Whole vehicle external flow field joint prediction method based on double-flow fusion and multi-head graph attention

Abstract

The application provides a whole vehicle external flow field joint prediction method based on double-flow fusion and multi-head graph attention, and relates to the technical field of vehicle dynamics analysis. The steps of the method comprise receiving a three-dimensional discrete point set of the whole vehicle shape; constructing a residual feature enhancement network to obtain a geometric high-dimensional feature vector; constructing a coordinate embedding network to obtain a high-dimensional coordinate embedding feature; adaptively weighting and fusing the geometric high-dimensional feature vector and the high-dimensional coordinate embedding feature; constructing a directed graph based on a k-nearest neighbor algorithm, splicing the aggregated features output by the multi-head, and obtaining global coupling features; inputting the global coupling features into a parallel first prediction branch and a second prediction branch; the first prediction branch outputs a three-dimensional pressure coefficient distribution map of the vehicle body surface through point-by-point regression; the second prediction branch fuses the global coupling features and key section embedding features, obtains section flow field prediction values through point-by-point regression, and outputs a key section two-dimensional flow field map.

Description

Technical Field

[0001] This invention relates to the field of vehicle dynamics analysis technology, and in particular to a method for joint prediction of the vehicle's external flow field based on dual-flow fusion and multi-head graph attention. Background Technology

[0002] As the automotive industry continues to evolve towards lower drag, lower energy consumption, and higher performance, vehicle aerodynamics has become a crucial factor influencing overall vehicle performance. During vehicle operation, airflow forms a complex three-dimensional flow structure on and around the vehicle body, generating corresponding pressure distribution characteristics. The pressure coefficient distribution on the vehicle body surface and the overall external flow field structure directly affect not only the vehicle's air resistance, lift, and lateral stability, but also key performance indicators such as energy consumption, driving stability, and wind noise. Therefore, during vehicle design and development, engineers typically need to obtain the pressure coefficient distribution on the vehicle body surface and the flow characteristics of the overall external flow field at multiple typical cross-sectional locations to optimize the aerodynamic design of the vehicle body shape.

[0003] However, existing flow field prediction schemes typically fail to achieve efficient and adaptive fusion of geometric structure information and spatial coordinate information during the feature extraction and fusion stages. This results in insufficient model representation of complex vehicle body surfaces and insufficient participation of spatial position information in modeling. In the prediction task stage, the prediction of the vehicle body surface pressure field and the prediction of the overall vehicle external flow field are generally separated into two independent models. This not only prevents the sharing and adaptive fusion of geometric features and coordinate information, but also severely severs the coupling information between geometry and flow field. This dual defect of insufficient feature fusion and separation of prediction tasks leads to computational redundancy and low efficiency. Furthermore, it makes it difficult to ensure the physical coordination and accuracy synchronization of the pressure field and flow field from the source. Summary of the Invention

[0004] The purpose of this invention is to provide a joint prediction method for the external flow field of a vehicle based on dual-flow fusion and multi-head graph attention, in order to solve the problem mentioned in the background art that the existing flow field prediction schemes have the dual defects of insufficient feature fusion and separation of prediction tasks, resulting in computational redundancy and low efficiency. Furthermore, the two prediction results lack physical consistency, making it difficult to ensure the physical coordination and accuracy synchronization of the pressure field and flow field from the source.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a method for joint prediction of the external flow field of a vehicle based on dual-stream fusion and multi-head graph attention, comprising the following steps: receiving a three-dimensional discrete point set of the vehicle's external shape, and using the three-dimensional coordinates of each point as an initial feature vector; constructing a residual feature enhancement network, and performing a layer-by-layer nonlinear transformation on the initial feature vector through a multi-layer residual stacking structure to gradually increase the feature dimension to the target high-dimensional space, thereby obtaining a geometric high-dimensional feature vector; constructing a coordinate embedding network, and performing a nonlinear mapping on the three-dimensional coordinates of each point to obtain a high-dimensional coordinate embedding feature, wherein the dimension of the high-dimensional coordinate embedding feature is consistent with that of the geometric high-dimensional feature vector; performing adaptive weighted fusion of the geometric high-dimensional feature vector and the high-dimensional coordinate embedding feature to obtain a fused feature; constructing a directed graph based on the k-nearest neighbor algorithm, and dividing the fused feature into multiple heads along the channel, based on the relationship between two adjacent nodes. Based on the feature similarity and relative spatial position, attention coefficients are calculated and normalized, then used as attention weights to aggregate neighbor features, resulting in aggregated features. The aggregated features from multiple outputs are concatenated to obtain global coupled features. These global coupled features are simultaneously input into a first prediction branch and a second prediction branch in parallel. The first prediction branch calculates the pressure coefficient at each point on the vehicle surface through point-by-point regression and outputs a three-dimensional pressure coefficient distribution map of the vehicle surface. The second prediction branch fuses the global coupled features with the key section embedding features obtained by mapping the three-dimensional coordinates of key section points of the vehicle through a coordinate embedding network. It obtains the predicted flow field value of the section through point-by-point regression, constructs a set of regular uniform grid nodes on the section plane, and uses radial basis function interpolation to reconstruct the predicted flow field value of the section into a regular grid, generating a regular two-dimensional flow field matrix and outputting a two-dimensional flow field map of the key section.

[0006] Optionally, the step of performing a layer-by-layer nonlinear transformation on the initial feature vector through a multi-layer residual stacking structure to gradually increase the feature dimension to the target high-dimensional space specifically includes: the residual stacking structure is composed of multiple one-dimensional convolutional residual units connected in series, and by stacking multiple residual units, the dimension of the initial feature vector is gradually increased to 1024 dimensions; wherein, in each residual unit, the input feature is processed by a first one-dimensional convolutional linear transformation and a first nonlinear activation function, then by a second one-dimensional convolutional linear transformation and a second nonlinear activation function, and is added to the input feature of the current residual unit to obtain the output feature of the current residual unit.

[0007] Optionally, the step of performing nonlinear mapping on the three-dimensional coordinates of each point to obtain high-dimensional coordinate embedding features specifically includes: the coordinate embedding network contains multiple fully connected layers; the three-dimensional coordinates of each point are sequentially input into the multiple fully connected layers, and a nonlinear activation function is applied after each layer except the output layer; through the layer-by-layer mapping of the fully connected layers, the three-dimensional coordinates are transformed into high-dimensional coordinate embedding features consistent with the dimension of the geometric high-dimensional feature vector.

