Airfoil flow field analysis method based on graph neural network MeshGraphNets

Abstract

The application discloses a kind of based on graph neural network MeshGraphNets wing flow field analysis method, comprising: the grid division of wing to be analyzed, constructs the grid structure graph model corresponding to wing;Obtain training sample set;Graph neural network model is constructed, and graph neural network model adopts MeshGraphNets network structure;According to the nonlinear partial differential equation and boundary condition corresponding to wing to be analyzed, construct embedded physical knowledge loss function, carry out unsupervised training to graph neural network model;The flow field of each node in preset time in the grid structure graph model corresponding to wing to be analyzed is acquired, the graph containing the flow field information of each node in preset time is input into graph neural network model, and the corresponding graph containing the flow field information of each node in next time is obtained;According to the flow field of each node in next time, determine the flow field of wing to be analyzed in next time.The application can realize efficient and fast inversion wing flow field, and improve wing flow field inversion prediction precision.

Description

Technical Field

[0001] This invention relates to the field of flow field inversion technology, and specifically to a method for analyzing the flow field of an airfoil based on MeshGraphNets. Background Technology

[0002] With the explosive growth of available data and computing resources, deep learning has made significant progress in fields including image recognition and natural language processing. It has also been 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 large flow datasets for offline "training," which is unavailable in airfoil flow field inversion problems. To address this, a new type of neural network with embedded physical knowledge (PINNs) has been proposed. PINNs serve as a general framework for solving forward and inverse partial differential equations. They encode existing physical prior information into a loss function for training and optimization, establishing a surrogate model that satisfies physical laws and compensates for the incompleteness and sparsity of noisy data. Compared to traditional numerical methods such as the finite element method and finite difference method, PINNs avoid the complex and tedious mesh construction process and the potential dimensionality explosion problem, saving solution time and computational costs, and enabling accurate prediction of the entire domain.

[0003] Existing embedded physical knowledge neural networks include those based on fully connected networks and those based on convolutional neural networks (CNNs). However, fully connected CNNs require a large number of points to represent high-dimensional domains, and the use of automatic differentiation during training results in high training costs and computation time. Furthermore, the model struggles to strictly adhere to initial conditions (IC) and boundary conditions (BC), and the use of fully connected networks limits the fitting accuracy of the embedded physical knowledge neural network. Therefore, existing fully connected CNNs are unsuitable for solving wing flow field inversion problems. Convolutional neural networks, on the other hand, suffer from inherent limitations in convolution operations, making it difficult to handle irregular domains with unstructured grids. Since wings are typically irregularly shaped, existing convolutional neural networks are also unsuitable for solving wing flow field inversion problems. Summary of the Invention

[0004] To address some or all of the technical problems existing in the prior art, this invention provides a wing flow field analysis method based on MeshGraphNets.

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

[0006] A method for analyzing the airfoil flow field based on MeshGraphNets is provided, the method comprising:

[0007] The wing to be analyzed is meshed, and a mesh structure diagram model of the wing is constructed based on the mesh.

[0008] Obtain the training sample set, which includes the graph corresponding to the wing to be analyzed, containing the flow field information of each node at a time.

[0009] A graph neural network model is constructed, which adopts the MeshGraphNets network structure.

[0010] Based on the nonlinear partial differential equations and boundary conditions corresponding to the wing to be analyzed, an embedded physical knowledge loss function is constructed, and the graph neural network model is trained unsupervised using the training sample set and the embedded physical knowledge loss function.

[0011] Obtain the flow field of each node in the mesh structure graph model corresponding to the wing to be analyzed at a preset time. Input the graph containing the flow field information of each node at the preset time into the trained graph neural network model to obtain the corresponding graph containing the flow field information of each node at the next time.

[0012] Based on the flow field of each node at the next moment, determine the flow field of the wing to be analyzed at the next moment.

[0013] In some possible implementations, an undirected isomorphic connected graph is used to model the mesh structure graph model corresponding to the wing.

[0014] In some possible implementations, a mesh structure diagram model corresponding to the wing is constructed based on the divided mesh, including:

[0015] Based on the divided grid, a node is used to represent an intersection point of the grid lines in the divided grid, and the coordinates of the intersection point are represented by the node eigenvalues;

[0016] Based on the divided grid, an edge is used to represent the grid line between two adjacent intersection points in the divided grid;

[0017] Based on the determined nodes, edges, and node feature values, construct the mesh structure graph model corresponding to the wing.

