CN-121705667-B - Electromagnetic field intelligent calculation method based on deep learning

CN121705667BCN 121705667 BCN121705667 BCN 121705667BCN-121705667-B

Abstract

The invention discloses an electromagnetic field intelligent calculation method based on deep learning, which comprises the following steps of inputting space-time vectors Is input into an MFF-PINN neural network, wherein the MFF-PINN neural network comprises Parallel sub-networks and linear superposition modules, the first The sub-network comprises a scale transformation module, a Fourier feature transformation module and an MLP processing module, wherein the scale transformation module firstly performs scale transformation on a time-space input vector, then performs Fourier feature transformation on the vector after the scale transformation, the Fourier feature transformation module performs Fourier transformation on the vector after the scale transformation based on an effective frequency matrix, and all the sub-networks share the Fourier feature transformation and input output obtained by the Fourier feature transformation to the first node MLP processing module in sub-network The outputs of the sub-networks are linearly superimposed. The invention obviously enhances the expression capability of the network to electromagnetic field high-frequency components and multi-scale characteristics.

Inventors

JIANG HAOLIN
SUN SHUHENG
LI YE

Assignees

南京信息工程大学

Dates

Publication Date: 20260505
Application Date: 20260213

Claims (8)

1. An electromagnetic field intelligent computing method based on deep learning is characterized by comprising the following steps: Space-time input vector Is input into an MFF-PINN neural network, wherein the MFF-PINN neural network comprises Parallel sub-networks and linear superposition modules, wherein , Indicating time of day Coordinates below; First, the The sub-network comprises a scale transformation module, a Fourier feature transformation module and an MLP processing module, wherein the scale transformation module firstly performs scale transformation on a time-space input vector and then performs Fourier feature transformation on the vector after the scale transformation, an effective frequency matrix is defined in the Fourier feature transformation module by utilizing a combination law of matrix multiplication and scalar multiplication, and the Fourier transformation is performed on the vector after the scale transformation based on the effective frequency matrix Input to the first An MLP processing module in the sub-network; Will be The output of the sub-network is linearly overlapped to obtain the moment Lower coordinates An electromagnetic field vector at which the magnetic field is generated, ; Training the loss function of an MFF-PINN neural network The expression of (2) is: ; Wherein, the Representing the function of the loss of physical information, Representing the initial conditional loss function of the device, Representing a boundary condition loss function; is a weight super parameter that balances the loss of physical information, Is a weight super parameter that balances the initial condition loss, Is a weight super parameter for balancing the loss of boundary conditions; The physical information loss function is constructed by adopting the following method: building maxwell's equations for describing two-dimensional TE waves: ; Wherein, the 、、 Representing electromagnetic field components in the x-axis direction, the y-axis direction and the z-axis direction respectively, Indicating the dielectric constant of the material, To represent permeability, to measure the fitting of the neural network output to the electromagnetic law, the following residual functions are constructed for the maxwell's equations set described above: ; Wherein, the , , The first residual function, the second residual function and the third residual function are respectively; , , representing the predicted electromagnetic field components of the MFF-PINN neural network in the x-axis, y-axis, and z-axis, respectively; in order to make the mean square value of three residual functions approach zero, the domain is solved in space-time Internal random sampling Each configuration point And thereby construct the following physical information loss function: ; Wherein, the 、、 Respectively represent the first And the first, second and third residual functions are corresponding to the configuration points.
2. A method for intelligent computation of electromagnetic field based on deep learning as defined in claim 1, wherein the first step The scale transformation module of the sub-network adopts scalar scale factors Multiplying the time space input vector element by element to obtain a vector after the scale transformation; scalar scale factor sequence composed of scalar scale factors For geometric progression, scalar scale factors From the base amplitude factor And (d) Individual scale base factors And (3) jointly determining: 。
3. The intelligent electromagnetic field computing method based on deep learning as claimed in claim 2, wherein the fourier feature transformation module performs the following processing on the vector after the scale transformation: ; Wherein, the For the vector after the scaling, Is a fourier feature transformation module that, For the output of the fourier feature transform module, Is the first to The Fourier characteristic transformation module performs Fourier transformation on the vector after the corresponding scale transformation based on the effective frequency matrix; wherein Is a Gaussian frequency matrix; is subjected to gaussian distribution , Is subjected to gaussian distribution , Is a fixed base scale hyper-parameter.
4. A method for intelligent calculation of electromagnetic field based on deep learning as defined in claim 1 is characterized by that the method for constructing initial condition loss function includes sampling in the region where initial condition acts Data points Constructing an initial conditional loss function based on the data points: ; Wherein, the Predicted first for MFF-PINN neural network The physical quantity at the data point is calculated, Is the first The data points correspond to the actual physical quantities.
5. A method for intelligent calculation of electromagnetic field based on deep learning as defined in claim 1 is characterized by that the method for constructing boundary condition loss function is implemented by sampling on the region acted by boundary condition Sampling points Boundary operators of the MFF-PINN neural network at the sampling points are calculated The mean square error between the result after action and zero, gets the boundary condition loss function: ; Wherein, the Predicted first for MFF-PINN neural network Physical quantities at the sampling points.
6. The intelligent electromagnetic field calculation method based on deep learning as claimed in claim 1, wherein the gradient-based optimization algorithm performs end-to-end training on the model, and calculates the total loss after the back propagation step starts to be executed Relative to the whole set of parameters A gradient of each of the trainable parameters, the Adam optimizer then performs the parameter update.
7. A computer device comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that the processor implements the steps of a deep learning based electromagnetic field intelligent computing method as claimed in any one of claims 1 to 6 when the computer program is executed by the processor.
8. A computer readable storage medium storing a computer program, wherein the computer program when executed by a processor implements the steps of a deep learning based electromagnetic field intelligent computing method as defined in any one of claims 1 to 6.