[0008] Optionally, the step of adaptively weighting and fusing the geometric high-dimensional feature vector with the high-dimensional coordinate embedding feature specifically includes: performing linear transformations on the geometric high-dimensional feature vector and the high-dimensional coordinate embedding feature respectively through two independent, trainable coefficient matrices; and adding the two feature vectors after linear transformation element by element to obtain the fused feature.

[0009] Optionally, the step of calculating and normalizing attention coefficients based on the feature similarity and relative spatial position between two adjacent nodes, and then using them as attention weights to weighted aggregate neighbor features, specifically includes: for any center node in the directed graph and neighbor nodes determined by the k-nearest neighbor algorithm, performing linear transformations on the features of the center node and neighbor nodes respectively through a learnable feature mapping matrix to obtain transformed feature vectors, and performing linear transformations on the relative spatial coordinate vectors between the two nodes through a learnable spatial position mapping matrix; concatenating the transformed center node features, neighbor node features, and spatial coordinate features into a joint vector, and then mapping this joint vector into a scalar through a learnable weight vector as the initial attention coefficient; normalizing the initial attention coefficients corresponding to all neighbor nodes of the center node to obtain the attention weights corresponding to each neighbor node; weighting and summing the transformed features of each neighbor node with the corresponding attention weights, and then performing a linear transformation through a learnable value mapping matrix to obtain the aggregated features of the center node under the current attention head.

[0010] Optionally, the step of calculating the pressure coefficient of each point on the vehicle surface by point-by-point regression specifically includes: independently mapping the feature vector corresponding to each point on the vehicle surface in the global coupling features to a scalar pressure coefficient value through a regression function, while maintaining the one-to-one correspondence between the features and the spatial points.

[0011] Optionally, the step of fusing the global coupling feature with the key section embedding feature obtained by the coordinate embedding network through the three-dimensional coordinate mapping of key section points of the whole vehicle specifically includes: obtaining discrete section point coordinates from the key section of the whole vehicle; inputting the section point coordinates into the coordinate embedding network to obtain the key section embedding feature; and concatenating the global coupling feature with the key section embedding feature to form a fused feature vector for section flow field prediction.

[0012] Optionally, the step of obtaining the cross-sectional flow field prediction value through point-by-point regression specifically includes: mapping the part of the spliced ​​fusion feature vector corresponding to each key cross-sectional point to a scalar flow field prediction value through a regression function.

[0013] Optionally, the step of constructing a set of regular uniform grid nodes on the cross-sectional plane and reconstructing the predicted cross-sectional flow field values ​​using radial basis function interpolation to generate a regular two-dimensional flow field matrix specifically includes: constructing a set of regular uniform grid nodes on the cross-sectional plane; using the key cross-sectional discrete points and the predicted cross-sectional flow field values ​​as known samples, calculating the interpolation weight at each regular grid node based on the radial basis function, wherein the radial basis function is determined according to the spatial distance between the grid node and the discrete point; and performing a weighted summation of the predicted values ​​at the discrete points according to the interpolation weights to calculate the flow field values ​​at all regular grid nodes, thereby forming a regular two-dimensional flow field data matrix.

[0014] On the other hand, the present invention also provides a joint prediction system for the external flow field of a vehicle based on dual-stream fusion and multi-head graph attention, comprising: a receiving module for receiving a set of three-dimensional discrete points of the vehicle's shape, using the three-dimensional coordinates of each point as an initial feature vector; an enhancement module for constructing a residual feature enhancement network, performing a layer-by-layer nonlinear transformation on the initial feature vector through a multi-layer residual stacking structure to gradually increase the feature dimension to the target high-dimensional space, thereby obtaining a geometric high-dimensional feature vector; an embedding module for constructing a coordinate embedding network, performing a nonlinear mapping on the three-dimensional coordinates of each point to obtain a high-dimensional coordinate embedding feature, wherein the high-dimensional coordinate embedding feature has the same dimension as the geometric high-dimensional feature vector; a fusion module for adaptively weightedly fusing the geometric high-dimensional feature vector and the high-dimensional coordinate embedding feature to obtain a fused feature; and a global coupling module for constructing a directed graph based on the k-nearest neighbor algorithm, dividing the fused feature into multiple heads along the channel, and so on. Based on the feature similarity and relative spatial position between two adjacent nodes, attention coefficients are calculated and normalized, and then used as attention weights to aggregate neighbor features to obtain aggregated features. The aggregated features output from multiple heads are concatenated to obtain global coupled features. A dual-branch prediction module is used to simultaneously input the global coupled features into a first prediction branch and a second prediction branch in parallel. The first prediction branch calculates the pressure coefficient of each point on the vehicle surface through point-by-point regression and outputs a three-dimensional pressure coefficient distribution map of the vehicle surface. The second prediction branch fuses the global coupled features with the key section embedding features obtained by the coordinate embedding network through the three-dimensional coordinate mapping of key section points of the whole vehicle. It obtains the predicted value of the cross-section flow field through point-by-point regression, constructs a set of regular uniform grid nodes on the cross-section plane, and uses the radial basis function interpolation method to reconstruct the predicted value of the cross-section flow field into a regular grid, generating a regular two-dimensional flow field matrix and outputting a two-dimensional flow field map of the key section.

[0015] Compared with the prior art, the beneficial effects of the present invention are: This application effectively solves the problem of inefficient fusion of geometric structure and spatial location information in existing technologies by constructing a geometric-coordinate dual-flow adaptive feature fusion mechanism, significantly enhancing the feature representation capability of complex curved surfaces and local structures of the entire vehicle. It employs an improved multi-head graph attention mechanism for global coupling modeling, which can fully capture the flow coupling relationship between different spatial regions, significantly improving the accuracy of flow field prediction. Based on this, this application integrates the prediction of the vehicle surface pressure coefficient and the flow field prediction of key sections into a unified joint prediction architecture, enabling the two tasks to share the feature extraction and global modeling process. This avoids redundant feature calculations and information fragmentation caused by separate predictions, ensuring the physical consistency and accuracy coordination of the pressure field and flow field prediction results. By performing two-dimensional flow field prediction on key sections and combining it with regular mesh reconstruction, the output dimension and computational complexity are effectively reduced, significantly improving prediction efficiency and engineering applicability. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the method steps of the present invention.

[0017] Figure 2 This is a schematic diagram of the overall process of the rapid prediction method for the external flow field of a vehicle according to the present invention.

[0018] Figure 3 This is a schematic diagram of the point-by-point regression structure of the pressure coefficient on the vehicle body surface according to the present invention.

[0019] Figure 4 This is a schematic diagram of the two-dimensional flow field prediction and planar homogenization interpolation process for the key cross-section of this invention.

[0020] Figure 5 This is a schematic diagram of the system structure of the present invention.

