A multi-fidelity deep learning model construction method, medium, equipment and application for super surface electromagnetic property estimation

Abstract

This invention belongs to the field of electronic information technology and discloses a method, medium, device, and application for constructing a multi-fidelity deep learning model for estimating the electromagnetic properties of metasurfaces. The method involves dividing the parameter space of the structural parameter vector of the metasurface to be estimated into multiple subsets, such that the parameter spaces corresponding to each subset are sequentially adjacent but do not overlap. Each subset is assigned a positive integer index value starting from 1. Within each subset, the high-fidelity electromagnetic response corresponding to the structural parameter vector is calculated using the finite element method, with the structural parameter vector as input and the high-fidelity electromagnetic response as output, forming a first-class training sample set. Within each subset, an adjoint fully connected deep learning model and a multi-fidelity deep learning model are constructed, and the adjoint fully connected deep learning model is trained using the first-class training sample set. For each subset with an index not equal to 1, the corresponding index of that subset is... The structure parameter vector in the first training sample set is used as the input to the accompanying fully connected deep learning model in the previous subset. The output of the accompanying fully connected deep learning model in the previous subset is regarded as the low-fidelity electromagnetic response of the current subset. The structure parameter vector and the low-fidelity electromagnetic response in the current subset are regarded as inputs, and the high-fidelity electromagnetic response is regarded as outputs, forming a second training sample set. In each subset with an index not equal to 1, a multi-fidelity deep learning model is trained using the second training sample set. The multi-fidelity deep learning model obtained by this invention can accurately estimate the electromagnetic properties of metasurfaces. Moreover, in order to achieve the same estimation accuracy performance index, compared with the ordinary deep learning model that only uses high-fidelity training samples, the multi-fidelity deep learning model can reduce the computational cost of calculating the high-fidelity electromagnetic response using the finite element method by 30%.

Description

Technical Field

[0001] This invention belongs to the field of electronic information technology, and in particular relates to a method, medium, device and application for constructing a multi-fidelity deep learning model for estimating the electromagnetic properties of metasurfaces. Background Technology

[0002] Currently, estimating the electromagnetic properties of metasurfaces using deep learning is a widely studied problem, encompassing fields such as wireless communication and electromagnetic simulation. A major research trend in estimating the electromagnetic properties of metasurfaces using deep learning is to improve the accuracy and efficiency of the estimation process. However, the use of multi-fidelity deep learning models has been less studied in terms of improving the accuracy and efficiency of the estimation process.

[0003] When using deep learning to estimate the electromagnetic properties of metasurfaces, the accuracy and efficiency of the model's estimation are typically determined by two key factors: the computational cost of building and training the model, and the deep learning model's ability to extract features from the data. Regarding the first factor, a higher computational cost generally leads to lower efficiency in estimating electromagnetic properties. This computational cost is typically manifested in two ways: first, the time spent performing precise numerical calculations when building a high-fidelity deep learning model's training sample set; and second, the necessary size of the training sample set for training the deep learning model. Regarding the second factor, a stronger ability to extract features results in higher accuracy and efficiency for the model. The ability to extract features usually depends on the type of forward operations performed by the model and the model's structure.

[0004] Generally, while using only high-fidelity training datasets can indeed yield deep learning models capable of accurately estimating the electromagnetic properties of metasurfaces, as mentioned earlier, training the model using only high-fidelity samples introduces excessive overhead when constructing the training dataset, thus reducing the efficiency of the deep learning model. Conversely, reducing the size of the training dataset to improve efficiency negatively impacts the accuracy of the deep learning model. This invention addresses this issue from a multi-fidelity perspective, using a method that combines high-fidelity and low-fidelity data to train a deep learning model. Furthermore, it constructs a deep learning model capable of simultaneously extracting and fusing features from both high-fidelity and low-fidelity training samples.

[0005] While low-fidelity training samples don't characterize the electromagnetic response as precisely as high-fidelity training samples, they can provide a rough representation. For example, they can depict the approximate pattern of the electromagnetic response's frequency variation and its general frequency band. These rough data patterns provide preliminary information for deep learning models, allowing multi-fidelity deep learning models to achieve better electromagnetic response estimation accuracy with fewer high-fidelity samples. Considering that obtaining high-fidelity samples using the finite element method is very time-consuming, models that utilize both high-fidelity and low-fidelity training samples can improve the efficiency of electromagnetic response estimation.