[0018] In some possible implementations, the graph neural network model includes: an encoder, a processor, and a decoder connected in sequence;

[0019] The encoder employs a multi-layer neural network, comprising an input layer, a hidden layer, and an output layer connected in sequence. The hidden layer comprises two layers, each with a ReLU activation function, and each hidden layer has 128 hidden units, used to encode the nodes and edges of the graph as features.

[0020] The processing program uses a graph network to predict potential feature changes in nodes and update the graph state.

[0021] The decoder uses the same multi-layer neural network as the encoder to decode node features and output corresponding prediction results.

[0022] In some possible implementations, the nonlinear partial differential equation corresponding to the wing is defined as follows:

[0023]

[0024] The embedded physical knowledge loss function is constructed as follows:

[0025]

[0026] Where X = (x, y) represents the coordinates of a point within the wing flow field, U represents the wing flow field, t represents time (t ∈ [0, T]), T represents a preset time interval, λ 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 U, and Θ represents the network parameters of the graph neural network model. Represents the residuals of nonlinear partial differential equations. U represents the predicted wing flow field at time l+1, as output by the graph neural network model. l Let l represent the airflow field at time l.

[0027] In some possible implementations, the graph neural network model is trained unsupervised using a training sample set and an embedded physical knowledge loss function, including:

[0028] Step S401: Input multiple training samples into the graph neural network model in sequence to obtain the graph output by the graph neural network model, which contains the flow field information of each node at the next time step.

[0029] Step S402: Calculate the embedded physical knowledge loss function based on the flow field information of each node in multiple training samples at one time and the flow field information of each node output by the graph neural network model at the next time.

[0030] Step S403: Determine whether the preset training stop condition has been met. If yes, use the current graph neural network model as the graph neural network model that has completed training. If no, update the network parameters of the graph neural network model using the embedded physical knowledge loss function and return to step S401.

[0031] In some possible implementations, the preset training stopping condition is that the calculated embedded physical knowledge loss function reaches its minimum value.

[0032] In some possible implementations, the network parameters of the graph neural network model are updated using the following formula:

[0033]

[0034] Where, Θ t+1 Θ represents the network parameters of the graph neural network model at the (t+1)th iteration. t Let L represent the network parameters of the graph neural network model at the t-th iteration, Δ[·] represent the optimizer, η represent the learning rate, and L represent the network parameters of the graph neural network model at the t-th iteration. f (Θ) represents the embedded physical knowledge loss function, and Θ represents the network parameters of the graph neural network model.

[0035] The main advantages of the technical solution of this invention are as follows:

[0036] The wing flow field analysis method based on MeshGraphNets of this invention utilizes MeshGraphNets to process the irregular domain of unstructured meshes and constructs a corresponding embedded physical knowledge loss function to physically constrain the graph neural network. This enables efficient and rapid inversion of the wing flow field, improves the accuracy of wing flow field inversion prediction, and reduces the training cost of the graph neural network. Attached Figure Description

[0037] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0038] Figure 1 This is a flowchart of a wing flow field analysis method based on MeshGraphNets according to an embodiment of the present invention;

[0039] Figure 2 This is a schematic diagram of the structure of an air wing according to an embodiment of the present invention. Detailed Implementation

[0040] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0041] The technical solutions provided by the embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0042] refer to Figure 1 An embodiment of the present invention provides a method for analyzing the airfoil flow field based on MeshGraphNets, the method comprising the following steps S1-S6:

[0043] Step S1: Mesh the wing to be analyzed and construct the corresponding mesh structure model of the wing based on the mesh.

[0044] In one embodiment of the present invention, the wing plane to be subjected to flow field inversion analysis is determined, and the wing plane is meshed using a preset meshing method. The meshing method is set according to the specific circumstances; generally, the finer the mesh, the higher the accuracy of the final wing flow field inversion prediction, but the higher the solution time and computational cost.

