Wing flow field analysis method based on embedded physical information implicit flow neural network

Abstract

The invention discloses a wing flow field analysis method based on an embedded physical information implicit flow neural network, and the method comprises the steps: obtaining a to-be-analyzed wing, constructing a coordinate system, and obtaining the coordinate information of a plurality of nodes of the wing in the coordinate system; acquiring a Reynolds number in a corresponding Navier-Stokes equation of the wing to be analyzed at a specified moment; and inputting the obtained coordinate information of the plurality of nodes, the time information at the specified moment and the Reynolds number into a pre-trained implicit flow neural network model to obtain the flow field information of the wing at the next moment output by the implicit flow neural network model. According to the method, the implicit flow neural network model is constructed by using the two networks so as to separately characterize the space complexity and the time complexity of wing flow field prediction analysis and establish a relation, and the implicit flow neural network model is physically limited by constructing a corresponding embedded physical information loss function; the method can achieve the efficient and rapid solution analysis of the wing flow field, and guarantees the prediction analysis precision of the wing flow field.

Description

Technical Field

[0001] The present invention relates to the technical field of flow field inversion, and in particular to a wing flow field analysis method based on an implicit flow neural network with embedded physical information. Background Art

[0002] With the explosive growth of available data and computing resources, deep learning has made great progress in fields including image recognition and natural language processing. It is also used to learn flow field features or directly capture the end-to-end mapping between sparse measurement data and high-resolution flow fields. However, deep learning models rely on a large amount of flow data sets for offline "training", which is not available in the wing flow field inversion problem. To this end, a physical embedded neural network (PINNs) is proposed. As a general framework for solving the forward and inverse problems of partial differential equations, it encodes the existing physical prior information into the loss function for training and optimization, establishes a proxy model that satisfies the physical laws, and makes up for the incompleteness and sparsity of noisy data. Compared with traditional numerical methods such as finite element method and finite difference, the physical embedded neural network avoids the complex and tedious process of grid establishment and the possible dimensional explosion problem, saves solution time and computational cost, and can accurately predict the entire domain.

[0003] Existing embedded physics knowledge neural networks include embedded physics knowledge neural networks based on fully connected networks and embedded physics knowledge neural networks based on convolutional neural networks. However, embedded physics knowledge neural networks based on fully connected networks require a large number of points to represent high-dimensional domains. Automatic differentiation calculations are used during training, which results in high training costs and computing time. The model is difficult to strictly enforce initial conditions (IC) and boundary conditions (BC). In addition, the use of fully connected networks will also limit the fitting accuracy of embedded physics knowledge neural networks, making it difficult for existing embedded physics knowledge neural networks based on fully connected networks to solve wing flow field inversion problems. Embedded physics information neural networks based on convolutional neural networks are difficult to handle irregular domains with unstructured grids due to the inherent limitations of the convolution operation of classical convolutional neural networks, and wings are usually irregular in shape, making it difficult for existing embedded physics knowledge neural networks based on convolutional neural networks to solve wing flow field inversion problems. Summary of the invention

[0004] In order to solve some or all of the technical problems existing in the above-mentioned prior art, the present invention provides a wing flow field analysis method based on an implicit flow neural network with embedded physical information.

[0005] The technical solution of the present invention is as follows:

[0006] A method for analyzing wing flow field based on an implicit flow neural network with embedded physical information is provided, the method comprising:

[0007] Obtain the wing to be analyzed, construct a coordinate system, and obtain coordinate information of multiple nodes of the wing in the coordinate system;

[0008] Obtain the Reynolds number in the Navier-Stokes equation corresponding to the wing to be analyzed at a specified time;

[0009] The acquired coordinate information of multiple nodes, the time information and the Reynolds number at the specified moment are input into the pre-trained implicit flow neural network model to obtain the flow field information of the wing at the next moment output by the implicit flow neural network model. The implicit flow neural network model is pre-trained based on a pre-constructed embedded physical information loss function. The implicit flow neural network model includes a flow field prediction network and a weight generation network. The input of the weight generation network is the time information and the Reynolds number at the specified moment. The weight generation network is used to output the weight parameters and bias parameters of the flow field prediction network according to the input time information and Reynolds number. The input of the flow field prediction network is the coordinate information of the node. The flow field prediction network uses the weight parameters and bias parameters output by the weight generation network as its own network parameters. The flow field prediction network is used to output the flow field information of the wing at the next moment according to the input node coordinate information.

[0010] In some optional implementations, the flow field prediction network and the weight generation network both use multi-layer perceptrons.

