Method for analyzing flow field of wing based on embedded physical information implicit flow neural network

Abstract

The application discloses a kind of wing flow field analysis methods based on embedding physical information implicit flow neural network, comprising: obtaining the wing to be analyzed, constructs coordinate system, obtains the coordinate information of multiple nodes of wing under coordinate system;Obtain the Reynolds number in the Navier-Stokes equation corresponding to the wing to be analyzed at a specified time;The coordinate information of the multiple nodes obtained, the time information at the specified time and the Reynolds number are input into the pre-trained implicit flow neural network model, and the flow field information of the wing at the next time output by the implicit flow neural network model is obtained.The application separates the space complexity and time complexity of wing flow field prediction analysis by using two networks to construct an implicit flow neural network model, and establishes a connection, and by constructing a corresponding embedded physical information loss function, the implicit flow neural network model is physically limited, which can realize efficient and rapid solution analysis of wing flow field, and ensure the prediction analysis accuracy of wing flow field.

Description

TECHNICAL FIELD

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

[0002] With the explosive growth of available data and computing resources, deep learning has made great progress in fields including image recognition, natural language processing, etc., and has also been used to learn flow field features or directly capture 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. For this reason, a physical knowledge neural network (PINN) is currently proposed, which, as a general framework for solving partial differential equation forward and inverse problems, encodes existing physical prior information into a loss function for training optimization, establishes a proxy model that satisfies the physical law, and makes up for the incompleteness and sparsity of noisy data. And compared with traditional numerical methods such as finite element method, finite difference method, etc., the embedded physical knowledge neural network avoids the complex and tedious process of grid establishment and the possible dimension explosion problem, saves solving time and computing cost, and can accurately predict the entire definition domain.

[0003] The existing embedded physical knowledge neural network includes an embedded physical knowledge neural network based on a fully connected network and an embedded physical knowledge neural network based on a convolutional neural network. However, the embedded physical knowledge neural network based on the fully connected network needs a large number of points to represent a high-dimensional domain, and in the training process, automatic differentiation calculation is used, the training cost and the calculation time are large, the model is difficult to strictly implement the initial condition (IC) and the boundary condition (BC), and the use of the fully connected network also limits the fitting accuracy of the embedded physical knowledge neural network, resulting in that the existing embedded physical knowledge neural network based on the fully connected network is difficult to be used for solving the wing flow field inversion problem. Due to the intrinsic limitation of the convolution operation of the classical convolutional neural network, the embedded physical information neural network based on the convolutional neural network is difficult to process irregular domains with unstructured grids, and wings are usually irregular in shape, resulting in that the existing embedded physical knowledge neural network based on the convolutional neural network is difficult to be used for solving the wing flow field inversion problem. SUMMARY

[0004] To solve part or all of the technical problems existing in the prior art, the present application provides a wing flow field analysis method based on an embedded physical information implicit flow neural network.

[0005] The technical scheme of the present application is as follows:

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

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

[0008] acquire a Reynolds number of the wing to be analyzed in a specified time instant in a Navier-Stokes equation;

[0009] input the acquired coordinate information of the multiple nodes, time information in the specified time instant, and the Reynolds number into a pre-trained implicit flow neural network model to obtain flow field information of the wing in a next time instant output by the implicit flow neural network model, the implicit flow neural network model being pre-trained based on a pre-constructed embedded physical information loss function, the implicit flow neural network model comprising a flow field prediction network and a weight generation network, an input of the weight generation network being the time information in the specified time instant and the Reynolds number, the weight generation network being configured to output weight parameters and bias parameters of the flow field prediction network according to the input time information and the Reynolds number, an input of the flow field prediction network being the coordinate information of the nodes, the flow field prediction network taking the weight parameters and the bias parameters output by the weight generation network as network parameters of itself, and the flow field prediction network being configured to output the flow field information of the wing in the next time instant according to the input coordinate information of the nodes.

[0010] In some optional embodiments, both the flow field prediction network and the weight generation network adopt a multi-layer perceptron.

