Multi-fidelity deep learning model construction method for metasurface electromagnetic characteristic estimation, medium, equipment and application

Abstract

The invention belongs to the technical field of electronic information, and discloses a multi-fidelity deep learning model construction method for estimating electromagnetic characteristics of a metasurface, a medium, equipment and application. A parameter space where a structure parameter vector of the metasurface to be estimated is located is divided into a plurality of subsets; enabling the parameter spaces corresponding to the subsets to be sequentially adjacent but not overlapped, and sequentially endowing each subset with a positive integer index value starting from 1; in each subset, calculating a high-fidelity electromagnetic response corresponding to the structure parameter vector by using a finite element method, taking the structure parameter vector as input, taking the high-fidelity electromagnetic response as output, and performing pairing to form a first type of training sample set; in each subset, constructing an adjoint full-connection deep learning model and a multi-fidelity deep learning model, and training the adjoint full-connection deep learning model by using the first type of training sample set; and for each subset of which the index is not 1, taking the structure parameter vector in the first type of training sample set corresponding to the subset as the input of the adjoint full-connection deep learning model in the previous subset, and taking the output of the adjoint full-connection deep learning model in the previous subset as the low-fidelity electromagnetic response of the current subset. Taking the structure parameter vector and the low-fidelity electromagnetic response in the current subset as input, taking the high-fidelity electromagnetic response as output, and pairing to form a second type of training sample set; in each subset of which the index is not 1, training a multi-fidelity deep learning model by using a second type of training sample set; the multi-fidelity deep learning model obtained by the invention can accurately estimate the electromagnetic characteristics of the metasurface, and in order to achieve the same estimation accuracy performance index, compared with a common deep learning model only using a high-fidelity training sample, the method has the advantages that the estimation accuracy is improved; the multi-fidelity deep learning model can reduce 30% of the calculation amount for calculating the high-fidelity electromagnetic response by using a finite element method.

Description

Technical Field

[0001] The present invention belongs to the field of electronic information technology, and in particular relates to a multi-fidelity deep learning model construction method, medium, equipment and application for estimating electromagnetic properties of metasurfaces. Background Art

[0002] Currently: Using deep learning to estimate the electromagnetic properties of metasurfaces is a widely studied problem, involving fields such as wireless communications and electromagnetic simulation. A major research trend in using deep learning to estimate the electromagnetic properties of metasurfaces is to improve the accuracy and efficiency of the electromagnetic property estimation process. For improving the accuracy and efficiency of the electromagnetic property estimation process, the use of multi-fidelity deep learning models has been less studied.

[0003] When using deep learning to estimate the electromagnetic properties of metasurfaces, the accuracy and efficiency of the model estimating the electromagnetic properties are usually determined by two key factors. The first is the computational cost paid to build and train the model, and the second is the ability of the deep learning model itself to extract features from the data. For the first factor, the higher the computational cost, the lower the efficiency of estimating electromagnetic properties. The computational cost is usually reflected in two aspects. The first aspect is the time-consuming execution of precise numerical calculation methods when building a high-fidelity deep learning model training sample set, and the second aspect is the size of the training sample set that must be guaranteed in order to train the deep learning model. For the second factor, the stronger the ability to extract features, the higher the accuracy and efficiency of the model. The ability to extract features usually depends on the type of forward operation of the model itself and the structure of the model.

[0004] Generally speaking, using only high-fidelity training sample sets can indeed obtain a deep learning model that can accurately estimate the electromagnetic properties of metasurfaces, but as mentioned above, using only high-fidelity samples for model training will introduce too much overhead when constructing the training sample set, thereby reducing the efficiency of the deep learning model. When the size of the training sample set is reduced in order to improve efficiency, the accuracy of the deep learning model will be affected. From the perspective of multi-fidelity, the present invention uses a method that combines high-fidelity and low-fidelity data to train a deep learning model, and constructs a deep learning model for this method that can extract and fuse features from both high-fidelity and low-fidelity training samples.

