A hyper-physical information neural network-based hypersonic target wake electron density flow field reconstruction method, system, device and medium

Abstract

A hyper-target wake electron density flow field reconstruction method, system, device and medium based on a physical information neural network, the method obtains electron density numerical values and two-dimensional electron density distribution through CFD simulation calculation, respectively stores them, and arranges a training set to train the training set under the supervision of a loss function by using a flow field reconstruction model, so as to obtain a flow field reconstruction model with trained weights, input the axis electron density vector data of an unknown two-dimensional distribution into the flow field reconstruction model with trained weights, and obtain the two-dimensional electron density distribution of the target wake flow field; the system, device and medium are used for realizing the above-mentioned hyper-target wake electron density flow field reconstruction method; the application has the advantages of strong practicability, good reliability and high accuracy, and can be widely applied to the fields of hypersonic vehicle experiment and design, plasma diagnosis, material science research, quantum computing and simulation, etc.

Description

Technical Field

[0001] This invention relates to the field of hypersonic flow field reconstruction technology, specifically to a method, system, device, and medium for reconstructing the electron density flow field of a hypersonic target wake based on a physical information neural network. Background Technology

[0002] Hypersonic targets generate ions and electrons during their flight, forming a plasma sheath at the nose and a wake plasma downstream. Experimental studies often require measuring electron density in the wake. In experimental settings such as wind tunnel shock tubes, researchers use probes to measure electron density at specific points in the flow field. However, because probes affect the surrounding flow field, only a few measurement points are designed along the wake axis in practice. Scientific research often requires electron density data for the entire flow field, which experimental measurement methods cannot meet.

[0003] Graph Convolutional Neural Network (GCN) models encode a batch of data into a set of nodes, which are then used as input to the model. The model structure typically consists of multiple layers of graph convolutional layers and activation layers. As a generalization of convolutional neural networks to graph-structured data, GCNs can achieve end-to-end learning of node feature information and structural information, demonstrating good performance on multiple public datasets. Despite their excellent performance in many fields, GCNs still face some challenges in application scenarios with unclear contours, complexity, and uncertainty. Particularly in wake applications, the electron density of the flow field within the head shock wave gradually stabilizes as the aircraft moves away from the shock, a characteristic that can pose difficulties for GCN modeling capabilities.

[0004] Similar techniques include image super-resolution, which aims to use multi-layer nonlinear transformations to extract high-level abstract features of data, learn the underlying distribution patterns of the data, and thus acquire the ability to make reasonable judgments or predictions about new data. Similarly, the nonlinear transformations in this method are implemented through multiple convolutional layers. Image super-resolution builds a network model using a combination of convolutional neural networks and multiple residual blocks, and designs a loss function based on prior knowledge to ultimately achieve image reconstruction and prediction capabilities. Image super-resolution can improve the enhancement effect of images such as flow fields and remote sensing images, and can obtain high-precision and high-efficiency remote sensing image target recognition results. However, for prediction functions, it is limited to enhancing local blurred features and cannot meet the application background of reconstructing vector data into matrix data.

[0005] Furthermore, both of the aforementioned approaches are based on convolutional layers, resulting in a large data requirement for both GNNs and image super-resolution. However, flow field experiments are costly in terms of both materials and time, making them unsuitable for such large data demands. Moreover, the networks are prone to overfitting when faced with limited data. While convolutional neural networks can perform translations and rotations, they struggle with more complex spatial transformations, such as scaling changes and nonlinear distortions. Although data augmentation can alleviate these issues, it cannot completely solve them. For physical property problems, convolutional neural networks are considered "black box" models, lacking interpretable working mechanisms and decision-making processes.

[0006] Zhu Rui (Zhu Rui. Research on Image Recognition Algorithm Based on Convolutional Neural Network [D]. Beijing University of Posts and Telecommunications, 2018.) proposed a research on image recognition algorithm based on convolutional neural networks. This research utilizes image recognition model compression and acceleration techniques based on convolutional neural networks to propose an image recognition algorithm with low complexity, high accuracy, high efficiency, and fast real-time performance. However, image recognition algorithms are prone to overfitting when faced with limited data. In the application scenario of wakes, the electron density of the flow field within the head shock gradually stabilizes as the aircraft moves away, posing challenges to graph convolutional neural networks. The output results may not satisfy the physical mechanism, lacking an interpretable working mechanism and decision-making process.

