A construction method of a high-degree-of-freedom metamaterial positive proxy model based on an artificial intelligence operator
The forward proxy model constructed by deep operator networks solves the problems of high computational resource consumption and limited degrees of freedom in traditional frequency-selective surface design, and achieves efficient and accurate electromagnetic response prediction, which is suitable for the rapid design of high-degree-of-freedom metamaterials.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- ZHEJIANG UNIV
- Filing Date
- 2025-11-17
- Publication Date
- 2026-08-04
AI Technical Summary
Traditional frequency selection surface design relies on analytical models and full-wave simulation, which is computationally expensive and has a long design cycle. It is difficult to meet the needs of rapid prediction of high-dimensional complex structures. Moreover, existing models have limited degrees of freedom at high resolution and do not consider frequency characteristics as display input.
A forward proxy model is constructed using the DeepONet deep operator network. Combined with the BranchNet branch network and the TrunkNet backbone network, the electromagnetic response prediction of high-degree-of-freedom metamaterials is achieved through multi-scale spatial feature extraction and nonlinear mapping of frequency points.
It significantly shortens the simulation calculation time, reduces the consumption of computing resources, and achieves efficient and accurate prediction of high-degree-of-freedom metamaterials in the 2-20GHz frequency band, with an average relative error of 0.0478 and a single prediction time of 6ms.
Smart Images
Figure CN121580792B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of electromagnetic metamaterial design technology, and in particular to a method for constructing a high-degree-of-freedom metamaterial forward proxy model based on artificial intelligence operators. Background Technology
[0002] Electromagnetic metamaterials are artificial two-dimensional planar or curved surface structures with longitudinal dimensions much smaller than the wavelength. By adjusting their geometric parameters and arrangement, precise control over the amplitude, phase, polarization, and other characteristics of electromagnetic waves can be achieved. Frequency selective surfaces (FSS), as an extension of electromagnetic metamaterials, are typically two-dimensional planar structures composed of periodic metallic patterns. They are divided into periodic patch type and periodic aperture type, and can exhibit controllable reflection or transmission characteristics for electromagnetic waves of different frequencies, polarization states, and incident angles.
[0003] Traditional FSS design primarily relies on analytical models and full-wave simulation, requiring extensive manual optimization and parameter scanning of structural parameters. This results in high computational costs and long design cycles, making it difficult to meet the rapid prediction needs of high-dimensional and complex structures. In recent years, the rapid development of artificial intelligence has also yielded significant results in areas such as the prediction of metasurface electromagnetic properties. In particular, the widespread application of deep neural networks in forward surrogate modeling can significantly improve modeling speed while maintaining high accuracy, alleviating the problems of high computational resource consumption and limited efficiency of full-wave simulation in traditional design.
[0004] A search revealed that the patent "A Forward Design Method for Metasurface Structural Units Based on Convolutional Neural Networks" (Publication No.: CN116882298A) discloses a forward prediction model for metasurfaces based on convolutional neural networks. This method establishes a mapping between structural parameters and absorption rate response, enabling rapid prediction of metasurface absorption performance and reducing the time consumption of iterative simulation and parameter optimization. While the proposed solution effectively improves the efficiency of electromagnetic performance prediction, its model is based on fixed structural parameter inputs and lacks the ability to express high-dimensional topological degrees of freedom. The patent "A Reverse Design Method for Encoded Metasurfaces Based on Joint Deep Learning and CST Simulation" (Publication No.: CN115270600A) uses a conditional variational autoencoder (CVAE) combined with simulation-generated data to achieve electromagnetic response modeling and design of encoded metasurfaces. Its training and evaluation data are both expressed in the basic form of a 16×16 encoded metasurface matrix, and closed-loop verification is completed in CST simulation, significantly reducing design and computational costs. However, the degrees of freedom of the metasurface structure in the above models are still limited under high-resolution requirements, and the model does not consider using frequency features as explicit input for training.
[0005] With the continuous development of artificial intelligence technology, the application of deep learning models in the electromagnetic field is constantly expanding. In recent years, deep operator networks have emerged, enabling the establishment of nonlinear mappings between input topology and output spectrum at the function space level, providing new technical support for high-degree-of-freedom modeling of frequency-selective surfaces. Therefore, this paper proposes a method for constructing a forward surrogate model of artificial intelligence operators for high-degree-of-freedom topologies, in order to achieve efficient prediction of the electromagnetic response of frequency-selective surfaces. Summary of the Invention
[0006] To address the shortcomings of existing technologies, this invention provides a method for constructing a high-degree-of-freedom metamaterial forward surrogate model based on artificial intelligence operators. The trained forward surrogate model can achieve high-precision electromagnetic response prediction of the frequency-selective surface transmission coefficient within the 2-20GHz operating frequency band.
