Method for obtaining equivalent electromagnetic parameters of honeycomb structure composite based on PINN

Abstract

The application discloses a kind of PINN-based honeycomb structure composite material equivalent electromagnetic parameter acquisition method, belong to electromagnetic calculation and artificial intelligence cross technical field.The method includes: simulation obtains the S parameter of honeycomb structure composite material, constructs S parameter simulation dataset;Physical driving neural network is constructed, and loss function is set;S parameter simulation dataset is input into the in physical driving neural network, network parameter is optimized through back propagation, loss function is minimized, and finally the equivalent electromagnetic parameter of honeycomb structure composite material is output.The application embeds the electromagnetic wave propagation physical equation based on Maxwell equations in honeycomb structure composite material into loss function, realizes the physical constraint of neural network, effectively overcome the problem of high computational complexity and low efficiency in the solving method of traditional composite material equivalent electromagnetic parameter, can realize the efficient solution to electromagnetic parameter under the condition of lacking sample data.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic computing and artificial intelligence, and in particular to a method for obtaining the equivalent electromagnetic parameters of a PINN-based honeycomb composite material. Background Technology

[0002] The electromagnetic properties of honeycomb composite materials mainly depend on their equivalent electromagnetic parameters. These materials are typically composed of a matrix medium and embedded media. By selecting different media types and designing differentiated topologies, directional attenuation of electromagnetic waves in specific frequency bands can be achieved. Inspired by the honeycomb structure in nature, its biomimetic configuration and the non-uniformity of heterogeneous media materials make traditional equivalent medium theory analysis methods cumbersome and computationally complex.

[0003] In recent years, to avoid the computational complexity of traditional methods, many researchers have used more advanced deep learning methods to study honeycomb composite absorbing materials. However, training network models using widely adopted deep learning methods requires a large amount of sample data to achieve good learning and prediction results. In the electromagnetic field, the electromagnetic properties of honeycomb composite absorbing materials are mainly determined by their equivalent electromagnetic parameters. The sample data for these equivalent electromagnetic parameters can generally only be obtained using traditional experimental measurement methods, which are often costly and time-consuming, making purely data-driven deep learning methods difficult to apply in practice.

[0004] In summary, there is currently no method that can achieve efficient prediction of equivalent electromagnetic parameters without complex mathematical derivations and extensive calculations, and with a limited amount of sample data. Summary of the Invention

[0005] The purpose of this invention is to address the problems of high computational complexity and low efficiency in traditional methods for solving the equivalent electromagnetic parameters of cellular composite materials, and the over-reliance on large-scale labeled data by purely data-driven deep learning methods. This invention provides a low-cost and high-efficiency method for obtaining the equivalent electromagnetic parameters of cellular composite materials based on PINN (Physics-Driven Neural Network). This method eliminates the need for complex mathematical derivations and extensive calculations, and can achieve efficient solution of electromagnetic parameters even in the absence of large amounts of sample data, providing a new approach for further improvements to electromagnetic modeling methods for cellular composite materials.

[0006] The technical solution adopted in this invention is as follows:

[0007] A method for obtaining equivalent electromagnetic parameters of PINN-based honeycomb composite materials, comprising the following steps:

[0008] Step S1. Establish an electromagnetic model of the honeycomb composite material and set excitation conditions. Test and obtain the S-parameters of the honeycomb composite material. Extract the reflection parameters and transmission parameters from the S-parameters to construct an S-parameter simulation dataset.

[0009] Step S2. Construct a physics-driven neural network and set the loss function;

[0010] The physical driving neural network is implemented using a deep neural network architecture.

[0011] The loss function includes the data loss term and physical constraint term of the deep neural network, and its expression is:

[0012] (1)

[0013] in, This represents the loss function for sample data in a deep neural network. Represents physical constraint terms. Represents the weighting coefficients of the physical constraint terms;

[0014] The physical constraints for:

[0015] (2)

[0016] Where i=1,2,3,…N represents the sample index in the S-parameter simulation dataset, and N is the total number of samples; The S-parameter simulation data of the honeycomb composite material before equivalence is represented. The real part of the S-parameters of the honeycomb composite material obtained from the calculation of the physical equation of electromagnetic wave propagation is represented. The imaginary part of the S-parameters of the honeycomb composite material obtained from the calculation of the physical equation of electromagnetic wave propagation is represented.

[0017] Step S3. Input the samples in the S-parameter simulation dataset into the physical driving neural network and optimize the network parameters through backpropagation; when the loss function is less than the set threshold, the real part prediction value and imaginary part prediction value of the equivalent relative permittivity of the honeycomb structure composite material are finally output.

