Electromagnetic field prediction method based on deep learning network model

Abstract

The application discloses an electromagnetic field prediction method based on a deep learning network model, belongs to the technical field of absorbing boundary in computational electromagnetics, constructs and trains an Autoformer model, applies a sequence decomposition mechanism and a sparse self-correlation mechanism to a WCS-FDTD framework based on an electromagnetic model, and more quickly and accurately updates electromagnetic field data, inputs acquired historical internal field domains and electromagnetic field data at corresponding absorbing boundaries into a trained neural network model for prediction, calculates electromagnetic field data of an internal field domain at a next moment based on predicted electromagnetic field data at the absorbing boundary at the next moment and electromagnetic field data of the internal field domain at a current moment, combines predicted electromagnetic field data at the absorbing boundary at the next moment with electromagnetic field data of the internal field domain at the next moment, generates input data at the next moment for iterative prediction, and finally obtains electromagnetic field data of a calculation domain at each moment.

Description

Technical Field

[0001] This invention belongs to the field of absorbing boundary technology in computational electromagnetics, specifically relating to an electromagnetic field prediction method based on a deep learning network model. Background Technology

[0002] The finite-difference time-domain (FDTD) method, as one of the core techniques in computational electromagnetics, has been widely applied in various fields. However, constrained by the Courant-Friedrichs-Lewy (CFL) condition, its time step is strongly correlated with the mesh size. In fine-structure simulation scenarios, to ensure numerical accuracy, the time step needs to be significantly compressed, which leads to a sharp increase in the number of iterations and thus significantly prolongs the computer simulation time. To address this issue, the weakly conditioned stable finite-difference time-domain (WCS-FDTD) method has been proposed. This method, through sub-time step decomposition and an explicit-implicit hybrid computation algorithm, decouples the computation process from the dependence on the mesh size in two directions, thereby significantly increasing the time step and effectively improving computational efficiency.

[0003] Open-domain problems in electromagnetic simulations are of significant research value, but solving these problems requires a large number of meshes to simulate a non-reflective wave environment. Due to limitations in computational resources, memory capacity, and computation time, computers cannot directly and efficiently solve these problems. Therefore, special methods are needed to truncate electromagnetic wave propagation and avoid reflection at specific locations, i.e., using absorbing boundaries for computation. Among these methods, the perfectly matched layer (PML) is the most widely used, with derivatives including the Berenger PML (BPML), unsplit PML (UPML), and convolutional PML (CPML). While CPML is favored by researchers for its high computational efficiency and optimal accuracy with the same number of layers, it still requires 5-10 layers to achieve complete electromagnetic wave absorption. Furthermore, the need to introduce auxiliary convolutional terms significantly increases the computational load, prolongs simulation time, and consumes substantial memory resources.

[0004] In recent years, with the rapid development of hardware technology, machine learning, and deep learning, many researchers have introduced related technologies into the study of absorbing boundaries to overcome the aforementioned challenges. For example, some researchers have proposed a model based on the Hyperbolic Tangent Based Function (HTBF) suitable for the two-dimensional FDTD framework, but it suffers from accumulated errors in long-term simulations. Other researchers have proposed an LSTM (Long Short-Term Memory) model for the two-dimensional FDTD framework, but its absorption efficiency and generalization ability have not yet reached ideal levels. Furthermore, no researchers have yet applied similar intelligent absorbing boundaries to the two-dimensional WCS-FDTD framework, indicating that there is still significant room for improvement in absorption efficiency, generalization ability, and simulation efficiency in this field.

[0005] In summary, there is an urgent need for a boundary absorption method that can overcome the shortcomings of existing technologies and achieve efficient simulation, efficient wave absorption, accurate calculation, and simplicity within the two-dimensional WCS-FDTD framework. Summary of the Invention

[0006] To address the shortcomings of existing technologies and achieve the goals of significantly improving simulation efficiency, reducing simulation time, and lowering memory resource consumption while ensuring absorption efficiency and generalization, this invention adopts the following technical solution:

[0007] The electromagnetic field prediction method based on deep learning network models includes the following steps:

[0008] Construct an electromagnetic model of the computational domain, including the internal field of the computational domain and the absorbing boundary surrounding the internal field, with an excitation source in the internal field;

[0009] Historical electromagnetic field data of the internal field and the corresponding absorption boundary at the current moment are collected as input data, and electromagnetic field data of the corresponding absorption boundary at the next moment are collected as label data to construct sample pairs and obtain a set of sample data.