[0007] To achieve the above objectives, the technical solution provided by the present invention is as follows: A method for constructing a high-degree-of-freedom metamaterial forward surrogate model based on artificial intelligence operators includes the following steps: Step 1: Construct a positive proxy model based on a neural network with DeepONet as its core; Step 2: Use Python in conjunction with HFSS to model and simulate the high degree of freedom metamaterial to obtain several pairs of data samples for training the positive surrogate model. Each pair of data samples includes the topological structure of the high degree of freedom metamaterial and the electromagnetic response values at n corresponding frequency points. Step 3: Using the topology and frequency points of the high-degree-of-freedom metamaterial in the training dataset as input and the electromagnetic response value corresponding to the frequency point as output, train the forward surrogate model until the model converges, completing the training and obtaining the high-degree-of-freedom metamaterial forward surrogate model based on artificial intelligence operators.
[0008] Furthermore, in step 1, the neural network architecture centered on the deep operator network includes a branch network (BranchNet) and a backbone network (TrunkNet): The branch network is used for multi-scale spatial features and adopts the ResNet-18 structure. A Squeeze-and-Excitation attention mechanism is introduced into the residual block of ResNet-18. The backbone network is used to receive inputs from n frequency points and establish a nonlinear mapping relationship between the information of the n frequency points and the corresponding electromagnetic response values. After normalizing the input n frequency points, the network periodically encodes the n frequency points through a sine and cosine embedding mechanism. Feature extraction and nonlinear transformation are performed using a multilayer perceptron. Finally, the high-dimensional features output from the branch network and the backbone network are fused by inner product through a deep operator structure to obtain the predicted electromagnetic response values for the corresponding n frequency points.
[0009] Furthermore, the topological structure of the high-degree-of-freedom metamaterial is input into the branch network, specifically as a binary topological image with pixels divided into 1×128×128. The frequency point information of the high degree of freedom metamaterial is input into the backbone network, specifically as 1×19 frequency sampling points; Specifically, the predicted electromagnetic response values at the n frequency points are the predicted electromagnetic response values at 19 frequency points with an interval of 1 GHz corresponding to the high degree of freedom metamaterial in the range of 2-20 GHz.
[0010] Furthermore, after fusing the high-dimensional features output by the branch network and the backbone network through inner product using a deep operator structure, a Sigmoid activation function is added to limit each electromagnetic response prediction value to the [0,1] interval, so as to ensure consistency with the electromagnetic response value range, eliminate abnormal data, and improve the numerical stability of the output results.
[0011] Furthermore, in step 2, the topology of the high-degree-of-freedom metamaterial is a number of frequency-selective topological units arranged periodically; each frequency-selective topological unit includes an RT5880 dielectric substrate and a perfect electrical conductor disposed on one side surface of the dielectric substrate; the electromagnetic response value is one of the S21 amplitude response value and the S11 amplitude response value.
[0012] Furthermore, the medium substrate is square, with a thickness of 2 mm and a side length of 10 mm.
[0013] Furthermore, each frequency-selective topology unit has a centrally symmetrical structure, consisting of 128×128 pixel units, with the number 1 representing the perfect electrical conductor region and the number 0 representing the dielectric region.
[0014] Furthermore, in step 3, the training dataset is divided into a training set, a test set, and a validation set in an 8:1:1 ratio for model training; The process until the model converges specifically involves calculating the loss using the predicted electromagnetic response values at n frequency points and the electromagnetic response values at those n frequency points, with the loss function employing... , y i Representing the iElectromagnetic response value at each frequency point y i 'representing the first i The model converges when the predicted electromagnetic response values at each frequency point are calculated until the loss value is minimized.
[0015] Furthermore, the optimizer used in the model training process is AdamW, the initial learning rate is set to 0.005, the learning rate scheduling strategy is ReduceLROnPlateau, the batch size is 64, and the activation function is... , x The input value is obtained by linearly combining the output of the previous layer with the weights and biases of the current layer in the neural network.
[0016] The beneficial effects of this invention are as follows: This invention provides a method for constructing a high-degree-of-freedom metamaterial forward surrogate model based on artificial intelligence operators. Compared with the traditional full-wave simulation method, this model significantly shortens the simulation calculation time and reduces the consumption of computing resources.