[0006] Based on the above analysis, the problems and defects of the existing technology are as follows: the current deep learning model structure can only extract features from high-fidelity training samples of metasurfaces. The training of such models can only use high-fidelity samples of metasurfaces, which makes the electromagnetic response estimation accuracy of such models low and the efficiency low.

[0007] The difficulty in solving the above problems and defects lies in the fact that, in order to utilize both low-fidelity and high-fidelity training samples simultaneously, a dedicated deep learning model needs to be constructed to extract and fuse features from the low-fidelity and high-fidelity training samples to estimate the electromagnetic properties of the metasurface. At the same time, in order to avoid using time-consuming methods such as the finite element method to obtain high-fidelity samples, the acquisition of low-fidelity samples cannot be done using methods such as the finite element method.

[0008] The significance of solving the above problems and defects is that the multi-fidelity deep learning model constructed in this invention can improve the accuracy of metasurface electromagnetic response estimation while keeping the size of the training sample set unchanged; or, in order to achieve specific electromagnetic response estimation performance, it can reduce the requirement for the size of the training sample set, thereby improving the estimation efficiency. Summary of the Invention

[0009] To address the problems existing in the prior art, this invention provides a method, medium, device, and application for constructing a multi-fidelity deep learning model for estimating the electromagnetic properties of metasurfaces.

[0010] This invention is implemented as follows: a method for constructing a multi-fidelity deep learning model for estimating the electromagnetic properties of metasurfaces, the method comprising:

[0011] The parameter space containing the structural parameter vector of the metasurface to be estimated is divided into multiple subsets, such that the parameter spaces corresponding to each subset are sequentially adjacent but do not overlap, and each subset is sequentially assigned a positive integer index value starting from 1.

[0012] In each subset, the high-fidelity electromagnetic response corresponding to the structural parameter vector is calculated using the finite element method. The structural parameter vector is regarded as the input and the high-fidelity electromagnetic response is regarded as the output, and the two are paired to form the first type of training sample set.

[0013] In each subset, construct an adjoint fully connected deep learning model and a multifidelity deep learning model, and train the adjoint fully connected deep learning model using the first type of training sample set;

[0014] For each subset whose index is not 1, the structure parameter vector in the first type of training sample set corresponding to the subset is used as the input of the accompanying fully connected deep learning model in the previous subset, the output of the accompanying fully connected deep learning model in the previous subset is regarded as the low-fidelity electromagnetic response of the current subset, the structure parameter vector and the low-fidelity electromagnetic response in the current subset are regarded as input, and the high-fidelity electromagnetic response is regarded as output, and they are paired to form the second type of training sample set;

[0015] In each subset where the index is not 1, a multi-fidelity deep learning model is trained using the second type of training sample set.

[0016] Furthermore, the method for constructing a multi-fidelity deep learning model for estimating the electromagnetic properties of metasurfaces specifically includes the following steps:

[0017] The first step is to sample a metasurface structure of size n in a given parameter space using a uniform sampling method. The parameter vector corresponding to the metasurface structure can be represented by a set X = {x1, x2, ..., xn}. n}express;

[0018] The second step is to divide the set X into N subsets X = {X1, X2, ..., X...} N The parameter spaces of each subset are sequentially adjacent but do not overlap, and the sizes of the N subsets are denoted as s1, s2, ..., s. N ;

[0019] The third step is to consider any subset X. i (1≤i≤N), calculate set X using the finite element method. i Each vector x in ij (1≤j≤s i The corresponding high-fidelity electromagnetic property vector z of the metasurface ij , obtain the set

[0020] Fourth step, for any subset X i (1≤i≤N), set X i The structural parameter vector in the set Z is taken as input. iThe high-fidelity electromagnetic property vector is regarded as the output, and the first type of training sample set is constructed.