[0045] The key to constructing a graph model is determining the nodes and edges in the graph model. Define a graph G = (V, E), where V represents the set of nodes in the graph, which is a collection of entity nodes that can store the characteristics of the nodes; E represents the set of edges in the graph, which is used to describe the connection relationships between nodes, and can represent different connection relationships of edges through the weight of the edges.

[0046] In one embodiment of the present invention, an undirected isomorphic connected graph is used to model the mesh structure graph model corresponding to the wing.

[0047] Specifically, in one embodiment of the present invention, constructing a mesh structure diagram model corresponding to the wing based on the divided mesh includes the following steps:

[0048] Step S101: Based on the divided grid, a node is used to represent an intersection point of the grid lines in the divided grid, and the coordinates of the intersection point are represented by the node eigenvalue.

[0049] Step S102: Based on the divided grid, use an edge to represent the grid line between two adjacent intersection points in the divided grid;

[0050] Step S103: Based on the determined nodes, edges, and node feature values, construct the mesh structure graph model corresponding to the wing.

[0051] In one embodiment of the present invention, each edge in the constructed mesh structure graph model has the same weight.

[0052] Step S2: Obtain the training sample set, which includes the graph corresponding to the wing to be analyzed, containing the flow field information of each node at a certain time.

[0053] In one embodiment of the present invention, a wing simulation model can be constructed based on the structure of the wing to be analyzed. Multiple simulation experiments under different physical parameters can be performed based on the wing simulation model to determine the flow field of each node in the mesh structure graph model corresponding to the wing to be analyzed at multiple times. Multiple training samples including the graph corresponding to the wing to be analyzed, which contains the flow field information of each node at a time, are obtained, and a training sample set including multiple training samples is acquired.

[0054] In one embodiment of the present invention, if there is corresponding historical real flow field data for the wing to be analyzed, multiple training samples including the graphs containing flow field information of each node at a certain time corresponding to the wing to be analyzed can be directly obtained from the historical real flow field data, and a training sample set including multiple training samples can be obtained.

[0055] Step S3: Construct a graph neural network model using the MeshGraphNets network structure.

[0056] In one embodiment of the present invention, the graph neural network model adopts a MeshGraphNets network structure, specifically including: an encoder, a processor, and a decoder connected in sequence. The encoder adopts a multilayer neural network (MLP), including an input layer, a hidden layer, and an output layer connected in sequence. There are two hidden layers, each with a ReLU activation function and 128 hidden units, used to encode the nodes and edges of the graph as features. The processor adopts a graph network (GN) to predict the latent feature changes of nodes and update the graph state, which includes the attributes of nodes, edges, and the entire graph. The decoder adopts the same multilayer neural network (MLP) as the encoder to decode the node features and output the corresponding prediction results.

[0057] In one embodiment of the present invention, the input of the graph neural network model is a graph containing the flow field information of each node at a certain time, and the output is a corresponding graph containing the flow field information of each node at the next time.

[0058] Step S4: Based on the nonlinear partial differential equations and boundary conditions corresponding to the wing to be analyzed, construct an embedded physical knowledge loss function, and use the training sample set and the embedded physical knowledge loss function to perform unsupervised training on the graph neural network model.

[0059] refer to Figure 2 Specifically, considering the two-dimensional discrete flow field of the wing plane, the corresponding nonlinear partial differential equation (PDE) for the wing is set as follows:

[0060]

[0061] Where X = (x, y) represents the coordinates of a point within the wing flow field, U represents the wing flow field, t represents time, t∈[0,T], T represents a preset time period, λ represents the Reynolds number in the Navier-Stokes equations (NS equations), Ω represents the wing flow field region, B(U,X) represents the boundary conditions, and f represents the nonlinear equation controlling the wing flow field U.

[0062] The two-dimensional rectangular coordinate system of the wing plane can be set according to the actual situation.

[0063] In one embodiment of the present invention, the boundary conditions satisfied by the wing flow field are determined according to the actual situation, and can be Dirichlet boundary conditions, Neumann boundary conditions, or Robin boundary conditions.

[0064] Furthermore, based on the aforementioned nonlinear partial differential equations, the embedded physical knowledge loss function is:

[0065]

[0066] Where Θ represents the network parameters of the graph neural network model. Represents the residuals of nonlinear partial differential equations. U represents the predicted wing flow field at time l+1, as output by the graph neural network model. l Let l represent the airflow field at time l.