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

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

[0013]

[0014] The embedded physical information loss function is:

[0015]

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

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

[0018] A set of training data is obtained, the training data including coordinate information of a plurality of nodes corresponding to an airfoil to be analyzed, a Reynolds number in a Navier-Stokes equation corresponding to the airfoil at a previous time in adjacent two time periods, and a flow field of the airfoil at a next time in the adjacent two time periods.

[0019] Based on the constructed embedded physical information loss function, the coordinate information in the training data in the set of training data is taken as an input of a flow field prediction network in the implicit flow neural network model, the time information and the Reynolds number at the previous time in the training data are taken as an input of a weight generation network in the implicit flow neural network model, and the flow field of the airfoil at the next time in the adjacent two time periods in the training data is taken as an output of the flow field prediction network, and the implicit flow neural network model is trained.

[0020] In some optional embodiments, based on the constructed embedded physical information loss function, the coordinate information in the training data in the set of training data is taken as an input of a flow field prediction network in the implicit flow neural network model, the time information and the Reynolds number at the previous time in the training data are taken as an input of a weight generation network in the implicit flow neural network model, and the flow field of the airfoil at the next time in the adjacent two time periods in the training data is taken as an output of the flow field prediction network, and the implicit flow neural network model is trained, and further comprising:

[0021] In step 321, the time information and the Reynolds number at the previous time in the training data are input into the weight generation network, the coordinate information in the training data is input into the flow field prediction network, and flow field information of the airfoil at the next time output by the flow field prediction network is obtained.

[0022] In step 322, the embedded physical information loss function is calculated according to the flow field of the airfoil at the next time in the adjacent two time periods in the training data and the flow field information of the airfoil at the next time corresponding to the training data output by the flow field prediction network.

[0023] Step 323, it is judged whether the preset training stop condition is reached, if yes, the current implicit flow neural network model is taken as the implicit flow neural network model completed training, if not, the network parameters of the weight generation network in the implicit flow neural network model are updated by using the calculated embedded physical information loss function, and step 321 is returned.

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

[0025] The output layer of the weight generation network is set as 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 scheme of the present application are as follows:

[0027] The wing flow field analysis method based on the embedded physical information implicit flow neural network of the present application can separate the space complexity and time complexity of the wing flow field prediction analysis and establish a connection by constructing an implicit flow neural network model with two networks, and can realize efficient and rapid solution and analysis of the wing flow field and guarantee the prediction and analysis accuracy of the wing flow field by constructing a corresponding embedded physical information loss function to physically limit the implicit flow neural network model. BRIEF DESCRIPTION OF DRAWINGS

[0028] In order to more clearly illustrate the technical scheme in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or prior art description will be briefly introduced below, and obviously, the drawings in the following description are only some embodiments of the present application, and those skilled in the art can obtain other drawings according to these drawings without creative labor.

[0029] Fig. 1 A flow chart of a wing flow field analysis method based on an embedded physical information implicit flow neural network provided by an embodiment of the present application;

[0030] Fig. 2 A structural schematic diagram of a wing provided by an embodiment of the present application;

[0031] Fig. 3 A structural schematic diagram of an implicit flow neural network model provided by an embodiment of the present application. DETAILED DESCRIPTION

[0032] In order to make the objects, technical solutions and advantages of the present application clearer, the technical solutions of the present application will be described below in connection with the embodiments of the present application and the corresponding drawings. Obviously, the described embodiments are only some of the embodiments of the present application, but not all the embodiments. Based on the embodiments of the present application, all other embodiments obtained by those of ordinary skill in the art without creative labor fall within the scope of protection of the present application.

[0033] The technical solutions provided by the embodiments of the present application will be described in detail below in connection with the drawings.

[0034] Reference Figs. 1-3 The embodiments of the present application provide a wing flow field analysis method based on an embedded physical information implicit flow neural network, which comprises the following steps:

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

[0036] In the embodiments of the present application, the wing to be analyzed is determined, and for the determined wing plane, an x-y coordinate system is constructed, and coordinate information of multiple nodes on the wing plane in the x-y coordinate system is determined.

[0037] In the embodiments of the present application, when the x-y coordinate system of the wing plane is constructed, the origin, x-axis direction and y-axis direction of the coordinate system can be specified according to actual conditions.

