Manufacturing-oriented periodic metamaterial electromagnetic response prediction method and related equipment

Abstract

The invention provides a manufacturing-oriented periodic metamaterial electromagnetic response prediction method, which comprises the following steps of: S1, acquiring a group of metamaterial training samples and a group of electromagnetic response training labels, defining microstructures in a metamaterial as nodes, and defining coupling connection between two adjacent microstructures as edges; each metamaterial training sample comprises a node feature, an edge code and an edge feature; s2, performing iterative training on the initial enhanced graph neural network model according to the group of metamaterial training samples and the group of electromagnetic response training labels so as to guide updating of the initial enhanced graph neural network model by using a loss function; and obtaining a target enhanced graph neural network model at the end of training, and S3, inputting the new metamaterial information into the target enhanced graph neural network model to obtain predicted electromagnetic response information. According to the method, rapid reasoning and prediction can be carried out on new metamaterial design according to manufacturing tolerance statistical distribution, and electromagnetic response evaluation can be rapidly given.

Description

Technical Field

[0001] The present invention relates to the field of metamaterial technology, and in particular to a manufacturing-oriented method for predicting electromagnetic responses of quasi-periodic metamaterials and related equipment. Background Art

[0002] Periodic and quasi-periodic structures possess unique electromagnetic wave manipulation properties and hold significant engineering applications in fields such as electromagnetic radiation, electromagnetic detection, and scattering suppression. According to the national standard GB / T32005-2015 "Terminology of Electromagnetic Metamaterials" (hereinafter referred to as the "Terminology Standard"), metamaterials are specialized composite materials or structures that, through the orderly structural design of key physical dimensions, possess extraordinary physical properties not possessed by conventional materials. Currently, electromagnetic metamaterials are widely used in fields such as aerospace equipment and 6G communications, and are beginning to be explored in areas such as quantum information.

[0003] Efficient and accurate evaluation of large-scale quasi-periodic arrays is a challenging area in electromagnetic simulation. Quasi-periodic arrays differ from fully periodic arrangements. Fully periodic refers to metamaterial microstructures, artificial structures with specific topological morphology and geometrical metrics at key physical scales within the metamaterial, replicated and extended across an infinitely large plane with a periodic pattern, with no actual differences between individual microstructures. Quasi-periodic structures, on the other hand, refer to microstructures with varying distances between them, or a combination of these two scenarios.

[0004] Quasi-periodic arrays possess unique technical advantages and characteristics compared to fully periodic arrays. However, in the practical evaluation and calculation of their electromagnetic response, due to limitations in modeling difficulty, electromagnetic simulation methods, and computing power, quasi-periodic arrays are often simplified to periodic arrangements and evaluated using traditional simulation or computational methods. These evaluation methods utilize the geometric repeatability of periodic cells and, based on Floquet's theorem, calculate the electromagnetic response of infinitely extended periodic structures using finite repeating cells under periodic boundary conditions. However, the periodic boundary method is essentially an equivalent approximation, applicable only to strictly periodic structures. For quasi-periodic structures with subtle differences, the evaluation results may differ due to the inability to perform equivalent simulations of the different array cells. Methods for electromagnetic simulation of quasi-periodic structures include the method of moments, fast multipole methods, and the domain decomposition method. Recently, researchers have proposed a parallel synthesis function method with a function reuse mechanism, drawing on the geometric similarity of quasi-periodic arrays. This method can, to a certain extent, overcome the challenges of balancing accuracy, efficiency, and memory consumption. Summary of the Invention

[0005] The embodiments of the present invention propose a manufacturing-oriented method for predicting the electromagnetic response of a quasi-periodic metamaterial, a computer device, and a computer-readable storage medium, to at least solve the problem of how to use node features, edge codes, and edge features containing physically meaningful spatial arrangement information as inputs to an enhanced graph neural network model, further facilitating the neural network's understanding of the electromagnetic physical model, making the intelligent evaluation method more based on the actual physical model and quickly providing an electromagnetic response evaluation.

[0006] According to one embodiment of the present invention, a manufacturing-oriented method for predicting the electromagnetic response of a quasi-periodic metamaterial is provided, which includes:

[0007] Step S1: Obtain a set of metamaterial training samples and a set of electromagnetic response training labels, each electromagnetic response training label corresponding to a metamaterial training sample; wherein the microstructures in the metamaterial are defined as nodes, the coupling connection between two adjacent microstructures is defined as edges, and the edge feature represents the electromagnetic coupling relationship between the two adjacent microstructures; each metamaterial training sample includes a node feature, an edge code, and an edge feature;

[0008] Step S2: iteratively training the initial enhanced graph neural network model to be trained based on the set of metamaterial training samples and the set of electromagnetic response training labels, so as to use a loss function to guide the update of the initial enhanced graph neural network model; and obtaining a target enhanced graph neural network model at the end of the training;

[0009] Step S3: Input the new metamaterial information into the target enhanced graph neural network model to obtain predicted electromagnetic response information.

[0010] According to another embodiment of the present invention, a computer device is provided, comprising a memory and a processor, wherein the memory stores a computer program; wherein the processor implements the steps of the above method when executing the computer program.

[0011] According to yet another embodiment of the present invention, a computer-readable storage medium storing a computer program is provided, wherein the computer program implements the steps of the above method when executed by a processor.