[0010] Construct a deep learning network model and train the deep learning network model based on the sample data;

[0011] Based on the electromagnetic model, the electromagnetic field data at different times is updated using the weakly conditionally stable finite-difference time-domain method. The acquired historical internal field data and the electromagnetic field data at the corresponding absorbing boundary are input into the trained deep learning network model for prediction. Based on the predicted electromagnetic field data at the absorbing boundary at the next time step and the electromagnetic field data of the internal field at the current time step, the electromagnetic field data of the internal field at the next time step is calculated. Then, the electromagnetic field data at the absorbing boundary at the next time step and the electromagnetic field data of the internal field at the next time step are combined to generate the input data for the next time step for iterative prediction, and finally the electromagnetic field data of the computational domain at each time step is obtained.

[0012] Furthermore, the computational domain is meshed, and the historical electromagnetic field data of the connected internal field grid and the absorbing boundary grid are used as the input data. The electromagnetic field data of the absorbing boundary grid connected to the internal field grid at the next moment is used as the label data. The deep learning network model is trained based on the input data and label data, so that the trained deep learning network model can predict the electromagnetic field data of the absorbing boundary grid connected to the internal field grid at the next moment using the historical electromagnetic field data at the internal field grid and the absorbing boundary grid connected to it. Based on the predicted electromagnetic field data of the absorbing boundary grid at the next moment and the electromagnetic field data of the internal field grid at the current moment, the electromagnetic field data of the internal field grid at the next moment is calculated. The predicted electromagnetic field data of the absorbing boundary grid at the next moment and the electromagnetic field data of the internal field grid at the next moment are combined to generate the input data for the next moment for iterative prediction, and finally the electromagnetic field data of the computational domain at each moment is obtained. In the simulation process, this invention predicts the electromagnetic field value on the absorbing boundary at the next time step by calculating historical data of the electromagnetic field values ​​of the field inside the domain and the absorbing boundary. Then, it substitutes the electromagnetic field value on the absorbing boundary at the next time step and the electromagnetic field value of the field inside the current time step into the weakly conditionally stable finite-difference time-domain method to obtain the electromagnetic field value of the field inside the next time step. This invention achieves the coupling of intelligent absorbing boundary and weakly conditionally stable finite-difference time-domain method for the first time.

[0013] Furthermore, an absorption boundary grid connected to the internal field grid is set for the absorption boundary. The direction from the excitation source to the absorption boundary is the horizontal direction, the direction perpendicular to the horizontal direction and upward is the vertical direction, and the directions perpendicular to the horizontal direction and the vertical direction and outward are the longitudinal direction. For two internal field grids and one absorption boundary grid connected in sequence, the electromagnetic field values ​​of the three grids at the current time step and the historical time step are collected as the input data based on the electric field of the grid in the horizontal and vertical directions and the magnetic field of the grid in the longitudinal direction. At the same time, the electromagnetic field value of the absorption boundary grid at the next time step is collected as the tag data.

[0014] Furthermore, the computational domain is a rectangular area, and the grid is a rectangular grid. For the non-corner points of the rectangular grid, the input data and the label data are collected from the three grids connected horizontally or vertically in sequence. For the corner points of the rectangular grid, the input data and the label data are collected from the three grids connected diagonally in sequence.

[0015] For the non-corner points of the rectangular grid, the sample data was collected as follows:

[0016]

[0017] For the corner points of the rectangular grid, the sample data was collected as follows:

[0018]

[0019] Where i and j represent the indices of the x and y coordinates of the grid nodes in the computational domain, respectively. This represents the electromagnetic field value at time step t for the node on the absorbing boundary with coordinate index (i,j) and the nodes in the internal field connected to it. This represents the vertical component of the magnetic field along the z-axis. This represents the horizontal component of the magnetic field along the x-axis. This represents the component of the electric field along the y-axis. This represents the electromagnetic field value at the absorbing boundary node with coordinate index (i,j) at time step t+1.

[0020] Furthermore, the deep learning network model includes an input projection layer, a sequence decomposition layer, an autocorrelation layer, a normalization layer, a forward propagation layer, a self-attention module, and an output layer. The input projection layer acquires the input data and projects it to obtain an input sequence. The sequence decomposition layer decomposes the acquired input sequence into a long-term trend component and a short-term fluctuation component, and after passing them through the autocorrelation layer, the two output sequences are added together. After layer normalization by the normalization layer, the sequence passes through the forward propagation layer and then through the self-attention module to enter the output layer, finally obtaining the predicted output data. The deep learning network model constructs a loss function using the predicted output data and the labeled data for model training. The Autoformer network described in this invention, through the sequence decomposition mechanism, enables it to model the long-term trend component and the short-term fluctuation component separately. It then utilizes the sparse autocorrelation mechanism to mine the potential patterns in the sequence, thereby achieving more accurate prediction results and exhibiting good generalization in complex scenarios.