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

[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 the embodiments of the present application, 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, inputting the obtained coordinate information of multiple nodes, time information at a specified time and Reynolds number into a pre-trained implicit flow neural network model to obtain flow field information of the wing at the next time output by the implicit flow neural network model.

[0042] In the embodiment of the present application, 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 comprises a flow field prediction network and a weight generation network, the input of the weight generation network is time information and a Reynolds number at a specified time, the weight generation network is configured to output weight parameters and bias parameters of the flow field prediction network according to the input time information and the Reynolds number, the input of the flow field prediction network is coordinate information of nodes, the flow field prediction network takes the weight parameters and the bias parameters output by the weight generation network as its own network parameters, and the flow field prediction network is configured to output flow field information of a wing at a next time according to the input coordinate information of nodes.

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

[0044] The wing flow field analysis method based on the embedded physical information implicit flow neural network provided in the embodiment of the present application can separate the space complexity and time complexity of the wing flow field prediction analysis and establish a connection by constructing an implicit flow neural network model using two networks, and can realize efficient and rapid solution and analysis of the wing flow field and ensure the prediction and analysis accuracy of the wing flow field by constructing a corresponding embedded physical information loss function to physically limit the implicit flow neural network model.

[0045] Further, in the embodiment of the present application, the flow field prediction network and the weight generation network in the implicit flow neural network model both adopt a multi-layer perceptron, the multi-layer perceptron comprises an input layer, a hidden layer and an output layer connected in sequence, and the hidden layer comprises one or more.

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

[0047] The network parameters of the flow field prediction network include weight parameters and bias parameters, and based on the above setting for the flow field prediction network, the network parameters φ of the flow field prediction network can be represented as:

[0048] φ={w m ,b m} 1≤m≤M ;

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

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

[0051] Hidden layer: 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] where 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 m-th layer, i.e., the input of the m-th hidden layer, N m (a m ) represents the output of the m-th layer, i.e., the output of the m-th hidden layer, σ represents a nonlinear activation function, a M represents the input of the output layer, and N M (a M ) represents the output of the output layer.

[0054] In the embodiments of the present application, the nonlinear activation function used by the multilayer perceptron described above can include any one of Sigmoid, Tanh and Relu.

[0055] It should be noted that in the embodiments of the present application, the number of layers of the multilayer perceptron used by the weight generation network can be different from the multilayer perceptron used by the flow field prediction network, and the remaining structure and algorithm principle can be the same as the multilayer perceptron used by the flow field prediction network described above, which will not be described here.

[0056] Further, in the embodiments of the present application, the embedded physical information loss function corresponding to the implicit flow neural network model is constructed according to the nonlinear partial differential equation and boundary conditions corresponding to the wing to be analyzed.

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

[0058]

[0059] Wherein, 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 a time variable, t [0, T], T represents a 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 a nonlinear equation for controlling the wing flow field U.

[0060] In the embodiment of the present application, the boundary condition satisfied by the wing flow field is determined according to the actual situation, which can be Dirichlet boundary condition, Neumann boundary condition, Robin boundary condition.

[0061] Further, based on the above-mentioned nonlinear partial differential equation, the embedded physical information loss function is represented as:

[0062]

[0063] Wherein, L f (Θ) represents the loss function value, Θ represents the network parameter of the implicit flow neural network model, represents the nonlinear partial differential equation residual, 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 application, 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 the embodiment of the present application, the nonlinear partial differential equation residual is represented as:

[0066]

[0067] Further, in the embodiment of the present application, 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 the coordinate information of a plurality of nodes corresponding to the wing to be analyzed, the Reynolds number in the Navier-Stokes equation corresponding to the wing at the previous time in the adjacent two time periods, and the flow field of the wing at the latter time in the adjacent two time periods;

[0069] 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 taken as the input of the flow field prediction network in the implicit flow neural network model, the time information and the Reynolds number at the previous moment in the training data are taken as the input of the weight generation network in the implicit flow neural network model, and the flow field of the airfoil at the next moment in the adjacent two moments in the training data is taken as the output of the flow field prediction network, and the implicit flow neural network model is trained.

