Method for constructing vehicle drag coefficient prediction model fusing convolution and physical information

Abstract

The application provides a method for constructing an automobile wind resistance coefficient prediction model by fusing convolution and physical information, and relates to the field of data processing. In the method, a vehicle body point cloud representation, wind resistance coefficient labeling data and flow field physical data are obtained and unified, a training set, a verification set and a test set are constructed; a dynamic graph structure is constructed based on neighborhood search and multi-layer edge convolution is performed to extract multi-scale geometric features, and a global feature vector is generated through global fusion; a double-branch prediction structure is constructed to output wind resistance coefficient prediction results and flow field prediction results; unified training targets are formed by fusing data fitting constraints and physical constraints, and parameters are updated, and optimal model parameters are determined by combining training optimization strategies to complete model construction. By implementing the scheme, the model can fully represent multi-scale geometric features in the vehicle body point cloud while introducing fluid mechanics constraints in the prediction process, and the problem of low prediction accuracy caused by pure data-driven methods is solved while ensuring prediction efficiency.

Description

Technical Field

[0001] This application relates to the technical field of data processing, specifically to a method for constructing a vehicle drag coefficient prediction model that integrates convolution and physical information. Background Technology

[0002] The drag coefficient is a core parameter for evaluating a vehicle's aerodynamic performance, directly impacting energy consumption, range, and driving stability. Currently, obtaining the drag coefficient primarily relies on wind tunnel testing or computational fluid dynamics (CFD) simulation. While wind tunnel testing can yield relatively accurate results in a controlled environment, it suffers from complex preparation, long cycles, and high costs, making it difficult to support rapid evaluation of various body styling options during the automotive design phase. Although CFD simulation reduces the cost of physical testing to some extent, it still requires complex mesh generation and numerical solutions, resulting in long computation times and heavy reliance on computational resources. It also suffers from inefficiency when facing the need for rapid iteration of multiple design options.

[0003] With the development of data-driven methods, machine learning-based drag coefficient prediction technology has been gradually introduced. This technology establishes a mapping relationship between vehicle body geometry and drag coefficient, enabling rapid estimation of the drag coefficient. However, these methods typically rely solely on labeled drag coefficient data for training, lacking a characterization of the physical processes of the flow field around the vehicle. This causes the model to tend to fit the data distribution during learning, neglecting fundamental fluid dynamics principles. This can easily lead to inconsistencies in the predicted flow field structure, thus affecting the reliability of the drag coefficient prediction. Furthermore, the complex three-dimensional structure of vehicle bodies makes it difficult for traditional feature extraction methods to simultaneously capture both local geometric details and the overall aerodynamic profile, limiting the model's ability to express key aerodynamic features.

[0004] Therefore, how to ensure prediction efficiency while enabling the model to fully represent the multi-scale geometric features in the vehicle point cloud, and also to introduce hydrodynamic constraints during the prediction process to avoid the problem of low prediction accuracy caused by pure data-driven methods, has become an urgent technical problem to be solved. Summary of the Invention

[0005] This application provides a method for constructing a vehicle drag coefficient prediction model that integrates convolution and physical information. This method ensures prediction efficiency while enabling the model to fully represent the multi-scale geometric features in the vehicle point cloud and to introduce hydrodynamic constraints during the prediction process, thus solving the problem of low prediction accuracy caused by pure data-driven methods.

[0006] The first aspect of this application provides a method for constructing a vehicle drag coefficient prediction model that integrates convolutional and physical information. The method includes: acquiring three-dimensional geometric data of a target vehicle and constructing a vehicle body point cloud representation; simultaneously acquiring drag coefficient annotation data and flow field physical data corresponding to the target vehicle; performing uniform normalization processing on the vehicle body point cloud representation, the drag coefficient annotation data, and the flow field physical data to generate a training set, a validation set, and a test set; performing a neighborhood search on each node based on the vehicle body point cloud representation to construct a neighborhood node set; constructing a dynamic graph structure based on the neighborhood node set; simultaneously performing multi-layer edge convolution operations on the dynamic graph structure; performing feature mapping and feature aggregation on the relative geometric relationships between nodes and neighborhood nodes to form a multi-scale geometric feature expression; performing global fusion processing on the multi-scale geometric feature expression to generate a global feature vector; and based on the global features... A bi-branch prediction structure is constructed using vectors to output drag coefficient prediction results and flow field prediction results. Data fitting constraints are constructed based on the drag coefficient prediction results and the drag coefficient labeled data, while physical constraints are constructed based on the flow field prediction results. The data fitting constraints and physical constraints are then fused to form a unified training objective. Backpropagation updates the feature extraction parameters corresponding to the dynamic graph structure and the prediction parameters corresponding to the bi-branch prediction structure, ensuring that the initial model fits the data distribution while satisfying the unified training objective. Based on the training set, the validation set, and the test set, the training process of the initial model is optimized using a learning rate scheduling strategy, regularization constraints, and a validation set early stopping mechanism to determine the optimal model parameters. Based on the optimal model parameters and the initial model, a vehicle drag coefficient prediction model integrating convolutional and physical information is constructed.