[0011] In some optional embodiments, the embedded physical information loss function is constructed according to the nonlinear partial differential equations and boundary conditions corresponding to the wing to be analyzed.

[0012] In some optional implementations, the nonlinear partial differential equation corresponding to the wing is set to:

[0013]

[0014] The embedded physical information loss function is:

[0015]

[0016] Where X = (x, y) represents the coordinates of a point in the wing flow field, U represents the wing flow field, t represents the time variable, t∈[0,T], T represents the preset time period, μ represents the Reynolds number in the Navier-Stokes equation, Ω represents the wing flow field area, B(U,X) represents the boundary condition, f represents the nonlinear equation controlling the wing flow field, and L f (Θ) represents the loss function value, Θ represents the network parameters of the implicit flow neural network model, represents the residual of the nonlinear partial differential equation, represents the wing flow field at time l+1 output by the implicit flow neural network model, U l represents the wing flow field at time l, and ‖·‖2 represents the 2-norm.

[0017] In some optional embodiments, the implicit flow neural network model is pre-trained in the following manner:

[0018] Acquire a training data set, the training data including coordinate information of multiple nodes corresponding to the wing to be analyzed, the Reynolds number in the Navier-Stokes equation corresponding to the wing at the previous moment between two adjacent moments, and the flow field of the wing at the latter moment between two adjacent moments;

[0019] Based on the constructed embedded physical information loss function, the coordinate information in the training data in the training data set is used as the input of the flow field prediction network in the implicit flow neural network model, the time information and Reynolds number of the previous moment in the training data are used as the input of the weight generation network in the implicit flow neural network model, and the flow field of the wing in the training data at the later moment of two adjacent moments is used as the output of the flow field prediction network to train the implicit flow neural network model.

[0020] In some optional embodiments, based on the constructed embedded physical information loss function, the coordinate information in the training data in the training data set is used as the input of the flow field prediction network in the implicit flow neural network model, the time information and Reynolds number of the previous moment in the training data are used as the input of the weight generation network in the implicit flow neural network model, and the flow field of the wing at the latter moment of two adjacent moments in the training data is used as the output of the flow field prediction network, and training the implicit flow neural network model further includes:

[0021] Step 321, inputting the time information and Reynolds number of the previous moment in the training data into the weight generation network, inputting the coordinate information in the training data into the flow field prediction network, and obtaining the flow field information of the wing at the next moment output by the flow field prediction network;

[0022] Step 322, calculating the embedded physical information loss function according to the flow field of the wing at the latter moment of two adjacent moments in the training data and the flow field information of the wing at the next moment corresponding to the training data output by the flow field prediction network;

[0023] Step 323, determine whether the preset training stop condition is reached. If so, use the current implicit flow neural network model as the implicit flow neural network model that has completed training. If not, use the calculated embedded physical information loss function to update the network parameters of the weight generation network in the implicit flow neural network model, and return to step 321.

[0024] In some optional embodiments, the method further comprises:

[0025] The output layer of the weight generation network is set to a linear output layer with a width of r, and the r-dimensional vector output by the weight generation network is converted into the weight parameters and bias parameters of the flow field prediction network through a preset mapping function.

[0026] The main advantages of the technical solution of the present invention are as follows:

[0027] The wing flow field analysis method based on the implicit flow neural network with embedded physical information of the present invention constructs an implicit flow neural network model by utilizing two networks to separately characterize and establish a connection between the spatial complexity and the temporal complexity of the wing flow field prediction analysis, and physically restricts the implicit flow neural network model by constructing a corresponding embedded physical information loss function, thereby achieving efficient and rapid solution and analysis of the wing flow field and ensuring the prediction and analysis accuracy of the wing flow field. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0029] Figure 1 A flowchart of a wing flow field analysis method based on an implicit flow neural network with embedded physical information provided by an embodiment of the present invention;

[0030] Figure 2 A schematic diagram of the structure of a wing provided by an embodiment of the present invention;

[0031] Figure 3 A schematic diagram of the structure of an implicit flow neural network model provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0032] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the specific embodiments of the present invention and the corresponding drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0033] The technical solution provided by the embodiments of the present invention is described in detail below with reference to the accompanying drawings.

[0034] refer to Figure 1-3 The embodiment of the present invention provides a wing flow field analysis method based on an implicit flow neural network with embedded physical information, the method comprising the following steps:

[0035] Step 1, obtain the wing to be analyzed, build a coordinate system, and obtain the coordinate information of multiple nodes of the wing in the coordinate system;

[0036] In an embodiment of the present invention, a wing to be subjected to flow field analysis is determined, an xy coordinate system is constructed for the determined wing plane, and coordinate information of multiple nodes on the wing plane in the xy coordinate system is determined.