[0070] In the embodiment of the application, when the training data set is acquired, a coordinate system and an airfoil simulation model can be constructed according to the structure of the airfoil to be analyzed, and a simulation experiment under different physical parameters is performed based on the airfoil simulation model to determine the coordinate information of the plurality of nodes of the airfoil to be analyzed, the flow field of the airfoil at different moments and the Reynolds number in the Navier-Stokes equation corresponding to the flow field.

[0071] Further, if the airfoil to be analyzed already has corresponding historical real flow field data, the coordinate information of the plurality of nodes of the airfoil, the flow field of the airfoil at different moments and the Reynolds number in the Navier-Stokes equation corresponding to the flow field can also be directly acquired from the historical real flow field data, thereby obtaining the training data set.

[0072] Further, in the embodiment of the application, 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 taken as the input of the flow field prediction network in the implicit flow neural network model, the time information and the Reynolds number at the previous moment in the training data are taken as the input of the weight generation network in the implicit flow neural network model, and the flow field of the airfoil at the next moment in the adjacent two moments in the training data is taken as the output of the flow field prediction network, and the implicit flow neural network model is trained, further comprising the following steps:

[0073] In step 321, the time information and the Reynolds number at the previous moment in the training data are input into the weight generation network, the coordinate information in the training data is input into the flow field prediction network, and the flow field information of the airfoil at the next moment output by the flow field prediction network is obtained.

[0074] In the embodiment of the application, the time information and the Reynolds number at the previous moment in the training data are input from the input layer of the weight generation network, processed through each layer in the weight generation network, and the network parameters of the flow field prediction network are output from the output layer of the weight generation network, and the network parameters are assigned to the flow field prediction network, the network parameters including 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, processed through each layer in the flow field prediction network, and the flow field of the airfoil at the next moment is output from the output layer of the flow field prediction network.

[0075] In the embodiment of the present application, 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] In step 322, the embedded physical information loss function is calculated according to the flow field of the wing at the later time of the two adjacent times in the training data and the flow field information of the wing at the next time output by the flow field prediction network corresponding to the training data.

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

[0078] In step 323, it is judged whether the preset training stop condition is reached. If yes, the current implicit flow neural network model is taken as the trained implicit flow neural network model. If no, the network parameters of the weight generation network in the implicit flow neural network model are updated using the calculated embedded physical information loss function, and the step 321 is returned.

[0079] In the embodiment of the present application, the training stop condition is set according to the actual situation, for example, the training iteration number reaches the set iteration number or the optimization index reaches the set threshold. The embedded physical information loss function can be taken as the optimization index.

[0080] Further, in the embodiment of the present application, the random gradient descent method or the adaptive momentum estimation method is used to 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 by the following formula:

[0082]

[0083] Wherein, 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, L f (Θ) represents the embedded physical information loss function, and Θ represents the network parameters of the implicit flow neural network model, specifically the network parameters of the weight generation network. The optimizer is, for example, Adam, SGD, etc., and the learning rate is set in advance to control the speed of network parameter update.

[0084] Further, in embodiments of the present application, the output of the weight generation network can be represented as:

[0085]

[0086] wherein parameterNet(t, μ; Θ) represents the output of the weight generation network, t and μ represent the time information and Reynolds number input to the weight generation network, Θ represents the network parameters of the weight generation network, w1, …, w M represent the weight parameters of the flow field prediction network whose output is the output of the weight generation network, b1, …, b M represent the bias parameters of the flow field prediction network whose output is the output of the weight generation network, and the superscript T represents the transpose.

[0087] Since the output dimension of the weight generation network is closely related to the input dimension, and the number of neurons, the number of layers and the output dimension of the flow field prediction network, it is 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 several thousand to tens of thousands. Therefore, in embodiments of the present application, the output of the weight generation network is processed by dimension reduction.

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

[0089] In embodiments of the present application, the 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, and the output of the linear output layer is an r-dimensional vector. One element of the r-dimensional vector corresponds to one basis vector of the subspace. By using a mapping function, the r-dimensional vector is converted into the required weight parameters and bias parameters.