[0021] Furthermore, in order to accelerate training and obtain better training results, it is necessary to unify the dimensions of the training data to achieve data normalization. During the training phase, the magnetic field values ​​of the input data and the magnetic field values ​​of the label data are multiplied by the vacuum wave impedance. During the prediction phase, the magnetic field values ​​of the input data are multiplied by the vacuum wave impedance, and the magnetic field values ​​in the output data are divided by the vacuum wave impedance to obtain the final predicted data. The vacuum wave impedance is the square root of the ratio of vacuum permeability to vacuum permittivity.

[0022] Furthermore, the weakly conditionally stable finite-difference time-domain method updates the electromagnetic field data at different time steps by dividing the time step into a first sub-time step and a second sub-time step using the weakly conditionally stable finite-difference time-domain method in each time step. For the first sub-time step, based on the electromagnetic field data of the grid, the time step size, the permittivity, the permeability, and the horizontal length of a single grid, the electromagnetic field values ​​on the grid nodes are updated row by row in the horizontal direction to obtain the electromagnetic field data of all grids in the first sub-time step. For the second sub-time step, based on the electromagnetic field data of the grid, the vertical time step size, the permittivity, the permeability, and the vertical width of a single grid, the electromagnetic field values ​​on the grid are updated column by column in the vertical direction to obtain the electromagnetic field data of all grids in the second sub-time step, i.e., updating the electromagnetic field data of one time step.

[0023] Each time step is divided into a first sub-time step and a second sub-time step; First sub-time step:

[0024]

[0025]

[0026]

[0027] Where i and j represent the indices of the x and y coordinates of the grid nodes in the computational domain, respectively. This represents the vertical component of the magnetic field along the z-axis. This represents the horizontal component of the magnetic field along the x-axis. This represents the component of the electric field along the y-axis. This indicates the time step size for a single-step simulation. Represents the dielectric constant. Indicates magnetic permeability, This represents the length of a single grid cell in the x-direction;

[0028] Second sub-time step:

[0029]

[0030]

[0031]

[0032] in, This represents the length of a single grid cell in the z-direction.

[0033] Furthermore, the data from the same grid in the input data are stacked in the time dimension as input data. Considering that the Autoformer model can use GPU for parallel computing, the electromagnetic field values ​​at different nodes at the same time are stacked together in an orderly manner, which greatly accelerates the single-step calculation process and significantly improves the computing efficiency.

[0034] Furthermore, during the iteration process, the input data of the trained deep learning network model is stored in a columnar stacked structure. During output, the electromagnetic field value is accurately assigned to its corresponding grid node. In the simulation process, the electromagnetic field data uses a columnar stacked data storage method, which facilitates the Autoformer network to perform electromagnetic field assignment calculations at the corresponding nodes. Moreover, the present invention uses the weakly conditionally stable finite-difference time-domain method to update the electromagnetic field data at different time steps. The weakly conditionally stable finite-difference time-domain method uses a tridiagonal matrix to solve for the electric field value in a columnar stacked structure, which can make some data completely fit the structure of the input data of the deep neural network model, thereby accelerating the calculation process of each simulation time step, saving computing resources, and improving simulation efficiency.

[0035] Furthermore, based on the center coordinates of the grid and the amplitude, frequency, time step number, and single-step time step size of the center coordinates, electromagnetic field data of the grid at different times are generated.

[0036] The advantages and beneficial effects of this invention are as follows:

[0037] This invention introduces the Autoformer model into the weakly conditionally stable finite-difference time-domain method for the first time. By using a prediction model based on a time series model, it simplifies the computation of the original CPML. Compared to the complex calculation of convolution terms required in CPML, this invention eliminates the need to calculate any auxiliary terms, significantly simplifying the computation process. It achieves the effect of replacing multiple layers of traditional CPML with a single intelligent absorbing boundary layer, thereby greatly simplifying the computation and reducing computational complexity. This invention uses the WCS-FDTD framework, which can overcome the limitations of the CFL conditions in other intelligent absorbing boundary FDTD frameworks during simulation. This allows for simulations at longer time steps, reducing simulation time and improving simulation efficiency. Attached Figure Description

[0038] Figure 1 This is a flowchart of a method according to an embodiment of the present invention.

[0039] Figure 2 This is a schematic diagram illustrating the principle of collecting training data through a reference electromagnetic simulation model in an embodiment of the present invention.

[0040] Figure 3 This is a schematic diagram of the framework of the Autoformer network in an embodiment of the present invention.

[0041] Figure 4 This is a WCS-FDTD simulation diagram of a single-excitation-source, single-layer intelligent absorbing boundary in Embodiment 1 of the present invention.