[0021] Fifth step, in each subset X i In (1≤i≤N), construct an adjoint fully connected deep learning model ADFC. i A multifidelity deep learning model MFNN i ;

[0022] Step 6, in each subset X i In (1≤i≤N), the first type of training sample set is used. Training accompanied by fully connected deep learning model ADFC i ;

[0023] Step 7: In each subset X with an index not equal to 1 i In (2≤i≤N), X i The structural parameter vector in the ADFC is used as the ADFC. i-1 The input is used to calculate the set X. i Each vector x in ij (1≤j≤s i The low-fidelity electromagnetic property vector y corresponding to the metasurface ij , obtain the set

[0024] Step 8: In each subset X with an index not equal to 1 i In (2≤i≤N), set X i The structural parameter vector and set Y in i The low-fidelity electromagnetic property vector in the set Z is taken as input. i The high-fidelity electromagnetic characteristic vector in the middle is regarded as the output, and the second type of training sample set is constructed.

[0025] Step 9: In each subset X with an index not equal to 1 i In (2≤i≤N), the second type of training sample set is used. Training a multi-fidelity deep learning model MFNN i ;

[0026] Step 10: For any subset X i When i=1, use ADFC i To estimate the electromagnetic properties of a metasurface, when i ≠ 1, use MFNN. i Estimate the electromagnetic properties of metasurfaces.

[0027] Furthermore, the ADFC model construction method for the multi-fidelity deep learning model construction method for estimating the electromagnetic properties of metasurfaces includes:

[0028] Step 1: Construct M fully connected layers FC1, FC2, ..., FC M M-1 batch normalized layers BN1, BN2, ..., BN M-1 M-1 activation layers RE1, RE2, ..., RE M-1 And an output layer OC that uses the Sigmoid function;

[0029] Step 2: Set FC1 as the first layer of ADFC, and FC1 is responsible for receiving x from the first type of training sample set;

[0030] Step 3: Configure the fully connected layer, batch normalized layer, activation layer, and output layer according to {FC1, BN1, RE1, FC2, ..., FC...} M The layers OC are connected in the order of OC, with the output of the previous layer serving as the input of the next layer.

[0031] Step 4: Set the electromagnetic properties of the metamaterial output by the OC layer neurons. The output of the OC layer neurons is the output of the ADFC model.

[0032] Furthermore, the MFNN model construction method for the multi-fidelity deep learning model construction method for estimating the electromagnetic properties of metasurfaces includes:

[0033] Step 1: Construct K fully connected layers K-1 batch normalization layers K-1 activation layers

[0034] Step 2, settings This is the first layer of the first branch of the MFNN network. Responsible for receiving x from the second type of training sample set;

[0035] Step 3: Arrange the K fully connected layers, K-1 batch normalized layers, and K-1 activation layers according to... The layers are connected sequentially, with the output of the previous layer serving as the input of the next layer.

[0036] Step 4: Construct L fully connected layers L-1 batch normalization layers L-1 activation layers

[0037] Step 5, Settings This is the first layer of the second branch of the MFNN network. Responsible for receiving y from the second type of training sample set;

[0038] Step 6: Arrange the L fully connected layers, L-1 batch normalized layers, and L-1 activation layers according to... The layers are connected sequentially, with the output of the previous layer serving as the input of the next layer.

[0039] Step 7: Construct an output layer OC that uses the Sigmoid function. Output and The outputs are summed and used as the input to the OC layer, and the output of the OC layer is the output of the MFNN model.

[0040] Furthermore, the ADFC model training method for the multi-fidelity deep learning model construction method for estimating the electromagnetic properties of metasurfaces includes:

[0041] Step 1: Take the x samples from the first training sample set as input to the ADFC model in turn, and use the ADFC model to perform forward propagation on the samples. For any x, obtain the floating-point numerical vector z′ generated by the output node neuron.

[0042] Step 2: Based on the floating-point numerical vector z′ and z in the first type of training sample set, calculate the loss function value l of the ADFC model using the mean squared error loss function;

[0043] Step 3: Calculate the gradient G corresponding to the trainable parameters in the ADFC model based on the loss function value l, and update the parameters in the ADFC model using gradient descent based on the gradient G.

[0044] Step 4: Repeat steps 1 to 3 to complete the training of the ADFC model.

[0045] Furthermore, the MFNN model training method for the multi-fidelity deep learning model construction method for estimating the electromagnetic properties of metasurfaces includes:

[0046] Step 1: Take the x and y samples from the second type of training sample set as input to the MFNN model in turn, and use the MFNN model to perform forward propagation on the samples. For any set of x and y, obtain the floating-point numerical vector z′ generated by the output node neuron.