[0037] In the embodiment of the present invention, when constructing the xy coordinate system of the wing plane, the origin, x-axis direction and y-axis direction of the coordinate system may be specifically specified according to actual conditions.

[0038] It should be noted that the number and position of nodes are specified in advance. When performing flow field analysis, the more node information is used, the higher the final prediction accuracy of the wing flow field analysis, but the required analysis cost and calculation cost are higher.

[0039] Step 2, obtaining the Reynolds number in the Navier-Stokes equation corresponding to the wing to be analyzed at a specified time;

[0040] In an embodiment of the present invention, according to the actual situation of the wing flow field analysis, the Reynolds number in the Navier-Stokes equation (NS equation) corresponding to the wing to be analyzed at a specified time is determined.

[0041] Step 3, input the acquired coordinate information of multiple nodes, the time information at a specified moment, and the Reynolds number into a pre-trained implicit flow neural network model to obtain the flow field information of the wing at the next moment output by the implicit flow neural network model.

[0042] In an embodiment of the present invention, an implicit flow neural network model is pre-trained based on a pre-constructed embedded physical information loss function. The implicit flow neural network model includes a flow field prediction network and a weight generation network. The input of the weight generation network is the time information and Reynolds number at a specified moment. The weight generation network is used to output the weight parameters and bias parameters of the flow field prediction network according to the input time information and Reynolds number. The input of the flow field prediction network is the coordinate information of the node. The flow field prediction network uses the weight parameters and bias parameters output by the weight generation network as its own network parameters. The flow field prediction network is used to output the flow field information of the wing at the next moment according to the input node coordinate information.

[0043] It should be noted that, in the embodiment of the present invention, the flow field includes a velocity field and a pressure field.

[0044] The wing flow field analysis method based on the implicit flow neural network with embedded physical information provided in an embodiment of the present invention utilizes two networks to construct an implicit flow neural network model to separately characterize and establish a connection between the spatial complexity and the temporal complexity of the wing flow field prediction analysis, and physically restricts the implicit flow neural network model by constructing a corresponding embedded physical information loss function. This can achieve efficient and rapid solution and analysis of the wing flow field and ensure the prediction and analysis accuracy of the wing flow field.

[0045] Furthermore, in an embodiment of the present invention, the flow field prediction network and the weight generation network in the implicit flow neural network model both adopt a multilayer perceptron, which includes an input layer, a hidden layer and an output layer connected in sequence, and the hidden layer includes one or more layers.

[0046] Specifically, the flow field prediction network is set to be an M-layer multilayer perceptron (MLP), and the mth layer of the multilayer perceptron has N m neurons, and the weight matrix of the mth layer is w m ∈R Nm×Nm-1 , the bias vector is b m ∈R Nm ;

[0047] The network parameters of the flow field prediction network include weight parameters and bias parameters. Based on the above settings for the flow field prediction network, the network parameter φ of the flow field prediction network can be expressed as:

[0048] φ={w m ,b m} 1≤m≤M ;

[0049] Based on the above settings for the flow field prediction network, the processing of the input layer, hidden layer and output layer of the flow field prediction network can be expressed as:

[0050] Input layer: N 0 (a 0)=a 0 ;

[0051] Hidden layers: N m (a m )=σ(w m N m-1 (a m-1 )+b m ), for 1≤m≤M-1;

[0052] Output layer: N M (a M )=w M N M-1 (a M-1 )+b M ;

[0053] Among them, a 0 represents the input of the input layer, N 0 (a 0 ) represents the output of the input layer, a m represents the input of the mth layer, that is, the input of the mth hidden layer, N m (a m ) represents the output of the mth layer, that is, the output of the mth hidden layer, σ represents the nonlinear activation function, a M represents the input of the output layer, N M (a M ) represents the output of the output layer.

[0054] In the embodiment of the present invention, the nonlinear activation function adopted by the above-mentioned multi-layer perceptron may include: any one of Sigmoid, Tanh and Relu.

[0055] It should be noted that in an embodiment of the present invention, the number of layers of the multilayer perceptron used in the weight generation network may be different from that of the multilayer perceptron used in the flow field prediction network, and the remaining structures and algorithm principles may be the same as those of the multilayer perceptron used in the above-mentioned flow field prediction network, and will not be repeated here.