[0007] Liu Chao (Liu Chao. Research and Implementation of Image Super-Resolution Reconstruction Algorithm Based on Deep Learning [D]. University of Electronic Science and Technology of China, 2023. DOI:10.27005 / d.cnki.gdzku.2022.001896.) proposed a research and implementation of an image super-resolution reconstruction algorithm based on deep learning. Specifically, he improved the generative adversarial network model based on multi-scale feature extraction. This model uses a densely connected multi-scale feature extraction module in the generator to extract image features, and uses a progressive two-stage reconstruction process instead of the original single-stage reconstruction process. This can accurately extract original features and high-level features, alleviate problems such as high computational complexity and gradient vanishing, and improve the feature expression ability of the network while effectively improving the quality of the reconstructed image. However, for physical property problems, convolutional neural networks are "black box" models, lacking interpretable working mechanisms and decision-making processes. Summary of the Invention

[0008] To overcome the shortcomings of the prior art, the present invention aims to provide a method, system, device, and medium for reconstructing the electron density flow field of a hypersonic target wake based on a physical information neural network. The method involves obtaining the electron density numerical value and the two-dimensional electron density distribution through CFD simulation calculations, storing these values, and organizing them to form a training set. A flow field reconstruction model is then trained on the training set under the supervision of a loss function to obtain a weighted flow field reconstruction model. The axial electron density vector data of the unknown two-dimensional distribution is input into the weighted flow field reconstruction model to obtain the two-dimensional electron density distribution of the target wake flow field. This method has the advantages of high practicality, high reliability, and high accuracy, and can be widely applied in fields such as hypersonic vehicle experiments and design, plasma diagnostics, materials science research, and quantum computing and simulation.

[0009] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0010] A method for reconstructing the electron density flow field of a hypersonic target wake based on a physical information neural network includes the following steps:

[0011] Step 1: Obtain the electron density values ​​on the central axis of the wake flow field of targets at different Mach numbers, store the electron density values ​​as vector data to obtain the axis electron density vector; obtain the two-dimensional distribution of electron density corresponding to the flow field where the central axis is located, store the two-dimensional distribution of electron density as matrix data; organize the vector data and matrix data into a training set.

[0012] Step 2: Construct a flow field reconstruction model, which includes a first fully connected layer, an activation layer, a deconvolution layer, a flattening layer, a second fully connected layer, a third fully connected layer, and a reconstructing layer; define the continuity equation in the NS equation as the loss function of the flow field reconstruction model;

[0013] Step 3: Use the flow field reconstruction model constructed in Step 2 to train the training set in Step 1 in the hypersonic target wake flow field at different Mach numbers. At the same time, use the loss function in Step 2 to supervise the training until the loss function converges, and obtain the flow field reconstruction model with trained weights.

[0014] Step 4: Using the unknown two-dimensional distribution of the axial electron density vector data as the input vector, the flow field reconstruction model with the weights trained in Step 3 is used to predict the input vector to obtain the two-dimensional electron density distribution of the target wake flow field.

[0015] In step 1, the electron density values ​​on the central axis and the two-dimensional distribution of electron density corresponding to the flow field where the central axis is located are obtained by CFD simulation calculations.

[0016] The flow field reconstruction model in step 2 is used to generate two-dimensional flow field data. The input layer receives vector data, the first fully connected layer increases the data volume, and the activation layer adjusts the data values. Two deconvolutional layers reconstruct features and increase the data dimension. A flattening layer flattens the high-dimensional data output by the deconvolutional layer into vector data. The data volume is normalized through the second and third fully connected layers. Finally, the data is reshaped through the reorganization layer and output to the desired size.

[0017] Step 2, which defines the continuity equation in the NS equations as the loss function of the flow field reconstruction model, specifically includes:

[0018] Spatial gradient features are extracted using the continuity equation of NS electrons in a steady fluid and discretized using the central difference method. The discretized continuity equation expression is used as a conservation term, and the mean square error between the true value and the predicted value of the conservation term constitutes the loss function. The loss function is combined with the flow field reconstruction model, so that the loss function propagates backward in the model and is used to optimize the model weights.

[0019] In step 4, the axial electron density vector data of the unknown two-dimensional distribution is the electron number density measured by the probe on the central axis of the blunt cone during the ground test.