[0047] Step 2: Based on the floating-point numerical vector z′ and z in the second type of training sample set, calculate the loss function value l of the MFNN model using the mean squared error loss function;

[0048] Step 3: Calculate the gradient G corresponding to the trainable parameters in the MFNN model based on the loss function value l, and update the parameters in the MFNN model using gradient descent based on the gradient G.

[0049] Step 4: Repeat steps 1 to 3 to complete the training of the MFNN model.

[0050] Another object of the present invention is to provide a computer device including a memory and a processor, the memory storing a computer program, which, when executed by the processor, causes the processor to perform the multi-fidelity deep learning model construction method for estimating the electromagnetic properties of metasurfaces.

[0051] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the method for constructing a multi-fidelity deep learning model for estimating the electromagnetic properties of metasurfaces.

[0052] Another objective of this invention is to provide an information data processing terminal, which is used to implement the multi-fidelity deep learning model construction method for estimating the electromagnetic properties of metasurfaces. The information data processing terminal includes: a wireless communication terminal and an electromagnetic simulation terminal.

[0053] The multi-fidelity deep learning model construction method was tested using a double-layer complementary transmissive metasurface structure. Compared to a conventional deep learning model trained only with a high-fidelity training sample set, the multi-fidelity deep learning model can achieve the same electromagnetic response estimation accuracy using only 70% of the high-fidelity training samples without introducing additional time-consuming numerical calculations based on methods such as finite element method. The size of its training sample set and the mean square error performance of the corresponding conventional or multi-fidelity deep learning models are shown in the attached figure. Figure 7 As shown in the figure, the dashed line represents the mean squared error performance of the deep learning model when only high-fidelity training samples are used, and the solid line represents the mean squared error performance of the multi-fidelity deep learning model. The lower the mean squared error value, the better the model's performance. Attached Figure Description

[0054] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the embodiments of this application will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0055] Figure 1 This is a flowchart of a method for constructing a multi-fidelity deep learning model for estimating the electromagnetic properties of metasurfaces, provided in an embodiment of the present invention.

[0056] Figure 2 This is a flowchart of the construction method of the ADFC fully connected deep learning model provided in the embodiment of the present invention;

[0057] Figure 3This is a flowchart of the construction method of the multi-fidelity deep learning model MFNN provided in the embodiments of the present invention;

[0058] Figure 4 This is a flowchart of the accompanying fully connected deep learning model training method provided in the embodiments of the present invention;

[0059] Figure 5 This is a flowchart of the multi-fidelity deep learning model training method provided in the embodiments of the present invention;

[0060] Figure 6 This is a scatter plot of the mean square error performance of the ordinary model and the multi-fidelity deep learning model provided in the embodiments of the present invention when estimating the electromagnetic response of a metasurface;

[0061] Figure 7 This is a mean squared error performance curve provided by an embodiment of the present invention, which shows the mean squared error performance curves that can be obtained when a regular model and the multi-fidelity deep learning model are trained using the same percentage of training sample set data. Detailed Implementation

[0062] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0063] To address the problems existing in the prior art, this invention provides a method, medium, device, and application for constructing a multi-fidelity deep learning model for estimating the electromagnetic properties of metasurfaces. The invention will be described in detail below with reference to the accompanying drawings.

[0064] like Figure 1 As shown, the method for constructing a multi-fidelity deep learning model for estimating the electromagnetic properties of metasurfaces provided by this invention includes the following steps:

[0065] S101: Divide the parameter space containing the structural parameter vector of the metasurface to be estimated into multiple subsets, such that the parameter spaces corresponding to each subset are adjacent but do not overlap, and assign positive integer index values ​​starting from 1 to each subset in sequence.

[0066] S102: In each subset, the high-fidelity electromagnetic response corresponding to the structural parameter vector is calculated using the finite element method. The structural parameter vector is regarded as the input and the high-fidelity electromagnetic response is regarded as the output. The samples are paired to form the first type of training sample set.

[0067] S103: In each subset, construct an adjoint fully connected deep learning model and a multifidelity deep learning model, and train the adjoint fully connected deep learning model using the first type of training sample set.