[0005] Although low-fidelity training samples will not accurately describe the electromagnetic response like high-fidelity training samples, they can roughly describe the electromagnetic response, such as describing the rough law of electromagnetic response changing with frequency, describing the approximate frequency band of electromagnetic response, etc. These rough data laws will provide preliminary information for the deep learning model, thereby enabling the multi-fidelity deep learning model to obtain better electromagnetic response estimation accuracy using fewer high-fidelity samples. Considering that obtaining high-fidelity samples using the finite element method is a very time-consuming operation, a model that simultaneously uses high-fidelity and low-fidelity training samples can improve the efficiency of electromagnetic response estimation.

[0006] Through the above analysis, the problems and defects of the existing technology are: the structure of the current deep learning model can only extract features from high-fidelity training samples of the metasurface, and the training of this type of model can only use high-fidelity samples of the metasurface, which makes the electromagnetic response estimation accuracy of this type of model low and the efficiency is also low.

[0007] The difficulty in solving the above problems and defects is: in order to be able to use both low-fidelity and high-fidelity training samples, it is necessary to construct a dedicated deep learning model to extract and fuse features from 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 finite elements to obtain high-fidelity samples, low-fidelity samples cannot be obtained using finite elements and other methods.

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

[0009] In response to the problems existing in the prior art, the present invention provides a multi-fidelity deep learning model construction method, medium, device and application for estimating the electromagnetic properties of metasurfaces.

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

[0011] The parameter space where the structural parameter vector of the hypersurface to be estimated is located is divided into multiple subsets, so that the parameter spaces corresponding to the subsets are adjacent but not overlapped in sequence, and each subset is assigned a positive integer index value starting from 1 in sequence;

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

[0013] In each subset, construct an accompanying fully connected deep learning model and a multi-fidelity deep learning model, and use the first type of training sample set to train the accompanying fully connected deep learning model;

[0014] For each subset whose index is not 1, the structural 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 structural 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 the pairs are formed into a second type of training sample set;

[0015] In each subset whose index is not 1, the second type of training sample set is used to train the multi-fidelity deep learning model.

[0016] Furthermore, the multi-fidelity deep learning model construction method for metasurface electromagnetic property estimation specifically includes the following steps:

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

[0018] The second step is to divide the set X into N subsets X = {X1, X2, ..., X N}, so that the parameter spaces corresponding to the subsets are adjacent but not overlapping in sequence, and the sizes of the N subsets are represented as s1, s2, ..., s N ;

[0019] The third step is to take any subset X. i (1≤i≤N), using the finite element method to calculate the set X i For each vector x ij (1≤j≤s i ) corresponds to the high-fidelity electromagnetic characteristic vector z of the metasurface ij , get the set

[0020] Step 4: For any subset X i (1≤i≤N), the set X i The structural parameter vector in is regarded as input, and the set Z iThe high-fidelity electromagnetic characteristic vector in is regarded as the output to construct the first type of training sample set

[0021] Step 5: In each subset X i (1≤i≤N), construct an accompanying fully connected deep learning model ADFC i and a multi-fidelity deep learning model MFNN i ;

[0022] Step 6: In each subset X i (1≤i≤N), use the first type of training sample set Training the ADFC deep learning model i ;

[0023] Step 7: In every subset X whose index is not 1 i (2≤i≤N), X i The structural parameter vector in is used as ADFC i-1 Input, calculate the set X i For each vector x ij (1≤j≤s i ) corresponds to the low-fidelity electromagnetic characteristic vector y of the metasurface ij , get the set

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

[0025] Step 9: In every subset X whose index is not 1 i (2≤i≤N), use the second type of training sample set Training a multi-fidelity deep learning model MFNN i ;

[0026] Step 10. For any subset X i , when i=1, use ADFC i Estimate the electromagnetic properties of the metasurface, when i≠1, using MFNN i Estimating the electromagnetic properties of metasurfaces.

[0027] Furthermore, the ADFC model construction method of the multi-fidelity deep learning model construction method for metasurface electromagnetic property estimation includes:

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

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

[0030] Step 3: Arrange the fully connected layer, batch normalization layer, activation layer, and output layer according to {FC1, BN1, RE1, FC2, ..., FC M , OC} are connected in sequence, and the output of the previous layer of network serves as the input of the next layer of network.