[0042] Figure 5 This is a WCS-FDTD simulation diagram of a traditional 6-layer CPML absorbing boundary with a single excitation source in Embodiment 1 of the present invention.

[0043] Figure 6 This is a comparison curve of the average relative error of each method at point A at different time periods in Embodiment 1 of the present invention.

[0044] Figure 7 This is a comparison curve of the average relative error of each method in Embodiment 1 of the present invention at point B in different time periods.

[0045] Figure 8 This is a comparison curve of the average relative error of each method in Embodiment 1 of the present invention across the entire computational domain.

[0046] Figure 9 This is a schematic diagram of electromagnetic simulation using multiple excitation point sources in Embodiment 2 of the present invention.

[0047] Figure 10 This is a comparison curve of the average relative error of each method at point A at different time periods in Embodiment 2 of the present invention.

[0048] Figure 11 This is a comparison curve of the average relative error of each method at point B at different time periods in Embodiment 2 of the present invention.

[0049] Figure 12 This is a comparison curve of the average relative error of each method in Embodiment 2 of the present invention across the entire computational domain.

[0050] Figure 13 This is a schematic diagram of electromagnetic simulation using multiple excitation point sources and multiple metals in Embodiment 3 of the present invention.

[0051] Figure 14 This is a comparison curve of the average relative error of each method in Embodiment 3 of the present invention at point A at different time periods.

[0052] Figure 15 This is a comparison curve of the average relative error of each method in Embodiment 3 of the present invention at point B in different time periods.

[0053] Figure 16 This is a comparison curve of the average relative error of the entire computational domain in Embodiment 3 of the present invention. Detailed Implementation

[0054] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0055] like Figure 1 As shown, the electromagnetic field prediction method based on a deep learning network model includes the following steps:

[0056] Step 1: Construct a reference electromagnetic simulation model for data acquisition, such as... Figure 2 As shown, the specific simulation parameters are: mesh size is... The size of the computational domain is The time step is A single-point source was set at its center as the excitation source, and the specific vibration expression is as follows:

[0057]

[0058] in, and These are the center coordinates in the x, y, and z directions, respectively. For time steps, This indicates the time step size for a single-step simulation. For amplitude, The frequency is specified. Additionally, to ensure the collected data is echo-free electromagnetic wave propagation data, the reference model employs 120 layers of CPML as the absorbing boundary.

[0059] Step 2: Simulate the reference electromagnetic simulation model and collect historical sample data for each set. The sample data collection process is as follows: Figure 2 As shown, the data collected in the first 600 ps of the reference electromagnetic simulation model is used to construct the training dataset. For a node (i, j) on the absorbing boundary, the electromagnetic field values ​​at time step t of two nodes in the computational domain connected sequentially and one node on the absorbing boundary, as well as the electromagnetic field value of the node on the absorbing boundary at time step t+1, are collected as a pair of sample data. Furthermore, the data collection methods differ between non-corner and corner locations. Specifically, the collection method for a pair of sample data is as follows:

[0060]

[0061]

[0062] Where i and j represent the indices of the x and y coordinates of the grid nodes in the computational domain, respectively. This represents the electromagnetic field value at time step t for the node on the absorbing boundary with coordinate index (i,j) and the nodes in the computational domain connected to it. This represents the component of the magnetic field along the z-axis (vertical) direction. This represents the component of the magnetic field along the x-axis (horizontally to the right). This indicates that the electric field is in the y-axis direction (the depth direction, i.e., pointing towards). Figure 2 The component in the outward direction, This represents the electromagnetic field value of the absorbing boundary node with coordinate index (i,j) at time step t+1 (the next time step);

[0063] Then stack the data from the same node along the time dimension. As input to sample data, This is then used as the output of the sample data, where N is a preset integer value (e.g., N=15). Considering that Autoformer can utilize GPUs for parallel computation, the electromagnetic field values ​​at different nodes (different i,j) at the same time are stacked together in an ordered manner to obtain... Then obtain the input data. This significantly accelerates the training process.

[0064] Again Figure 1 The Autoformer model is established using the following structural form:

[0065] The dimension of the feature vectors in the model is set to 27;

[0066] The sequence decomposition module uses a moving average to calculate the long-term trend sequence, and subtracts the long-term trend sequence from the original sequence to obtain the short-term fluctuations;

[0067] The autocorrelation layer employs a sparse autocorrelation mechanism;

[0068] The activation function used is the hyperbolic tangent (tanh) activation function.