[0090] In embodiments of the present application, 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", and the like, are used solely to distinguish one entity or action from another, without necessarily requiring or implying any actual such relationship or order between such entities or actions. Moreover, the terms "comprises", "comprising", or any other variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but can also include other elements not expressly listed or inherent to such process, method, article, or apparatus. In addition, "front", "rear", "left", "right", "upper", "lower", and the like, are all referred to the placement state shown in the drawings.

[0092] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present application, and are not limited thereto; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that the technical solutions recorded in the foregoing embodiments can still be modified, or some technical features can be replaced by equivalents; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for analyzing the flow field of an airfoil based on an implicit flow neural network with embedded physical information, characterized in that, include: Obtain the wing to be analyzed, construct a coordinate system, and obtain the coordinate information of multiple nodes of the wing in the coordinate system; Obtain the Reynolds number in the Navier-Stokes equations for the wing to be analyzed at a specified time. The coordinate information of multiple nodes, the time information at a specified time, and the Reynolds number are input into a pre-trained implicit flow neural network model to obtain the flow field information of the wing at the next time step, which is 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 at a specified time step and the Reynolds number. The weight generation network is used to output the weight parameters and bias parameters of the flow field prediction network based on the input time information and the Reynolds number. The input of the flow field prediction network is the coordinate information of the nodes. 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 time step based on the input coordinate information of the nodes.

2. The wing flow field analysis method based on an implicit flow neural network with embedded physical information as described in claim 1, characterized in that, Both the flow field prediction network and the weight generation network employ a multilayer perceptron.

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

4. The wing flow field analysis method based on an implicit flow neural network with embedded physical information as described in claim 3, characterized in that, The nonlinear partial differential equation corresponding to the wing is set as follows: The embedded physical information loss function is: Where X = (x, y) represents the coordinates of a point within the wing flow field, U represents the wing flow field, t represents the time variable, t ∈ [0, T], T represents the preset time interval, μ represents the Reynolds number in the Navier-Stokes equations, Ω represents the wing flow field region, B(U, X) represents the boundary conditions, f represents the nonlinear equation controlling the wing flow field, and L f (Θ) represents the loss function value, and Θ represents the network parameters of the implicit flow neural network model. Represents the residuals of nonlinear partial differential equations. U represents the wing flow field at time l+1, as output by the implicit flow neural network model. l Let ||·||2 represent the wing flow field at time l, and let ||·||2 represent the 2-norm.

5. The wing flow field analysis method based on an implicit flow neural network with embedded physical information as described in claim 4, characterized in that, The implicit stream neural network model is pre-trained in the following manner: Obtain a training dataset, which includes the coordinate information of multiple nodes corresponding to the wing to be analyzed, the Reynolds number in the Navier-Stokes equations for the wing at the previous time step between two adjacent time steps, and the flow field of the wing at the next time step between two adjacent time steps. Based on the constructed embedded physical information loss function, the coordinate information in the training data in the training dataset 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. The flow field of the wing in the training data at the next moment between 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 an implicit flow neural network with embedded physical information as described in claim 5, characterized in that, Based on the constructed embedded physical information loss function, the coordinate information in the training data of the training dataset is used as the input to 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 to the weight generation network in the implicit flow neural network model. The flow field of the wing at the next moment between two adjacent moments in the training data is used as the output of the flow field prediction network. The implicit flow neural network model is trained, further including: Step 321: Input the time information and Reynolds number of the previous moment in the training data into the weight generation network, and input the coordinate information in the training data into the flow field prediction network to obtain the flow field information of the wing at the next moment output by the flow field prediction network. Step 322: Calculate the embedded physical information loss function based on the flow field of the wing at the next time step between two adjacent time steps in the training data, and the flow field information of the wing at the next time step corresponding to the training data output by the flow field prediction network. Step 323: Determine whether the preset training stop condition has been met. If yes, use the current implicit flow neural network model as the implicit flow neural network model that has completed training. If no, update the network parameters of the weight generation network in the implicit flow neural network model using the calculated embedded physical information loss function, and return to step 321.

7. The wing flow field analysis method based on an implicit flow neural network with embedded physical information according to any one of claims 1-6, characterized in that, The method further includes: The output layer of the weight generation network is set as a linear output layer with a width of r. 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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