[0056] Furthermore, in an embodiment of the present invention, the embedded physical information loss function corresponding to the implicit flow neural network model is constructed according to the nonlinear partial differential equations and boundary conditions corresponding to the wing to be analyzed.

[0057] Specifically, in the embodiment of the present invention, the two-dimensional discrete flow field of the wing plane is considered, and the nonlinear partial differential equation (PDE) corresponding to the wing is set as:

[0058]

[0059] Among them, X = (x, y) represents the coordinates of a point in the wing flow field, U represents the wing flow field, that is, the objective function of the fluid mechanics model, t represents the time variable, t∈[0,T], T represents the preset time period, μ represents the Reynolds number in the Navier-Stokes equation, Ω represents the wing flow field area, B(U,X) represents the boundary condition, and f represents the nonlinear equation controlling the wing flow field U.

[0060] In the embodiment of the present invention, the boundary conditions satisfied by the wing flow field are determined according to actual conditions, and may be Dirichlet boundary conditions, Neumann boundary conditions, or Robin boundary conditions.

[0061] Furthermore, based on the nonlinear partial differential equation set above, the embedded physical information loss function is expressed as:

[0062]

[0063] Among them, L f (Θ) represents the loss function value, Θ represents the network parameters of the implicit flow neural network model, represents the residual of the nonlinear partial differential equation, represents the wing flow field at time l+1 output by the implicit flow neural network model, U l represents the wing flow field at time l, and ‖·‖2 represents the 2-norm.

[0064] It should be noted that in the embodiment of the present invention, since the network parameters of the flow field prediction network in the implicit flow neural network model are generated by the weight generation network, the network parameters Θ of the above-mentioned implicit flow neural network model represent the network parameters of the weight generation network, and the network parameters specifically include weight parameters and bias parameters.

[0065] Further, in an embodiment of the present invention, the nonlinear partial differential equation residual is expressed as:

[0066]

[0067] Furthermore, in an embodiment of the present invention, the implicit flow neural network model is pre-trained by the following steps:

[0068] Step 31, obtaining a training data set, the training data including coordinate information of multiple nodes corresponding to the wing to be analyzed, the Reynolds number in the Navier-Stokes equation corresponding to the wing at the previous moment between two adjacent moments, and the flow field of the wing at the next moment between two adjacent moments;

[0069] Step 32, based on the constructed embedded physical information loss function, the coordinate information in the training data in the training data set is used as the input of the flow field prediction network in the implicit flow neural network model, the time information and Reynolds number of the previous moment in the training data are used as the input of the weight generation network in the implicit flow neural network model, and the flow field of the wing in the training data at the later moment of two adjacent moments is used as the output of the flow field prediction network to train the implicit flow neural network model.

[0070] In an embodiment of the present invention, when obtaining a training data set, a coordinate system and a wing simulation model can be constructed according to the structure of the wing to be analyzed, and multiple simulation experiments under different physical parameters are performed based on the wing simulation model to determine the coordinate information of multiple nodes of the wing to be analyzed, as well as the flow field of the wing at different times and the corresponding Reynolds number in the Navier-Stokes equations.

[0071] Furthermore, if the wing to be analyzed already has corresponding historical real flow field data, the coordinate information of multiple nodes of the wing, as well as the flow field of the wing at different times and the corresponding Reynolds number in the Navier-Stokes equations can be directly obtained from the historical real flow field data to obtain a training data set.

[0072] Further, in an embodiment of the present invention, in step 32, based on the constructed embedded physical information loss function, the coordinate information in the training data in the training data set is used as the input of the flow field prediction network in the implicit flow neural network model, the time information and Reynolds number of the previous moment in the training data are used as the input of the weight generation network in the implicit flow neural network model, and the flow field of the wing in the training data at the latter moment of two adjacent moments is used as the output of the flow field prediction network, and the implicit flow neural network model is trained, further comprising the following steps:

[0073] Step 321, input the time information and Reynolds number of the previous moment in the training data into the weight generation network, input the coordinate information in the training data into the flow field prediction network, and obtain the flow field information of the wing at the next moment output by the flow field prediction network;

[0074] In an embodiment of the present invention, the time information and Reynolds number of the previous moment in the training data are input from the input layer of the weight generation network. After being processed by each layer in the weight generation network, the weight generation network outputs the network parameters of the flow field prediction network from the output layer, and the network parameters are assigned to the flow field prediction network. The network parameters include weight parameters and bias parameters. After obtaining the network parameters of the flow field prediction network, the coordinate information in the training data is input from the input layer of the flow field prediction network. After being processed by each layer in the flow field prediction network, the flow field prediction network outputs the flow field of the wing at the next moment from the output layer.