[0069]

[0070] Step 3: Use the collected training dataset for the Autoformer network. For example... Figure 3As shown, the Autoformer network architecture adopts an improved Autoformer network architecture. The structure from input to output is as follows: input projection layer, sequence decomposition layer, autocorrelation layer, normalization layer, forward propagation layer, self-attention module, and output layer. The input projection layer consists of multiple fully connected layers. The sequence decomposition layer decomposes the input sequence of this layer into long-term trend components and short-term fluctuation components. The autocorrelation layer calculates the input sequence of this layer through sparse autocorrelation and then adds the two output sequences of this layer. The normalization layer uses a layer normalization algorithm. The forward propagation layer consists of multiple fully connected layers, activation functions, and residual structures. The self-attention module uses a sparse attention mechanism. The output layer consists of multiple fully connected layers and activation functions.

[0071] An Adaptive Moment Estimation (Adam) optimizer is used, with an initial learning rate of 0.003. A hybrid loss function is employed for training, the formula of which is:

[0072]

[0073] in, Represents the loss function. The weight parameters of the neural network, This indicates the number of samples contained in the training set of the dataset. This represents the true value of the electromagnetic field, i.e., the label value used to train the network. Indicates input The corresponding electromagnetic field predictions from the Autoformer network.

[0074] In actual training, to accelerate training and achieve better results, it is necessary to standardize the dimensions of the training data, thereby achieving data normalization. Specifically, this involves multiplying the magnetic field value in the input and label values ​​by the vacuum wave impedance. ,in It is the vacuum permittivity. This is the free magnetic permeability. Correspondingly, in the prediction phase, the magnetic field value in the input needs to be multiplied by... The magnetic field value in the output value is divided by Then, it is used as the predicted value of the electromagnetic field.

[0075] Step 4: Build the model to be simulated, and leave 1 mesh layer to integrate the Autoformer network here as an absorbing boundary.

[0076] Step 5: Integrate the trained Autoformer network into the WCS-FDTD computational framework for simulation calculations. In each simulation time step, calculate the electromagnetic field value for the next time step. The specific calculation process is as follows:

[0077] During the initial N time steps of the simulation, the electromagnetic field values ​​at all nodes are updated using the weakly conditionally stable finite-difference time-domain method at each time step. The specific calculation process is as follows:

[0078] First time step:

[0079] (1-1)

[0080] (1-2)

[0081] (1-3)

[0082] in, This indicates the time step size for a single-step simulation. Represents the dielectric constant. Indicates magnetic permeability, This represents the length of a single grid cell in the x-direction;

[0083] Second sub-time step:

[0084] (2-1)

[0085] (2-2)

[0086] (2-3)

[0087] in, This represents the length of a single grid cell in the z-direction;

[0088] Each time step iteration is divided into two sub-time steps. In the first sub-time step, the implicit equation (1-1) is first used to calculate... Then, use the two explicit equations (1-2) and (1-3) to calculate... and In the second sub-time step, in the first sub-time step, the implicit equation (2-1) is first used to calculate... Then, use the two explicit equations (2-2) and (2-3) to calculate... and .

[0089] Then, the electromagnetic field values ​​of the absorbing boundary and its surrounding nodes are saved. Finally, at the end of the (N-1)th time step iteration, the result is obtained. ;

[0090] When the current iteration time step is greater than or equal to N, in each iteration of time step: first, input the historical data of the electromagnetic field values ​​of the absorbing boundary node and its surrounding nodes into the model for prediction, and use the obtained values ​​as the electromagnetic field values ​​of the absorbing boundary node in the next time step; then, substitute these values ​​and the values ​​of the field inside the computational domain in this time step into the weakly conditionally stable finite-difference time-domain method to calculate the electromagnetic field values ​​of the field inside the computational domain in the next time step; then, combine the electromagnetic field values ​​of the absorbing boundary and the electromagnetic field values ​​of the field inside the computational domain in the next time step to obtain the complete electromagnetic field values ​​for the next time step; finally, transfer the input sequence from... Updated to Then, proceed to the next iteration in the time step.

[0091] During the simulation iteration process, considering the parallel architecture of Autoformer, the electromagnetic field values ​​at different nodes (different i, j) at the same time are stacked together in an orderly manner to obtain... Then, stack them in the time domain to obtain the input data. This allows the GPU to perform parallel computations on all nodes at the absorbing boundary, greatly improving computation speed.

[0092] Furthermore, the data input to the Autoformer model is stored in a columnar stacked structure, allowing the program to accurately assign electromagnetic field values ​​to their corresponding nodes during output. The weakly conditional finite-difference time-domain method uses a tridiagonal matrix to solve for the electric field values ​​in a columnar stacked structure, ensuring that some data perfectly matches the structure of the Autoformer model's input data. This accelerates the calculation process at each simulation time step, saves computational resources, and improves simulation efficiency.

