sub-curve sequence after all samples are output by autoregression to the maximum number of sub-curves M max , fill the insufficient part with zero; fill the sub-curves in the dataset label to the maximum number of sub-curves M max ; During the model training process, multiple loss functions are introduced to collaboratively constrain the generation accuracy, structural consistency of sub-curves, and the reconstruction effect of the overall curve, thereby improving the stability and generalization ability of the generation module.

9. A method for predicting performance of a frequency selective surface according to claim 8, characterized in that: The multiple loss functions are as follows: 1) Normalized sub-curve reconstruction error L norm , which is calculated as follows: Where B is the index of the sample in the current training batch, and index m represents the mth sub-curve in the sample; represents the mth true normalized sub-curve label in the Bth sample, The prediction result of the mth normalized sub-curve obtained after the model predicts and decodes the Bth sample; 2) Continuity prediction head loss L cont , which is calculated as follows: Where, Whether the output of the continuity prediction head during the mth autoregression needs to continue to generate the true label of the next sub-curve; is the predicted probability of the mth autoregressive output of the continuous prediction head; 3) Amplitude, bias, left endpoint, right endpoint loss L A 、L b 、L l 、L r , which is calculated as follows: Where k (B,m) is the true label of the amplitude A, bias b, left endpoint l, and right endpoint r of the mth true sub-curve in the Bth sample, is the model's predicted value of the amplitude A, bias b, left endpoint l, and right endpoint r of the m-th sub-curve in the B-th sample; 4) Combined curve regularization term L comb , which is calculated as follows: Where y B is the true complete performance curve label of the Bth sample, is the complete performance curve of the Bth sample finally predicted by the model; The overall loss of the model is: L total =L norm +λ1L cont +λ2L A +λ3L b +λ4L l +λ5L r +λ6L comb Where λ1, λ2, λ3, λ4, λ5, and λ6 are weight coefficients.

10. An electronic device, characterized in that: The electronic device includes a processor and a memory, wherein the memory stores at least one instruction, at least one program, a code set, or an instruction set, and the at least one instruction, the at least one program, the code set, or the instruction set is loaded and executed by the processor to implement the method according to any one of claims 1 to 9.

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