[0012] The beneficial effects of the present invention are:

[0013] The present invention is aimed at the electromagnetic response evaluation of quasi-periodic metamaterials, and specifically designs an enhanced graph neural network model. It also uses the spatial arrangement information containing physical meaning (i.e., the microstructure physical parameter characteristics, edge coding, and edge characteristics included in the node characteristics) and the frequency domain sampling information (i.e., the frequency compression characteristics included in the node characteristics) as the input of the enhanced graph neural network model, which further facilitates the neural network's understanding of the electromagnetic physical model, making the intelligent evaluation method more based on the actual physical model. At the same time, this method is more oriented towards actual production and manufacturing, and can use the uncertainty of precision, tolerance, etc. in the production and manufacturing process as the noise in the input of the enhanced graph neural network model (for example, the statistical distribution characteristics of the tolerance of the outer ring outer radius, inner ring radius, outer ring inner radius, dielectric thickness, and microstructure unit size in the actual manufacturing process as noise) to quickly evaluate its impact on the overall electromagnetic response. Compared with traditional calculation methods, the present invention redefines the characteristics of nodes and edges in the enhanced graph neural network model based on the physical model, and incorporates frequency and spatial information, quasi-periodic structure difference information, differentiated microstructure mutual coupling, and other information into the model. At the same time, since the electromagnetic response evaluation of this intelligent periodic metamaterial is based on training with a large amount of existing simulation or measurement data, the constitutive relationship between the microstructure topology and electromagnetic response of the electromagnetic metamaterial has been internalized as the network parameters of the enhanced graph neural network model. Therefore, it is possible to make rapid inferences and predictions on the design of new metamaterials and quickly provide electromagnetic response evaluations. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0015] Figure 1 This is a flowchart of a manufacturing-oriented method for predicting the electromagnetic response of a quasi-periodic metamaterial according to an embodiment of the present invention.

[0016] Figure 2 A schematic diagram of a periodic metamaterial according to an embodiment is shown.

[0017] Figure 3 A schematic diagram of defining node and edge concepts in a microstructure set according to an embodiment.

[0018] Figure 4 for Figure 3 Schematic diagram of the physical parameters of each microstructure in the set of microstructures shown.

[0019] Figure 5 Specific training flowchart for training the initial enhanced graph neural network model to obtain the target enhanced graph neural network model.

[0020] Figure 6 Schematic diagram of the specific structure of the enhanced graph neural network model.

[0021] Figure 7 Schematic diagram of the specific structure of the decoding layer in the enhanced graph neural network model.

[0022] Figure 8 A typical loss function numerical curve graph during the training process of the enhanced graph neural network model is shown.

[0023] Figure 9 (a), (b) and (c) show the difference between the predicted value of an electromagnetic response S11 parameter in the validation set and the true value (i.e., label value) after the 1st, 21st and 41st rounds of training iterations of the enhanced graph neural network model, respectively.

[0024] Figure 10 (a), (b) and (c) show the difference comparison between the predicted value of another electromagnetic response S21 parameter in the validation set and the true value (i.e., label value) after the 1st, 21st and 41st rounds of training iterations of the enhanced graph neural network model, respectively. DETAILED DESCRIPTION

[0025] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention are within the scope of protection of the present invention.

[0026] In traditional electromagnetic metamaterial simulations, the Floquet theorem is used to calculate the electromagnetic response of an infinitely extended plane using the same metal microstructure, subject to periodic boundary conditions. However, in actual engineering design and manufacturing, certain quasi-periodic metamaterial designs, because they do not meet periodic boundary conditions, can only approximate the electromagnetic response using traditional methods. This invention utilizes the mining of relationships between nodes in an enhanced graph neural network, combining the physical parameter information between different electromagnetic microstructures with the feature information of the edges in the enhanced graph neural network. By leveraging the training and learning of electromagnetic responses in a previous training set, this method allows for rapid electromagnetic response evaluation of quasi-periodic metamaterials.

[0027] Specifically, if Figure 1 As shown, a manufacturing-oriented method 100 for predicting electromagnetic response of a quasi-periodic metamaterial includes the following steps:

[0028] Step S1: Obtain a set of metamaterial training samples and a set of electromagnetic response training labels, where each electromagnetic response training label corresponds to a metamaterial training sample; wherein, the microstructures in the metamaterial are defined as nodes, and the coupled connection between two adjacent microstructures is defined as an edge, and the edge feature represents the electromagnetic coupling relationship between two adjacent microstructures; each metamaterial training sample includes node features, edge encodings, and edge features;

[0029] Step S2: Iteratively train the initial enhanced graph neural network model to be trained according to the set of metamaterial training samples and the set of electromagnetic response training labels, so as to use the loss function to guide the update of the initial enhanced graph neural network model; and obtain the target enhanced graph neural network model at the end of the training;

[0030] Step S3: Input the new metamaterial information into the target enhanced graph neural network model to obtain the predicted electromagnetic response information. The new metamaterial information also includes node features, edge encodings, and edge features.

[0031] In this embodiment, specifically, the node features include microstructural physical parameter features and frequency compression features, and the microstructural physical parameter features and frequency compression features together serve as the input of the initial enhanced graph neural network model; or

[0032] The node features include microstructural physical parameter features and wavelength compression features, and the microstructural physical parameter features and wavelength compression features together serve as the input of the initial enhanced graph neural network model.

[0033] In this embodiment, more specifically, the frequency compression features include Q frequency features obtained by compressing frequencies F1, F2,..., F P using a preset frequency compression method, where Q < P; P is P uniformly or non-uniformly spaced frequency points taken on the S21 or S11 curve at a certain frequency interval within a preset working frequency band; preferably, the frequency compression features specifically include the starting frequency, intermediate frequency, ending frequency, frequency mean, and frequency variance obtained by compressing frequencies F1, F2,..., F P ; or

[0034] The wavelength compression features include Q wavelength features obtained by compressing wavelengths λ1, λ2,..., λ P ; the wavelengths λ1, λ2,..., λ P are respectively obtained by transforming frequencies F1, F2,..., F P ; preferably, the wavelength compression features specifically include the starting wavelength, intermediate wavelength, ending wavelength, wavelength mean, and wavelength variance obtained by compressing wavelengths λ1, λ2,..., λ PThe minimum wavelength, median wavelength, maximum wavelength, wavelength mean, and wavelength variance obtained by compression. As a non-limiting illustration, P is equal to 1001.