[0068] S104: For each subset whose index is not 1, the structure parameter vector in the first type of training sample set corresponding to the subset is used as the input of the accompanying fully connected deep learning model in the previous subset, the output of the accompanying fully connected deep learning model in the previous subset is regarded as the low-fidelity electromagnetic response of the current subset, the structure parameter vector and the low-fidelity electromagnetic response in the current subset are regarded as input, and the high-fidelity electromagnetic response is regarded as output, and they are paired to form the second type of training sample set;

[0069] S105: In each subset where the index is not 1, train a multi-fidelity deep learning model using the second type of training sample set.

[0070] The method for constructing a multi-fidelity deep learning model for estimating the electromagnetic properties of metasurfaces provided in this invention can also be implemented by those skilled in the art using other steps. Figure 1 The method for constructing a multi-fidelity deep learning model for estimating the electromagnetic properties of metasurfaces provided by this invention is merely a specific embodiment.

[0071] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0072] The method for constructing a multi-fidelity deep learning model for estimating the electromagnetic properties of metasurfaces provided by this invention specifically includes the following steps:

[0073] The first step is to sample a metasurface structure of size n in a given parameter space using a uniform sampling method. The parameter vector corresponding to the metasurface structure can be represented by a set X = {x1, x2, ..., xn}. n}express;

[0074] The second step is to divide the set X into N subsets X = {X1, X2, ..., X...} M The parameter spaces of each subset are sequentially adjacent but do not overlap, and the sizes of the N subsets are denoted as s1, s2, ..., s. N ;

[0075] The third step is to consider any subset X. i (1≤i≤N), calculate set X using the finite element method. i Each vector x in ij (1≤j≤s i The corresponding high-fidelity electromagnetic property vector z of the metasurface ij , obtain the set

[0076] Fourth step, for any subset X i (1≤i≤N), set X i The structural parameter vector in the set Z is taken as input.i The high-fidelity electromagnetic property vector is regarded as the output, and the first type of training sample set is constructed.

[0077] Fifth step, in each subset X i In (1≤i≤N), construct an adjoint fully connected deep learning model ADFC. i A multifidelity deep learning model MFNN i ;

[0078] Step 6, in each subset X i In (1≤i≤N), the first type of training sample set is used. Training accompanied by fully connected deep learning model ADFC i ;

[0079] Step 7: In each subset X with an index not equal to 1 i In (2≤i≤N), X i The structural parameter vector in the ADFC is used as the ADFC. i-1 The input is used to calculate the set X. i Each vector x in ij (1≤j≤s i The low-fidelity electromagnetic property vector y corresponding to the metasurface ij , obtain the set

[0080] Step 8: In each subset X with an index not equal to 1 i In (2≤i≤N), set X i The structural parameter vector and set Y in i The low-fidelity electromagnetic property vector in the set Z is taken as input. i The high-fidelity electromagnetic characteristic vector in the middle is regarded as the output, and the second type of training sample set is constructed.

[0081] Step 9: In each subset X with an index not equal to 1 i In (2≤i≤N), the second type of training sample set is used. Training a multi-fidelity deep learning model MFNN i ;

[0082] Step 10: For any subset X i When i=1, use ADFC i To estimate the electromagnetic properties of a metasurface, when i ≠ 1, use MFNN. i Estimate the electromagnetic properties of metasurfaces.

[0083] like Figure 2As shown, the ADFC model construction method provided in this embodiment of the invention includes:

[0084] Step 1: Construct M fully connected layers FC1, FC2, ..., FC M M-1 batch normalized layers BN1, BN2, ..., BN M-1 M-1 activation layers RE1, RE2, ..., RE M-1 And an output layer OC that uses the Sigmoid function;

[0085] Step 2: Set FC1 as the first layer of ADFC, and FC1 is responsible for receiving x from the first type of training sample set;

[0086] Step 3: Configure the fully connected layer, batch normalized layer, activation layer, and output layer according to {FC1, BN1, RE1, FC2, ..., FC...} M The layers OC are connected in the order of OC, with the output of the previous layer serving as the input of the next layer.

[0087] Step 4: Set the electromagnetic properties of the metamaterial output by the OC layer neurons. The output of the OC layer neurons is the output of the ADFC model.

[0088] like Figure 3 As shown, the MFNN model construction method provided in this embodiment of the invention includes:

[0089] Step 1: Construct K fully connected layers K-1 batch normalization layers K-1 activation layers

[0090] Step 2, settings This is the first layer of the first branch of the MFNN network. Responsible for receiving x from the second type of training sample set;

[0091] Step 3: Arrange the K fully connected layers, K-1 batch normalized layers, and K-1 activation layers according to... The layers are connected in sequence, with the output of the previous layer serving as the input of the next layer.