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

[0032] Furthermore, the MFNN model construction method of the multi-fidelity deep learning model construction method for metasurface electromagnetic property estimation includes:

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

[0034] Step 2: Set up It is the first layer network of the first branch of MFNN. Responsible for receiving x in the second type of training sample set;

[0035] Step 3: Place K fully connected layers, K-1 batch normalization layers, and K-1 activation layers according to The output of the previous network layer is used as the input of the next network layer.

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

[0037] Step 5: Set up is the first layer network of the second branch of MFNN, Responsible for receiving y in the second type of training sample set;

[0038] Step 6: Place L fully connected layers, L-1 batch normalization layers, and L-1 activation layers according to The output of the previous network layer is used as the input of the next network layer.

[0039] Step 7: Construct an output layer OC using the Sigmoid function. The output and The outputs of the OC layer are added together and used as the input of the OC layer. The output of the OC layer is the output of the MFNN model.

[0040] Furthermore, the ADFC model training method of the multi-fidelity deep learning model construction method for metasurface electromagnetic property estimation includes:

[0041] Step 1: Take x in the first class of training sample sets as the input of the ADFC model in turn, use the ADFC model to perform forward propagation operations on the samples, and obtain the floating-point value vector z′ generated by the output node neuron for any x;

[0042] Step 2, according to the floating point numerical vector z′ and z in the first type of training sample set, use the mean square error loss function to calculate the loss function value l of the model ADFC;

[0043] Step 3, calculating the gradient G corresponding to the trainable parameters in the model ADFC according to the loss function value l, and updating the parameters in the ADFC model using the gradient descent method according to 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 of the multi-fidelity deep learning model construction method for metasurface electromagnetic property estimation includes:

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

[0047] Step 2, according to the floating point value vector z′ and z in the second type of training sample set, use the mean square error loss function to calculate the loss function value l of the model MFNN;

[0048] Step 3: Calculate the gradient G corresponding to the trainable parameters in the model MFNN according to the loss function value l, and update the parameters in the MFNN model using the gradient descent method according to 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, the computer device comprising a memory and a processor, the memory storing a computer program, and when the computer program is executed by the processor, the processor performs the following steps:

[0051] The parameter space where the structural parameter vector of the hypersurface to be estimated is located is divided into multiple subsets, so that the parameter spaces corresponding to the subsets are adjacent but not overlapped in sequence, and each subset is assigned a positive integer index value starting from 1 in sequence;

[0052] In each subset, the finite element method is used to calculate the high-fidelity electromagnetic response corresponding to the structural parameter vector, and the structural parameter vector is regarded as input and the high-fidelity electromagnetic response is regarded as output, and they are paired to form the first type of training sample set;

[0053] In each subset, construct an accompanying fully connected deep learning model and a multi-fidelity deep learning model, and use the first type of training sample set to train the accompanying fully connected deep learning model;

[0054] For each subset whose index is not 1, the structural 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 structural 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 the pairs are formed into a second type of training sample set;

[0055] In each subset whose index is not 1, the second type of training sample set is used to train the multi-fidelity deep learning model.

[0056] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, the processor executes the following steps:

[0057] The parameter space where the structural parameter vector of the hypersurface to be estimated is located is divided into multiple subsets, so that the parameter spaces corresponding to the subsets are adjacent but not overlapped in sequence, and each subset is assigned a positive integer index value starting from 1 in sequence;

[0058] In each subset, the finite element method is used to calculate the high-fidelity electromagnetic response corresponding to the structural parameter vector, and the structural parameter vector is regarded as input and the high-fidelity electromagnetic response is regarded as output, and they are paired to form the first type of training sample set;

[0059] In each subset, construct an accompanying fully connected deep learning model and a multi-fidelity deep learning model, and use the first type of training sample set to train the accompanying fully connected deep learning model;

[0060] For each subset whose index is not 1, the structural 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 structural 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 the pairs are formed into a second type of training sample set;

[0061] In each subset whose index is not 1, the second type of training sample set is used to train the multi-fidelity deep learning model.