[0035] The preset frequency compression method includes but is not limited to frequency compression using a statistical method, frequency compression using a Fourier transform method, frequency compression using a Fourier series method, or frequency-wavelength conversion method.

[0036] Figure 2 A schematic diagram of a periodic metamaterial according to an embodiment is shown. Figure 3 FIG. 1 is a schematic diagram of defining the concepts of nodes and edges in a microstructure set according to an embodiment. Figure 2 As shown, each metamaterial is a quasi-periodic structure, and the quasi-periodic structure includes a plurality of periodically arranged microstructure sets, each microstructure set includes a plurality of microstructures with similar shapes, the sizes of the plurality of microstructures are all different or partially different, and the distances between every two adjacent microstructures in the plurality of microstructures are all different or partially different; each microstructure in the microstructure set is defined as a node, and the coupling connection between every two adjacent microstructures in the plurality of microstructures is defined as an edge.

[0037] The edge features include the distance d1 between two adjacent microstructures and the angle θ1 between the microstructure polarization response and the defined edge, such as Figure 3 As shown; each electromagnetic response training label includes the corresponding sample metamaterial in F1, F2, ..., F P P S11 and / or S21 values ​​obtained by actual testing or simulation at the frequency.

[0038] The sensitivity analysis in the prior art mechanically forms multiple possible values ​​of the input according to a certain step size, and performs simulation analysis by using permutations and combinations as input, which does not truly and accurately reflect the actual production and manufacturing process.

[0039] With the development of electromagnetic metamaterial technology, the design of electromagnetic microstructures has become more sophisticated, and the impact of uncertainties such as tolerances in the manufacturing process on electromagnetic response has begun to become apparent. This invention can better address the tolerance distribution in actual manufacturing processes. Before the validation dataset is input into the enhanced graph neural network model, the invention can add noise with the same statistical distribution characteristics to the physical dimensions of the node features in the validation dataset, simulating the statistical distribution of measured values ​​generated in the actual manufacturing process. The enhanced graph neural network model can then be used to rapidly evaluate the electromagnetic response.

[0040] The present invention can use tolerance information such as line width and line spacing of microstructures during the manufacturing process (for example, the statistical distribution characteristics of the tolerances of the microstructure's outer ring outer radius, inner ring radius, outer ring inner radius, dielectric thickness, and microstructure unit size) as part of the node features in the enhanced graph neural network. Leveraging the training and learning of electromagnetic responses in the previous training set, this method can quickly assess the electromagnetic response of the resulting impact. This method has a faster iteration cycle than the sensitivity analysis used in the prior art and can quickly assess the electromagnetic response of the statistical distribution characteristics of the tolerances of different physical parameters of the microstructure during the actual manufacturing process.

[0041] Specifically, in this embodiment, the node feature includes a first microstructure physical parameter feature and a frequency compression feature, and the method further includes:

[0042] Using the statistical distribution characteristics of the tolerance of the first microstructure physical parameter in the actual manufacturing process as noise, and adding the noise with the statistical distribution law to the first microstructure physical parameter characteristics respectively, to obtain the second microstructure physical parameter characteristics;

[0043] Inputting the node features, edge codes, and edge features including the second microstructure physical parameter features and the frequency compression features into the target enhanced graph neural network model to obtain evaluated electromagnetic response information;

[0044] Preferably, the first microstructure physical parameter characteristic and the second microstructure physical parameter characteristic both include but are not limited to the outer radius R1 of the outer ring, the inner radius R3 of the inner ring, the inner radius R2 of the outer ring, the dielectric thickness d and the microstructure unit size L, such as Figure 4 shown.

[0045] Preferably, the noise includes but is not limited to white noise or Gaussian noise.

[0046] Figure 5 The specific training flow chart for training the initial enhanced graph neural network model to obtain the target enhanced graph neural network model. Figure 5 As shown, the loss function is a complex domain loss function; Figure 1 Step S2 shown specifically includes:

[0047] Step S21, obtaining a training set and a validation set divided according to a certain ratio, wherein the training set includes multiple groups of metamaterial training samples and multiple groups of electromagnetic response training labels; the validation set includes multiple groups of metamaterial verification samples and multiple groups of electromagnetic response verification labels, and each electromagnetic response verification label corresponds to a metamaterial verification sample;

[0048] Step S23: Input a group of metamaterial training samples and a group of electromagnetic response training labels in the training set into the initial enhanced graph neural network model to be trained to obtain first predicted electromagnetic response information; calculate a first error value using a complex domain loss function based on the first predicted electromagnetic response information and the corresponding electromagnetic response training labels; adjust the parameters of the initial enhanced graph neural network model based on the first error value; and repeat this step until all groups of data in the training set are trained. As a non-limiting illustration, the parameters of the initial enhanced graph neural network model include but are not limited to weights, biases, convolution parameters, etc.

[0049] Step S25: input a group of metamaterial verification samples and a group of electromagnetic response verification labels in the verification set into the adjusted initial enhanced graph neural network model to obtain second predicted electromagnetic response information; calculate a second error value using a complex domain loss function based on the second predicted electromagnetic response information and the corresponding electromagnetic response verification label; save the adjusted initial enhanced graph neural network model when the second error value meets a preset condition; and do not save the adjusted initial enhanced graph neural network model when the second error value does not meet the preset condition; loop through this step until all groups of data in the verification set are verified; each metamaterial verification sample also includes node features, edge codes, and edge features;

[0050] Step S27, taking step S23 and step S25 as one iteration, and looping through step S23 and step S25 until the current number of iterations reaches the total number of iterations, and determining the saved initial enhanced graph neural network model as the trained target enhanced graph neural network model.