[0021] In the diagram: 10 - Receiver module, 20 - Enhancement module, 30 - Embedding module, 40 - Fusion module, 50 - Global coupling module, 60 - Dual-branch prediction module. Detailed Implementation

[0022] The present invention will now be clearly and completely described in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0023] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be used interchangeably where appropriate for the embodiments of this application described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0024] Those skilled in the art will understand that, unless explicitly stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in the specification of this application means the presence of features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. It should be understood that when we say an element is “connected” or “coupled” to another element, it can be directly connected or coupled to the other element, or there may be intermediate elements. Furthermore, “connected” or “coupled” as used herein can include wireless connections or wireless coupling. The term “and / or” as used herein includes all or any units and all combinations of one or more associated listed items.

[0025] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless specifically defined as herein.

[0026] It should be understood that the sequence number and size of each step in this embodiment do not imply the order of execution. The execution order of each process is determined by its function and internal logic, and should not constitute any limitation on the implementation process of this application embodiment.

[0027] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0028] Please refer to Figures 1-4This invention discloses a method for jointly predicting the external flow field of a vehicle based on dual-flow fusion and multi-head graph attention. The method includes the following steps: receiving a set of three-dimensional discrete points of the vehicle's external shape, and using the three-dimensional coordinates of each point as an initial feature vector; constructing a residual feature enhancement network, performing a layer-by-layer nonlinear transformation on the initial feature vector through a multi-layer residual stacking structure to gradually increase the feature dimension to the target high-dimensional space, obtaining a geometric high-dimensional feature vector; constructing a coordinate embedding network, performing nonlinear mapping on the three-dimensional coordinates of each point to obtain a high-dimensional coordinate embedding feature, wherein the high-dimensional coordinate embedding feature has the same dimension as the geometric high-dimensional feature vector; adaptively weighting and fusing the geometric high-dimensional feature vector and the high-dimensional coordinate embedding feature to obtain a fused feature; constructing a directed graph based on the k-nearest neighbor algorithm, dividing the fused feature into multiple heads along the channel, and determining the heads based on the feature similarity and proximity between adjacent nodes. For spatial location, attention coefficients are calculated and normalized, then used as attention weights to aggregate neighbor features, resulting in aggregated features. The aggregated features from multiple outputs are concatenated to obtain global coupled features. These global coupled features are simultaneously input into a first prediction branch and a second prediction branch in parallel. The first prediction branch calculates the pressure coefficients at various points on the vehicle surface through point-by-point regression and outputs a three-dimensional pressure coefficient distribution map of the vehicle surface. The second prediction branch fuses the global coupled features with the key section embedding features obtained by mapping the three-dimensional coordinates of key cross-section points of the vehicle through a coordinate embedding network. It obtains the predicted cross-section flow field value through point-by-point regression, constructs a set of regular uniform grid nodes on the cross-section plane, and uses radial basis function interpolation to reconstruct the predicted cross-section flow field value into a regular grid, generating a regular two-dimensional flow field matrix and outputting a two-dimensional flow field map of the key cross-section.

[0029] Specifically, the system receives a three-dimensional discrete point set of the vehicle's exterior shape. In this embodiment, the vehicle's exterior shape can be obtained through CAD models, three-dimensional scan data, or discrete surface point cloud data, and then processed through surface discretization to form a point set of the vehicle's surface. ,in, This indicates the number of discrete points on the vehicle body surface.

[0030] The input point set is initialized with features by using the 3D coordinates of each point as the initial feature vector. Next, a residual feature enhancement network is constructed. This network adopts a residual structure based on one-dimensional convolution. Through multi-layer stacking of residuals, the initial feature vector is subjected to a layer-by-layer nonlinear transformation, gradually increasing the feature dimension to the target high-dimensional space (1024 dimensions), and outputting a geometrically high-dimensional feature vector. Simultaneously, an independent coordinate embedding network is constructed, consisting of multiple fully connected layers, which performs nonlinear mapping on the three-dimensional coordinates of each point to generate high-dimensional coordinate embedding features consistent with the geometric high-dimensional feature vector dimension. ,in .

[0031] Adaptive weighted fusion of high-dimensional geometric feature vectors and high-dimensional coordinate embedding features: through two trainable linear mapping matrices. and Perform linear transformations on both separately, and then add the transformed results element-wise to obtain the fused features. ,in and As a trainable linear mapping matrix, the model adaptively learns the importance weights of geometric features and spatial location features for subsequent prediction tasks during model training. This fusion method allows the model to dynamically adjust the contribution of the two feature channels, avoiding feature redundancy or conflict that may be introduced by fixed splicing, thereby more effectively fusing geometric structure and spatial location information.

[0032] In the global feature modeling stage, a directed graph is constructed based on the k-nearest neighbor algorithm (k ranges from 8 to 32). Nodes in the graph represent points on the vehicle surface, and edges connect each point to its k nearest neighbors in 3D space. The fused features are segmented into multiple heads along the channel direction (e.g., the number of heads m is 8). Within each head, attention coefficients are calculated based on the feature similarity and relative spatial position between adjacent nodes. After normalization, these coefficients are used as weights to aggregate neighbor features, resulting in the aggregated features for each head. Finally, the outputs of all heads are concatenated to form the global coupled features. .

[0033] The globally coupled features are simultaneously fed into the first and second prediction branches in parallel. The first prediction branch uses a point-by-point regression method to independently map the pressure coefficient to each point on the vehicle surface. ,in The first prediction branch maintains a one-to-one correspondence between features and spatial points, ultimately outputting a three-dimensional pressure coefficient distribution map of the vehicle body surface. The second prediction branch first obtains discrete cross-sectional point coordinates from key cross-sections of the vehicle, maps them to key cross-sectional embedded features through the coordinate embedding network, then fuses the global coupling features with these embedded features, and finally obtains the cross-sectional flow field prediction value through point-by-point regression. Subsequently, a set of regular uniform grid nodes is constructed on the cross-sectional plane, and the discrete prediction values ​​are reconstructed into a regular grid using radial basis function interpolation to generate a regular two-dimensional flow field matrix. Finally, a two-dimensional flow field map of the key cross-section is output, thus completing a full joint prediction of the vehicle's external flow field.