[0007] A second aspect of this application provides an apparatus for constructing a vehicle drag coefficient prediction model that integrates convolutional and physical information. The apparatus includes an acquisition module and a processing module. The acquisition module acquires three-dimensional geometric data of a target vehicle and constructs a vehicle body point cloud representation. It also acquires drag coefficient annotation data and flow field physical data corresponding to the target vehicle, and performs uniform normalization processing on the vehicle body point cloud representation, the drag coefficient annotation data, and the flow field physical data to generate a training set, a validation set, and a test set. The processing module performs a neighborhood search on each node based on the vehicle body point cloud representation to construct a neighborhood node set. It then constructs a dynamic graph structure based on the neighborhood node set and performs multi-layer edge convolution operations on the dynamic graph structure. It performs feature mapping and feature aggregation on the relative geometric relationships between nodes and neighborhood nodes to form a multi-scale geometric feature expression. The processing module further performs global fusion processing on the multi-scale geometric feature expression to generate a global feature vector. The processing module is further configured to construct a dual-branch prediction structure based on the global feature vector, so as to output the drag coefficient prediction result and the flow field prediction result through the dual-branch prediction structure; the processing module is further configured to construct data fitting constraints based on the drag coefficient prediction result and the drag coefficient labeled data, and construct physical constraints based on the flow field prediction result, and perform fusion processing on the data fitting constraints and the physical constraints to form a unified training objective, and update the feature extraction parameters corresponding to the dynamic graph structure and the prediction parameters corresponding to the dual-branch prediction structure through backpropagation, so that the initial model satisfies the unified training objective while fitting the data distribution; the processing module is further configured to optimize the training process of the initial model based on the training set, the validation set and the test set, combined with the learning rate scheduling strategy, regularization constraints and the validation set early stopping mechanism, to determine the optimal model parameters, so as to complete the construction of the vehicle drag coefficient prediction model that integrates convolution and physical information according to the optimal model parameters and the initial model.

[0008] A third aspect of this application provides an electronic device including a processor, a memory, a user interface, and a network interface. The memory is used to store instructions, and both the user interface and the network interface are used to communicate with other devices. The processor is used to execute the instructions stored in the memory to cause the electronic device to perform the method described above.

[0009] A fourth aspect of this application provides a non-transitory computer-readable storage medium storing instructions that, when executed, perform the method described above.

[0010] In summary, one or more technical solutions provided in this application have at least the following technical effects or advantages: By using the vehicle body point cloud representation as a unified input and combining neighborhood search and dynamic graph structure construction, the model can adaptively characterize the complex 3D geometry of the vehicle body. Through multi-layer edge convolution operations, it extracts local surface morphology features, regional contour features, and overall vehicle semantic features layer by layer, significantly improving the ability to express the aerodynamic shape of the vehicle body and avoiding the problem of traditional parametric methods being unable to describe complex shapes. By performing global fusion processing on multi-scale geometric feature representations and generating global feature vectors, the geometric information scattered across nodes and levels is integrated at the vehicle level, providing a unified and high-dimensional feature foundation for subsequent predictions. This ensures that the drag coefficient prediction results and flow field prediction results are generated in the same geometric semantic space, enhancing the consistency and correlation between different prediction tasks. By constructing a dual-branch prediction structure, the model directly outputs the drag coefficient prediction results, achieving efficient mapping from vehicle body geometry to aerodynamic performance indicators. Simultaneously, it outputs the flow field prediction results, enabling the model to explicitly characterize the external flow state of the vehicle body. This introduces intermediate physical quantities in the prediction stage, compensating for the information loss caused by single scalar prediction and improving the model's expressive completeness.

[0011] By simultaneously constructing data fitting constraints and physical constraints, and fusing them into a unified training objective, the model can not only fit the labeled drag coefficient data but also satisfy the basic laws of fluid mechanics. This effectively avoids the physical inconsistency problem common in purely data-driven methods, significantly improving the physical rationality and engineering credibility of the prediction results. By introducing a division of labor mechanism between training, validation, and test sets, and combining learning rate scheduling strategies, regularization constraints, and early stopping mechanisms on the validation set, the entire initial model training process is controlled. This achieves a balance between training efficiency, convergence stability, and generalization ability, avoiding overfitting and improving adaptability to unknown vehicle body shapes. Therefore, it is convenient to ensure prediction efficiency while enabling the model to fully represent the multi-scale geometric features in the vehicle body point cloud and to introduce fluid mechanics constraints during the prediction process, solving the problem of low prediction accuracy caused by purely data-driven methods. Attached Figure Description

[0012] Figure 1 A flowchart illustrating the method for constructing a vehicle drag coefficient prediction model that integrates convolutional and physical information, as provided in this application embodiment; Figure 2 A schematic diagram of the module for constructing a vehicle drag coefficient prediction model that integrates convolutional and physical information, as provided in an embodiment of this application. Figure 3 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application.

[0013] Explanation of reference numerals in the attached figures: 21. Acquisition module; 22. Processing module; 31. Processor; 32. Communication bus; 33. User interface; 34. Network interface; 35. Memory. Detailed Implementation

[0014] To enable those skilled in the art to better understand the technical solutions in this specification, the technical solutions in the embodiments of this specification will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments.

[0015] In the description of the embodiments of this application, the words "for example" or "for instance" are used to indicate examples, illustrations, or explanations. Any embodiment or design that is described as "for example" or "for instance" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design options. Rather, the use of the words "for example" or "for instance" is intended to present the relevant concepts in a specific manner.

[0016] In the description of the embodiments of this application, the term "multiple" means two or more. For example, multiple systems means two or more systems, and multiple screen terminals means two or more screen terminals. In addition, the terms "comprising," "including," "having," and variations thereof all mean "including but not limited to," unless otherwise specifically emphasized.