[0093] Example 1

[0094] This embodiment is used to verify the basic performance of the present invention, and its simulation model has the same parameter settings as the training set. For example... Figure 4 , Figure 5 As shown, the internal field size of the computational domain is 60 mm. 60mm, grid size is The time step is The sinusoidal point source is located at the center. When using this method, one mesh layer is reserved to integrate the Autoformer network here as an absorbing boundary. Figure 4 This is a schematic diagram showing the integration of the Autoformer network into the WCS-FDTD computing framework. Figure 5 This is a schematic diagram of a 6-layer CPML.

[0095] To quantitatively evaluate the absorption effect of this method, the relative error is defined as follows:

[0096]

[0097] in, Let be the electric field value of the method to be measured. This is a reference electric field value that is approximately non-reflective, obtained using multilayer CPML (e.g., 120 layers). The maximum value of the reference electric field throughout the entire simulation process.

[0098] Figure 6 , Figure 7 The relative errors at observation points A and B (600 ps-1000 ps and 3600 ps-4000 ps) are shown respectively. For point A, the traditional 1-layer CPML and 6-layer CPML show errors of -11 dB and -37 dB respectively. For comparison, the relative errors of the HTBF model and LSTM model in the integrated 2D WCS-FDTD framework are also given. The maximum errors of the HTBF model and LSTM model are -31 dB and -34 dB respectively. Meanwhile, the maximum error of this invention is only -40 dB, lower than the errors of traditional CPML and other machine learning-driven absorption boundaries. For point B, the maximum relative errors of the traditional 1-layer CPML, 6-layer CPML, HTBF model, LSTM model, and this method are -9 dB, -35 dB, -28 dB, -32 dB, and -40 dB respectively, demonstrating that this invention achieves the best absorption effect.

[0099] Figure 8 The relative average errors of these five methods across the entire computational domain were compared. The traditional 1-layer CPML had an average error of -13dB, indicating poor absorption performance. Furthermore, the average errors of the other methods were: -37dB for 6-layer CPML, -30dB for the HTBF model, -32dB for the LSTM model, and -39dB for our proposed method. Therefore, our invention achieves the lowest absorption error. Compared to the traditional 6-layer CPML, its absorption performance is improved by 2dB. Moreover, compared to the HTBF model and the LSTM model, improvements are achieved by 9dB and 7dB, respectively. This demonstrates that our invention has superior absorption performance.

[0100] To evaluate computational efficiency, tests were conducted in an example hardware environment (a workstation equipped with a multi-core CPU and a GPU supporting parallel computing). In a comparative single-step simulation, the traditional 1-layer CPML and 6-layer CPML took 0.00694 seconds and 0.01187 seconds, respectively. The present invention, however, took only 0.00464 seconds. Clearly, compared to the traditional CPML, the present invention achieves a similar absorption effect to the 6-layer CPML while reducing computation time by 60.9%. Although slower than HTBF and LSTM models, it offers higher accuracy. These results demonstrate that the present invention significantly improves overall computational efficiency while maintaining the highest accuracy, especially by reducing memory consumption after simplifying boundary calculations.

[0101] Example 2

[0102] This embodiment is used to verify the generalization ability of the model of the present invention, and a new scenario with multiple excitation sources and an increased computational domain size is constructed. Figure 9 One sinusoidal point source is placed at the center of the computational domain, and four other sinusoidal point sources form a square, with one mesh layer reserved to integrate the Autoformer as an absorbing boundary. The internal field size of the computational domain is set to 140 mm. The simulation parameters were 140mm, and the rest were the same as in Example 1. The key difference was that the Autoformer model trained in the scenario of Example 1 was used directly without any retraining.

[0103] Figure 10 and Figure 11 The relative errors of different methods were compared. The maximum relative error of the 1-layer traditional CPML reached -7dB at point A and -8dB at point B, while the 6-layer CPML reached -35dB at point A and -36dB at point B. The LSTM model... Figure 9 The error reached -30dB at point A and -32dB at point B. However, in long-term simulations, the error of the HTBF model gradually accumulated, reaching -13dB at point A and -11dB at point B. In contrast, this invention exhibited the lowest error, reaching -38dB at point A and -37dB at point B.

[0104] also, Figure 12The average relative error across the entire computational domain is also demonstrated. The maximum average relative error of a single-layer traditional CPML reaches -13dB, while the HTBF model, through gradual error accumulation over long-term simulations, also reaches -13dB. Notably, this invention achieves an average relative error of -38dB, outperforming the LSTM model (-33dB) and the traditional 6-layer CPML (-37dB). Furthermore, for single-step computation, the traditional 1-layer CPML and 6-layer traditional CPML require 0.03508 seconds and 0.04565 seconds, respectively, while the LSTM model and this invention require only 0.01535 seconds and 0.02752 seconds, respectively. The above analysis demonstrates that when simulating more complex scenarios than those in the training set, this invention maintains good absorption efficiency while requiring less computation time compared to traditional CPML, which preliminarily proves the generalization ability of this invention.