[0062] Another object of the present 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.

[0063] The multi-fidelity deep learning model construction method was tested using a double-layer complementary wave-transparent metasurface structure. Compared with the ordinary 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 elements. The scale of the training sample set and the mean square error performance of the corresponding ordinary or multi-fidelity deep learning model are shown in the attached figure. Figure 7 The dotted line in the figure represents the mean square error performance of the deep learning model when only high-fidelity training samples are used, and the solid line represents the mean square error performance of the multi-fidelity deep learning model. The lower the mean square error value, the better the performance of the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following is a brief introduction to the drawings required for use in the embodiments of the present application. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0065] Figure 1 It is a flow chart of a method for constructing a multi-fidelity deep learning model for estimating electromagnetic properties of a metasurface provided by an embodiment of the present invention;

[0066] Figure 2It is a flow chart of a method for constructing the accompanying fully connected deep learning model ADFC model provided by an embodiment of the present invention;

[0067] Figure 3 It is a flow chart of a method for constructing the multi-fidelity deep learning model MFNN model provided in an embodiment of the present invention;

[0068] Figure 4 is a flow chart of the accompanying fully connected deep learning model training method provided by an embodiment of the present invention;

[0069] Figure 5 is a flow chart of the multi-fidelity deep learning model training method provided by an embodiment of the present invention;

[0070] Figure 6 is a scatter plot of mean square error performance when estimating the electromagnetic response of a metasurface using a common model and the multi-fidelity deep learning model provided in an embodiment of the present invention;

[0071] Figure 7 It is a mean square error performance curve diagram provided by an embodiment of the present invention that can be obtained when a common model and the multi-fidelity deep learning model are trained using the same percentage of training sample set data. DETAILED DESCRIPTION

[0072] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0073] In response to the problems existing in the prior art, the present invention provides a multi-fidelity deep learning model construction method, medium, device and application for metasurface electromagnetic property estimation. The present invention is described in detail below in conjunction with the accompanying drawings.

[0074] like Figure 1 As shown, the multi-fidelity deep learning model construction method for metasurface electromagnetic property estimation provided by the present invention comprises the following steps:

[0075] S101: Divide the parameter space where the structural parameter vector of the hypersurface to be estimated is located into multiple subsets, so that the parameter spaces corresponding to the respective subsets are adjacent in sequence but do not overlap, and assign a positive integer index value starting from 1 to each subset in sequence;

[0076] S102: In each subset, a high-fidelity electromagnetic response corresponding to a structural parameter vector is calculated using a finite element method, and the structural parameter vector is regarded as an input, and the high-fidelity electromagnetic response is regarded as an output, and the two are paired to form a first type of training sample set;

[0077] S103: in each subset, construct an accompanying fully connected deep learning model and a multi-fidelity deep learning model, and use the first type of training sample set to train the accompanying fully connected deep learning model;

[0078] S104: for each subset whose index is not 1, the structural 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 structural 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 the pairs are formed into a second type of training sample set;

[0079] S105: In each subset whose index is not 1, use the second type of training sample set to train a multi-fidelity deep learning model.

[0080] The multi-fidelity deep learning model construction method for metasurface electromagnetic property estimation provided by the present invention can also be implemented by other steps by ordinary technicians in the industry. Figure 1 The multi-fidelity deep learning model construction method for estimating the electromagnetic properties of metasurfaces provided by the present invention is only a specific embodiment.