[0020] A hypersonic target wake electron density flow field reconstruction system based on physical information neural network includes:

[0021] Data acquisition module: The electron density values ​​on the central axis of the wake flow field of targets at different Mach numbers and the two-dimensional distribution of electron density corresponding to the flow field where the central axis is located are obtained by CFD simulation calculation. The electron density values ​​are stored as vector data to obtain the axis electron density vector; the two-dimensional distribution of electron density is stored as matrix data. Finally, the vector data and matrix data are organized into a training set.

[0022] The deep learning module consists of two main parts: First, constructing the flow field reconstruction model and defining its loss function. The flow field reconstruction model is constructed using a first fully connected layer, activation layer, deconvolution layer, flattening layer, second fully connected layer, third fully connected layer, and reconstruction layer. The loss function is defined by the continuity equation in the NS equations. Second, training and supervising the flow field reconstruction model. The flow field reconstruction model is trained under the supervision of the loss function.

[0023] Prediction module: Using the unknown two-dimensional distribution of axis electron density vector data as the input vector of the flow field reconstruction model, the trained flow field reconstruction model reconstructs the input vector to obtain the two-dimensional electron density distribution of the target wake flow field where the vector data is located.

[0024] A hypersonic target wake electron density flow field reconstruction device based on physical information neural network includes:

[0025] Memory: Used to store computer programs that implement the hypersonic target wake electron density flow field reconstruction method based on physical information neural networks as described above;

[0026] Processor: Used to implement the hypersonic target wake electron density flow field reconstruction method based on physical information neural network as described above when executing the computer program.

[0027] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of a hypersonic target wake electron density flow field reconstruction method based on a physical information neural network.

[0028] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0029] Step 1 of this invention utilizes the electron density on the central axis of the hypersonic target wake flow field to reconstruct the flow field, which is consistent with the actual experimental setup and has strong practicality. The flow field data can be reconstructed through the central axis measurement data. Therefore, the reconstructed flow field data is highly correlated with the experimental data and has high accuracy.

[0030] Step 2 of this invention uses the Navier-Stokes equations to define the loss function of the flow field reconstruction model. Compared with existing graph convolutional neural networks and image super-resolution techniques, it has an interpretable physical mechanism and the advantage of being easier to converge with a small amount of training data.

[0031] Step 3 of this invention uses a training set composed of hypersonic target wake flow field data of different Mach numbers to train the flow field reconstruction model, which has the advantage of being adaptable to different application backgrounds.

[0032] Step 4 of this invention can obtain the complete two-dimensional electron density distribution of the target wake flow field, which can provide reliable data support for the calculation of the target's electromagnetic scattering, stimulated electromagnetic radiation, and infrared and ultraviolet radiation characteristics.

[0033] In summary, through the above methods, this invention can obtain the complete two-dimensional electron density distribution of the target wake flow field, solving the problem that the probe will affect the surrounding flow field during the experiment, resulting in a small number of measurement points designed on the wake axis. This invention has the advantages of strong practicality, high reliability, and high accuracy, and can be widely used in many fields such as hypersonic vehicle experiments and design, plasma diagnostics, materials science research, and quantum computing and simulation. Attached Figure Description

[0034] Figure 1 This is a flowchart of the method of the present invention.

[0035] Figure 2 This is a structural diagram of the physical information coupled flow field reconstruction model of the present invention.

[0036] Figure 3 This invention provides a geometric model of a hypersonic aircraft used for simulating the electron density of its wake.

[0037] Figure 4 The convergence process of the training loss function for the flow field reconstruction model of this invention.

[0038] Figure 5 The two-dimensional wake electron number density prediction results and true values ​​of the present invention are shown.

[0039] Figure 6 For the present invention Figure 6 A schematic diagram of electron density data extraction.

[0040] Figure 7 This is a comparison chart showing the effects of a convolutional neural network (CNN) and the flow field reconstruction model provided by this invention.

[0041] Figure 8 This is a graph showing the correlation between the prediction results and the true values ​​of this invention. Detailed Implementation

[0042] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0043] See Figure 1 A method for reconstructing the electron density flow field of a hypersonic target wake based on a physical information neural network includes the following steps:

[0044] Step 1: Obtain the electron density values ​​on the central axis of the wake flow field of targets at different Mach numbers, store the electron density values ​​as vector data to obtain the axis electron density vector; obtain the two-dimensional distribution of electron density corresponding to the flow field where the central axis is located, store the two-dimensional distribution of electron density as matrix data; organize the vector data and matrix data into a training set.