[0034] This application effectively solves the problem of inefficient fusion of geometric structure and spatial location information in existing technologies by constructing a geometric-coordinate dual-flow adaptive feature fusion mechanism, significantly enhancing the feature representation capability of complex curved surfaces and local structures of the entire vehicle. It employs an improved multi-head graph attention mechanism for global coupling modeling, which can fully capture the flow coupling relationship between different spatial regions, significantly improving the accuracy of flow field prediction. Based on this, this application integrates the prediction of the vehicle surface pressure coefficient and the flow field prediction of key sections into a unified joint prediction architecture, enabling the two tasks to share the feature extraction and global modeling process. This avoids redundant feature calculations and information fragmentation caused by separate predictions, ensuring the physical consistency and accuracy coordination of the pressure field and flow field prediction results. By performing two-dimensional flow field prediction on key sections and combining it with regular mesh reconstruction, the output dimension and computational complexity are effectively reduced, significantly improving prediction efficiency and engineering applicability.

[0035] In some embodiments, the step of performing a layer-by-layer nonlinear transformation on the initial feature vector through a multi-layer residual stacking structure to gradually increase the feature dimension to the target high-dimensional space specifically includes: the residual stacking structure is composed of multiple one-dimensional convolutional residual units connected in series, and by stacking multiple residual units, the dimension of the initial feature vector is gradually increased to 1024 dimensions; wherein, in each residual unit, the input feature is processed by a first one-dimensional convolutional linear transformation and a first nonlinear activation function, then by a second one-dimensional convolutional linear transformation and a second nonlinear activation function, and is added to the input feature of the current residual unit to obtain the output feature of the current residual unit.

[0036] Specifically, the residual stacking structure consists of multiple residual units connected in series based on one-dimensional convolution. Each residual unit performs the following operations: the input features first undergo a first one-dimensional convolutional linear transformation, then pass through a non-linear activation function (e.g., ReLU), followed by a second one-dimensional convolutional linear transformation and a second non-linear activation function to obtain intermediate features; then, these intermediate features are added to the input features of the current residual unit (i.e., a skip connection) to become the output features of this residual unit. By stacking multiple such residual units, the feature dimension is gradually increased from the initial three dimensions to 1024 dimensions.

[0037] For the Layer residual element, its calculation form is: ;in and It is a linear mapping matrix. It is a nonlinear activation function. Through a multi-layer residual stacking structure, the geometric feature representation capability is progressively improved, and the feature dimension is increased to 1024 dimensions, resulting in a high-dimensional geometric feature representation. Residual structures can effectively alleviate the vanishing gradient problem in deep network training, while enhancing the ability to represent complex geometric details.

[0038] In practice, the number of residual units can be adjusted according to the network depth requirements. For example, four residual units can be used, with the kernel size of each unit set to 1×3 and the stride to 1. The number of channels increases layer by layer until it reaches 1024 dimensions.

[0039] The residual feature enhancement network in this application employs a stacked, cascaded one-dimensional convolutional residual unit. The one-dimensional convolution slides along the channel dimension, enabling the capture of local dependencies between adjacent feature channels under parameter sharing conditions. Compared to fully connected layers, this reduces the number of parameters and lowers the risk of overfitting. Residual skip connections allow direct addition of the input and output of each unit, ensuring smooth gradient backpropagation in deep networks and allowing the network to learn identity mappings, thus maintaining training stability while increasing depth. By stacking multiple such units, the feature dimension is progressively expanded to 1024 dimensions, fully preserving and enhancing the ability to depict the geometric details of complex vehicle surfaces (such as curvature abrupt changes and edge features) without introducing redundant computation or overfitting due to excessive dimensionality. This gives the geometric feature extraction branch efficient, scalable, and deeply malleable representation capabilities, laying a solid foundation for the stable convergence and accurate prediction of the overall framework.

[0040] In some embodiments, the step of performing nonlinear mapping on the three-dimensional coordinates of each point to obtain high-dimensional coordinate embedding features specifically includes: the coordinate embedding network contains multiple fully connected layers; the three-dimensional coordinates of each point are sequentially input into the multiple fully connected layers, and a nonlinear activation function is applied after each layer except the output layer; through the layer-by-layer mapping of the fully connected layers, the three-dimensional coordinates are transformed into high-dimensional coordinate embedding features consistent with the dimension of the geometric high-dimensional feature vector.

[0041] Specifically, the coordinate embedding network is designed as a multi-layer fully connected network containing three fully connected layers with 256, 512, and 1024 neurons in each layer, respectively. For the three-dimensional coordinates (x, y, z) of each point, the first fully connected layer is fed into a ReLU activation function, outputting 256-dimensional features; then, the second fully connected layer is fed into a ReLU activation function, outputting 512-dimensional features; finally, the third fully connected layer (the output layer, without an activation function) is fed into the third fully connected layer, outputting 1024-dimensional high-dimensional coordinate embedding features. The calculation formula is as follows: .

[0042] in This coordinate embedding network performs a layer-by-layer nonlinear transformation on the original 3D spatial coordinates through a multi-layer fully connected structure, enabling a richer expression of spatial location information in the high-dimensional feature space and effectively enhancing the geometric structure's ability to perceive spatial location. Through this layer-by-layer nonlinear mapping, the 3D spatial coordinates are encoded as high-dimensional coordinate embedding features that are completely consistent with the dimensions of the geometric high-dimensional feature vector, providing aligned spatial location information for subsequent adaptive weighted fusion.

[0043] The coordinate embedding network in this application transforms absolute spatial coordinates into high-dimensional embedding features through layer-by-layer nonlinear mapping, and this embedding dimension is strictly aligned with the geometric high-dimensional feature vector. Compared to directly using the original 3D coordinates or simple concatenation, this high-dimensional embedding allows coordinate information to participate in subsequent fusion in a richer expressive form: each fully connected layer, combined with an activation function, can generate a nonlinear combination of coordinate basis functions, which can encode the absolute position priors of different regions of the vehicle body (such as the front stagnation zone, the top flow acceleration zone, and the rear separation zone). At the same time, the output layer does not have an activation function, ensuring that the value range of the embedded features is unrestricted, which is beneficial for linear adaptive weighting with geometric features. Through channels independent of geometric feature branches, the coordinate embedding network avoids feature coupling, enabling the model to learn independent representations of local shape and global position separately, and finally achieves the best balance between the two in the fusion stage, significantly improving the model's sensitivity to the spatial layout of the vehicle's external flow field.

[0044] In some embodiments, the step of adaptively weighting and fusing the geometric high-dimensional feature vector with the high-dimensional coordinate embedding feature specifically includes: performing linear transformations on the geometric high-dimensional feature vector and the high-dimensional coordinate embedding feature respectively through two independent, trainable coefficient matrices; and adding the two feature vectors after linear transformation element by element to obtain the fused feature.