[0017] To address the aforementioned technical issues, this application provides a method for constructing a vehicle drag coefficient prediction model that integrates convolutional and physical information, referring to... Figure 1 , Figure 1 This is a flowchart illustrating the method for constructing a vehicle drag coefficient prediction model that integrates convolutional and physical information, as provided in this application embodiment. The method is applied to a server and includes steps S110 to S160, as follows:

[0018] S110. Acquire the three-dimensional geometric data of the target vehicle and construct the vehicle body point cloud representation. At the same time, acquire the drag coefficient annotation data and flow field physical data corresponding to the target vehicle. Perform unified normalization processing on the vehicle body point cloud representation, drag coefficient annotation data and flow field physical data to generate training set, validation set and test set.

[0019] Specifically, a server refers to a computing device with data processing and network communication capabilities, whose main functions are to provide computing services, data storage services, and model inference services. Convolution refers to a dynamic graph convolutional neural network, the core of which lies in constructing a dynamically updatable graph structure for point cloud data and performing edge convolution operations on this graph structure to extract features. Physical information refers to a physical information neural network, the core of which lies in introducing physical constraints during the neural network training process, ensuring that the model output not only meets data fitting requirements but also satisfies the physical laws of the corresponding domain.

[0020] First, the 3D geometric data of the target vehicle undergoes format conversion and surface sampling processing to unify the conversion of geometric models from different sources into a vehicle body point cloud representation. The 3D geometric data includes triangular mesh models, surface models, or computer-aided design models composed of the vehicle's outer surfaces. Format conversion involves uniformly parsing geometric files output by different modeling software or simulation platforms into readable sets of vertices, faces, and topological relationships, and then further converting them into discrete point sets that retain only the spatial coordinates of the vehicle's outer surfaces. Surface sampling processing involves extracting representative spatial points along the vehicle's outer surfaces according to preset rules. This ensures that the discrete points cover the front, roof, side, rear, and additional component areas, while avoiding geometric imbalances caused by excessively dense or sparse local point counts. The preset point count scale ensures that the number of points retained for each vehicle sample remains consistent after conversion, facilitating subsequent batch training. Spatial distribution density refers to the density of point distribution within a unit surface area, requiring overall uniformity while appropriately increasing the sampling density in areas with significant curvature variations to preserve key geometric details. Surface sampling points can be generated by combining surface area-weighted sampling with curvature-compensated sampling, where the probability of a single triangular facet being selected can be written as:

[0021] in, Indicates the first The probability of a triangular facet being selected for surface sampling; Indicates the first The area of ​​each triangular facet; This indicates the total number of triangular facets on the outer surface of the vehicle body; This represents the sum of the areas of all triangular facets. The principle reflected in this formula is that the larger the surface area, the higher the probability of it being sampled, thus ensuring that large areas are not distorted due to insufficient sampling. After surface sampling, outlier removal and duplicate point merging must be performed on the vehicle body point cloud representation. Outliers are isolated points caused by model damage, sampling errors, or coordinate resolution errors, whose spatial positions are significantly deviated from the vehicle's outer surface; duplicate points are points with multiple highly overlapping or very close overlapping coordinates, leading to local density variations. Outliers can be identified based on the average distance from their neighborhood. If the average distance from a point to its neighborhood points is significantly greater than the overall mean, it is determined to be an outlier. The determination metric can be written as:

[0022] in, Indicates the first Average neighborhood distance of each sampling point; This indicates the number of neighboring points included in the statistics; Indicates the first The three-dimensional coordinates of each sampling point; Indicates the first The corresponding sampling point of the th sampling point Coordinates of neighboring points; This represents the calculation of Euclidean distance. The principle reflected in this formula is that normal surface points maintain a continuous distribution with surrounding points. If the average distance of the neighborhood is too large, the point may not belong to the actual outer surface of the vehicle body. After the above processing, a complete, uniform, and density-controlled point cloud representation of the vehicle body is obtained, providing a foundation for subsequent dynamic map structure construction.

[0023] Subsequently, the drag coefficient labeled data underwent a working condition consistency check to ensure that the drag coefficient labeled data of different vehicle samples were under a unified evaluation standard. The drag coefficient labeled data comes from wind tunnel test results or computational fluid dynamics simulation results; essentially, it is a dimensionless air resistance characterization value under a certain inflow condition and reference area definition. The working condition consistency check involves checking whether the inflow velocity, inflow direction, air density, reference windward area, and drag calculation standard corresponding to the drag coefficient are consistent for the same batch of vehicle samples. If discrepancies exist, recalculation or removal of inconsistent samples is required. The reference area is the base area used to normalize drag in the definition of the drag coefficient, using the vehicle's projected windward area; the inflow condition refers to the flow state of air acting on the vehicle, and at least the velocity and direction conditions should be consistent. The drag coefficient itself can be characterized by the following formula:

[0024] in, Indicates the drag coefficient; This indicates the air resistance experienced by the vehicle; Indicates air density; Indicates the incoming flow velocity; This represents the reference frontal area. The principle behind this formula is to normalize actual air resistance as a proportion relative to hydrodynamic pressure and the vehicle's reference area, thus facilitating comparisons between different vehicle models. In practice, it is necessary to convert the data corresponding to each vehicle sample... A one-to-one mapping relationship is established between the vehicle body point cloud representation and the vehicle body point cloud representation. This means ensuring that each vehicle body point cloud representation corresponds to only one drag coefficient label value that has been verified under operating conditions, and that the same point cloud does not correspond to multiple conflicting label values. If multiple sets of duplicate measurement results exist for the same vehicle sample, a consistency screening process can be used to take the average label value. The averaging process can be written as follows:

[0025] in, This indicates the final drag coefficient value for the same vehicle sample. This indicates the number of times the vehicle sample was repeatedly measured or simulated; Indicates the first The drag coefficient is obtained from multiple measurements or simulations. The principle reflected in this formula is that averaging multiple results reduces the impact of random fluctuations on the labeled value, thereby enhancing the stability of subsequent monitoring signals.