[0045] Step 2: Construct a flow field reconstruction model, which includes a first fully connected layer, an activation layer, a deconvolution layer, a flattening layer, a second fully connected layer, a third fully connected layer, and a reconstructing layer; define the continuity equation in the NS equation as the loss function of the flow field reconstruction model;

[0046] Step 3: Use the flow field reconstruction model constructed in Step 2 to train the training set in Step 1 in the hypersonic target wake flow field at different Mach numbers. At the same time, use the loss function in Step 2 to supervise the training until the loss function converges, and obtain the flow field reconstruction model with trained weights.

[0047] Step 4: Using the unknown two-dimensional distribution of the axial electron density vector data as the input vector, the flow field reconstruction model with the weights trained in Step 3 is used to predict the input vector to obtain the two-dimensional electron density distribution of the target wake flow field.

[0048] In step 1, the electron density values ​​on the central axis of the wake flow field of targets at different Mach numbers, as well as the two-dimensional distribution of electron density corresponding to the flow field where the central axis is located, are obtained by CFD simulation calculation.

[0049] The hypersonic vehicle geometric model established using this model was used to perform CFD simulation of the target flow field. During the simulation, the target flow field was simulated using... A model was used to describe the turbulent kinetic energy in the fluid, and the Gupta 11 component chemical reaction model was used to describe the changes in the content and degree of reaction of each component in the fluid. Initial Mach numbers were set to 11 Ma, 12 Ma, ..., 18 Ma for simulation. The simulation ended after the electron density residuals converged, and the simulation results were obtained. The electron density values ​​on the central axis were extracted as 1×n vector data, and the overall flow field was saved as an n×n matrix.

[0050] The flow field reconstruction model in step 2 is used to generate two-dimensional flow field data. The input layer receives vector data, the first fully connected layer increases the data volume, and the activation layer adjusts the data values. Two deconvolutional layers reconstruct features and increase the data dimension. A flattening layer flattens the high-dimensional data output by the deconvolutional layer into vector data. The data volume is normalized through the second and third fully connected layers. Finally, the data is reshaped through the reorganization layer and output to the desired size.

[0051] Step 2, which defines the continuity equation in the NS equations as the loss function of the flow field reconstruction model, specifically includes:

[0052] Spatial gradient features are extracted using the continuity equation of NS electrons in a steady fluid and discretized using the central difference method. The discretized continuity equation expression is used as a conservation term, and the mean square error between the true value and the predicted value of the conservation term constitutes the loss function. The loss function is combined with the flow field reconstruction model, so that the loss function propagates backward in the model and is used to optimize the model weights.

[0053] In step 4, the axial electron density vector data of the unknown two-dimensional distribution is the electron number density measured by the probe on the central axis of the blunt cone during the ground test.

[0054] A hypersonic target wake electron density flow field reconstruction system based on physical information neural network includes:

[0055] Data acquisition module: The electron density values ​​on the central axis of the wake flow field of targets at different Mach numbers and the two-dimensional distribution of electron density corresponding to the flow field where the central axis is located are obtained by CFD simulation calculation. The electron density values ​​are stored as vector data to obtain the axis electron density vector; the two-dimensional distribution of electron density is stored as matrix data. Finally, the vector data and matrix data are organized into a training set.

[0056] The deep learning module consists of two main parts: First, constructing the flow field reconstruction model and defining its loss function. The flow field reconstruction model is constructed using a first fully connected layer, activation layer, deconvolution layer, flattening layer, second fully connected layer, third fully connected layer, and reconstruction layer. The loss function is defined by the continuity equation in the NS equations. Second, training and supervising the flow field reconstruction model. The flow field reconstruction model is trained under the supervision of the loss function.

[0057] Prediction module: Using the unknown two-dimensional distribution of axis electron density vector data as the input vector of the flow field reconstruction model, the trained flow field reconstruction model reconstructs the input vector to obtain the two-dimensional electron density distribution of the target wake flow field where the vector data is located.

[0058] A hypersonic target wake electron density flow field reconstruction device based on physical information neural network includes:

[0059] Memory: Used to store computer programs that implement the hypersonic target wake electron density flow field reconstruction method based on physical information neural networks as described above;

[0060] Processor: Used to implement the hypersonic target wake electron density flow field reconstruction method based on physical information neural network as described above when executing the computer program.