[0045] Specifically, for each point i, a geometrically high-dimensional feature vector has been obtained. and high-dimensional coordinate embedding features Each is achieved through two independent, trainable coefficient matrices. and A linear transformation is performed on both, resulting in two 2048-dimensional vectors; then these two vectors are added element-wise to obtain the fused feature. The calculation formula is as follows: , .

[0046] During model training, and The parameters are adaptively adjusted through backpropagation, thereby learning the importance weights of geometric features and spatial location features for subsequent prediction tasks. This fusion method avoids feature redundancy or conflict caused by traditional simple splicing, enabling the model to dynamically balance the information contribution of local geometry and global absolute position.

[0047] This application achieves adaptive weighted fusion of geometric high-dimensional features and coordinate embedding features by performing linear transformations on the geometric high-dimensional features and coordinate embedding features respectively using two independent trainable coefficient matrices, and then summing them element-wise. Compared with the traditional approach of splicing and then connecting to a linear layer, this application assigns weight matrices to the two types of features, enabling the model to dynamically adjust the contribution ratio of geometric and positional information for different points or channels. For example, in the stagnation area at the front of the vehicle, absolute coordinates play a dominant role in the prediction of pressure peaks, and the model can automatically increase the coefficients of the coordinate embedding features; near the rearview mirror, local curvature changes affect flow separation, and the coefficients of geometric features are increased accordingly. This channel-level adaptive weighting avoids the limitation of expressive power caused by a fixed fusion ratio. At the same time, because the matrix dimension is 2048×1024, the output fused features are upgraded to 2048 dimensions, providing a richer feature capacity for subsequent multi-head attention. It effectively solves the problem of difficult coordination and fusion of geometric and spatial information in traditional methods, and significantly improves the accuracy of flow field prediction under complex curved surfaces and local structural changes.

[0048] In some embodiments, the step of calculating attention coefficients and normalizing them based on the feature similarity and relative spatial position between two adjacent nodes, and then using them as attention weights to weighted aggregate neighbor features, specifically includes: for any center node in the directed graph and neighbor nodes determined by the k-nearest neighbor algorithm, performing linear transformations on the features of the center node and neighbor nodes respectively through a learnable feature mapping matrix to obtain transformed feature vectors, and performing linear transformations on the relative spatial coordinate vectors between the two nodes through a learnable spatial position mapping matrix; concatenating the transformed center node features, neighbor node features, and spatial coordinate features into a joint vector, and then mapping this joint vector into a scalar through a learnable weight vector as the initial attention coefficients; normalizing the initial attention coefficients corresponding to all neighbor nodes of the center node to obtain the attention weights corresponding to each neighbor node; weighting and summing the transformed features of each neighbor node with the corresponding attention weights, and then performing a linear transformation through a learnable value mapping matrix to obtain the aggregated features of the center node under the current attention head.

[0049] Specifically, the fusion features The channel is divided into m segments (e.g., m=8) along the channel dimension, and each segment is fed into an attention head for calculation. Let the set of points on the vehicle surface be... The k-nearest neighbor algorithm is used to construct a directed graph. , among which, nodes ,side , Point The set of k nearest neighbors in three-dimensional space.

[0050] In each attention head, for node i and its neighboring nodes... The attention coefficient is defined as: ;in The node features are the input. The feature mapping matrix; This is a spatial location mapping matrix; This is the attention weight vector; For nodes and The relative spatial coordinate vectors between points, that is, for points and points , Defined as: .

[0051] Then, the neighboring nodes are normalized using... Point Weighting percentage: .

[0052] Then output each node in the head. The characteristics are: ;in This is a value mapping matrix used for feature fusion.

[0053] In the above calculation process These are all parameters that can be learned during the training process. These are hyperparameters that can be adjusted according to the task.

[0054] Concatenate all the headers to obtain the final output feature: Through the aforementioned geometric adaptive graph attention mechanism, the model considers both feature similarity and spatial geometric relationships during the global feature modeling process, thereby enhancing its ability to express complex curved surfaces and aerodynamic coupling structures of the vehicle and providing high-quality global feature inputs for subsequent prediction of vehicle surface pressure coefficient and key section flow field.

[0055] To capture global flow coupling, this application segments the fused features into multiple heads along the channel. Each head independently learns different feature subspaces and spatial relationship weights. The concatenation of these heads integrates various attention modes, enhancing the model's expressive power. Within each head, the features of the central node and its neighboring nodes are first linearly transformed and their relative spatial coordinates mapped. Then, these three features are concatenated and mapped to scalar attention coefficients via a weight vector. Both feature similarity (semantic relevance) and spatial proximity (geometric constraints) are considered, enabling the attention mechanism to accurately identify node pairs with strong aerodynamic coupling in the flow field. Normalization ensures the weight sum is 1, achieving selective aggregation. Finally, a learnable value mapping matrix is ​​used for another linear transformation, adapting the output features to the feature distribution of different layers. The entire process learns multiple parameters, including feature mapping, spatial mapping, attention weights, and value mapping, endowing the model with powerful graph structure modeling capabilities. This allows the model to capture the flow influence between distant regions on the vehicle surface, providing physically consistent global coupling features for subsequent point-by-point regression.

[0056] In some embodiments, the step of calculating the pressure coefficient of each point on the vehicle surface by point-by-point regression specifically includes: independently mapping the feature vector corresponding to each point on the vehicle surface in the global coupling features to a scalar pressure coefficient value through a regression function, while maintaining the one-to-one correspondence between the features and the spatial points.

[0057] Specifically, a multilayer perceptron is constructed as a regression function, with the global coupled features at each point as input. The pressure coefficient at that point is mapped to a scalar value through two fully connected layers. ,in .

[0058] Importantly, this invention does not employ global pooling; instead, it maintains a one-to-one correspondence between the features of each point and its original spatial location, thereby avoiding the loss of local geometric information caused by feature compression. Finally, by mapping the predicted pressure coefficient values ​​of all points back to the vehicle surface according to the spatial coordinates of the original 3D point cloud, a complete 3D pressure coefficient distribution map of the vehicle surface can be generated. This distribution map can clearly reflect key aerodynamic features such as stagnation points, low-pressure areas, and separation zones.