[0051] Specifically, the first error value and the second error value are both calculated by the following complex domain loss function Spara_Loss complex To calculate:

[0052]

[0053] Among them, S21 i_complex At frequency F i The electromagnetic transmission response training label of the complex data type under frequency F i are frequencies F1, F2, ..., F P Any one of , 1≤i≤P; First predicted electromagnetic transmission response information of a complex data type; or S21 i_complex At frequency F i Under the Electromagnetic Transmission Response Validation tab, second predicted electromagnetic transmission response information of a complex data type;

[0054] Or the first error value and the second error value are both calculated by the following complex domain loss function Spara_Loss complex To calculate:

[0055]

[0056] Among them, S11 i_complex At frequency F i The electromagnetic reflection response training label of the complex data type is First predicted electromagnetic reflection response information of a complex data type; or S11 i_complex At frequency F i Under the Complex Data Type Electromagnetic Reflection Response Validation tab, second predicted electromagnetic reflection response information of a complex data type;

[0057] P is P uniform or non-uniform frequency points taken on the S21 or S11 curve at a certain frequency interval within the preset working frequency band; as a non-limiting illustration, P is equal to 1001.

[0058]

[0059] Among them, S21 i_real is the real part of the label value of the i-th S21 parameter, is the real part of the predicted value of the i-th S21 parameter; S21 i_imag is the imaginary part of the label value of the i-th S21 parameter, is the imaginary part of the predicted value of the i-th S21 parameter; or

[0060]

[0061] Among them, S11 i_real is the real part of the label value of the i-th S11 parameter, is the real part of the predicted value of the i-th S11 parameter; S11 i_imag is the imaginary part of the label value of the i-th S21 parameter, is the imaginary part of the predicted value of the i-th S11 parameter;

[0062] The real part value and imaginary part value of the label value are respectively the real part value and imaginary part value of the electromagnetic response training label of the training set or the electromagnetic response verification label of the verification set, and the real part value and imaginary part value of the predicted value are respectively the real part value and imaginary part value of the first predicted electromagnetic response information or the second predicted electromagnetic response information.

[0063] The above description describes the design of a loss function in the complex domain. It's worth noting that the electromagnetic response S11 or S21 parameters, used as training labels, are complex numbers. Unlike traditional methods of calculating loss functions, this method directly calculates the difference between the predicted S11 or S21 parameters and the actual S11 or S21 parameters in the complex domain. This calculation method more accurately describes the difference between the two, thus better guiding the training direction of enhanced graph neural network models.

[0064] More specifically, in this embodiment, the node feature is defined as: N is the number of nodes, that is Figure 2 or Figure 3 The number of microstructures in the microstructure set shown; F1 is the number of features in each node, that is, the number of microstructure physical parameter features. Figure 4 As shown, the microstructure physical parameter characteristics include but are not limited to the outer radius R1 of the outer ring, the inner radius R3 of the inner ring, the inner radius R2 of the outer ring, the dielectric thickness d and the microstructure unit size L, that is, the number of microstructure physical parameter characteristics is 5.

[0065] The edge coding is defined as a set of {i, j}; {i, j} represents the edge from node i to node j, and node j is any node adjacent to node i among the N nodes representing the spatial arrangement information of the multiple microstructures; 1≤i≤N, 1≤j≤N; i, j, and N are all natural numbers.

[0066] In a specific embodiment, each metamaterial is a quasi-periodic structure, wherein the quasi-periodic structure includes a plurality of periodically arranged microstructure sets; each microstructure set includes but is not limited to a 3×3 microstructure, a 5×5 microstructure, a 9×9 microstructure, or an 11×11 microstructure; as a non-limiting explanation, Figure 3 The 3×3 microstructures included in each microstructure set are taken as an example for description.

[0067] The edge code is:

[0068]

[0069] The edges between two adjacent nodes represented by the edge code "set of {i, j}" are 1-2, 2-1, 1-4, 4-1, 2-3, 3-2, 2-5, 5-2, 3-6, 6-3, 4-5, 5-4, 4-7, 7-4, 5-6, 6-5, 5-8, 8-5, 6-9, 9-6, 7-8, 8-7, 8-9, 9-8. N = 9; the features contained in each edge include but are not limited to the distance between two adjacent nodes (i.e., the distance d1 between two adjacent microstructures), the angle θ1 between the microstructure polarization response and the defined edge, as shown in Figure 5. Figure 3 shown.

[0070] Specifically, if Figure 2 The schematic diagram of the quasi-periodic metamaterial shown is shown. Each metamaterial is a quasi-periodic structure. The quasi-periodic structure includes multiple microstructure sets arranged periodically. Each microstructure set includes multiple microstructures with similar shapes. The sizes of the multiple microstructures are different or partially different. The distance between each two adjacent microstructures in the multiple microstructures is different or partially different. Each microstructure set includes but is not limited to 3×3 microstructures, 5×5 microstructures, 9×9 microstructures, or 11×11 microstructures. For example, each microstructure set includes 3×3 microstructures. When all 9 microstructures are the same, Figure 4 The outer ring radius R1, inner ring radius R3, outer ring inner radius R2, dielectric thickness d and microstructure unit size L are 3.49mm, 2.00mm, 3.52mm, 0.18mm and 7.18mm respectively. Figure 4 The outer ring outer radius R1, inner ring radius R3, outer ring inner radius R2, dielectric thickness d and microstructure unit size L are shown in the following table.