[0105] Example 3

[0106] This embodiment is used to verify the robustness of the present invention in complex electromagnetic environments. A simulation model with multiple point sources, a large computational domain, multiple mesh sizes, and multiple metals was constructed. Figure 13 This embodiment incorporates fine structures in both the x and z directions. ), and placed two metallic scatterers in the computational domain, one of which was located within a fine structure, and extended the simulation time step to ), The remaining simulation parameters are the same as in Example 2. This complex scenario places extremely high demands on the absorption boundary, as it not only needs to absorb the complex scattered waves generated by the fine structure and metallic body, but also requires the present invention to adapt to simulation states with large time steps.

[0107] Figure 14 , Figure 15 Error analysis at specified observation points is presented. The HTBF model initially exhibits good absorption performance. However, its error accumulates over time, leading to performance degradation. Its maximum relative error reaches -10 dB at point A and -11 dB at point B. Other methods remain stable. The maximum relative errors at point A for the 1-layer CPML, 6-layer CPML, and LSTM models are -9 dB, -35 dB, and -28 dB, respectively, and at point B, they are -8 dB, -34 dB, and -25 dB, respectively. In contrast, the relative errors of this invention reach -41 dB at point A and -38 dB at point B, demonstrating superior absorption performance.

[0108] Figure 16The average relative errors of these methods were discussed. The HTBF model gradually accumulated errors after 9000 ps, ​​eventually reaching -13 dB. The LSTM model's error increased to -27 dB, while the present invention maintained a low error (-37 dB), comparable to the traditional 6-layer CPML (-36 dB). Clearly, the present invention exhibits excellent absorption performance at larger time steps. It is worth noting that... The time step size breaks through the CFL limitation of the FDTD framework, which significantly expands the application scope of the smart absorption boundary.

[0109] Furthermore, for single-step simulation, this invention takes 0.02537 seconds, slightly longer than the 0.01875 seconds required by the LSTM model, but significantly shorter than the 0.04857 seconds for a 1-layer CPML and the 0.06307 seconds for a 6-layer CPML. Clearly, compared to traditional CPML, this invention achieves absorption performance comparable to a 6-layer CPML while reducing computation time by 59.79%. Compared to the LSTM model, its absorption performance is improved by 11 dB.

[0110] In addition, with the computing scale increasing from 60mm 60mm increased to 140mm At 140mm, the additional time cost decreased from 52.13% to 35.25%, indicating that the efficiency gap narrows at larger scales.

[0111] In summary, this invention combines the Autoformer network with the WCS-FDTD method to achieve a highly efficient intelligent absorbing boundary that can replace the traditional multi-layer CPML with only a single-layer mesh. Verification through multiple embodiments demonstrates that this invention has significant advantages in terms of accuracy, efficiency, stability, and generalization ability.

[0112] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An electromagnetic field prediction method based on a deep learning network model, characterized in that... Includes the following steps: Construct an electromagnetic model of the computational domain, including the internal field of the computational domain and the absorbing boundary surrounding the internal field, with an excitation source in the internal field; Historical electromagnetic field data of the internal field and the corresponding absorbing boundary at the current moment are collected as input data. Electromagnetic field data of the corresponding absorbing boundary at the next moment are collected as label data to construct sample pairs and obtain a set of sample data. An absorbing boundary grid connected to the internal field grid is set for the absorbing boundary to integrate the Autoformer network as the absorbing boundary. The direction from the excitation source to the absorbing boundary is defined as the horizontal direction, the direction perpendicular to the horizontal direction and upward is defined as the vertical direction, and the directions perpendicular to the horizontal direction and the vertical direction and outward are defined as the longitudinal direction. For two internal field grids and one absorbing boundary grid connected in sequence, based on the electric field of the grid in the horizontal and vertical directions and the magnetic field of the grid in the longitudinal direction, the electromagnetic field values ​​of the three grids at the current time step and the historical time step are collected as the input data. At the same time, the electromagnetic field value of the absorbing boundary grid at the next time step is collected as the label data. Construct an Autoformer deep learning network model and train the Autoformer deep learning network model based on the sample data; Based on the electromagnetic model, the electromagnetic field data at different times is updated using the weakly conditionally stable finite-difference time-domain method. The acquired historical internal field data and the electromagnetic field data at the corresponding absorbing boundary are input into the trained Autoformer deep learning network model for prediction. Based on the predicted electromagnetic field data at the absorbing boundary at the next time step and the electromagnetic field data of the internal field at the current time step, the electromagnetic field data of the internal field at the next time step is calculated. Then, the electromagnetic field data at the absorbing boundary at the next time step and the electromagnetic field data of the internal field at the next time step are combined to generate the input data for the next time step for iterative prediction, and finally the electromagnetic field data of the computational domain at each time step is obtained.