[0059] This application employs a point-by-point regression method to predict the pressure coefficient of the vehicle body surface, explicitly maintaining a one-to-one correspondence between features and spatial points, and avoiding global pooling. This effectively solves the problem of local information loss caused by global pooling, a common issue in existing data-driven methods. Global pooling compresses the features of all points into a single vector, thus erasing the details of pressure differences between different regions (such as the A-pillar and the rearview mirror), resulting in low spatial resolution of the prediction results. Furthermore, the globally coupled features of each vehicle body surface point are independently mapped to the pressure coefficient of that point through a regression function, essentially training a local regressor for each point, which can fully preserve the pressure change information caused by local geometric differences. The regression function typically uses a multilayer perceptron, which can fit a highly nonlinear mapping relationship. This structure ensures that the pressure coefficient prediction results are not only accurate in overall trend but also accurately reflect the influence of subtle features on the vehicle body surface (such as edges, gaps, and pits) on aerodynamic pressure, thereby generating a high-resolution, physically realistic three-dimensional pressure coefficient distribution map of the vehicle body surface, greatly enhancing its guiding value for aerodynamic optimization design.

[0060] In some embodiments, the step of fusing the global coupling feature with the key section embedding feature obtained by the coordinate embedding network from the three-dimensional coordinate mapping of key section points of the whole vehicle specifically includes: obtaining discrete section point coordinates from the key section of the whole vehicle; inputting the section point coordinates into the coordinate embedding network to obtain the key section embedding feature; and concatenating the global coupling feature with the key section embedding feature to form a fused feature vector for section flow field prediction.

[0061] Specifically, firstly, several typical cross-sections are selected based on the engineering analysis requirements, such as longitudinal symmetry planes (xz plane) or transverse characteristic planes (yz plane). Discrete sampling point sets are then generated on these cross-sections at a certain density. For these cross-sectional points, a coordinate embedding network is used to perform a nonlinear mapping of their three-dimensional coordinates to obtain the key cross-sectional embedding features corresponding to each cross-sectional point.

[0062] At the same time, the previously calculated global coupling features of the vehicle body surface are... Perform global average pooling or global max pooling to obtain a single global feature vector. Then, for each cross-section point j, concatenate this global feature vector with its embedded features to form a fused feature vector, which is the input feature used for cross-section flow field prediction.

[0063] This application generates discrete sampling points from key cross-sections of the vehicle and uses the same coordinate embedding network as the vehicle body points to obtain the embedding features of the cross-section points, ensuring the consistency of the feature space. Then, the global coupling features are concatenated with these embedding features to form a fusion vector for predicting the cross-sectional flow field. Since the global coupling features have already encoded the coupling relationship of the global flow on the vehicle body surface, and the cross-sectional embedding features provide precise positional information of the cross-sectional plane, the concatenation and fusion allows the model to fully utilize the overall influence of the vehicle shape on the flow when predicting the cross-sectional flow field, while maintaining the local spatial resolution within the cross-section. Unlike vehicle body pressure prediction, the features of the cross-sectional points do not undergo graph attention, but parameter reuse and information alignment are achieved by sharing the coordinate embedding network. This fusion strategy fundamentally ensures the physical synergy between the vehicle body pressure field and the cross-sectional flow field—both are based on the same set of global features, avoiding contradictory results that are easily generated by separate predictions (such as the cross-sectional velocity field corresponding to the low-pressure area of ​​the vehicle body appearing as high pressure), providing complete and inherently consistent input for subsequent interpolation and reconstruction.

[0064] In some embodiments, the step of obtaining the cross-sectional flow field prediction value by point-by-point regression specifically includes: mapping the part of the spliced ​​fusion feature vector corresponding to each key cross-sectional point to a scalar flow field prediction value through a regression function.

[0065] Specifically, a cross-sectional regression function is constructed, and the fused vector is input into the regression function h. The output is a scalar value, which is the predicted flow field value (which can be pressure, velocity, or other aerodynamic parameters) at the sampling point of that cross-section. Since different cross-sectional points have different spatial locations and different embedding features, each point can obtain a predicted value independently. This process ensures that the cross-sectional flow field prediction and the vehicle surface pressure field prediction share the global features extracted by the same backbone network, realizing the collaborative utilization of information.

[0066] In this application, the fused vector for each cross-section point includes global coupling features and the point's position embedding. The regression function can infer the velocity or pressure at that point based on a combination of global flow information and local coordinates. This point-by-point independent regression method preserves the differences between different locations within the cross-section, avoiding the detail ambiguity caused by global averaging or pooling. Simultaneously, because the regression function shares parameters across all cross-section points, the model can learn general mapping rules from a limited set of cross-section training samples. This ensures that the cross-section flow field prediction not only aligns with the vehicle body pressure field in macroscopic trends but also captures fine structures such as boundary layers and separated vortices in microscopic distribution, providing high-quality discrete sample points for subsequent regular grid reconstruction.

[0067] In some embodiments, the step of constructing a set of regular uniform grid nodes on the cross-sectional plane and reconstructing the predicted cross-sectional flow field values ​​using radial basis function interpolation to generate a regular two-dimensional flow field matrix specifically includes: constructing a set of regular uniform grid nodes on the cross-sectional plane; using the key cross-sectional discrete points and the predicted cross-sectional flow field values ​​as known samples, calculating the interpolation weight at each regular grid node based on the radial basis function, wherein the radial basis function is determined according to the spatial distance between the grid node and the discrete point; and performing a weighted summation of the predicted values ​​at the discrete points according to the interpolation weights to calculate the flow field values ​​at all regular grid nodes, thereby forming a regular two-dimensional flow field data matrix.

[0068] Specifically, since the discrete sampling points of the cross-section may be unevenly distributed on the plane, direct display would lead to image discontinuities or numerical fluctuations. Therefore, a regular and uniform set of grid nodes is first constructed on the cross-sectional plane. ,in, This represents the total number of uniform grid nodes on the cross-sectional plane.

[0069] Then, the radial basis function interpolation method is used for reconstruction: for each regular grid node Using known discrete sampling points and their predicted flow field values ​​as samples, the interpolation weight of each sample point to the grid node is calculated. This weight is determined by the radial basis function (such as Gaussian function, multiple quadratic function) based on the distance.

[0070] The interpolated flow field values ​​at the grid nodes can be expressed as: Where M represents the interpolated flow field value at the regular grid node, h represents the normalization coefficient in the interpolation process, used for scaling the neighborhood weights. Represents the spatial location of discrete sampling points in the neighborhood. The radial function response value formed at that location.

[0071] This function mapping relationship allows for the smooth expansion of the flow field values ​​at discrete prediction points, resulting in a continuous distribution across regular grid nodes, thus achieving a homogeneous reconstruction of the cross-sectional flow field. After sequentially performing the above interpolation calculations on all regular grid nodes on the cross-sectional plane, a regular two-dimensional flow field matrix can be obtained. Where M and N represent the number of nodes in the cross-sectional mesh in two directions, respectively. This interpolation process can effectively eliminate local numerical fluctuations caused by uneven distribution of discrete sampling points, making the final generated two-dimensional flow field map more spatially smooth and continuous. At the same time, it improves the flow field visualization effect and the stability of subsequent aerodynamic performance analysis, thus making it more conducive for engineers to conduct intuitive analysis and optimization design of the aerodynamic structural characteristics of the whole vehicle.