[0071]

[0072] Furthermore, the initial enhanced graph neural network model includes but is not limited to an input layer, multiple graph attention network convolutional layers, and a decoding layer. For ease of understanding, as a non-limiting illustration, the structure of the initial enhanced graph neural network model of a specific embodiment is as follows: Figure 6 shown.

[0073] Figure 6 The number 10 in the neural input layer of the middle enhancement graph represents five microstructure physical parameter features (i.e., outer radius of the outer ring, inner radius of the inner ring, dielectric thickness, and microstructure unit size) and five frequency compression features (i.e., starting frequency, middle frequency, ending frequency, frequency mean, and frequency variance). Figure 6 The number 2 in the edge encoding of the neural input layer of the enhanced graph represents: the edge encoding is:

[0074]

[0075] The edges between two adjacent nodes represented by the edge code "set of {i, j}" are 1-2, 2-1, 1-4, 4-1, 2-3, 3-2, 2-5, 5-2, 3-6, 6-3, 4-5, 5-4, 4-7, 7-4, 5-6, 6-5, 5-8, 8-5, 6-9, 9-6, 7-8, 8-7, 8-9, 9-8. Correspondingly, Figure 6 The number of edge codes in is 24.

[0076] Figure 6The number 2 in the edge feature of the neural input layer of the enhanced graph represents: the distance d1 between two adjacent microstructures (i.e., nodes), and the angle θ1 between the microstructure polarization response and the defined edge, as shown in Figure 3 shown.

[0077] Figure 6 The number 2 in the decoding layer represents the real and imaginary parts of the predicted electromagnetic response. Figure 2 or Figure 3 The 3×3 microstructure shown is used to illustrate the Figure 6 The number of nodes N in is 9. Figure 6 The total number of convolutional layers in the multiple graph attention networks is 2.

[0078] In one embodiment of the present invention, the input layer of the initial enhanced graph neural network model is {e 1,2 ,...,e i,j ,...,e N,N-1}}, F2 is the number of edge features of adjacent nodes; the output of the previous graph attention network convolutional layer is used as the input of the next graph attention network convolutional layer. Or the input layer of the initial enhanced graph neural network model is Edge encoding "set of {i, j}", {e 1,2 ,...,e i,j ,...,e N,N-1}},

[0079] The training process of the initial enhanced graph neural network model is as follows:

[0080] When the input is passed to the sth graph attention network convolutional layer, the updated node features are obtained

[0081] n s represents the sth layer; 1≤s≤M, M is the total number of convolutional layers of multiple graph attention networks; among them, for the i-th node The calculation formula is as follows:

[0082]

[0083] Where σ is the activation function (activation function includes but is not limited to ELU function), W is the dimension The weight coefficient matrix, h j is the characteristic of any node adjacent to node i among N nodes; a ij Described by the following numerical expression:

[0084]

[0085] Among them, exp represents the exponential function with e as the base, is the characteristic of any node among N nodes, is the characteristic of any node adjacent to node i among the N nodes; Both represent the attention coefficient, Θ represents the convolution parameter; e i,j and e i,k are all feature information of edges; e i,j represents the edge features of adjacent nodes, e i,k Represents all node edge features;

[0086] The decoding layer is used to transform the feature data output by the Mth graph attention network convolutional layer into 2P-dimensional feature data, and the 2P-dimensional feature data is used as P frequency points F1, F2, ..., F P The corresponding real and imaginary values ​​of P predicted electromagnetic response information. The dimension change includes but is not limited to dimension increase. P=1001.

[0087] More specifically, the network structure of the decoding layer is as follows Figure 7 As shown, as a non-limiting explanation, the decoding layer extracts global features from node features and edge features through a multi-layer perceptron to simulate the transformation from the microstructure physical topological parameters of the electromagnetic metamaterial to the constitutive relationship of the electromagnetic response. The 2002-dimensional feature data output by the decoding layer serves as the real and imaginary parts of 1001 S11 or S21 parameters corresponding to 1001 frequency points respectively.

[0088] Please refer to the typical loss function numerical curve in the training process of the enhanced graph neural network model described in the embodiment of the present invention as shown in the technical solution attached. Figure 8 As shown in the figure, after sufficient enhanced graph neural network training, it can be observed that the values ​​of the training set loss function and the validation set loss function basically reach a stable value after a monotonically decreasing state and no longer change.

[0089] Technical solution attached Figure 9 (a), (b) and (c) respectively show the difference between the predicted value and the true value (i.e., label value) of an electromagnetic response S11 parameter in the validation set after the 1st, 21st and 41st rounds of training iterations of the enhanced graph neural network model. Figure 10 (a), (b) and (c) show the difference comparison between the predicted value of another electromagnetic response S21 parameter in the validation set and the true value (i.e., label value) after the 1st, 21st and 41st rounds of training iterations of the enhanced graph neural network model, respectively.

[0090] By the attached Figure 9 and 10It can be seen that for electromagnetic metamaterial microstructures with different electromagnetic response S11 and S21 parameters, the enhanced graph neural network model can give relatively accurate predictions after a certain number of network training iterations, that is, the predicted values ​​of the electromagnetic response S11 or S21 parameters given by the enhanced graph neural network model are slightly different from the true values, and the two are relatively close; the enhanced graph neural network model described in the present invention can better give relatively accurate predictions.