[0061] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of a hypersonic target wake electron density flow field reconstruction method based on a physical information neural network.

[0062] The application effects of the present invention will be described in detail below with reference to the embodiments.

[0063] See Figure 1 and Figure 2 A method for reconstructing the electron density flow field of a hypersonic target wake based on a physical information neural network includes the following steps:

[0064] Step 1: Simulate the electron density of the target wake at different Mach numbers using CFD simulation methods. Figure 3This is a geometric schematic of a blunt cone model with a base diameter of 1m and a semi-cone angle of 8°. After obtaining the target flow field, the electron density values ​​along the central axis of the target wake flow field are acquired and stored as vector data. The two-dimensional distribution of the electron density in the flow field along the central axis is obtained and stored as a matrix; the dataset covers flow field electron density data from 11 Ma to 18 Ma, and the two-dimensional flow field and the corresponding central axis data are organized into a training set.

[0065] Step 2: The flow field reconstruction model generates two-dimensional flow field data. The input layer receives vector data, the first fully connected layer increases the data volume, and the activation layer adjusts the data values. Two deconvolutional layers reconstruct features and increase the data dimension. A flattening layer flattens the high-dimensional data output from the deconvolutional layers into vector data. The second and third fully connected layers normalize the data volume, and finally, a remodeling layer reshapes the data, outputting the data at the desired size. A pre-constructed loss function is used for supervised training of the flow field reconstruction model. The loss function provides feedback to the model output during backpropagation, facilitating model improvement during training. The input data, processed by the trained flow field reconstruction model, can be reconstructed from vector data into two-dimensional flow field data through the model's expansion and remodeling functions.

[0066] Furthermore, the loss function based on physical information is constructed in the near-wake flow field of the hypersonic target, and the Navier-Stokes equations are typically used to describe the spatial distribution of various parameters in the flow field. The continuity equations describing the physical quantities in the Navier-Stokes equations are:

[0067]

[0068] in, The density in the flow field, Indicates time, It represents a physical quantity of component m in a fluid.

[0069] In a steady fluid, removing the time gradient, and considering the two-dimensional case, expanding the above continuity equation yields a conservation expression:

[0070]

[0071] The above expression remains conserved within the flow field region, and therefore can be used as a loss function to supervise the training of the flow field reconstruction model. When representing electrons, physical quantity exist Directional components, physical quantity exist Directional component. The above equation can be expressed using a central difference with the surrounding four points:

[0072] The expression within the trace domain is:

[0073]

[0074]

[0075] The expression for the wake boundary is:

[0076]

[0077]

[0078] in, Indicates the difference step size. and Let represent the difference coordinates. The continuity equation in the Navier-Stokes equations is defined as the loss function of the flow field reconstruction model; therefore, we have:

[0079]

[0080] The above loss function can capture the spatial characteristics of drastically changing physical quantities, such as the parameter gradients at locations like shock wave profiles and post-stagnation points. Furthermore, traditional loss calculation methods ensure the accuracy of the output values. Therefore, the loss function combines the aforementioned spatial gradient term with the traditional mean squared error loss term:

[0081] This network will calculate the residual modules for the entire smooth region, incorporating spatial physics differential loss. The specific calculation method is as follows:

[0082]

[0083] in, Represents the data sample number. This represents the total number of data samples. physical quantity In the x-direction component, physical quantity Component in the y-direction. The formula for the mean square error between the predicted and true values.

[0084] The evaluated loss value is inserted into the flow field reconstruction model to supervise its training based on the reconstruction results. For the non-uniform spatial distribution of wake plasma density, the physical information extraction flow field reconstruction model has a theoretical advantage in training and predicting plasma density.

[0085] Step 3: Use the training set consisting of the hypersonic target wake flow field data of Mach 11-18 from Step 1 to train the flow field reconstruction model constructed in Step 2. Simultaneously, use the loss function from Step 2 to supervise the training until the loss function converges. The convergence status is as follows: Figure 4 At this point, a flow field reconstruction model with trained weights is obtained;

[0086] Step 4: Using the unknown two-dimensional distribution of the axial electron density vector from Step 1 as the input vector, the flow field reconstruction model trained in Step 3 is used to reconstruct the input vector to obtain the two-dimensional electron density distribution of the target wake flow field after reconstruction.