[0072] This application employs radial basis function interpolation to reconstruct the predicted flow field values ​​of discrete cross-sections using a regular grid, generating a regular two-dimensional flow field matrix. Since the original sampling points on key cross-sections may be unevenly distributed, directly displaying these discrete values ​​would produce jagged or mottled images, which is detrimental to engineering analysis. This application first constructs a regular uniform grid on the cross-sectional plane, and then uses the discrete predicted points as known samples, calculating the interpolation weight of each grid node based on radial basis functions (such as Gaussian functions or multiple quadratic functions). The weight depends on the spatial distance between the grid node and the discrete point. Radial basis function interpolation has advantages such as good smoothness and strong adaptability to irregular data, enabling the generation of continuous and naturally transitioning flow field contour maps. Simultaneously, a normalization coefficient is introduced to adjust the neighborhood influence radius, avoiding oversmoothing or overfitting. The resulting regular two-dimensional flow field matrix can be directly input into standard visualization tools (such as Matplotlib and ParaView) to generate contour maps, cloud maps, or streamline maps, greatly facilitating engineers' intuitive identification of key aerodynamic features such as vortex core locations, separation lines, and reattachment zones, providing a clear and reliable basis for shape optimization decisions.

[0073] Please refer to Figure 5On the other hand, the present invention also provides a joint prediction system for the external flow field of a vehicle based on dual-stream fusion and multi-head graph attention, comprising: a receiving module 10, used to receive a set of three-dimensional discrete points of the vehicle's shape, and using the three-dimensional coordinates of each point as an initial feature vector; an enhancement module 20, used to construct a residual feature enhancement network, and to perform a layer-by-layer nonlinear transformation on the initial feature vector through a multi-layer residual stacking structure, gradually increasing the feature dimension to the target high-dimensional space to obtain a geometric high-dimensional feature vector; an embedding module 30, used to construct a coordinate embedding network, and to perform nonlinear mapping on the three-dimensional coordinates of each point to obtain a high-dimensional coordinate embedding feature, wherein the high-dimensional coordinate embedding feature has the same dimension as the geometric high-dimensional feature vector; a fusion module 40, used to perform adaptive weighted fusion of the geometric high-dimensional feature vector and the high-dimensional coordinate embedding feature to obtain a fused feature; and a global coupling module 50, used to construct a directed graph based on the k-nearest neighbor algorithm, and to segment the fused feature along the channel into multiple The system calculates attention coefficients based on the feature similarity and relative spatial position between adjacent nodes, normalizes them, and uses them as attention weights to aggregate neighbor features, resulting in aggregated features. The aggregated features output from multiple heads are then concatenated to obtain global coupled features. A dual-branch prediction module 60 simultaneously inputs the global coupled features into a first prediction branch and a second prediction branch in parallel. The first prediction branch calculates the pressure coefficients at various points on the vehicle surface through point-by-point regression and outputs a three-dimensional pressure coefficient distribution map of the vehicle surface. The second prediction branch fuses the global coupled features with key section embedding features obtained by mapping the three-dimensional coordinates of key cross-section points of the vehicle using a coordinate embedding network. It then obtains the predicted cross-section flow field value through point-by-point regression, constructs a set of regular uniform grid nodes on the cross-section plane, and uses radial basis function interpolation to reconstruct the predicted cross-section flow field value using a regular grid, generating a regular two-dimensional flow field matrix and outputting a two-dimensional flow field map of the key cross-section.

[0074] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause an electronic device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0075] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, database, or other media used in the embodiments provided by this invention can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and RAMbus dynamic RAM (RDRAM), etc.

[0076] The above are merely embodiments of the present invention and do not limit the patent scope of the present invention. Any equivalent modifications made based on the content of the present invention's specification and drawings, or direct or indirect applications in related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A method for joint prediction of the external flow field of a vehicle based on dual-flow fusion and multi-head graph attention, characterized by the following steps: include: Receive the three-dimensional discrete point set of the vehicle's exterior shape, and use the three-dimensional coordinates of each point as the initial feature vector; A residual feature enhancement network is constructed, and the initial feature vector is subjected to a layer-by-layer nonlinear transformation through a multi-layer residual stacking structure to gradually increase the feature dimension to the target high-dimensional space, thereby obtaining a geometrically high-dimensional feature vector. A coordinate embedding network is constructed to perform nonlinear mapping on the three-dimensional coordinates of each point to obtain high-dimensional coordinate embedding features, wherein the dimensions of the high-dimensional coordinate embedding features are consistent with those of the geometric high-dimensional feature vector. The geometric high-dimensional feature vector and the high-dimensional coordinate embedding feature are adaptively weighted and fused to obtain the fused feature; A directed graph is constructed based on the k-nearest neighbor algorithm. The fused features are divided into multiple heads along the channel. Based on the feature similarity and relative spatial position between two adjacent nodes, the attention coefficient is calculated and normalized, and then used as the attention weight to aggregate the neighbor features to obtain aggregated features. The aggregated features output by the multiple heads are spliced ​​together to obtain global coupled features. The global coupling features are simultaneously input into the first and second prediction branches in parallel. The first prediction branch calculates the pressure coefficient of each point on the vehicle surface through point-by-point regression and outputs a three-dimensional pressure coefficient distribution map of the vehicle surface. The second prediction branch fuses the global coupling features with the key section embedding features obtained by mapping the three-dimensional coordinates of key section points of the whole vehicle through the coordinate embedding network. It obtains the predicted value of the cross-section flow field through point-by-point regression, constructs a set of regular uniform grid nodes on the cross-section plane, and uses the radial basis function interpolation method to reconstruct the predicted value of the cross-section flow field into a regular grid, generating a regular two-dimensional flow field matrix and outputting a two-dimensional flow field map of the key section.

2. The method for joint prediction of the vehicle external flow field based on dual-stream fusion and multi-head graph attention as described in claim 1, characterized in that, The step of performing a layer-by-layer nonlinear transformation on the initial feature vector through a multi-layer residual stacking structure to gradually increase the feature dimension to the target high-dimensional space specifically includes: The residual stacking structure is composed of multiple one-dimensional convolutional residual units connected in series. By stacking multiple residual units, the dimension of the initial feature vector is gradually increased to 1024 dimensions. In each residual unit, the input features are processed by a first one-dimensional convolutional linear transformation and a first non-linear activation function, then by a second one-dimensional convolutional linear transformation and a second non-linear activation function, and finally added to the input features of the current residual unit to obtain the output features of the current residual unit.