[0018] Preferably, in the loss function, the real part of the equivalent S-parameters and the virtual part The calculation method is as follows:

[0019] The physical equations for electromagnetic wave propagation in the honeycomb structure composite material, based on Maxwell's equations, are as follows:

[0020] (3)

[0021] (4)

[0022] (5)

[0023] Where Γ represents the reflection coefficient and T represents the transmission coefficient. This represents the total reflection coefficient. This represents the total transmission coefficient.

[0024] (1) When the incident plane wave is vertically polarized, the formula for calculating the relative permittivity of the honeycomb composite material is as follows:

[0025] (6)

[0026] (7)

[0027] (8)

[0028] in, This indicates the relative permeability of the honeycomb composite material. The relative permittivity of the honeycomb composite material is represented by θ; the incident angle is θ; and the thickness of the dielectric plate is d. The wave number in free space; These are intermediate quantities in the calculation process and have no actual physical meaning. It is the imaginary unit.

[0029] (2) When the incident plane wave is parallel polarized, the formula for calculating the relative permittivity of the honeycomb structure composite material is as follows:

[0030] (9)

[0031] (10)

[0032] (11)

[0033] Based on the polarization mode of the incident wave set in the excitation conditions of step S1, the real part prediction value and imaginary part prediction value of the equivalent relative permittivity output by the physical driving neural network are substituted into formulas (3)-(8) or (3)-(5) and (9)-(11) respectively to calculate the real part of the equivalent S-parameter. and the virtual part .

[0034] Preferably, the loss function for the sample data in the deep neural network is:

[0035] (12)

[0036] in, The loss function for a single sample.

[0037] Preferably, the physical driving neural network is composed of one input layer, M hidden layers and one output layer stacked in series;

[0038] The input data of the input layer is samples from the S-parameter simulation dataset; the output data of the output layer is the predicted real and imaginary parts of the equivalent relative permittivity; each hidden layer is connected to an activation function to improve the fitting ability to complex solution spaces.

[0039] Preferably, the physical driving neural network uses the Adam optimizer to iteratively update the trainable parameters.

[0040] Compared with the prior art, the significant advantages of this invention are:

[0041] (1) The present invention provides a method for obtaining equivalent electromagnetic parameters of honeycomb composite materials based on physical-driven neural networks. This method effectively solves the problems of high computational complexity and low efficiency in traditional methods for solving equivalent electromagnetic parameters of composite materials. It provides a method for solving equivalent electromagnetic parameters that does not require complex mathematical derivation and significantly reduces computational burden.

[0042] (2) The method of the present invention uses a physical-driven neural network to solve the equivalent electromagnetic parameters of honeycomb composite materials. The physical equation is embedded in the loss function of the deep neural network, which solves the problem that the pure data-driven deep learning method relies too much on large-scale labeled data. It can achieve efficient prediction of equivalent electromagnetic parameters under the condition of lacking a large amount of sample data. Attached Figure Description

[0043] Figure 1 This is a schematic diagram of the physical-driven neural network model of the present invention.

[0044] Figure 2 This is a schematic diagram of a honeycomb structure according to an embodiment of the present invention.

[0045] Figure 3 This is a flowchart of the physical-driven neural network for solving equivalent electromagnetic parameters according to the present invention. Detailed Implementation

[0046] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0047] This embodiment of the electromagnetic modeling method for honeycomb composite materials based on a physics-driven neural network includes the following steps:

[0048] Step S1. Establish an electromagnetic model of the honeycomb composite material and set excitation conditions. Test and obtain the S-parameters of the honeycomb composite material. Extract the reflection parameters and transmission parameters from the S-parameters to construct an S-parameter simulation dataset.

[0049] Specifically, an electromagnetic model of a honeycomb composite material was established in ANSYS HFSS software, a professional electromagnetic field simulation tool based on the finite element method, and the model was simulated and analyzed.

[0050] The electromagnetic model of the honeycomb structural unit of the honeycomb composite material, established in ANSYS HFSS software, is as follows: Figure 2 As shown, based on the geometric dimensions, dielectric properties, and periodic structural characteristics of the cellular structure unit, a three-dimensional model containing the cell periodic boundary conditions and wave port excitation (including the polarization mode and angle of the incident wave) is constructed in the HFSS environment, thus obtaining the electromagnetic model of the cellular structure composite material.

[0051] Set the frequency sweep analysis type to cover the required operating frequency band, perform electromagnetic field calculations, and obtain the S-parameters of the honeycomb composite material at different frequency points within the operating frequency band; extract its reflection and transmission parameters to characterize the electromagnetic reflection and transmission characteristics of the material; then, normalize and standardize the extracted reflection and transmission parameters to construct the S-parameter simulation dataset.

[0052] Step S2. Construct a physical-driven neural network and set the loss function.