[0087] The electron density distribution of the target wake flow field is obtained using the trained flow field reconstruction model, with reference to... Figure 5 The predicted flow fields for Mach 12, 14, 16, and 18 are presented, with the true electron density distribution obtained through CFD simulation shown on the right. The electron density generated by the hypersonic target varies in the flow fields at the four different Mach numbers. As the Mach number increases, the compression and heating effects of the airflow become more intense, leading to the ionization of more air molecules and a significant increase in electron density. At lower Mach numbers, ionization is mainly concentrated near the shock layer. As the Mach number increases, the ionization region expands to a larger area, and the electron density inside the shock layer increases significantly.

[0088] from Figure 6 Based on the prediction results, the flow field reconstruction model proposed in this invention performs better in predicting the electron density along the straight line at y = 4m, which includes the abrupt change in electron density caused by the head shock. Furthermore, the straight line at y = 0m passes through the post-stagnant point of the hypersonic target flow field, where the spatial gradient of electron density is larger, making the advantages of this model even more pronounced.

[0089] Figure 7 The Pearson correlation coefficients of the convolutional neural network (CNN) and this model for reconstructing the two-dimensional flow fields at 11 Ma, 13 Ma, 15 Ma, and 17 Ma are shown. Where cov represents covariance, this model still outperforms convolutional neural networks in comparison with Pearson correlation coefficients, indicating that this model can take into account both small-scale features and overall structure. Figure 7 The Pearson correlation demonstrates that this invention outperforms the correlation lines of convolutional neural networks at different Mach numbers, especially in locations with higher electron density where the flow field reconstruction model is closer to the true value.

[0090] In summary, compared with existing technologies:

[0091] In step 1 of this embodiment, the flow field is reconstructed using the electron density on the central axis of the hypersonic target wake flow field. This is consistent with the actual experimental setup and has strong practicality. The flow field data can be reconstructed using the central axis measurement data. Therefore, the reconstructed flow field data is highly correlated with the experimental data and has high accuracy.

[0092] In step 2, the loss function of the flow field reconstruction model is defined using the Navier-Stokes equations. Compared with existing graph convolutional neural networks and image super-resolution techniques, it has an interpretable physical mechanism and is easier to converge with a small amount of training data.

[0093] In step 3, the flow field reconstruction model is trained using a training set composed of hypersonic target wake flow field data at different Mach numbers, which has the advantage of being adaptable to different application backgrounds.

[0094] Step 4 yields the complete two-dimensional electron density distribution of the target wake flow field, providing reliable data support for calculating the target's electromagnetic scattering, stimulated electromagnetic radiation, and infrared and ultraviolet radiation characteristics.

[0095] The above method can obtain the complete two-dimensional electron density distribution of the target wake flow field, which solves the problem that the probe will affect the surrounding flow field in the experiment, resulting in a small number of measurement points designed on the wake axis. This method has the advantages of strong practicality, high reliability and high accuracy, and is widely used in many fields such as hypersonic vehicle experiment and design, plasma diagnostics, materials science research and quantum computing and simulation.

[0096] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for reconstructing the electron density flow field of a hypersonic target wake based on a physical information neural network, characterized in that: Includes the following steps: Step 1: Obtain the electron density values ​​on the central axis of the wake flow field of targets at different Mach numbers, store the electron density values ​​as vector data to obtain the axis electron density vector; obtain the two-dimensional distribution of electron density corresponding to the flow field where the central axis is located, store the two-dimensional distribution of electron density as matrix data; organize the vector data and matrix data into a training set. Step 2: Construct a flow field reconstruction model, which includes a first fully connected layer, an activation layer, a deconvolution layer, a flattening layer, a second fully connected layer, a third fully connected layer, and a reconstructing layer; define the continuity equation in the NS equation as the loss function of the flow field reconstruction model; The definition of the continuity equation in the NS equations as the loss function of the flow field reconstruction model specifically includes: The continuity equations describing physical quantities in the Navier-Stokes equations are: in, This represents the density in the flow field. Indicates time, Represents electron, A physical quantity representing electrons in a fluid; In a steady fluid, removing the time gradient, and considering the two-dimensional case, expanding the above continuity equation yields a conservation expression: The above expression can be represented using the central difference with the surrounding four points: The expression within the trace domain is: The expression for the wake boundary is: in, Indicates the difference step size. and Represents difference coordinates; The continuity equation in the Navier-Stokes equations is defined as the loss function of the flow field reconstruction model; therefore, we have: The flow field reconstruction model incorporates the residual module, which calculates the entire smooth region, with spatial physical quantity differential loss, resulting in the loss function of the flow field reconstruction model: in, Indicates the data sample number. This represents the total number of data samples. Representing physical quantities In the x-direction component, Representing physical quantities In the y-direction component, This represents the mean squared error between the predicted and true values. Step 3: Use the flow field reconstruction model constructed in Step 2 to train the training set in Step 1 in the hypersonic target wake flow field at different Mach numbers. At the same time, use the loss function in Step 2 to supervise the training until the loss function converges, and obtain the flow field reconstruction model with trained weights. Step 4: Using the unknown two-dimensional distribution of the axial electron density vector data as the input vector, the flow field reconstruction model with the weights trained in Step 3 is used to predict the input vector to obtain the two-dimensional electron density distribution of the target wake flow field.