[0017] The forward proxy model of this invention, combined with artificial intelligence operators, uses frequency as the explicit input. The average relative error on the validation set is 0.0478, and the average single prediction time is 6ms. It achieves efficient and accurate prediction of S21 parameters of high-degree-of-freedom metamaterials in the 2-20GHz frequency band, providing an efficient and feasible technical solution for rapid modeling and intelligent design of complex electromagnetic structures. Attached Figure Description
[0018] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with embodiments of the invention to further explain the invention and do not constitute a limitation thereof.
[0019] Figure 1 This is a training framework for a high-degree-of-freedom metamaterial positive surrogate model based on artificial intelligence operators in an embodiment of the present invention; Figure 2 This is a dataset example for a method of constructing a high-degree-of-freedom metamaterial positive proxy model based on artificial intelligence operators in an embodiment of the present invention; Figure 3 This is a schematic diagram of the Trunk Net subnetwork of a high-degree-of-freedom metamaterial forward proxy model based on artificial intelligence operators in an embodiment of the present invention. Figure 4 This is a schematic diagram of the Branch Net subnetwork of a high-degree-of-freedom metamaterial forward proxy model based on artificial intelligence operators in an embodiment of the present invention. Figure 5To illustrate the training of the positive proxy model in this embodiment of the invention, (a) is a trend graph of the model loss changing with the number of iterations, and (b) is the coefficient of determination (Test R) of the test set. 2 The curve showing how the number of iterations changes; Figure 6 These are test examples of the trained model on the validation set in this embodiment of the invention; Figure 7 This is an operation diagram of the electromagnetic response prediction interface designed in an embodiment of the present invention. Detailed Implementation
[0020] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that those skilled in the art can make various improvements or modifications to the following embodiments without departing from the spirit and essence of the present invention, and all such improvements or modifications shall fall within the protection scope of the present invention.
[0021] like Figure 1 As shown, this invention provides a method for constructing a high-degree-of-freedom metamaterial forward surrogate model based on artificial intelligence operators, comprising the following steps: Step 1: Construct a positive proxy model based on a neural network with DeepONet as its core; Step 2: Use Python in conjunction with HFSS to model and simulate high-degree-of-freedom metamaterials, obtaining 36,216 pairs of data samples. Each pair of data samples includes the topology of the high-degree-of-freedom metamaterial with a resolution of 128×128 and the corresponding S21 curve values of 19 points in the 2-20GHz frequency band with a sampling interval of 1GHz. The data samples are divided into training set, test set and validation set in an 8:1:1 ratio to train the surrogate model. Step 3: Using the topology and frequency points of the high-degree-of-freedom metamaterial in the training dataset as input, and the electromagnetic response value corresponding to the frequency point as output, the output is normalized by the Sigmoid layer, and the forward surrogate model is trained until the model converges, thus completing the training and obtaining the high-degree-of-freedom metamaterial forward surrogate model based on artificial intelligence operators.
[0022] Specifically, the step of "until the model converges" involves calculating the loss by comparing the predicted S21 value output by the positive proxy model with the true S21 value of the topology. The loss function is... ,in y i Representing the i The true value of each data point S21 y i 'representing the first iThe model is trained for 100 iterations. The optimizer is AdamW, the initial learning rate is set to 0.005, the learning rate scheduling strategy is ReduceLROnPlateau, the batch size is 64, and the activation function is... , x The input value is obtained by linearly combining the output of the previous layer with the weights and biases of the current layer in the neural network.
[0023] After training, the topological structure and frequency information of the high-degree-of-freedom metamaterial are input into the network to obtain the high-precision S21 value corresponding to the structure.
[0024] like Figure 2 The image shows a dataset example of a high-degree-of-freedom metamaterial forward proxy model based on artificial intelligence operators provided by the present invention. The topological structure of the high-degree-of-freedom metamaterial is a number of periodically arranged frequency-selective topological units. The frequency-selective topological unit includes an RT5880 dielectric substrate and a perfect electrical conductor disposed on one side surface of the dielectric substrate. The dielectric substrate is square, with a thickness of 2 mm and a side length of 10 mm. The structure of the frequency-selective topological unit is centrally symmetrical and consists of 128×128 pixel units, with the number 1 representing the perfect electrical conductor region and the number 0 representing the dielectric region. Figure 2 The curve on the right is the S21 amplitude curve corresponding to this high-degree-of-freedom metamaterial, with a frequency range of 2-20 GHz and a frequency sampling interval of 1 GHz. In this example, the relative permittivity of the RT5880 dielectric is 2.2.