[0081] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0082] The multi-fidelity deep learning model construction method for metasurface electromagnetic property estimation provided by the present invention specifically includes the following steps:

[0083] In the first step, a uniform sampling method is used to sample a hypersurface structure of size n in a given parameter space. The parameter vector corresponding to the hypersurface structure can be represented by a set X = {x1, x2, ..., x n}express;

[0084] The second step is to divide the set X into N subsets X = {X1, X2, ..., X N}, so that the parameter spaces corresponding to the subsets are adjacent but not overlapping in sequence, and the sizes of the N subsets are represented as s1, s2, ..., s N ;

[0085] The third step is to take any subset X. i (1≤i≤N), using the finite element method to calculate the set X i For each vector x ij (1≤j≤s i ) corresponds to the high-fidelity electromagnetic characteristic vector z of the metasurface ij , we get the set Z i =

[0086] Step 4: For any subset X i (1≤i≤N), the set X i The structural parameter vector in is regarded as input, and the set Z i The high-fidelity electromagnetic characteristic vector in is regarded as the output to construct the first type of training sample set

[0087] Step 5: In each subset X i (1≤i≤N), construct an accompanying fully connected deep learning model ADFC i and a multi-fidelity deep learning model MFNN i ;

[0088] Step 6: In each subset X i (1≤i≤N), use the first type of training sample set Training the ADFC deep learning model i ;

[0089] Step 7: In every subset X whose index is not 1 i (2≤i≤N), X i The structural parameter vector in is used as ADFC i-1 Input, calculate the set X i For each vector x ij (1≤j≤s i ) corresponds to the low-fidelity electromagnetic characteristic vector y of the metasurface ij , get the set

[0090] Step 8: In every subset X whose index is not 1 i (2≤i≤N), the set X i The structural parameter vector and set Y in i The low-fidelity electromagnetic characteristic vector in is taken as input, and the set Z i The high-fidelity electromagnetic characteristic vector in is regarded as the output to construct the second type of training sample set

[0091] Step 9: In every subset X whose index is not 1 i (2≤i≤N), use the second type of training sample set Training a multi-fidelity deep learning model MFNN i ;

[0092] Step 10. For any subset X i , when i=1, use ADFC iEstimate the electromagnetic properties of the metasurface, when i≠1, using MFNN i Estimating the electromagnetic properties of metasurfaces.

[0093] like Figure 2 As shown, the ADFC model construction method provided by the embodiment of the present invention includes:

[0094] Step 1: construct M fully connected layers FC1, FC2, ..., FC M , M-1 batch normalization layers BN1, BN2, ..., BN M-1 , M-1 activation layers RE1, RE2, ..., RE M-1 And an output layer OC using the Sigmoid function;

[0095] Step 2: Set FC1 as the first layer network of ADFC, and FC1 is responsible for receiving x in the first type of training sample set;

[0096] Step 3: Arrange the fully connected layer, batch normalization layer, activation layer, and output layer according to {FC1, BN1, RE1, FC2, ..., FC M , OC} are connected in sequence, and the output of the previous layer of network serves as the input of the next layer of network.

[0097] Step 4: Set the OC layer neurons to output the electromagnetic properties of the metamaterial. The output of the OC layer neurons is the output of the ADFC model.

[0098] like Figure 3 As shown, the MFNN model construction method provided by the embodiment of the present invention includes:

[0099] Step 1: Construct K fully connected layers K-1 batch normalization layers K-1 activation layers

[0100] Step 2: Set up It is the first layer network of the first branch of MFNN. Responsible for receiving x in the second type of training sample set;

[0101] Step 3: Place K fully connected layers, K-1 batch normalization layers, and K-1 activation layers according to The output of the previous network layer is used as the input of the next network layer.

[0102] Step 4: Construct L fully connected layers L-1 batch normalization layers L-1 activation layer

[0103] Step 5: Set up is the first layer network of the second branch of MFNN, Responsible for receiving y in the second type of training sample set;

[0104] Step 6: Place L fully connected layers, L-1 batch normalization layers, and L-1 activation layers according to The output of the previous network layer is used as the input of the next network layer.

[0105] Step 7: Construct an output layer OC using the Sigmoid function. The output and The outputs of the OC layer are added together and used as the input of the OC layer. The output of the OC layer is the output of the MFNN model.