[0053] Specifically, the physical driving neural network is implemented using a deep neural network architecture; it consists of one input layer, M hidden layers, and one output layer stacked in series; the input data of the input layer is sample data from the S simulation parameter dataset; the output data of the output layer is the real part prediction value and the imaginary part prediction value of the equivalent relative permittivity; each hidden layer is connected to an activation function to improve the fitting ability to complex solution spaces.

[0054] The physical-driven neural network uses the Adam optimizer to iteratively update the trainable parameters in order to balance convergence speed and accuracy.

[0055] The loss function includes the data loss term and the physical constraint term of the deep neural network.

[0056] Figure 1 The diagram shown is a schematic of the physical-driven neural network model of the present invention. The essential difference between the physical-driven neural network of the present invention and the traditional deep neural network is the calling of the loss function within the model. By adding physical constraint terms, the neural network can achieve efficient prediction of equivalent electromagnetic parameters based on a small amount of sample data.

[0057] The total loss function in the physical-driven neural network is:

[0058] (1)

[0059] in, This represents the loss function for sample data in a deep neural network. Indicated in the physical constraint terms, The weighting coefficients for physical constraint terms are used to measure the importance of physical constraint terms within the overall loss term. Take 1.

[0060] The loss function for the sample data in the deep neural network is:

[0061] (2)

[0062] Where i = 1, 2, 3, ... N represents the sample number, and N is the total number of samples; It is the loss function for a single sample.

[0063] The physical constraints for:

[0064] (3)

[0065] in, The S-parameter simulation data of the honeycomb composite material before equivalence is represented. The real part of the S-parameters of the honeycomb composite material obtained from the calculation of the physical equation of electromagnetic wave propagation is represented. This represents the imaginary part of the S-parameters of the honeycomb composite material obtained from the calculation of the physical equations of electromagnetic wave propagation.

[0066] Real part of the equivalent S-parameter and the virtual part The calculation method is as follows:

[0067] The physical equations for electromagnetic wave propagation in the honeycomb structure composite material, based on Maxwell's equations, are as follows:

[0068] (4)

[0069] (5)

[0070] (6)

[0071] Where Γ represents the reflection coefficient and T represents the transmission coefficient. This represents the total reflection coefficient. This represents the total transmission coefficient.

[0072] (1) When the incident plane wave is vertically polarized, the formula for calculating the relative permittivity of the honeycomb composite material is as follows:

[0073] (7)

[0074] (8)

[0075] (9)

[0076] in, This represents the relative permeability of the honeycomb composite material, which is taken as 1 in this example; The relative permittivity of the honeycomb composite material is represented by θ; the incident angle is θ; and the thickness of the dielectric plate is d. The wave number in free space; These are intermediate quantities in the calculation process and have no actual physical meaning. It is the imaginary unit.

[0077] (2) When the incident plane wave is parallel polarized, the formula for calculating the relative permittivity of the honeycomb structure composite material is as follows:

[0078] (10)

[0079] (11)

[0080] (12)

[0081] The equivalent relative permittivity output by the physical driving neural network. Substituting the real and imaginary predicted values ​​into formulas (4)-(9) or (4)-(6) and (10)-(12) respectively, the real part of the equivalent S-parameter is calculated. and the virtual part The loss value is calculated by comparing it with the simulated S-parameters.

[0082] Step S4. Input the S-parameter simulation dataset into the physical driving neural network and optimize the network parameters through backpropagation; when the loss function is less than the set threshold, the real part prediction value and imaginary part prediction value of the equivalent relative permittivity of the honeycomb structure composite material are finally output.

[0083] Figure 3This is a flowchart illustrating the process of solving for equivalent electromagnetic parameters using a physical-driven neural network according to the present invention. The S-parameter simulation data serves as the input to the physical-driven neural network, and the output consists of the predicted real and imaginary parts of the equivalent relative permittivity. These predicted real and imaginary parts are then substituted into the physical constraint equations within the loss function to calculate the predicted S-parameters. Finally, the input S-parameter simulation data and the predicted S-parameters are squared, and this squared error is used as the return value of the loss function of the physical-driven neural network for backpropagation. The network parameters are then reassigned based on the gradient to minimize the loss function. When the loss function is less than a set threshold, the output is the required equivalent relative permittivity.

[0084] Step S5. Using the equivalent relative permittivity obtained in step S4, establish an equivalent electromagnetic model of the honeycomb composite material in the finite element simulation software ANSYS HFSS.

[0085] Specifically, an equivalent plate model with the same dimensions as the honeycomb composite material is established in the HFSS 3D modeling environment; periodic boundary conditions are applied at the boundary of the equivalent plate model to simulate the electromagnetic behavior of an infinitely large periodic structure; an excitation source is set on the surface of the equivalent plate model, and the frequency scanning range and solution settings are defined; after performing electromagnetic simulation, the S-parameters of the equivalent plate model are extracted to evaluate its electromagnetic characteristics.