2. The method for reconstructing the electron density flow field of a hypersonic target wake based on a physical information neural network according to claim 1, characterized in that: In step 1, the electron density values ​​on the central axis and the two-dimensional distribution of electron density corresponding to the flow field where the central axis is located are obtained by CFD simulation calculations.

3. The method for reconstructing the electron density flow field of a hypersonic target wake based on a physical information neural network according to claim 1, characterized in that: The flow field reconstruction model in step 2 is used to generate two-dimensional flow field data. The input layer receives vector data, the first fully connected layer increases the data volume, and the activation layer adjusts the data values. Two deconvolutional layers reconstruct features and increase the data dimension. A flattening layer flattens the high-dimensional data output by the deconvolutional layer into vector data. The data volume is normalized through the second and third fully connected layers. Finally, the data is reshaped through the reorganization layer and output to the desired size.

4. The method for reconstructing the electron density flow field of a hypersonic target wake based on a physical information neural network according to claim 1, characterized in that: Step 2, which defines the continuity equation in the NS equations as the loss function of the flow field reconstruction model, specifically includes: Spatial gradient features are extracted using the continuity equation of NS electrons in a steady fluid and discretized using the central difference method. The discretized continuity equation expression is used as a conservation term, and the mean square error between the true value and the predicted value of the conservation term constitutes the loss function. The loss function is combined with the flow field reconstruction model, so that the loss function propagates backward in the model and is used to optimize the model weights.

5. The method for reconstructing the electron density flow field of a hypersonic target wake based on a physical information neural network according to claim 1, characterized in that: In step 4, the axial electron density vector data of the unknown two-dimensional distribution is the electron number density measured by the probe on the central axis of the blunt cone during the ground test.

6. A system for performing the hypersonic target wake electron density flow field reconstruction method based on a physical information neural network as described in claim 1, characterized in that: include: Data acquisition module: The electron density values ​​on the central axis of the wake flow field of targets at different Mach numbers and the two-dimensional distribution of electron density corresponding to the flow field where the central axis is located are obtained by CFD simulation calculation. The electron density values ​​are stored as vector data to obtain the axis electron density vector; the two-dimensional distribution of electron density is stored as matrix data. Finally, the vector data and matrix data are organized into a training set. The deep learning module consists of two parts: First, constructing the flow field reconstruction model and defining its loss function. The flow field reconstruction model is constructed using a first fully connected layer, activation layer, deconvolution layer, flattening layer, second fully connected layer, third fully connected layer, and reconstruction layer. The loss function is defined by the continuity equation in the NS equation. Second, training and supervising the flow field reconstruction model. The flow field reconstruction model is trained under the supervision of the loss function. Prediction module: Using the unknown two-dimensional distribution of axis electron density vector data as the input vector of the flow field reconstruction model, the trained flow field reconstruction model reconstructs the input vector to obtain the two-dimensional electron density distribution of the target wake flow field where the vector data is located.

7. A hypersonic target wake electron density flow field reconstruction device based on physical information neural network, characterized in that: include: Memory: Used to store computer programs implementing the hypersonic target wake electron density flow field reconstruction method based on physical information neural network as described in any one of claims 1-5; Processor: Used to implement the hypersonic target wake electron density flow field reconstruction method based on physical information neural network as described in any one of claims 1-5 when executing the computer program.

8. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program that, when executed by a processor, implements a hypersonic target wake electron density flow field reconstruction method based on a physical information neural network as described in any one of claims 1-5.

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