[0091] The beneficial technical effects of the present invention include but are not limited to the following:

[0092] 1. Compared with the prior art, the present invention uses machine learning methods to predict the performance of electromagnetic metamaterials. In the prior art, the electromagnetic response is often only predicted for fully periodic microstructures, that is, for electromagnetic metamaterials with the same physical topology or parameters for each microstructure. However, the enhanced graph neural network model described in the present invention can predict the electromagnetic response for quasi-periodic metamaterials, that is, each metamaterial is a quasi-periodic structure, the quasi-periodic structure includes a plurality of periodically arranged microstructure sets, each microstructure set includes a plurality of microstructures with similar shapes, the sizes of the plurality of microstructures are all different or partially different, the distance between each two adjacent microstructures in the plurality of microstructures is all different or partially different, each microstructure in the microstructure set is defined as a node, and the coupling connection between each two adjacent microstructures in the plurality of microstructures is defined as an edge.

[0093] 2. Compared with the prior art, the present invention uses machine learning methods to predict the performance of electromagnetic metamaterials. In the prior art, only the physical topological parameters of a single microstructure with the same structure in the entire period are input, or the pattern images of multiple or single microstructures are input. However, the present invention not only inputs the physical topological parameters of a single microstructure, but also inputs the adjacent arrangement information of the microstructures, the operating frequency compression information, etc. into the enhanced graph neural network model. In other words, the enhanced graph neural network model is customized and the spatial arrangement information and frequency compression information of the microstructures are both used as inputs with actual physical meaning, thereby transferring physical information to the enhanced graph neural network model to the greatest extent possible.

[0094] 3. Compared with the prior art, the present invention is a method for predicting the electromagnetic response of metamaterials that is manufacturing-oriented. It can modify the input of the enhanced graph neural network model based on the statistical distribution characteristics of tolerances such as line width and line spacing in the actual manufacturing process (such as the tolerance of the outer radius of the outer ring, the radius of the inner ring, the inner radius of the outer ring, the thickness of the medium, and the size of the microstructure unit). It can quickly evaluate the actual impact of the current manufacturing process on the metamaterial design. Specifically, the node features include the first microstructure physical parameter features and the frequency compression features. The method further includes: using the statistical distribution characteristics of the tolerance of the first microstructure physical parameter in the actual manufacturing process as noise, adding the noise of the statistical distribution law to the first microstructure physical parameter features respectively, and obtaining the second microstructure physical parameter features; inputting the node features, edge coding, and edge features including the second microstructure physical parameter features and the frequency compression features into the target enhanced graph neural network model to obtain the evaluation electromagnetic response information.

[0095] 4. Compared to the prior art, the present invention customizes the design of a complex-domain loss function, directly comparing the predicted electromagnetic response value with the labeled electromagnetic response value in the complex domain. Unlike the prior art, which converts the complex-data type electromagnetic response to real numbers before comparison, the present invention fully utilizes the amplitude and phase information of the S11 or S21 parameters in the complex-domain comparison. In the prior art, however, the conversion of the complex-domain electromagnetic response to the real-domain results in phase information loss, making it impossible to more accurately calculate the difference between the predicted and true electromagnetic response values ​​as achieved in the present invention.

[0096] 5. Compared with the prior art, the present invention is that in the modeling of periodic metamaterials, the physical distance dimensions between adjacent microstructures, the coupling relationship between microstructures, the angular relationship between the polarization direction of the microstructure and the horizontal and vertical polarizations, etc. (that is, the distance between two adjacent microstructures included in the edge features, the angle between the polarization response of the microstructure and the defined edge, etc.) can be used as edge feature inputs to enhance the graph neural network model, thereby maximizing the direct input of beneficial and key physical information into the enhanced graph neural network model; unlike the prior art that directly inputs microstructure images, the input information in the prior art has no direct relationship with the physical information.

[0097] 6. Compared with the prior art, the present invention includes a graph attention network convolution layer in the designed enhanced graph neural network model. The global features extracted by the graph attention network convolution layer include both node features (i.e., the physical parameter features of a single microstructure) and edge features (i.e., the coupling relationship features between adjacent microstructures).

[0098] 7. Compared with the prior art, the present invention not only inputs the characteristic information of the physical parameters and spatial arrangement of the electromagnetic metamaterial into the enhanced graph neural network model, but also inputs the frequency compression characteristic information into the enhanced graph neural network model. The frequency compression characteristic includes the frequency F1, F2, ..., F1 using a preset frequency compression method. P The Q frequency features obtained by compression are as follows: The preset frequency compression method includes but is not limited to frequency compression using a statistical method, frequency compression using a Fourier transform method, frequency compression using a Fourier series method, or frequency-wavelength conversion method.

[0099] The innovations of the present invention include but are not limited to the following:

[0100] 1. The innovation of this invention lies in its ability to rapidly evaluate the electromagnetic response of periodic metamaterials. By treating each periodic microstructure within a periodic metamaterial as a single node, the physical parameters of the microstructure can be independently characterized as node features. The coupling relationships between microstructures can be characterized by the edges between nodes. Rapid evaluation of the electromagnetic response of periodic metamaterials is achieved through an enhanced graph neural network model.

[0101] 2. Compared with the comparative document CN202010531141.1, the difference between the present invention and the comparative document CN202010531141.1 is that the present invention uses physical quantities such as microstructure physical parameters and operating frequency as node features, and inputs the adjacent coupling relationship of different microstructures in the quasi-periodic metamaterial into the enhanced graph neural network model as edge features. However, the graph neural network model of the comparative document does not contain any physical meaning, but only approximates the performance characteristics of the n+1th unit based on the distance between the nodes in the knowledge graph, which is essentially different from the enhanced graph neural network model of the present invention that contains actual physical parameter information. Moreover, the comparative document is still limited to the prediction of physical properties of metamaterial periodic structures with exactly the same microstructure, and cannot carry out electromagnetic response prediction for quasi-periodic metamaterial structures.