[0067] The residuals of the nonlinear partial differential equations are expressed as:

[0068]

[0069] Furthermore, in one embodiment of the present invention, unsupervised training of the graph neural network model is performed using a training sample set and an embedded physical knowledge loss function, including the following steps S401-S403:

[0070] Step S401: Input multiple training samples into the graph neural network model in sequence to obtain the graph output by the graph neural network model, which contains the flow field information of each node at the next time step.

[0071] In one embodiment of the present invention, a graph containing the flow field information of each node at a certain time in the training samples is input from the input end of the graph neural network model, processed sequentially through the parameters of each layer in the graph neural network model, and output from the output end of the graph neural network model. The information output from the output end is the corresponding graph containing the flow field information of each node at the next time.

[0072] In one embodiment of the present invention, the graph neural network model may be an untrained or incompletely trained model. Each layer of the model is set with initialization parameters, and the parameters of each layer can be continuously updated and adjusted during the training process of the model.

[0073] Step S402: Calculate the embedded physical knowledge loss function based on the flow field information of each node in multiple training samples at one time and the flow field information of each node output by the graph neural network model at the next time.

[0074] Specifically, based on the embedded physical knowledge loss function constructed above, the embedded physical knowledge loss function is calculated according to the flow field information of each node in multiple training samples at one time and the flow field information of each node output by the graph neural network model at the next time.

[0075] Step S403: Determine whether the preset training stop condition has been met. If yes, use the current graph neural network model as the graph neural network model that has completed training. If no, update the network parameters of the graph neural network model using the embedded physical knowledge loss function and return to step S401.

[0076] In one embodiment of the present invention, the preset training stopping condition is that the calculated embedded physical knowledge loss function reaches its minimum value.

[0077] Furthermore, in one embodiment of the present invention, stochastic gradient descent or adaptive momentum estimation can be used to train and update the network parameters of the graph neural network model.

[0078] Specifically, the network parameters of a graph neural network model can be updated using the following formula:

[0079]

[0080] Where, Θ t+1 Θ represents the network parameters of the graph neural network model at the (t+1)th iteration. t Let L represent the network parameters of the graph neural network model at the t-th iteration, Δ[·] represent the optimizer, η represent the learning rate, and L represent the network parameters of the graph neural network model at the t-th iteration. f(Θ) represents the embedded physical knowledge loss function, and Θ represents the network parameters of the graph neural network model. The optimizer can be, for example, Adam or SGD, and the learning rate needs to be preset to control the speed of parameter updates.

[0081] Step S5: Obtain the flow field of each node in the mesh structure graph model corresponding to the wing to be analyzed at a preset time. Input the graph containing the flow field information of each node at the preset time into the trained graph neural network model to obtain the corresponding graph containing the flow field information of each node at the next time.

[0082] Specifically, the flow field of each node in the grid structure graph model corresponding to the wing to be analyzed is obtained at a preset time. The graph containing the flow field information of each node at the preset time is determined. The graph containing the flow field information of each node at the preset time is input into the trained graph neural network model to obtain the graph output by the graph neural network model, which contains the flow field information of each node at the next time.

[0083] Step S6: Determine the flow field of the wing to be analyzed at the next moment based on the flow field of each node at the next moment.

[0084] Specifically, based on the graph output by the graph neural network model, which contains the flow field information of each node at the next time step, the flow field of each node at the next time step can be directly obtained. Based on the flow field of each node at the next time step, the flow field of the wing to be analyzed at the next time step can be determined by numerical calculation methods or a trained deep learning model, thus completing the solution of the wing flow field inversion problem.

[0085] An embodiment of the present invention provides a wing flow field analysis method based on MeshGraphNets. By utilizing MeshGraphNets graph neural networks to process the irregular domain of unstructured meshes and constructing a corresponding embedded physical knowledge loss function to physically constrain the graph neural network, it can achieve efficient and fast inversion of wing flow field, improve the accuracy of wing flow field inversion prediction, and reduce the training cost of graph neural networks.

[0086] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Additionally, the terms "front," "back," "left," "right," "upper," and "lower" in this document refer to the placement shown in the accompanying drawings.