Description

Electromagnetic field intelligent calculation method based on deep learning Technical Field The invention belongs to the field of electromagnetic field calculation, and particularly relates to an electromagnetic field intelligent calculation method based on deep learning. Background The accurate solution of Maxwell's equations has fundamental and key roles in the modern scientific and engineering fields of antenna design, electromagnetic compatibility analysis, electromagnetic stealth and the like. Currently, electromagnetic field simulation and prediction techniques for this system of equations mainly include traditional numerical calculation methods and emerging methods based on deep learning, which have been rapidly developed in recent years. Of the conventional numerical methods, the time-Domain finite difference Method (FINITE DIFFERENCE TIME Domain, FDTD), the finite element Method (FINITE ELEMENT Method, FEM), and the moment Method (Method of Moments, moM) are most widely used. The core idea is to discretize the continuous physical space into grid or patch units, thereby solving maxwell's equations approximately in algebraic form. Therefore, the reliability and efficiency of the calculation result is highly dependent on the quality of the grid or patch generation. Taking the FDTD algorithm based on the differential form of maxwell's equations as an example, in a multi-scale electromagnetic problem, in order to reduce the effect of the inherent numerical dispersion error on the solution accuracy, a Yee grid cell that is much smaller than the electrical size is typically required. Such fine meshing often results in mesh numbers of hundreds of millions or more, which can pose significant challenges for memory consumption and computational speed. Meanwhile, under the limitation of the stability condition of the Brownian condition (Courant-Friedrichs-Lewy), the excessively dense space dispersion inevitably brings hundreds of millions of time iteration steps, and the pressure of simulation time is further amplified. In addition, for targets with complex surface geometries, it is difficult for conventional FDTDs to avoid step approximation errors, and even with conformal mesh techniques, it is difficult to completely eliminate this effect, so that the accuracy and reliability of simulation results still face significant challenges. In order to thoroughly solve the influence of discrete unit generation on Maxwell's equation set numerical solution, a physical information neural network (Physics-Informed Neural Network, PINN) based on deep learning, which is rapidly developed in recent years, gradually becomes a novel research paradigm capable of replacing the traditional numerical algorithm, and is widely focused. PINN the core idea is to explicitly embed the dominant equations, boundary conditions, and initial conditions into the loss function of the neural network, driving the network to learn the solutions that satisfy the partial differential equation (PARTIAL DIFFERENTIAL Equation, PDE) by minimizing the physical residuals. The multi-layer perceptron (Multilayer Perceptron, MLP) is considered under this framework as a generic function approximator, enabling the solution of various types of mathematical physical equations to be implemented in a unified and flexible manner. By virtue of the mesh-free characteristic, PINN is widely applied in various fields such as hydrodynamics, acoustics, electrostatic magnetism, low-frequency electromagnetic problems, single-frequency electromagnetic analysis and the like, and has great development potential. However, when the classical PINN architecture is used to solve the high-frequency transient electromagnetic problem, its inherent spectral bias characteristics often lead to reduced solving efficiency, difficult convergence and even inability to accurately capture high-frequency details. Therefore, a brand new technical solution is needed in the art, which can fundamentally overcome the problem of PINN of spectrum bias, so that the device has the capability of efficiently representing the transient response and wide spectrum components of rapid change in the time domain electromagnetic field. The invention aims at solving the technical problems and aims at constructing an innovative PINN framework. According to the structure, the multi-scale Fourier feature mapping is introduced, so that the learning and expression capacity of the neural network to the high-frequency transient field component is remarkably improved, and the excellent performances of high precision, no grid and suitability for complex electromagnetic process simulation are realized when the time domain Maxwell equation is solved. Disclosure of Invention The invention aims to solve the problems in the prior art, and provides an electromagnetic field intelligent computing method based on deep learning. The invention provides an electromagnetic field intelligent computing method based on deep learning,