[0026] Subsequently, spatial registration processing is performed on the flow field physical data to ensure that the flow field velocity distribution and pressure distribution are in the same spatial coordinate system as the vehicle body point cloud representation. Flow field physical data describes the flow state of air around the vehicle body at different spatial locations. The flow field velocity distribution reflects the magnitude and direction of air velocity at each sampling location, while the flow field pressure distribution reflects the pressure changes of air on the vehicle body surface and adjacent areas. Spatial registration processing involves transforming the original coordinate system of the flow field physical data to the vehicle body coordinate system where the vehicle body point cloud representation resides, avoiding misalignment between geometric and physical field positions. If the original flow field data originates from the simulation mesh coordinate system, while the vehicle body point cloud representation originates from the design model coordinate system, a rigid transformation or similarity transformation is required to achieve unification. The transformation relationship can be written as:

[0027] in, Indicates the transformed first... The coordinates of each flow field sampling point in the vehicle body coordinate system; Indicates the first before conversion The original coordinates of each flow field sampling point; This represents the coordinate rotation matrix, used to correct for attitude differences; This represents the translation vector, used to correct positional offsets. The principle reflected in this formula is that by unifying rotation and translation relationships, data originally located under different reference frames are mapped to a common geometric reference. After coordinate unification, the flow field physical data needs to be aligned to the surface sampling points corresponding to the vehicle body point cloud representation according to a preset sampling method. The preset sampling method refers to interpolating the corresponding flow field velocity and pressure values ​​from neighboring flow field sampling points around each surface sampling point, thereby establishing a point-to-point alignment relationship. The inverse distance weighted interpolation relationship can be written as:

[0028] in, The point cloud representation of the vehicle body Interpolation results corresponding to each surface sampling point; Indicates the first The physical quantity is taken at each flow field sampling point. This physical quantity can be either a velocity component or a pressure value. Indicates the first The flow field sampling point for the first The interpolation weights for each surface sampling point range from 0 to 1; This indicates the number of neighboring flow field sampling points involved in the interpolation; This represents the distance attenuation index; the larger the value, the stronger the influence of the flow field sampling point that is closer to the sample. This represents a very small positive number to prevent the denominator from being zero. The principle reflected in this formula is that the closer the flow field sampling point is to the surface sampling point, the greater its contribution to the physical quantity of the flow field at that point, thereby achieving precise alignment between the physical data of the flow field and the point cloud representation of the vehicle body.

[0029] Next, uniform normalization is performed on the vehicle body point cloud representation, drag coefficient annotation data, and flow field physical data to eliminate numerical scale differences between different data and form a unified data representation. The purpose of uniform normalization is to ensure that geometric coordinates, flow field velocity, flow field pressure, and drag coefficient are within a relatively stable numerical range when entering the subsequent training process, preventing any one type of value from dominating the parameter update process due to excessive magnitude. For the spatial coordinates in the vehicle body point cloud representation and the velocity and pressure in the flow field physical data, normalization can be performed using a minimum to maximum value range scaling method, the expression of which is:

[0030] in, This represents the normalized value; This represents the original value before normalization. This indicates the minimum value of this type of data in the current sample set or the current field; This indicates the maximum value of this type of data in the current sample set or the current field; This indicates the prevention of extremely small positive numbers with a denominator of zero. The principle reflected in this formula is to compress the original data into a uniform numerical range, reducing the numerical bias between different orders of magnitude. For wind resistance coefficient labeled data, mean centering and dispersion scaling can be used for uniform normalization, and its expression is:

[0031] in, This indicates the normalized drag coefficient value. This represents the original drag coefficient value. This represents the overall mean of the drag coefficient data. The standard deviation represents the overall dispersion of the drag coefficient data. This indicates the use of extremely small positive numbers to prevent the denominator from being zero. The principle reflected in this formula is to adjust the drag coefficient annotation data to near the zero center and control its fluctuation range, thereby improving the stability of model training. Unified data representation means that after the above regularization, the vehicle body point cloud representation, drag coefficient annotation data, and flow field physical data all meet the unified requirements for subsequent processing in terms of structural organization and numerical space.