[0092] Step 4: Construct L fully connected layers L-1 batch normalization layers L-1 activation layers

[0093] Step 5, Settings This is the first layer of the second branch of the MFNN network. Responsible for receiving y from the second type of training sample set;

[0094] Step 6: Arrange the L fully connected layers, L-1 batch normalized layers, and L-1 activation layers according to... The layers are connected sequentially, with the output of the previous layer serving as the input of the next layer.

[0095] Step 7: Construct an output layer OC that uses the Sigmoid function. Output and The outputs are summed and used as the input to the OC layer, and the output of the OC layer is the output of the MFNN model.

[0096] like Figure 4 As shown, the ADFC model training method provided in this embodiment of the invention includes:

[0097] Step 1: Take the x samples from the first training sample set as input to the ADFC model in turn, and use the ADFC model to perform forward propagation on the samples. For any x, obtain the floating-point numerical vector z′ generated by the output node neuron.

[0098] Step 2: Based on the floating-point numerical vector z′ and z in the first type of training sample set, calculate the loss function value l of the ADFC model using the mean squared error loss function;

[0099] Step 3: Calculate the gradient G corresponding to the trainable parameters in the ADFC model based on the loss function value l, and update the parameters in the ADFC model using gradient descent based on the gradient G.

[0100] Step 4: Repeat steps 1 to 3 to complete the training of the ADFC model.

[0101] like Figure 5 As shown, the MFNN model training method provided in this embodiment of the invention includes:

[0102] Step 1: Take the x and y samples from the second type of training sample set as input to the MFNN model in turn, and use the MFNN model to perform forward propagation on the samples. For any set of x and y, obtain the floating-point numerical vector z′ generated by the output node neuron.

[0103] Step 2: Based on the floating-point numerical vector z′ and z in the second type of training sample set, calculate the loss function value l of the MFNN model using the mean squared error loss function;

[0104] Step 3: Calculate the gradient G corresponding to the trainable parameters in the MFNN model based on the loss function value l, and update the parameters in the MFNN model using gradient descent based on the gradient G.

[0105] Step 4: Repeat steps 1 to 3 to complete the training of the MFNN model.

[0106] The technical effects of the present invention will be described in detail below with reference to specific embodiments.

[0107] Example 1:

[0108] Take a two-layer complementary transparent metasurface structure as an example. The bottom surface of this structure is coated with a square-ring-shaped copper layer, and the top surface is also coated with copper, but its shape is complementary to the bottom surface. A dielectric layer with a relative permittivity of 1.1 and a relative permeability of 1 is filled between the bottom and top metal layers. A total of 2500 metasurface structures were collected using a random sampling method to construct the dataset. For the first type of training sample set, there are 2000 metasurface structure parameter vectors and 2000 high-fidelity electromagnetic responses obtained using the finite element method. The remaining metasurface structures and their electromagnetic responses are used to test the performance of the deep learning model. For the second type of training sample set, there are 2000 metasurface structure parameter vectors and 2000 high-fidelity electromagnetic responses obtained using the finite element method, as well as 2000 low-fidelity electromagnetic responses generated using the ADFC model. The remaining metasurface structures and their electromagnetic responses are used to test the performance of the deep learning model. The finite element method is not required when generating the low-fidelity electromagnetic responses using ADFC. A multi-fidelity model is constructed using the aforementioned multi-fidelity deep learning method for estimating the electromagnetic properties of metasurfaces. For both the structural parameter vector and the low-fidelity electromagnetic response, four fully connected layers and other supporting layers are used for feature extraction. The extracted features are then fused and output. For a typical deep learning model using only a high-fidelity training dataset, four fully connected layers and other supporting layers are used for feature extraction and output.

[0109] Figure 6 The average mean square error of the ordinary model and the multi-fidelity deep learning model in estimating the electromagnetic response of the metasurface is shown, and 120 samples are randomly selected to show their mean square error. For the scatter points in the figure, the horizontal axis is the index of the randomly selected sample, the vertical axis is the mean square error, and the straight line in the figure represents the average mean square error of the test sample set. Figure 7 The figure illustrates the mean squared error performance of the standard model and the multi-fidelity deep learning model when using the same percentage of data. The horizontal axis represents the percentage of data samples used during training relative to the total training dataset, and the vertical axis represents the mean squared error of the electromagnetic response estimation of the trained model on the test sample set. The figure shows that the multi-fidelity model can achieve the same performance as the standard model using only 70% of the training data, indicating that the multi-fidelity model has higher estimation efficiency.