[0106] like Figure 4 As shown, the ADFC model training method provided by the embodiment of the present invention includes:

[0107] Step 1: Take x in the first class of training sample sets as the input of the ADFC model in turn, use the ADFC model to perform forward propagation operations on the samples, and obtain the floating-point value vector z′ generated by the output node neuron for any x;

[0108] Step 2, according to the floating point numerical vector z′ and z in the first type of training sample set, use the mean square error loss function to calculate the loss function value l of the model ADFC;

[0109] Step 3, calculating the gradient G corresponding to the trainable parameters in the model ADFC according to the loss function value l, and updating the parameters in the ADFC model using the gradient descent method according to the gradient G;

[0110] Step 4: Repeat steps 1 to 3 to complete the training of the ADFC model.

[0111] like Figure 5 As shown, the MFNN model training method provided by the embodiment of the present invention includes:

[0112] Step 1: Take x and y in the second type of training sample set as the input of the MFNN model in turn, use the MFNN model to perform forward propagation operation on the samples, and obtain the floating-point numerical vector z′ generated by the output node neuron for any set of x and y;

[0113] Step 2, according to the floating point value vector z′ and z in the second type of training sample set, use the mean square error loss function to calculate the loss function value l of the model MFNN;

[0114] Step 3: Calculate the gradient G corresponding to the trainable parameters in the model MFNN according to the loss function value l, and update the parameters in the MFNN model using the gradient descent method according to the gradient G;

[0115] Step 4: Repeat steps 1 to 3 to complete the training of the MFNN model.

[0116] The technical effects of the present invention are described in detail below in conjunction with specific embodiments.

[0117] Embodiment 1:

[0118] Take a double-layer complementary wave-transmitting metasurface structure as an example. The bottom surface of the wave-transmitting structure is coated with metal copper in the shape of a square ring, and the top surface is also coated with metal copper, but its shape is complementary to the bottom surface. A dielectric layer is filled between the bottom and top metal layers, with a relative dielectric constant of 1.1 and a relative magnetic permeability of 1. A total of 2500 metasurface structures were collected using a random sampling method to construct a data set. For the first type of training sample set, it contains 2000 metasurface structure parameter vectors and 2000 high-fidelity electromagnetic responses obtained using the finite element numerical 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, it contains 2000 metasurface structure parameter vectors and 2000 high-fidelity electromagnetic responses obtained using the finite element numerical 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. There is no need to use the finite element numerical method in the process of using ADFC to generate low-fidelity electromagnetic responses. A multi-fidelity model is constructed using the multi-fidelity deep learning construction method for metasurface electromagnetic property estimation, wherein for the structural parameter vector and the low-fidelity electromagnetic response, there are 4 fully connected layers and other matching layers to extract features, and the extracted features are fused and output. For an ordinary deep learning model that only uses a high-fidelity training sample set, 4 fully connected layers and other matching layers are used to extract and output features.

[0119] 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 scattered 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 7The figure shows the mean square error performance that can be obtained by the ordinary model and the multi-fidelity deep learning model when using the same percentage of data, wherein the horizontal axis represents the percentage of data samples used in training in the total training data set samples, and the vertical axis represents the mean square error of the electromagnetic response estimation of the trained model on the test sample set. The figure shows that the multi-fidelity model can obtain the same performance as the ordinary model using only 70% of the training data, indicating that the multi-fidelity model has a higher estimation efficiency.

[0120] It should be noted that the embodiments of the present invention can be implemented by hardware, software, or a combination of software and hardware. The hardware part can be implemented using dedicated logic; the software part can be stored in a memory and executed by an appropriate instruction execution system, such as a microprocessor or dedicated design hardware. It can be understood by a person of ordinary skill in the art that the above-mentioned devices and methods can be implemented using computer executable instructions and / or contained in a processor control code, such as a carrier medium such as a disk, CD or DVD-ROM, a programmable memory such as a read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. Such code is provided on the carrier medium. The device and its modules of the present invention can be implemented by hardware circuits such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, etc., or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., can also be implemented by software executed by various types of processors, and can also be implemented by a combination of the above-mentioned hardware circuits and software, such as firmware.

[0121] The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with the technical field within the technical scope disclosed by the present invention and within the spirit and principle of the present invention should be covered by the protection scope of the present invention.