[0075] In an embodiment of the present invention, the network parameters of the flow field prediction network in the implicit flow neural network model are generated by the weight generation network, and the network parameters of the weight generation network in the implicit flow neural network model are initialization parameters. During the training process of the implicit flow neural network model, the network parameters of the weight generation network can be continuously updated and learned.

[0076] Step 322, calculating the embedded physical information loss function according to the flow field of the wing at the later moment of two adjacent moments in the training data and the flow field information of the wing at the next moment corresponding to the training data output by the flow field prediction network;

[0077] In an embodiment of the present invention, based on the embedded physical information loss function constructed as described above, the embedded physical information loss function is calculated according to the flow field of the wing at the latter moment of two adjacent moments in the training data input into the implicit flow neural network model, and the flow field information of the wing at the next moment corresponding to the training data output by the flow field prediction network.

[0078] Step 323, determine whether the preset training stop condition is reached. If so, use the current implicit flow neural network model as the implicit flow neural network model to complete the training. If not, use the calculated embedded physical information loss function to update the network parameters of the weight generation network in the implicit flow neural network model, and return to step 321.

[0079] In an embodiment of the present invention, the training stop condition is specifically set according to the actual situation, for example, the number of training iterations reaches a set number of iterations or the optimization index reaches a set threshold. Among them, the embedded physical information loss function can be used as the optimization index.

[0080] Furthermore, in one embodiment of the present invention, a stochastic gradient descent method or an adaptive momentum estimation method is used to train and update the network parameters of the implicit flow neural network model.

[0081] Specifically, the network parameters of the implicit flow neural network model can be updated using the following formula:

[0082]

[0083] Among them, Θ t+1 represents the network parameters of the implicit flow neural network model at the t+1th iteration, Θ t represents the network parameters of the implicit flow neural network model at the tth iteration, Δ[·] represents the optimizer, η represents the learning rate, and L f (Θ) represents the embedded physical information loss function, Θ represents the network parameters of the implicit flow neural network model, specifically the network parameters of the weight generation network. Among them, the optimizer is, for example, Adam, SGD, etc., and the learning rate is pre-set to control the speed of updating the network parameters.

[0084] Furthermore, in an embodiment of the present invention, the output of the weight generation network can be expressed as:

[0085]

[0086] Among them, parameterNet(t,μ;Θ) represents the output of the weight generation network, t and μ represent the time information and Reynolds number of the input weight generation network, Θ represents the network parameters of the weight generation network, w1,…,w M Represents the weight parameters of the flow field prediction network output by the weight generation network, b1,…,b M Represents the bias parameter of the flow field prediction network output by the weight generation network. The superscript T represents transposition.

[0087] Since the output dimension of the weight generation network is closely related to the input dimension, as well as the number of neurons, the number of layers, and the output dimension of the flow field prediction network, it is very challenging to directly learn the mapping from the input parameters to the weight parameters and bias parameters of the flow field prediction network. When the complexity of the flow field prediction network increases, the output dimension of the weight generation network will also increase dramatically, and may even reach thousands to tens of thousands. For this reason, in an embodiment of the present invention, the output of the weight generation network is subjected to dimensionality reduction processing.

[0088] Specifically, in an embodiment of the present invention, the output layer of the weight generation network is set to a linear output layer with a width of r, and the r-dimensional vector output by the weight generation network is converted into weight parameters and bias parameters of the flow field prediction network through a preset mapping function.

[0089] In an embodiment of the present invention, a linear output layer with a width of r set at the end of the weight generation network corresponds to a subspace with a rank of r. The output of the linear output layer is an r-dimensional vector. An element of the r-dimensional vector corresponds to a basis vector of the subspace. By utilizing a mapping function, the r-dimensional vector is converted into the required weight parameters and bias parameters.

[0090] In the embodiment of the present invention, the mapping function is implemented by using a fully connected layer.

[0091] It should be noted that, in this article, relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In addition, "front", "back", "left", "right", "upper" and "lower" in this article are all referenced to the placement state shown in the accompanying drawings.