[0032] Then, integrity verification is performed on the data after unified normalization to filter out valid sample sets that simultaneously possess vehicle body point cloud representation, drag coefficient annotation data, and flow field physical data. Integrity verification is not simply checking for file existence, but rather screening from three levels: sample consistency, field integrity, and spatial correspondence. Sample consistency means that the three types of data for the same vehicle sample must share the same vehicle identifier; field integrity means that the vehicle body point cloud representation must have a specified number of surface sampling points, the drag coefficient annotation data must have valid annotation values, and the flow field physical data must cover the specified surface sampling area; spatial correspondence means that the flow field physical data, after alignment, must be able to establish a mapping relationship with the surface sampling points in the vehicle body point cloud representation. A sample validity determination function can be constructed to automatically screen each vehicle sample, and its expression can be written as:

[0033] in, Indicates the first The validity determination results of individual vehicle samples; Indicates the first The criteria for determining whether a vehicle sample has a qualified vehicle body point cloud representation are set to 1 if the criteria are met, and 0 otherwise. Indicates the first Whether a vehicle sample has qualified drag coefficient labeling data; Indicates the first The criteria for determining whether a vehicle sample has qualified flow field physical data; Indicates the first This formula determines whether a vehicle sample possesses a valid spatial correspondence. The principle behind this formula is that a vehicle sample is only included in the valid sample set when the vehicle body point cloud representation, drag coefficient annotation data, flow field physical data, and spatial correspondence all meet the requirements. This method avoids missing, mismatched, or failed-registration data from entering the subsequent training process.

[0034] Finally, the valid sample set is shuffled and partitioned to generate training, validation, and test sets. Shuffling involves randomizing the order of vehicle samples in the valid sample set to avoid order bias caused by the original data being arranged by vehicle type, platform, or generation time. Partitioning involves dividing the shuffled valid sample set into independent training, validation, and test sets, ensuring that the same vehicle sample and its highly similar variants do not simultaneously enter multiple subsets. The training set drives the model to learn parameters, the validation set monitors the model's generalization trend during training and triggers an early stopping mechanism, and the test set evaluates the final generalization ability after model construction. If the total number of valid samples is... The number of samples in the training set, validation set, and test set can be expressed as follows:

[0035] in, Indicates the number of samples in the training set; Indicates the number of samples in the validation set; Indicates the number of samples in the test set; This represents the total number of valid samples. Indicates the proportion of the training set partition; Indicates the proportion of the validation set partition; This indicates a floor function. The principle behind this formula is to first allocate training and validation samples proportionally from the total sample size, then allocate the remaining samples to the test set, ensuring that the three subsets have no overlap and that the total number of samples is conserved. In practice, the partitioning ratio can be set to approximately 7:2:1, thus ensuring sufficient training while reserving a sufficient sample size for the validation and test sets. After this processing, the training, validation, and test sets required for subsequent model training, performance screening, and generalization evaluation are formed.

[0036] S120. Based on the vehicle body point cloud representation, perform a neighborhood search for each node to construct a set of neighborhood nodes, and construct a dynamic graph structure based on the set of neighborhood nodes. At the same time, perform multi-layer edge convolution operations on the dynamic graph structure to perform feature mapping and feature aggregation on the relative geometric relationship between the node and the neighborhood nodes to form a multi-scale geometric feature representation.

[0037] Specifically, each node in the vehicle body point cloud representation is uniformly numbered, and a neighborhood search is performed on each node based on a preset neighborhood determination method to generate a set of neighboring nodes corresponding to the node, and to establish the adjacency relationship between the node and its neighboring nodes. Nodes in the vehicle body point cloud representation refer to discrete sampling points distributed on the outer surface of the vehicle body. Each node carries three-dimensional spatial coordinate information to represent the local geometric position of the vehicle body. Uniform numbering refers to assigning a unique index to all nodes so that the same node can be stably referenced in subsequent neighborhood search, dynamic graph structure construction, and edge convolution operations. The preset neighborhood determination method refers to the rules for determining which nodes around a central node should be considered its neighboring nodes, including a fixed number of neighboring points method and a fixed spatial radius method. The fixed number of neighboring points method is suitable for controlling the size of the neighborhood participating in the operation for each central node, while the fixed spatial radius method is suitable for maintaining true geometric proximity. If the fixed number of neighboring points method is used, the nodes closest to the central node can be selected according to Euclidean distance from nearest to farthest to form a set of neighboring nodes. The distance expression is:

[0038] in, Indicates the first The node and the first Euclidean distance between nodes; Indicates the first The three-dimensional coordinates of each node; Indicates the first The three-dimensional coordinates of each node; This represents the L2 norm operation, used to calculate straight-line distances in three-dimensional space. The principle reflected in this formula is that nodes that are spatially closer are more likely to belong to the same local geometric region on the vehicle's outer surface, and therefore are preferentially included in the neighborhood node set. If for the ... Select the node that is closest to it. If there are n nodes, then the set of its neighboring nodes can be expressed as:

[0039] in, Indicates the first The set of neighboring nodes corresponding to each node; This indicates selecting the smallest distance from all candidate distances. One corresponding node; This indicates the preset number of neighboring nodes. The principle reflected in this formula is to construct a uniformly sized local observation range for each node, ensuring a consistent input format for subsequent feature extraction processes of different nodes. Adjacency refers to the connection established between the central node and its neighboring nodes. This relationship does not represent a physical link, but rather indicates that information exchange between them is allowed in subsequent graph operations. After this step, the originally independent nodes are organized into node relationship units with the central node as the core and the set of neighboring nodes as the local environment.