3. The method for joint prediction of the vehicle external flow field based on dual-stream fusion and multi-head graph attention as described in claim 2, characterized in that, The step of performing a nonlinear mapping of the three-dimensional coordinates of each point to obtain high-dimensional coordinate embedding features specifically includes: The coordinate embedding network contains multiple fully connected layers; The three-dimensional coordinates of each point are sequentially input into multiple fully connected layers, and a non-linear activation function is applied after each layer except the output layer. Through the layer-by-layer mapping of the fully connected layers, the three-dimensional coordinates are transformed into high-dimensional coordinate embedding features that are consistent with the dimensions of the geometric high-dimensional feature vector.

4. The method for joint prediction of the vehicle external flow field based on dual-stream fusion and multi-head graph attention as described in claim 3, characterized in that, The step of adaptively weighting and fusing the high-dimensional geometric feature vector with the high-dimensional coordinate embedding feature specifically includes: Linear transformations are performed on the geometric high-dimensional feature vector and the high-dimensional coordinate embedding feature using two independent, trainable coefficient matrices, respectively. The two feature vectors after linear transformation are added element by element to obtain the fused feature.

5. The method for joint prediction of the vehicle external flow field based on dual-stream fusion and multi-head graph attention as described in claim 4, characterized in that, The step of calculating attention coefficients based on the feature similarity and relative spatial position between two adjacent nodes, and then normalizing them to serve as attention weights for weighted aggregation of neighbor features specifically includes: For any central node and neighboring nodes determined by the k-nearest neighbor algorithm in a directed graph, the features of the central node and neighboring nodes are linearly transformed by a learnable feature mapping matrix to obtain the transformed feature vectors. The relative spatial coordinate vectors between the two nodes are linearly transformed by a learnable spatial position mapping matrix. The transformed features of the central node, neighboring nodes, and spatial coordinates are concatenated into a joint vector, and then a learnable weight vector is used to map this joint vector into a scalar, which serves as the initial attention coefficient. The initial attention coefficients of all neighboring nodes of the central node are normalized to obtain the attention weights of each neighboring node. The transformed features of each neighboring node are weighted and summed with their corresponding attention weights, and then linearly transformed through a learnable value mapping matrix to obtain the aggregated features of the central node under the current attention head.

6. The method for joint prediction of the vehicle external flow field based on dual-stream fusion and multi-head graph attention as described in claim 5, characterized in that, The step of calculating the pressure coefficient at each point on the vehicle body surface through point-by-point regression specifically includes: The feature vector corresponding to each point on the vehicle surface in the global coupling features is independently mapped to a scalar pressure coefficient value through a regression function, while maintaining the one-to-one correspondence between the features and the spatial points.

7. The method for joint prediction of the vehicle external flow field based on dual-stream fusion and multi-head graph attention as described in claim 5, characterized in that, The specific steps of fusing the global coupling features with the key section embedding features obtained by the coordinate embedding network through the 3D coordinate mapping of key section points of the whole vehicle include: Obtain discrete cross-sectional coordinates from key cross-sections of the vehicle; The coordinates of the cross-section points are input into the coordinate embedding network to obtain the key cross-section embedding features; The global coupling feature is concatenated with the key section embedding feature to form a fused feature vector for section flow field prediction.

8. The method for joint prediction of the vehicle external flow field based on dual-stream fusion and multi-head graph attention as described in claim 7, characterized in that, The step of obtaining the predicted cross-sectional flow field value through point-by-point regression specifically includes: The portion of the fused feature vector formed by splicing that corresponds to each key cross-section point is mapped to a scalar flow field prediction value through a regression function.

9. The method for joint prediction of the vehicle external flow field based on dual-stream fusion and multi-head graph attention as described in claim 8, characterized in that, The steps of constructing a regular uniform grid node set on the cross-sectional plane, and reconstructing the predicted cross-sectional flow field value using the radial basis function interpolation method to generate a regular two-dimensional flow field matrix specifically include: Construct a regular and uniform set of grid nodes on the cross-sectional plane; Using the key cross-section discrete points and the predicted cross-section flow field values ​​as known samples, the interpolation weight at each regular grid node is calculated based on the radial basis function, wherein the radial basis function is determined according to the spatial distance between the grid node and the discrete point; The predicted values ​​of discrete points are weighted and summed according to the interpolation weights to calculate the flow field values ​​on all regular grid nodes, thereby forming a regular two-dimensional flow field data matrix.

10. A joint prediction system for the external flow field of a vehicle based on dual-stream fusion and multi-head graph attention, characterized in that, include: The receiving module is used to receive a set of three-dimensional discrete points of the vehicle's exterior shape and use the three-dimensional coordinates of each point as the initial feature vector. The enhancement module is used to construct a residual feature enhancement network. It performs a layer-by-layer nonlinear transformation on the initial feature vector through a multi-layer residual stacking structure, gradually increasing the feature dimension to the target high-dimensional space to obtain a geometrically high-dimensional feature vector. An embedding module is used to construct a coordinate embedding network, which performs nonlinear mapping on the three-dimensional coordinates of each point to obtain high-dimensional coordinate embedding features. The high-dimensional coordinate embedding features have the same dimension as the geometric high-dimensional feature vector. The fusion module is used to adaptively weight and fuse the geometric high-dimensional feature vector with the high-dimensional coordinate embedding feature to obtain the fused feature; The global coupling module is used to construct a directed graph based on the k-nearest neighbor algorithm, divide the fused features into multiple heads along the channel, calculate the attention coefficient based on the feature similarity and relative spatial position between two adjacent nodes, normalize it and use it as attention weight to aggregate neighbor features to obtain aggregated features, and concatenate the aggregated features output by multiple heads to obtain global coupling features. The dual-branch prediction module is used to simultaneously input the global coupling features into a first prediction branch and a second prediction branch in parallel. The first prediction branch calculates the pressure coefficient of each point on the vehicle surface through point-by-point regression and outputs a three-dimensional pressure coefficient distribution map of the vehicle surface. The second prediction branch fuses the global coupling features with the key section embedding features obtained by mapping the three-dimensional coordinates of key section points of the whole vehicle through a coordinate embedding network. It obtains the predicted flow field value of the section through point-by-point regression, constructs a set of regular uniform grid nodes on the section plane, and uses the radial basis function interpolation method to reconstruct the predicted flow field value of the section through a regular grid, generating a regular two-dimensional flow field matrix and outputting a two-dimensional flow field map of the key section.

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