[0087] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for analyzing the airfoil flow field based on MeshGraphNets, characterized in that, include: The wing to be analyzed is meshed, and a mesh structure diagram model of the wing is constructed based on the mesh. Obtain a training sample set, which includes a graph corresponding to the wing to be analyzed, containing flow field information of each node at a time. The node represents the intersection of grid lines in the divided grid. A graph neural network model is constructed, which adopts the MeshGraphNets network structure. Based on the nonlinear partial differential equations and boundary conditions corresponding to the wing to be analyzed, an embedded physical knowledge loss function is constructed, and the graph neural network model is trained unsupervised using the training sample set and the embedded physical knowledge loss function. Obtain the flow field of each node in the mesh structure graph model corresponding to the wing to be analyzed at a preset time. Input the graph containing the flow field information of each node at the preset time into the trained graph neural network model to obtain the corresponding graph containing the flow field information of each node at the next time. Based on the flow field of each node at the next moment, determine the flow field of the wing to be analyzed at the next moment; The nonlinear partial differential equation corresponding to the wing is set as follows: ； The embedded physical knowledge loss function is constructed as follows: ； in, This represents the coordinates of a point within the airflow field of the wing. Indicates the airflow field of the wing. Indicates time, , Indicates a preset time period. Represents the Reynolds number in the Navier-Stokes equations. Indicates the airflow field region of the wing. Indicate boundary conditions, Indicates the control of the airfoil flow field The nonlinear equation, This represents the network parameters of the graph neural network model. Represents the residuals of nonlinear partial differential equations. , This represents the output of the graph neural network model. Predicting the wing flow field at any given time. express The airflow field of the wing at any given moment.

2. The wing flow field analysis method based on MeshGraphNets according to claim 1, characterized in that, An undirected isomorphic connected graph is used to model the mesh structure graph model corresponding to the wing.

3. The wing flow field analysis method based on MeshGraphNets according to claim 2, characterized in that, Based on the divided grid, construct the corresponding mesh structure diagram model of the wing, including: Based on the divided grid, a node is used to represent an intersection point of the grid lines in the divided grid, and the coordinates of the intersection point are represented by the node eigenvalues; Based on the divided grid, an edge is used to represent the grid line between two adjacent intersection points in the divided grid; Based on the determined nodes, edges, and node feature values, construct the mesh structure graph model corresponding to the wing.

4. The wing flow field analysis method based on MeshGraphNets according to claim 1, characterized in that, The graph neural network model includes: an encoder, a processor, and a decoder connected in sequence; The encoder employs a multi-layer neural network, comprising an input layer, a hidden layer, and an output layer connected in sequence. The hidden layer comprises two layers, each with a ReLU activation function, and each hidden layer has 128 hidden units, used to encode the nodes and edges of the graph as features. The processing program uses a graph network to predict potential feature changes in nodes and update the graph state. The decoder uses the same multi-layer neural network as the encoder to decode node features and output corresponding prediction results.

5. The wing flow field analysis method based on MeshGraphNets according to claim 1, characterized in that, Unsupervised training of the graph neural network model is performed using a training sample set and an embedded physical knowledge loss function, including: Step S401: Input multiple training samples into the graph neural network model in sequence to obtain the graph output by the graph neural network model, which contains the flow field information of each node at the next time step. Step S402: Calculate the embedded physical knowledge loss function based on the flow field information of each node in multiple training samples at one time and the flow field information of each node output by the graph neural network model at the next time. Step S403: Determine whether the preset training stop condition has been met. If yes, use the current graph neural network model as the graph neural network model that has completed training. If no, update the network parameters of the graph neural network model using the embedded physical knowledge loss function and return to step S401.

6. The wing flow field analysis method based on MeshGraphNets according to claim 5, characterized in that, The preset training stopping condition is that the calculated embedded physical knowledge loss function reaches its minimum value.

7. The wing flow field analysis method based on MeshGraphNets according to claim 5, characterized in that, The network parameters of the graph neural network model are updated using the following formula: ； in, Indicates the first The network parameters of the graph neural network model at the next iteration. Indicates the first The network parameters of the graph neural network model at the next iteration. Indicates the optimizer, Indicates the learning rate. This represents the loss function of embedded physical knowledge.

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