[0040] A dynamic graph structure is constructed based on adjacency relationships, with each node serving as a central node and the set of neighboring nodes as local association units. The association relationships between nodes and their neighbors are represented by node-connecting edges. A dynamic graph structure is a graph representation where nodes are the basic elements, node-connecting edges are the relationship carriers, and the connections between nodes can be adjusted according to feature changes. Unlike static graph structures, dynamic graph structures are not fixed throughout the training process; instead, they allow for recalculation of similarity and proximity between nodes at different levels based on current node features, thus dynamically reconstructing the connection relationships. Node-connecting edges are graph relationship units pointing from the central node to neighboring nodes, used to express the association channels between the central node and neighboring nodes that allow feature interactions. If all nodes are numbered... The dynamic graph structure can then be represented as a combination of a set of nodes and a set of edges:

[0041] in, Indicates the first The dynamic graph structure corresponding to the layer; The set of nodes consists of all nodes in the vehicle body point cloud representation. Indicates the first The edge set of a layer consists of the edges connecting the central node and its neighboring nodes. This formula reflects the principle that, given the same set of nodes, the edge sets at different levels can change based on updates to node characteristics, thus giving the graph structure a dynamic nature. For any central node... The nodes connecting the edges can be written as:

[0042] in, Indicates the first In the layer, the first A set of node-connecting edges established with each node as the center node; Indicates from the central node To neighboring nodes An edge connecting a node; Indicates the first The first in the layer The set of neighboring nodes of each node. The principle reflected in this formula is that each central node establishes local association units with its neighboring nodes through several node connection edges, and the combination of all local association units constitutes the vehicle-level dynamic graph structure. In this way, the discrete nodes in the front, roof, side, rear, and additional component areas are no longer scattered, but are organized in the form of a graph as a structured expression that can transmit hierarchical features.

[0043] Edge convolution is performed on the dynamic graph structure to extract node features and relative geometric relationships for each central node and its corresponding set of neighboring nodes. Feature mapping is then applied to these node features and relative geometric relationships to generate corresponding edge feature representations. Edge convolution refers to the operation of extracting, mapping, and encoding the feature differences between the central node and its neighboring nodes around each connecting edge. Node features are vectors used to describe the node state at the current level. In the initial layer, these are taken as the node's three-dimensional coordinates; in higher layers, they evolve into information vectors containing geometric semantics. Relative geometric relationships refer to the local geometric differences between the central node and its neighboring nodes, focusing on describing their relative displacement, relative direction, and local morphological change trends. In the initial layer, relative geometric relationships can be initially constructed from the positional differences of neighboring nodes relative to the central node, expressed as:

[0044] in, Indicates the first The neighboring node relative to the first The position difference vector of each central node; Indicates the first The coordinates of the central node; Indicates the first The coordinates of the neighboring nodes. This formula reflects the principle that edge convolution operations consider not only the absolute position of the nodes themselves, but also the spatial offset of each node relative to another within its local neighborhood, thus making it easier to characterize surface undulations, contour transitions, and convex structures. If the node features of the current layer are denoted as... When generating edge feature representation for a node connection edge, the center node feature and feature difference can be fed together into the feature mapping function, with the expression as follows:

[0045] in, Indicates the first Central node in the layer With neighboring nodes Corresponding edge feature representation; Indicates the first The feature mapping function of the layer is implemented by a multilayer perceptron structure with shared parameters; Indicates the first Central node in the layer Node characteristics; Indicates the first Neighborhood nodes in the layer Node characteristics; This represents the relative feature difference between neighboring nodes and the central node. The principle reflected in this formula is to encode the current state of the central node and the relative changes in its neighborhood into the edge feature representation, thereby preserving local positional semantics while highlighting local difference patterns. Through this processing, the smooth transition of the front region, the truncated contraction of the rear region, the gradually changing curvature of the roof region, and the abrupt protrusions of the additional component regions can all be prominently represented in the edge feature representation.

[0046] Feature aggregation is performed on the edge feature representations to generate node feature update results for each central node at the current level. The dynamic graph structure is then updated based on these node feature update results, allowing the relationships between nodes to dynamically adjust as node features change. Feature aggregation refers to the process of uniformly summarizing all edge feature representations corresponding to the same central node, enabling local geometric information scattered across multiple node connections to be attributed to the central node. Feature aggregation methods include maximum aggregation, average aggregation, and summation aggregation. Maximum aggregation emphasizes the most significant local geometric differences and is suitable for highlighting edges, corners, and local convexities. If maximum aggregation is used, the node feature update results at the current level can be written as:

[0047] in, Indicates the first Central node in the layer The node feature update results; Indicates the first Layer node connection edge Edge feature representation; This indicates that the edge feature representations corresponding to all neighboring nodes are aggregated using a dimension-wise maximum aggregation method. The principle reflected in this formula is to allow the edge feature representations that best reflect local geometric saliency to dominate the new features of the central node, thereby enhancing the model's sensitivity to key morphological differences. After the node feature update is completed, the nodes are no longer simply represented by their initial coordinates, but begin to carry information such as local surfaces, contour edges, and regional semantics. Subsequently, the similarity between nodes is recalculated using the new node features, thereby updating the neighboring node set and edge set. At this point, the dynamic graph structure no longer completely relies on the original coordinate proximity relationships, but begins to consider semantic similarity. For example, two nodes that are spatially distant but both belong to the tail-end contraction region may be more easily organized into the same neighborhood relationship at higher levels. If the feature distance is recalculated based on the node features of the current layer, it can be written as:

[0048] in, Indicates the first The first in the layer The node and the first Feature distance between nodes; and They represent the first The expression reflects the principle that, at higher levels, whether nodes should be adjacent depends not only on their coordinate distance but also on their proximity in the geometric semantic space. Through this update process, the dynamic graph structure gains the ability to dynamically adjust as node features change.