[0102] 3. The innovation of this invention also lies in its manufacturing-oriented electromagnetic response prediction method for periodic metamaterials. This method uses the statistically derived tolerance distributions of specific metamaterial microstructure parameters, such as line width and line spacing, during the manufacturing process (for example, the statistical distribution characteristics of the tolerances of the microstructure's outer ring outer radius, inner ring radius, outer ring inner radius, dielectric thickness, and microstructure unit size). This distribution probability is then independently applied to the physical parameter inputs in the node features. By enhancing the predictions of the graph neural network model, the impact of these tolerance distributions during the manufacturing process on the final electromagnetic response is estimated. This truly enables manufacturing-oriented electromagnetic response assessment. Unlike sensitivity analysis used in the prior art, this method directly influences the inputs of the enhanced graph neural network model based on the statistical distribution of the different tolerances of various physical parameters of the microstructure during the manufacturing process, and also takes into account the coupling between adjacent microstructures caused by these inputs. Unlike prior sensitivity analysis, which mechanically transforms the input into multiple possible values ​​according to a certain step size and then uses them as inputs for simulation analysis through permutations and combinations, it does not accurately reflect the actual manufacturing process.

[0103] 4. The present invention also personalizes the loss function of the complex data type. The present invention directly calculates the difference between the predicted and actual S11 or S21 parameters in the complex domain, unlike the prior art that converts the electromagnetic response of the complex data type into real numbers before comparison. The present invention directly calculates in the complex domain, not only considering the amplitude information of the S11 or S21 parameters, but also taking into account the phase information of the S11 or S21 parameters. Compared with the prior art, it can more accurately evaluate the difference between the predicted and the actual S11 or S21 parameters (the actual or true S11 or S21 parameters refer to the electromagnetic response as the label value), and better guide the training of the enhanced graph neural network model.

[0104] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A manufacturing-oriented method for predicting the electromagnetic response of periodic metamaterials, characterized in that: include: Step S1: Obtain a set of metamaterial training samples and a set of electromagnetic response training labels, each electromagnetic response training label corresponding to a metamaterial training sample; wherein the microstructures in the metamaterial are defined as nodes, the coupling connection between two adjacent microstructures is defined as edges, and the edge feature represents the electromagnetic coupling relationship between the two adjacent microstructures; each metamaterial training sample includes a node feature, an edge code, and an edge feature; Step S2: iteratively training the initial enhanced graph neural network model to be trained based on the set of metamaterial training samples and the set of electromagnetic response training labels, so as to use a loss function to guide the update of the initial enhanced graph neural network model; and obtaining a target enhanced graph neural network model at the end of the training; Step S3: Input the new metamaterial information into the target enhanced graph neural network model to obtain predicted electromagnetic response information.

2. The method according to claim 1, wherein: The node features include microstructure physical parameter features and frequency compression features, and the microstructure physical parameter features and frequency compression features are used together as inputs to the initial enhanced graph neural network model; or The node features include microstructure physical parameter features and wavelength compression features, which together serve as input to the initial enhanced graph neural network model.

3. The method according to claim 2, wherein: The frequency compression features include using a preset frequency compression method to compress frequencies F1, F2,..., F P to obtain Q frequency features, where Q < P; P is P evenly or unevenly spaced frequency points taken on the S21 or S11 curve at a certain frequency interval within a preset operating frequency band; preferably, the frequency compression features specifically include the starting frequency, intermediate frequency, ending frequency, frequency mean, and frequency variance obtained by compressing frequencies F1, F2,..., F P ; or The wavelength compression characteristics include wavelengths λ1, λ2, ..., λ P The Q wavelength characteristics obtained by compression are the wavelengths λ1, λ2, ..., λ P The frequencies F1, F2, ..., F P Preferably, the wavelength compression characteristics specifically include wavelengths λ1, λ2, ..., λ P The minimum wavelength, median wavelength, maximum wavelength, wavelength mean and wavelength variance obtained by compression; The edge features include the distance between two adjacent microstructures and the angle between the microstructure polarization response and the defined edge; each electromagnetic response training label includes the corresponding sample metamaterial in F1, F2, ..., F P P S11 and / or S21 values ​​obtained by actual testing or simulation at the frequency.

4. The method according to claim 3, wherein: The preset frequency compression method includes frequency compression using a statistical method, frequency compression using a Fourier transform method, frequency compression using a Fourier series method, or frequency-wavelength conversion method.

5. The method according to claim 3, wherein: Each metamaterial is a quasi-periodic structure, which includes a plurality of periodicly arranged microstructure sets, each microstructure set includes a plurality of microstructures with similar shapes, the sizes of the plurality of microstructures are all different or partially different, and the distances between every two adjacent microstructures in the plurality of microstructures are all different or partially different; each microstructure in the microstructure set is defined as a node, and the coupling connection between every two adjacent microstructures in the plurality of microstructures is defined as an edge.

6. The method according to claim 1, characterized in that The node feature includes a first microstructure physical parameter feature and a frequency compression feature, and the method further includes: Using the statistical distribution characteristics of the tolerance of the first microstructure physical parameter in the actual manufacturing process as noise, and adding the noise with the statistical distribution law to the first microstructure physical parameter characteristics respectively, to obtain the second microstructure physical parameter characteristics; Inputting the node features, edge codes, and edge features including the second microstructure physical parameter features and the frequency compression features into the target enhanced graph neural network model to obtain evaluated electromagnetic response information; Preferably, the first microstructure physical parameter characteristic and the second microstructure physical parameter characteristic both include an outer ring outer radius, an inner ring radius, an outer ring inner radius, a dielectric thickness, and a microstructure unit size.