[0025] like Figure 3 The diagram shows the specific principle of the Trunk Net sub-network of a high-degree-of-freedom metamaterial forward proxy model based on artificial intelligence operators in an embodiment of the present invention: The input is a 1×128×128 FSS topological encoding structure. An improved structure based on the ResNet-18 backbone network is used to effectively extract multi-scale spatial features in the topological structure. An SE-Identity block attention mechanism is introduced after each residual module to enhance the model's attention to key features. The input topological structure first passes through a 7×7 convolutional layer with a stride of 2, and the output feature size becomes 64×64×64; then it passes through a 3×3 max pooling layer, which further downsamples the output feature size to 64×32×32; then it passes through multiple stacked 3×3 convolutional blocks, and the channel dimension is gradually increased to 128, 256 and 512 dimensions, finally obtaining a deep feature representation of size 512×4×4. Through adaptive average pooling, the final 512 features are obtained. Then, further dimensionality reduction is performed in a multilayer perceptron to obtain the feature vector output by the Branch net. b 1, b 2…,b p ].
[0026] like Figure 4 The diagram shown illustrates the specific principle of a Branch Net subnetwork for a high-degree-of-freedom metamaterial forward surrogate model based on artificial intelligence operators in an embodiment of the present invention: the input is the frequency point corresponding to the electromagnetic response curve to be predicted. f The value, using the formula Normalize it, among which f min 2GHz f max The frequency is 20 GHz. Periodic encoding is performed using a sine-cosine embedding mechanism. The encoded vector is then input into a multilayer perceptron module containing three fully connected layers. Each fully connected layer is followed by a ReLU activation function and a Dropout layer. Finally, the output feature vector is obtained through a LayerNorm layer. t 1(y), t 2(y),…, t p [y] is consistent with the output dimension of Branch Net to enable tensor inner product operations.
[0027] like Figure 5 As shown in (a), the model loss gradually converges during the iteration process, and the training process is very stable; Figure 5 (b) shows the coefficient of determination for the test set. R 2 The trend of change with training rounds, where the coefficient of determination is defined as... In the formula It is the actual value. These are model predictions. It is the average of all true values. R 2 The value of ranges from negative infinity to 1, with the closer the value is to 1, the stronger the model's ability to interpret data variations. As can be seen from the graph, in the later stages of training, the model's... R 2 The value has exceeded 0.99, indicating that the model has a good fit.
[0028] Figure 6 The examples shown are test cases of the trained model on the validation set in this embodiment of the invention. The model's average relative error RE on the entire test set of 3621 samples is 0.0478, calculated using the following formula: This is used to quantify the overall degree of agreement between the predicted curve and the actual curve. In this example, k =3621, S i Indicates the firsti The true values of the |S21| parameter of a high-degree-of-freedom metamaterial topology. The corresponding predicted value is shown. In the curve graph on the right, the blue solid line is the true |S21| curve, and the red dots represent the model's predicted values. It can be seen that the predicted results are highly consistent with the true curve, demonstrating the model's excellent fitting and generalization capabilities.
[0029] like Figure 7 As shown, to improve the engineering usability of the model, this invention developed a graphical user interface (GUI) based on the wxPython framework. This interface can load the topology file of the frequency selection unit and automatically call the trained forward surrogate model to perform inference calculations. The system can output the comparison results of the predicted S21 curve in real time and supports saving and exporting the results. On a personal computer, the average prediction time per attempt is approximately 6 ms, significantly improving electromagnetic design efficiency compared to traditional full-wave simulation methods.
[0030] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. For those skilled in the art, various equivalent substitutions or adjustments can be made to the specific structure, network parameters, or implementation methods based on the technical solutions and improvement ideas of the present invention without departing from the spirit and essence of the invention; all such substitutions or adjustments should be considered to fall within the protection scope of the present invention. The embodiments described in this invention are mainly used to illustrate the technical principles and implementation process and are not intended to limit the scope of protection. Where there is no conflict, the various embodiments of the present invention and their technical features can be arbitrarily combined to achieve efficient prediction and design in different application scenarios.