[0092] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A wing flow field analysis method based on implicit flow neural network with embedded physical information, characterized in that: include: Obtain the wing to be analyzed, construct a coordinate system, and obtain coordinate information of multiple nodes of the wing in the coordinate system; Obtain the Reynolds number in the Navier-Stokes equation corresponding to the wing to be analyzed at a specified time; The acquired coordinate information of multiple nodes, the time information and the Reynolds number at the specified moment are input into the pre-trained implicit flow neural network model to obtain the flow field information of the wing at the next moment output by the implicit flow neural network model. The implicit flow neural network model is pre-trained based on a pre-constructed embedded physical information loss function. The implicit flow neural network model includes a flow field prediction network and a weight generation network. The input of the weight generation network is the time information and the Reynolds number at the specified moment. The weight generation network is used to output the weight parameters and bias parameters of the flow field prediction network according to the input time information and Reynolds number. The input of the flow field prediction network is the coordinate information of the node. The flow field prediction network uses the weight parameters and bias parameters output by the weight generation network as its own network parameters. The flow field prediction network is used to output the flow field information of the wing at the next moment according to the input node coordinate information.

2. The wing flow field analysis method based on implicit flow neural network with embedded physical information according to claim 1 is characterized in that: The flow field prediction network and the weight generation network both use multi-layer perceptrons.

3. The wing flow field analysis method based on implicit flow neural network with embedded physical information according to claim 1 is characterized in that: The embedded physical information loss function is constructed according to the nonlinear partial differential equations and boundary conditions corresponding to the wing to be analyzed.

4. The wing flow field analysis method based on implicit flow neural network with embedded physical information according to claim 3 is characterized in that: The nonlinear partial differential equation corresponding to the wing is assumed to be: The embedded physical information loss function is: Where X = (x, y) represents the coordinates of a point in the wing flow field, U represents the wing flow field, t represents the time variable, t∈[0,T], T represents the preset time period, μ represents the Reynolds number in the Navier-Stokes equation, Ω represents the wing flow field area, B(U,X) represents the boundary condition, f represents the nonlinear equation controlling the wing flow field, and L f (Θ) represents the loss function value, Θ represents the network parameters of the implicit flow neural network model, represents the residual of the nonlinear partial differential equation, represents the wing flow field at time l+1 output by the implicit flow neural network model, U l represents the wing flow field at time l, and ||·||2 represents the 2-norm.

5. The wing flow field analysis method based on implicit flow neural network with embedded physical information according to claim 4 is characterized in that: The implicit flow neural network model is pre-trained in the following way: Acquire a training data set, the training data including coordinate information of multiple nodes corresponding to the wing to be analyzed, the Reynolds number in the Navier-Stokes equation corresponding to the wing at the previous moment between two adjacent moments, and the flow field of the wing at the latter moment between two adjacent moments; Based on the constructed embedded physical information loss function, the coordinate information in the training data in the training data set is used as the input of the flow field prediction network in the implicit flow neural network model, the time information and Reynolds number of the previous moment in the training data are used as the input of the weight generation network in the implicit flow neural network model, and the flow field of the wing in the training data at the later moment of two adjacent moments is used as the output of the flow field prediction network to train the implicit flow neural network model.

6. The wing flow field analysis method based on implicit flow neural network with embedded physical information according to claim 5 is characterized in that: Based on the constructed embedded physical information loss function, the coordinate information in the training data in the training data set is used as the input of the flow field prediction network in the implicit flow neural network model, the time information and Reynolds number of the previous moment in the training data are used as the input of the weight generation network in the implicit flow neural network model, and the flow field of the wing at the latter moment of two adjacent moments in the training data is used as the output of the flow field prediction network, and the implicit flow neural network model is trained, further comprising: Step 321, inputting the time information and Reynolds number of the previous moment in the training data into the weight generation network, inputting the coordinate information in the training data into the flow field prediction network, and obtaining the flow field information of the wing at the next moment output by the flow field prediction network; Step 322, calculating the embedded physical information loss function according to the flow field of the wing at the latter moment of two adjacent moments in the training data and the flow field information of the wing at the next moment corresponding to the training data output by the flow field prediction network; Step 323, determine whether the preset training stop condition is reached. If so, use the current implicit flow neural network model as the implicit flow neural network model that has completed training. If not, use the calculated embedded physical information loss function to update the network parameters of the weight generation network in the implicit flow neural network model, and return to step 321.

7. The wing flow field analysis method based on implicit flow neural network with embedded physical information according to any one of claims 1 to 6, characterized in that: The method further comprises: The output layer of the weight generation network is set to a linear output layer with a width of r, and the r-dimensional vector output by the weight generation network is converted into the weight parameters and bias parameters of the flow field prediction network through a preset mapping function.

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