7. The method according to claim 1, characterized in that The loss function is a complex domain loss function; the step S2 specifically includes: Step S21, obtaining a training set and a validation set divided according to a certain ratio, wherein the training set includes multiple groups of metamaterial training samples and multiple groups of electromagnetic response training labels; the validation set includes multiple groups of metamaterial verification samples and multiple groups of electromagnetic response verification labels, and each electromagnetic response verification label corresponds to a metamaterial verification sample; Step S23: Input a set of metamaterial training samples and a set of electromagnetic response training labels in the training set into the initial enhanced graph neural network model to be trained to obtain first predicted electromagnetic response information; calculate a first error value using a complex domain loss function based on the first predicted electromagnetic response information and the corresponding electromagnetic response training labels; adjust the parameters of the initial enhanced graph neural network model based on the first error value; and repeat this step until all groups of data in the training set are trained. Step S25: input a group of metamaterial verification samples and a group of electromagnetic response verification labels in the verification set into the adjusted initial enhanced graph neural network model to obtain second predicted electromagnetic response information; calculate a second error value using a complex domain loss function based on the second predicted electromagnetic response information and the corresponding electromagnetic response verification labels; save the adjusted initial enhanced graph neural network model if the second error value meets a preset condition; and do not save the adjusted initial enhanced graph neural network model if the second error value does not meet the preset condition; and repeat this step until all groups of data in the verification set are verified; Step S27, taking step S23 and step S25 as one iteration, and looping through step S23 and step S25 until the current number of iterations reaches the total number of iterations, and determining the saved initial enhanced graph neural network model as the trained target enhanced graph neural network model.

8. The method according to claim 7, characterized in that The first error value and the second error value are both calculated by the following complex domain loss function Spara_Loss complex To calculate: Among them, S21 i_complex At frequency F i The electromagnetic transmission response training label under the complex data type, the frequency F i are frequencies F1, F2, ..., F P Any one of , 1≤i≤P; First predicted electromagnetic transmission response information of a complex data type; or S21 i_complex At frequency F i Under the Electromagnetic Transmission Response Validation tab, second predicted electromagnetic transmission response information of a complex data type; Or the first error value and the second error value are both calculated by the following complex domain loss function Spara_Loss complex To calculate: Among them, S11 i_complex At frequency F i The electromagnetic reflection response training label of the complex data type is First predicted electromagnetic reflection response information of a complex data type; or S11 i_complex At frequency F i Under the Complex Data Type Electromagnetic Reflection Response Validation tab, second predicted electromagnetic reflection response information of a complex data type; P is P uniform or non-uniform frequency points taken on the S21 or S11 curve at a certain frequency interval within the preset working frequency band; Among them, S21 i_real is the real part of the label value of the i-th S21 parameter, is the real part of the predicted value of the i-th S21 parameter; S21 i_imag is the imaginary part of the label value of the i-th S21 parameter, is the imaginary part of the predicted value of the i-th S21 parameter; or Among them, S11 i_real is the real part of the label value of the i-th S11 parameter, is the real part of the predicted value of the i-th S11 parameter; S11 i_imag is the imaginary part of the label value of the i-th S21 parameter, is the imaginary part of the predicted value of the i-th S11 parameter; The real part value and imaginary part value of the label value are respectively the real part value and imaginary part value of the electromagnetic response training label of the training set or the electromagnetic response verification label of the verification set, and the real part value and imaginary part value of the predicted value are respectively the real part value and imaginary part value of the first predicted electromagnetic response information or the second predicted electromagnetic response information.

9. The method according to claim 5, characterized in that Also includes: The node characteristics are defined as: N is the number of nodes, that is, the number of microstructures in the microstructure set; F1 is the number of features in each node, that is, the number of microstructure physical parameter features; The edge code is defined as a set of {i, j}; {i, j} represents an edge from node i to node j, and node j is any node adjacent to node i among the N nodes representing the spatial arrangement information of the multiple microstructures; 1≤i≤N,1≤j≤N; i, j, and N are all natural numbers.

10. The method according to claim 9, characterized in that Also includes: The initial enhanced graph neural network model includes an input layer, multiple graph attention network convolutional layers and a decoding layer; the input layer of the initial enhanced graph neural network model is F2 is the number of adjacent node edge features; The output of the previous graph attention network convolutional layer serves as the input of the next graph attention network convolutional layer; The training process of the initial enhanced graph neural network model is as follows: When the input is passed to the sth graph attention network convolutional layer, the updated node features are obtained n s represents the sth layer; 1≤s≤M, M is the total number of convolutional layers of multiple graph attention networks; among them, for the i-th node The calculation formula is as follows: Among them, σ is the activation function, W is the dimension The weight coefficient matrix, h j is the characteristic of any node adjacent to node i among N nodes; a ij Described by the following numerical expression: Among them, exp represents the exponential function with e as the base, is the characteristic of any node among N nodes, is the characteristic of any node adjacent to node i among the N nodes; Both represent the attention coefficient, Θ represents the convolution parameter; e i,j and e i,k are all feature information of edges; e i,j represents the edge features of adjacent nodes, e i,k Represents all node edge features; the LeakyReLU activation function is an improved ReLu activation function; The decoding layer is used to transform the feature data output by the Mth graph attention network convolutional layer into 2P-dimensional feature data, and the 2P-dimensional feature data is used as P frequency points F1, F2, ..., F P The corresponding real and imaginary values ​​of the P predicted electromagnetic response information respectively.

11. A computer device comprising a memory and a processor, wherein the memory stores a computer program; When the processor executes the computer program, the steps of the method according to any one of claims 1 to 10 are implemented.

12. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, wherein when the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 10 are implemented.

Images