Claims
1. A method for constructing a high-degree-of-freedom metamaterial forward surrogate model based on artificial intelligence operators, characterized in that, Includes the following steps: Step 1: Construct a positive proxy model based on a neural network with DeepONet as its core; Step 2: Model and simulate the high degree of freedom metamaterial to obtain several pairs of data samples. Each pair of data samples includes the topological structure of the high degree of freedom metamaterial and the electromagnetic response values at n corresponding frequency points, which are used as training datasets. Step 3: Using the topology and frequency points of the high-degree-of-freedom metamaterial in the training dataset as input and the electromagnetic response value corresponding to the frequency point as output, train the forward surrogate model until the model converges, complete the training, and obtain the high-degree-of-freedom metamaterial forward surrogate model based on artificial intelligence operators. In step 1, the neural network architecture centered on the deep operator network includes a branch network (Branch Net) and a trunk network (Trunk Net): The branch network is used to extract multi-scale spatial features in the topology. It adopts the ResNet-18 structure and introduces the Squeeze-and-Excitation attention mechanism in the residual block of ResNet-18. The backbone network is used to receive inputs from n frequency points and establish a nonlinear mapping relationship between the information of the n frequency points and the corresponding electromagnetic response values. After normalizing the input n frequency points, the network periodically encodes the n frequency points through a sine and cosine embedding mechanism. Feature extraction and nonlinear transformation are performed using a multilayer perceptron. Finally, the high-dimensional features output from the branch network and the backbone network are fused by inner product through a deep operator structure to obtain the predicted electromagnetic response values for the corresponding n frequency points.
2. The method for constructing a high-degree-of-freedom metamaterial forward surrogate model based on artificial intelligence operators according to claim 1, characterized in that, The topological structure of the high degree of freedom metamaterial is input into the branch network, specifically a binary topological image with pixels divided into 1×128×128; The frequency point information of the high degree of freedom metamaterial is input into the backbone network, specifically as 1×19 frequency sampling points; Specifically, the predicted electromagnetic response values at the n frequency points are the predicted electromagnetic response values at 19 frequency points with an interval of 1 GHz corresponding to the high degree of freedom metamaterial in the range of 2-20 GHz.
3. The method for constructing a high-degree-of-freedom metamaterial forward surrogate model based on artificial intelligence operators according to claim 1, characterized in that, After fusing the high-dimensional features output by the branch network and the backbone network through inner product using a deep operator structure, a Sigmoid activation function is added to limit each electromagnetic response prediction value to the [0,1] interval.
4. The method for constructing a high-degree-of-freedom metamaterial forward surrogate model based on artificial intelligence operators according to claim 1, characterized in that, In step 2, the topology of the high-degree-of-freedom metamaterial is a number of frequency-selective topological units arranged periodically; each frequency-selective topological unit includes an RT5880 dielectric substrate and a perfect electrical conductor disposed on one side surface of the dielectric substrate; the electromagnetic response value is one of the S21 amplitude response value and the S11 amplitude response value.
5. The method for constructing a high-degree-of-freedom metamaterial forward surrogate model based on artificial intelligence operators according to claim 4, characterized in that, The medium substrate is square, with a thickness of 2 mm and a side length of 10 mm.
6. The method for constructing a high-degree-of-freedom metamaterial forward surrogate model based on artificial intelligence operators according to claim 4, characterized in that, Each frequency-selective topology unit has a centrally symmetrical structure, consisting of 128×128 pixel units, with the number 1 representing the perfect electrical conductor region and the number 0 representing the dielectric region.
7. The method for constructing a high-degree-of-freedom metamaterial forward surrogate model based on artificial intelligence operators according to claim 1, characterized in that, In step 3, the training dataset is divided into a training set, a test set, and a validation set in an 8:1:1 ratio for model training. The process until the model converges specifically involves calculating the loss using the predicted electromagnetic response values at n frequency points and the electromagnetic response values at those n frequency points. The loss function adopts... y i y represents the electromagnetic response value at the i-th frequency point. i ' represents the predicted electromagnetic response value at the i-th frequency point. The model converges when the loss value is reduced to the minimum.
8. The method for constructing a high-degree-of-freedom metamaterial forward surrogate model based on artificial intelligence operators according to claim 1, characterized in that, The optimizer used in the model training process is AdamW, with an initial learning rate of 0.005, a learning rate scheduling strategy of ReduceLROnPlateau, a batch size of 64, and an activation function of [function name missing]. x is the input value obtained by linearly combining the output of the previous layer and the weights and biases of the current layer in the neural network.