[0110] It should be noted that embodiments of the present invention can be implemented in hardware, software, or a combination of both. The hardware portion can be implemented using dedicated logic; the software portion can be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or dedicated-design hardware. Those skilled in the art will understand that the above-described devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuitry such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field-programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of the above-described hardware circuitry and software, such as firmware.

[0111] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for constructing a multi-fidelity deep learning model for estimating the electromagnetic properties of metasurfaces, characterized in that, The method for constructing a multi-fidelity deep learning model for estimating the electromagnetic properties of metasurfaces includes: The parameter space containing the structural parameter vectors of the metasurface to be estimated is divided into multiple subsets, such that the parameter spaces corresponding to each subset are sequentially adjacent but do not overlap. Each subset is assigned a positive integer index value starting from 1, corresponding to the first and second steps: The first step is to sample a metasurface structure of size n in a given parameter space using a uniform sampling method. The parameter vector corresponding to the metasurface structure can be represented by a set X = {x1, x2, ..., xn}. n }express; The second step is to divide the set X into N subsets X = {X1, X2, ..., X...} M The parameter spaces of each subset are sequentially adjacent but do not overlap, and the sizes of the N subsets are denoted as s1, s2, ..., s. N ; In each subset, the high-fidelity electromagnetic response corresponding to the structural parameter vector is calculated using the finite element method. The structural parameter vector is treated as input, and the high-fidelity electromagnetic response is treated as output. These are paired to form the first type of training sample set, corresponding to steps three and four: The third step is to consider any subset X. i (1≤i≤N), calculate set X using the finite element method. i Each vector x in ij (1≤j≤s i The corresponding high-fidelity electromagnetic property vector z of the metasurface ij , obtain the set Fourth step, for any subset X i (1≤i≤N), set X i The structural parameter vector in the set Z is taken as input. i The high-fidelity electromagnetic property vector is regarded as the output, and the first type of training sample set is constructed. In each subset, construct a companion fully connected deep learning model and a multi-fidelity deep learning model, and train the companion fully connected deep learning model using the first type of training sample set, corresponding to steps five and six: Fifth step, in each subset X i In (1≤i≤N), construct an adjoint fully connected deep learning model ADFC. i A multifidelity deep learning model MFNN i ; Step 6, in each subset X i In (1≤i≤N), the first type of training sample set is used. Training accompanied by fully connected deep learning model ADFC i ; For each subset with an index other than 1, the structure parameter vector in the first type of training sample set corresponding to that subset is used as the input of the accompanying fully connected deep learning model in the previous subset. The output of the accompanying fully connected deep learning model in the previous subset is regarded as the low-fidelity electromagnetic response of the current subset. The structure parameter vector and low-fidelity electromagnetic response in the current subset are regarded as inputs, and the high-fidelity electromagnetic response is regarded as outputs. These are paired to form the second type of training sample set, corresponding to steps seven and eight: Step 7: In each subset X with an index not equal to 1 i In (2≤i≤N), X i The structural parameter vector in the ADFC is used as the ADFC. i-1 The input is used to calculate the set X. i Each vector x in ij (1≤j≤s i The low-fidelity electromagnetic property vector y corresponding to the metasurface ij , obtain the set Step 8: In each subset X with an index not equal to 1 i In (2≤i≤N), set X i The structural parameter vector and set Y in i The low-fidelity electromagnetic property vector in the set Z is taken as input. i The high-fidelity electromagnetic characteristic vector in the middle is regarded as the output, and the second type of training sample set is constructed. In each subset where the index is not 1, a multi-fidelity deep learning model is trained using the second type of training sample set, corresponding to steps nine and ten: Step 9: In each subset X with an index not equal to 1 i In (2≤i≤N), the second type of training sample set is used. Training a multi-fidelity deep learning model MFNN i ; Step 10: For any subset X i When i=1, use ADFC i To estimate the electromagnetic properties of a metasurface, when i ≠ 1, use MFNN. i Estimate the electromagnetic properties of metasurfaces.