Claims

1. A method for constructing a multi-fidelity deep learning model for estimating electromagnetic properties of metasurfaces, characterized in that: The multi-fidelity deep learning model construction method for metasurface electromagnetic property estimation includes: The parameter space where the structural parameter vector of the hypersurface to be estimated is located is divided into multiple subsets, so that the parameter spaces corresponding to the subsets are adjacent but not overlapped in sequence, and each subset is assigned a positive integer index value starting from 1 in sequence; In each subset, the finite element method is used to calculate the high-fidelity electromagnetic response corresponding to the structural parameter vector, and the structural parameter vector is regarded as input and the high-fidelity electromagnetic response is regarded as output, and they are paired to form the first type of training sample set; In each subset, construct an accompanying fully connected deep learning model and a multi-fidelity deep learning model, and use the first type of training sample set to train the accompanying fully connected deep learning model; For each subset whose index is not 1, the structural 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 structural 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 the pairs are formed into a second type of training sample set; In each subset whose index is not 1, the second type of training sample set is used to train the multi-fidelity deep learning model.

2. The method for constructing a multi-fidelity deep learning model for estimating electromagnetic properties of a metasurface according to claim 1, characterized in that: The multi-fidelity deep learning model construction method for metasurface electromagnetic property estimation is specifically The following steps are involved: In the first step, a uniform sampling method is used to sample a hypersurface structure of size n in a given parameter space. The parameter vector corresponding to the hypersurface structure can be represented by a set X = {x1, x2, ..., x n }express; The second step is to divide the set X into N subsets X = {X1, X2, ..., X N }, so that the parameter spaces corresponding to the subsets are adjacent but not overlapping. The sizes of the N subsets are represented by s1, s2, ..., s N ; The third step is to take any subset X. i (1≤i≤N), using the finite element method to calculate the set X i For each vector x ij (1≤j≤s i ) corresponds to the high-fidelity electromagnetic characteristic vector z of the metasurface ij , get the set Step 4: For any subset X i (1≤i≤N), the set X i The structural parameter vector in is regarded as input, and the set Z i The high-fidelity electromagnetic characteristic vector in is regarded as the output to construct the first type of training sample set Step 5: In each subset X i (1≤i≤N), construct an accompanying fully connected deep learning model ADFC i and a multi-fidelity deep learning model MFNN i ; Step 6: In each subset X i (1≤i≤N), use the first type of training sample set Training the ADFC deep learning model i ; Step 7: In every subset X whose index is not 1 i (2≤i≤N), X i The structural parameter vector in is used as ADFC i-1 Input, calculate the set X i For each vector x ij (1≤j≤s i ) corresponds to the low-fidelity electromagnetic characteristic vector y of the metasurface ij , get the set Step 8: In every subset X whose index is not 1 i (2≤i≤N), the set X i The structural parameter vector and set Y in i The low-fidelity electromagnetic characteristic vector in is taken as input, and the set Z i The high-fidelity electromagnetic characteristic vector in is regarded as the output to construct the second type of training sample set Step 9: In every subset X whose index is not 1 i (2≤i≤N), use the second type of training sample set Training a multi-fidelity deep learning model MFNN i ; Step 10. For any subset X i , when i=1, use ADFC i Estimate the electromagnetic properties of the metasurface, when i≠1, using MFNN i Estimating the electromagnetic properties of metasurfaces.

3. The method for constructing a multi-fidelity deep learning model for estimating electromagnetic properties of a metasurface according to claim 2, wherein: The ADFC model construction method comprises: Step 1: construct M fully connected layers FC1, FC2, ..., FC M , M-1 batch normalization layers BN1, BN2, …, BN M-1 , M-1 activation layers RE1,RE2,…,RE M-1 And an output layer OC using the Sigmoid function; Step 2: Set FC1 as the first layer network of ADFC, and FC1 is responsible for receiving x in the first type of training sample set; Step 3: Arrange the fully connected layer, batch normalization layer, activation layer, and output layer according to {FC1, BN1, RE1, FC2, …, FC M ,OC} are connected in sequence, and the output of the previous layer of network serves as the input of the next layer of network. Step 4: Set the OC layer neurons to output the electromagnetic properties of the metamaterial. The output of the OC layer neurons is the output of the ADFC model.