[0086] This invention models the electromagnetic wave propagation physical equations based on Maxwell's equations in honeycomb composite materials using a physical-driven neural network. Combined with the S-parameters of the honeycomb composite materials obtained from simulation, it accurately simulates the process of solving the equivalent electromagnetic parameters of the physical equations. This effectively overcomes the problems of high computational complexity and low efficiency in traditional methods for solving equivalent electromagnetic parameters of composite materials. At the same time, it solves the problem that pure data-driven deep learning methods rely too much on large-scale labeled data.

[0087] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

[0088] It should be understood that, in order to simplify the present invention and help those skilled in the art understand its various aspects, in the above description of exemplary embodiments of the present invention, various features of the present invention are sometimes described in a single embodiment or with reference to a single figure. However, the present invention should not be construed as including all features in the exemplary embodiments as essential technical features of the claims of this patent.

Claims

1. A method for obtaining equivalent electromagnetic parameters of PINN-based honeycomb composite materials, characterized in that, Includes the following steps: Step S1. Establish an electromagnetic model of the honeycomb composite material and set excitation conditions. Test and obtain the S-parameters of the honeycomb composite material. Extract the reflection parameters and transmission parameters from the S-parameters to construct an S-parameter simulation dataset. Step S2. Construct a physics-driven neural network and set the loss function; The physical driving neural network is implemented using a deep neural network architecture; the physical driving neural network consists of one input layer, M hidden layers and one output layer stacked in sequence. The input data of the input layer is samples from the S-parameter simulation dataset; the output data of the output layer is the predicted real part and the predicted imaginary part of the equivalent relative permittivity; each hidden layer is connected to an activation function to improve the fitting ability to complex solution spaces. The loss function includes the data loss term and physical constraint term of the deep neural network, and its expression is: （1） （2） in, This represents the loss function for sample data in a deep neural network. Represents physical constraint terms. The weight coefficients of the physical constraint terms are represented; i=1,2,3,…N represent the sample numbers in the S-parameter simulation dataset, and N is the total number of samples; The S-parameter simulation data of the honeycomb composite material before equivalence is represented. The real part of the S-parameters of the honeycomb composite material obtained from the calculation of the physical equation of electromagnetic wave propagation is represented. The imaginary part of the S-parameters of the honeycomb composite material obtained from the calculation of the physical equation of electromagnetic wave propagation is represented. The loss function for the sample data in the deep neural network is: in, The loss function for a single sample; Step S3. Input the samples in the S-parameter simulation dataset into the physical driving neural network and optimize the network parameters through backpropagation; when the loss function is less than the set threshold, the real part prediction value and imaginary part prediction value of the equivalent relative permittivity of the honeycomb structure composite material are finally output.

2. The method for obtaining equivalent electromagnetic parameters of a PINN-based honeycomb composite material as described in claim 1, characterized in that, In the loss function, the real part of the equivalent S-parameter and the virtual part The calculation method is as follows: The physical equations for electromagnetic wave propagation in the honeycomb structure composite material, based on Maxwell's equations, are as follows: （3） （4） （5） Where Γ represents the reflection coefficient and T represents the transmission coefficient. This represents the total reflection coefficient. This represents the total transmission coefficient; (1) When the incident plane wave is vertically polarized, the formula for calculating the relative permittivity of the honeycomb composite material is as follows: （6） （7） （8） in, This indicates the relative permeability of the honeycomb composite material. The relative permittivity of the honeycomb composite material is represented by θ; the incident angle is θ; and the thickness of the dielectric plate is d. The wave number in free space; These are intermediate quantities in the calculation process and have no actual physical meaning. The imaginary unit; (2) When the incident plane wave is parallel polarized, the formula for calculating the relative permittivity of the honeycomb structure composite material is as follows: （9） （10） （11） in, This indicates the relative permeability of the honeycomb composite material. The relative permittivity of the honeycomb composite material is represented by θ; the incident angle is θ; and the thickness of the dielectric plate is d. The wave number in free space; These are intermediate quantities in the calculation process and have no actual physical meaning. The imaginary unit; Based on the polarization mode of the incident wave set in the excitation conditions of step S1, the real part prediction value and imaginary part prediction value of the equivalent relative permittivity output by the physical driving neural network are substituted into formulas (3)-(8) or (3)-(5) and (9)-(11) respectively to calculate the real part of the equivalent S-parameter. and the virtual part .

3. The method for obtaining equivalent electromagnetic parameters of a PINN-based honeycomb composite material as described in claim 2, characterized in that, The physical-driven neural network uses the Adam optimizer to iteratively update the trainable parameters.

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