[0049] Based on the updated dynamic graph structure, multi-layer edge convolution operations are repeatedly performed to extract local surface geometric features, regional contour geometric features, and whole-vehicle semantic geometric features from the vehicle body point cloud representation layer by layer. Local surface geometric features refer to features that characterize small-scale surface undulations, edge transitions, curvature changes, and protrusions of additional components; regional contour geometric features refer to features that characterize the overall contour relationships of larger regions such as the front, roof, side, and rear regions; whole-vehicle semantic geometric features refer to high-level features that reflect the aerodynamic shape characteristics and cross-regional correlation patterns of the entire vehicle. As the number of layers increases, nodes can continuously expand their perception range through repeated information transmission and neighborhood updates, thus gradually evolving from perceiving only local neighborhoods to perceiving region-level and even whole-vehicle-level structures. If the node feature update process of a layer is denoted as a composite operator, then the entire hierarchical recursive relation can be written as:

[0050] in, Indicates the first The node feature matrix of all nodes in the layer; Indicates the first Layer edge convolution and feature aggregation combined operation; Indicates the first The node feature matrix of all nodes in the layer; Indicates the first The dynamic graph structure of the layers. This formula reflects the principle that the output of each layer is built upon the node features of the previous layer and the dynamic graph structure of the current layer; therefore, there is a strict dependency between layers. In implementation, lower layers focus more on local surface geometry, intermediate layers focus more on regional contour geometry, and higher layers focus more on the semantic geometry of the entire vehicle. For example, the first layer might highlight local fold lines at the door edges, local surface changes in the wheel arches, and sensor envelope protrusions; the second layer begins to integrate the front windward curve, the rear tapering curve, and the roof transition shape; the third and higher layers further establish the overall styling relationship between the front, roof, and rear regions. Through this progressive layering, the model can fully learn the hierarchical geometric rules of the vehicle's exterior shape, from details to the whole.

[0051] The local surface geometric features, region contour geometric features, and whole-vehicle semantic geometric features output from the convolutional operations of each layer are integrated to form a multi-scale geometric feature representation. Multi-scale geometric feature representation refers to the comprehensive feature representation obtained by fusing node features from multiple levels in a unified manner. This representation includes detailed responses at the local surface level, structural responses at the region contour level, and global responses at the whole-vehicle semantic level. The integration process is not a simple addition; instead, it first performs layer alignment, followed by feature concatenation or weighted fusion. Layer alignment ensures that the node features output from different levels maintain correspondence in node order and feature dimension mapping. Feature concatenation concatenates node features from different levels along the feature dimension to preserve the independence of information from each layer. If we consider the first layer as an example... Layer to the first If the node features of a layer are taken as input, then the multi-scale geometric feature representation of a single node can be written as:

[0052] in, Indicates the first Multi-scale geometric feature representation of each node; Indicates feature concatenation operation; They represent the first The node at the th Layer to the first Node feature update results in the layer; This indicates the total number of convolutional layers. The principle reflected in this formula is to retain all the geometric information extracted from different layers, enabling subsequent global fusion processing to see not only subtle changes in the local areas of the vehicle body but also the comprehensive pattern of region contours and overall vehicle semantics. If this integration is completed for all nodes, a multi-scale geometric feature representation matrix at the vehicle level can be formed, providing direct input for the next step of global fusion processing to generate global feature vectors. After this step, the entire vehicle point cloud representation has evolved from a set of original discrete coordinates into a multi-scale geometric feature representation system that combines local geometric recognition capabilities, region contour organization capabilities, and overall vehicle semantic expression capabilities.

[0053] S130. Perform global fusion processing on the multi-scale geometric feature representation to generate a global feature vector.

[0054] Specifically, the node features of each node at different levels in the multi-scale geometric feature representation are uniformly organized, and hierarchical alignment processing is performed on the node features to establish the correspondence between the same node at different levels. Node features refer to the feature vector corresponding to each node after the convolution operation at each layer; node features at different levels represent geometric information at different scales, with lower layers focusing more on local surface undulations and edge transitions, and higher layers focusing more on regional contour relationships and the semantic structure of the entire vehicle. Unified organization refers to rearranging and storing all node features corresponding to the same node in layers 1 to L according to a unified index order to avoid node identity confusion due to layer switching. Hierarchical alignment processing ensures that the node features of the same node at different levels can correspond one-to-one, so that subsequent feature splicing processing targets the semantic evolution results of the same physical location node at different levels, rather than a mixed combination of different nodes. The node at the th The node features of a layer are denoted as Then the node feature sequence of the same node across all levels can be represented as:

[0055] in, Indicates the first The hierarchical node feature sequence after unified organization; They represent the first The node characteristics of a node in layers 1 to L; This represents the total number of convolutional layers. The principle reflected in this formula is to collect the representation results of the same node at different layers in a fixed order, so that it can subsequently participate in the fusion process as a complete hierarchical semantic trajectory. In implementation, it is necessary to first verify whether the node indices in the output of each layer are consistent. If there is node rearrangement in the middle, index restoration must be performed based on the original node number to ensure that the node features of each node in each layer strictly fall under the same node identifier.