4. The method for constructing a multi-fidelity deep learning model for estimating electromagnetic properties of a metasurface according to claim 2, wherein: The MFNN model construction method comprises: Step 1: Construct K fully connected layers K-1 batch normalization layers K-1 activation layers Step 2: Set up It is the first layer network of the first branch of MFNN. Responsible for receiving x in the second type of training sample set; Step 3: Place K fully connected layers, K-1 batch normalization layers, and K-1 activation layers according to The output of the previous network layer is used as the input of the next network layer. Step 4: Construct L fully connected layers L-1 batch normalization layers L-1 activation layer Step 5: Set up is the first layer network of the second branch of MFNN, Responsible for receiving y in the second type of training sample set; Step 6: Place L fully connected layers, L-1 batch normalization layers, and L-1 activation layers according to The output of the previous network layer is used as the input of the next network layer. Step 7: Construct an output layer OC using the Sigmoid function. The output and The outputs of the OC layer are added together and used as the input of the OC layer. The output of the OC layer is the output of the MFNN model.

5. The method for constructing a multi-fidelity deep learning model for estimating electromagnetic properties of a metasurface according to claim 2, wherein: The ADFC model training method comprises: Step 1: Take x in the first class of training sample sets as the input of the ADFC model in turn, use the ADFC model to perform forward propagation operations on the samples, and obtain the floating-point value vector z′ generated by the output node neuron for any x; Step 2, according to the floating point numerical vector z′ and z in the first type of training sample set, use the mean square error loss function to calculate the loss function value l of the model ADFC; Step 3, calculating the gradient G corresponding to the trainable parameters in the model ADFC according to the loss function value l, and updating the parameters in the ADFC model using the gradient descent method according to the gradient G; Step 4: Repeat steps 1 to 3 to complete the ADFC model.

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

7. A computer device, characterized in that: The computer device includes a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor performs the following steps: The parameter space where the structural parameter vector of the hypersurface to be estimated is located is divided into multiple subsets, so that the parameter spaces corresponding to the subsets are adjacent but not overlapped in sequence, and each subset is assigned a positive integer index value starting from 1 in sequence; In each subset, the finite element method is used to calculate the high-fidelity electromagnetic response corresponding to the structural parameter vector, and the structural parameter vector is regarded as input and the high-fidelity electromagnetic response is regarded as output, and they are paired to form the first type of training sample set; In each subset, construct an accompanying fully connected deep learning model and a multi-fidelity deep learning model, and use the first type of training sample set to train the accompanying fully connected deep learning model; For each subset whose index is not 1, the structural 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 structural 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 the pairs are formed into a second type of training sample set; In each subset whose index is not 1, the second type of training sample set is used to train the multi-fidelity deep learning model.

8. A computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, the processor executes the following steps: The parameter space where the structural parameter vector of the hypersurface to be estimated is located is divided into multiple subsets, so that the parameter spaces corresponding to the subsets are adjacent but not overlapped in sequence, and each subset is assigned a positive integer index value starting from 1 in sequence; In each subset, the finite element method is used to calculate the high-fidelity electromagnetic response corresponding to the structural parameter vector, and the structural parameter vector is regarded as input and the high-fidelity electromagnetic response is regarded as output, and they are paired to form the first type of training sample set; In each subset, construct an accompanying fully connected deep learning model and a multi-fidelity deep learning model, and use the first type of training sample set to train the accompanying fully connected deep learning model; For each subset whose index is not 1, the structural 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 structural 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 the pairs are formed into a second type of training sample set; In each subset whose index is not 1, the second type of training sample set is used to train the multi-fidelity deep learning model.

9. 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 any one of claims 1 to 6, and the information data processing terminal includes: a wireless communication terminal and an electromagnetic simulation terminal.

Images