2. The method for constructing a multi-fidelity deep learning model for estimating the electromagnetic properties of metasurfaces as described in claim 1, characterized in that, The ADFC model construction method includes: Step 1: Construct M fully connected layers FC1, FC2, ..., FC M M-1 batch normalized layers BN1, BN2, ..., BN M-1 M-1 activation layers RE1, RE2, ..., RE M-1 And an output layer OC that uses the Sigmoid function; Step 2: Set FC1 as the first layer of ADFC, and L1 is responsible for receiving x from the first type of training sample set; Step 3: Configure the fully connected layer, batch normalized layer, activation layer, and output layer according to {FC1, BN1, RE1, FC2, ..., FC...} M The layers OC are connected in the order of OC, with the output of the previous layer serving as the input of the next layer. Step 4: Set the electromagnetic properties of the metamaterial output by the OC layer neurons. The output of the OC layer neurons is the output of the ADFC model.

3. The method for constructing a multi-fidelity deep learning model for estimating the electromagnetic properties of metasurfaces as described in claim 1, characterized in that, The MFNN model construction method includes: Step 1: Construct K fully connected layers K-1 batch normalization layers K-1 activation layers Step 2, settings This is the first layer of the first branch of the MFNN network. Responsible for receiving x from the second type of training sample set; Step 3: Arrange the K fully connected layers, K-1 batch normalized layers, and K-1 activation layers according to... The layers are connected in sequence, with the output of the previous layer serving as the input of the next layer. Step 4: Construct L fully connected layers L-1 batch normalization layers L-1 activation layers Step 5, Settings This is the first layer of the second branch of the MFNN network. Responsible for receiving y from the second type of training sample set; Step 6: Arrange the L fully connected layers, L-1 batch normalized layers, and L-1 activation layers according to... The layers are connected sequentially, with the output of the previous layer serving as the input of the next layer. Step 7: Construct an output layer OC that uses the Sigmoid function. Output and The outputs are summed and used as the input to the OC layer, and the output of the OC layer is the output of the MFNN model.

4. The method for constructing a multi-fidelity deep learning model for estimating the electromagnetic properties of metasurfaces as described in claim 1, characterized in that, The ADFC model training method includes: Step 1: Take the x samples from the first training sample set as input to the ADFC model in turn, and use the ADFC model to perform forward propagation on the samples. For any x, obtain the floating-point numerical vector z′ generated by the output node neuron. Step 2: Based on the floating-point numerical vector z′ and z in the first type of training sample set, calculate the loss function value l of the ADFC model using the mean squared error loss function; Step 3: Calculate the gradient G corresponding to the trainable parameters in the ADFC model based on the loss function value l, and update the parameters in the ADFC model using gradient descent based on the gradient G. Step 4: Repeat steps 1 to 3 to complete the ADFC model.

5. The method for constructing a multi-fidelity deep learning model for estimating the electromagnetic properties of metasurfaces as described in claim 1, characterized in that, The MFNN model training method includes: Step 1: Take the x and y samples from the second type of training sample set as input to the MFNN model in turn, and use the MFNN model to perform forward propagation on the samples. For any set of x and y, obtain the floating-point numerical vector z′ generated by the output node neuron. Step 2: Based on the floating-point numerical vector z′ and z in the second type of training sample set, calculate the loss function value l of the MFNN model using the mean squared error loss function; Step 3: Calculate the gradient G corresponding to the trainable parameters in the MFNN model based on the loss function value l, and update the parameters in the MFNN model using gradient descent based on the gradient G. Step 4: Repeat steps 1 to 3 to complete the MFNN model.

6. A computer device, characterized in that, The computer device includes a memory and a processor. The memory stores a computer program, which, when executed by the processor, causes the processor to perform a method for constructing a multi-fidelity deep learning model for estimating the electromagnetic properties of metasurfaces as described in claim 1.

7. A computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the method for constructing a multi-fidelity deep learning model for estimating the electromagnetic properties of metasurfaces as described in claim 1.

8. An information data processing terminal, characterized in that, The information data processing terminal is used to implement the multi-fidelity deep learning model construction method for estimating the electromagnetic properties of metasurfaces as described in claim 1. The information data processing terminal includes: a wireless communication terminal and an electromagnetic simulation terminal.

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