2. The electromagnetic field prediction method based on a deep learning network model according to claim 1, characterized in that: The computational domain is meshed, and historical electromagnetic field data of the connected internal field grid and absorbing boundary grid are used as input data. The next-moment electromagnetic field data of the absorbing boundary grid connected to the internal field grid is used as label data. The Autoformer deep learning network model is trained based on the input and label data. The trained Autoformer deep learning network model predicts the electromagnetic field data of the absorbing boundary grid connected to the internal field grid at the next moment using the historical electromagnetic field data of the internal field grid and its connected absorbing boundary grid. Based on the predicted electromagnetic field data of the absorbing boundary grid at the next moment and the electromagnetic field data of the internal field grid at the current moment, the electromagnetic field data of the internal field grid at the next moment is calculated. The predicted electromagnetic field data of the absorbing boundary grid at the next moment is combined with the electromagnetic field data of the internal field grid at the next moment to generate the input data for the next moment. Iterative prediction is then performed to obtain the computational domain electromagnetic field data at each moment.

3. The electromagnetic field prediction method based on a deep learning network model according to claim 1, characterized in that: The computational domain is a rectangular area, and the grid is a rectangular grid. For the non-corner points of the rectangular grid, the input data and the label data are collected from the three grids connected horizontally or vertically in sequence. For the corner points of the rectangular grid, the input data and the label data are collected from the three grids connected diagonally in sequence.

4. The electromagnetic field prediction method based on a deep learning network model according to claim 1, characterized in that: The Autoformer deep learning network model includes an input projection layer, a sequence decomposition layer, an autocorrelation layer, a normalization layer, a forward propagation layer, a self-attention module, and an output layer. The input projection layer acquires the input data and projects it to obtain the input sequence. The sequence decomposition layer decomposes the acquired input sequence into long-term trend components and short-term fluctuation components, and after passing them through the autocorrelation layer, the two output sequences are added together. After layer normalization by the normalization layer, the sequence passes through the forward propagation layer and then through the self-attention module to enter the output layer, finally obtaining the predicted output data. The Autoformer deep learning network model constructs a loss function using the predicted output data and the label data for model training.

5. The electromagnetic field prediction method based on a deep learning network model according to claim 4, characterized in that: During the training phase, the magnetic field values ​​of the input data and the label data are multiplied by the vacuum wave impedance. During the prediction phase, the magnetic field values ​​of the input data are multiplied by the vacuum wave impedance, and the magnetic field values ​​in the output data are divided by the vacuum wave impedance to obtain the final predicted data. The vacuum wave impedance is the square root of the ratio of vacuum permeability to vacuum permittivity.

6. The electromagnetic field prediction method based on a deep learning network model according to claim 1, characterized in that: Updating electromagnetic field data at different time steps using the weakly conditionally stable finite-difference time-domain method involves dividing each time step into a first sub-time step and a second sub-time step. For the first sub-time step, based on the electromagnetic field data of the grid, the time step size, dielectric constant, permeability, and the horizontal length of a single grid, the electromagnetic field values ​​on the grid are updated row by row along the horizontal direction to obtain the electromagnetic field data of all grids in the first sub-time step. For the second sub-time step, based on the electromagnetic field data of the grid, the vertical time step size, dielectric constant, permeability, and the vertical width of a single grid, the electromagnetic field values ​​on the grid are updated column by column along the vertical direction to obtain the electromagnetic field data of all grids in the second sub-time step, thus updating the electromagnetic field data of one time step.

7. The electromagnetic field prediction method based on a deep learning network model according to claim 1, characterized in that: The input data is stacked in the time dimension, with data from the same grid stacked together as the sample input data.

8. The electromagnetic field prediction method based on a deep learning network model according to claim 1, characterized in that: During the iteration process, the input data of the trained deep learning network model is stored in a columnar stacked structure, and the electromagnetic field value is assigned to its corresponding grid during output.

9. The electromagnetic field prediction method based on a deep learning network model according to claim 2, characterized in that: Based on the center coordinates of the grid and the amplitude, frequency, time step number, and single-step time step size of the center coordinates, electromagnetic field data of the grid at different times are generated.

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