[0056] Feature stitching is performed on node features that have completed hierarchical alignment to form composite node features containing multi-layered information. This allows the composite node features to simultaneously represent local surface geometry, regional contour geometry, and overall vehicle semantic geometry. Feature stitching refers to sequentially concatenating node features of the same node at different levels along the feature dimension to form a higher-dimensional comprehensive feature vector. Composite node features are node-level comprehensive expressions that retain both low-level details and high-level semantics. Local surface geometry refers to details such as small-scale surface undulations, polygonal edges, and protrusions of additional components near the node's location; regional contour geometry refers to the contour relationships of larger structural areas such as the front, roof, side, and rear regions; and overall vehicle semantic geometry refers to high-level features that, after cross-regional combination, provide a holistic description of the vehicle's aerodynamic shape. If a direct stitching method is used, then the... The characteristics of a composite node can be written as:

[0057] in, Indicates the first The characteristics of a composite node; Indicates feature concatenation operation; They represent the first The formula reflects the principle that by preserving and combining the multi-layered representation results side-by-side along the feature dimension, a single node can simultaneously possess the ability to recognize surface details, regional structure, and the semantics of the entire vehicle. In implementation, a unified dimensional mapping can be performed on the node features at different levels before splicing, ensuring that the node features at each level have similar representation scales and preventing any one layer from having an excessively high dimension that dominates the overall composite node features after splicing. If the... Layer node features need to be mapped to a unified dimensional space first, which can be written as:

[0058] in, Indicates the first The node at the th The node features of the layer after dimensional unification; Indicates the first The linear mapping matrix of the layer is used to map the original features to a uniform dimension; Indicates the first Layer bias vector; Indicates the first The node at the th The original node features of the layer. The principle reflected in this formula is that features from different layers are first projected onto a unified representation space, and then feature splicing is performed, which can reduce splicing deviations caused by inconsistencies in feature scales at different layers.

[0059] Embedding processing is performed on composite node features to suppress irrelevant disturbances and enhance highly relevant node features associated with the vehicle's aerodynamic shape. Embedding processing involves projecting the original composite node features into a new feature subspace using a trainable mapping function. Within this subspace, disturbances weakly correlated with drag coefficients and flow field evolution are suppressed, while key features highly correlated with the vehicle's aerodynamic shape are preserved and enhanced. Irrelevant disturbances refer to feature components formed by local noise, sampling errors, non-critical small-scale surface fluctuations, or geometric details that contribute very little to aerodynamic performance. Highly relevant node features are those that remain after embedding processing and are closely related to the vehicle's aerodynamic shape, such as the frontal curve transition, the contraction trend between the roof and rear, the outward or inward expansion of the side panels, and the local disturbance contours introduced by additional components. Embedding processing can be implemented using a nonlinear mapping function, the general expression of which can be written as:

[0060] in, Indicates the first Highly relevant node features after embedding processing; This represents the embedding mapping function, which is implemented by a multilayer perceptron or a combination of linear mapping and nonlinear activation. Indicates the first The formula describes the composite node features of a given node. The principle reflected in this formula is that high-dimensional composite node features are compressed into a more discriminative representation space through trainable mapping. If the embedding process is combined with a gating enhancement mechanism, key node features can be further strengthened through node weights, and its expression can be written as:

[0061] in, Indicates the first The relevance weight of each node ranges from 0 to 1. The specific value is set according to the specific situation and will not be elaborated here. This represents the Sigmoid activation function, used to compress weights to a range between 0 and 1; This represents the weight generation vector; Indicates the bias term; This represents the characteristics of highly correlated nodes after correlation weight modulation; This represents the basic embedding result. The principle reflected in this formula is to first estimate the contribution of each node to the overall aerodynamic shape of the vehicle, and then use this contribution to weight the node features, so that the expression of nodes in key areas is highlighted, while the expression of nodes in irrelevant areas is weakened. In practice, this step is particularly helpful in distinguishing the nodes most sensitive to airflow organization in the front, rear, and additional component areas from a large number of ordinary surface nodes.

[0062] Global fusion processing is performed on the highly correlated node features of each node to uniformly converge node features across the entire vehicle, forming a holistic representation of local surface geometry, regional contour relationships, and overall vehicle semantic structure. Global fusion processing means moving beyond a single node or localized unit and uniformly converging all nodes across the entire vehicle. The goal of this unified convergence is to compress the key geometric information scattered across the front, roof, side, rear, and additional component regions into a single holistic representation, enabling subsequent prediction branches to directly utilize this holistic representation for drag coefficient and flow field prediction. This holistic representation needs to retain two capabilities: sensitivity to significant local geometric patterns and the ability to summarize overall distribution trends. The former helps capture key configurations such as local protrusions, sharp edge transitions, and rear truncations, while the latter helps reflect the continuous streamline trend of the entire vehicle from front to rear. To retain both capabilities, global fusion processing can simultaneously employ global average convergence and global maximum convergence, then combine them. The expression can be written as:

[0063] in, This represents the global average convergence result, used to reflect the overall distribution trend of highly correlated node features across the entire vehicle. This represents the total number of nodes in the vehicle body point cloud representation; Indicates the first Highly relevant node characteristics of each node; This represents the global maximum convergence result, used to highlight the most significant local aerodynamic response characteristics across the entire vehicle. This indicates that a dimension-wise maximum value operation is performed on all node features; This represents the overall expression after global fusion. This represents the splicing operation. The principle reflected in this formula is that global average convergence focuses on the overall morphological trend, while global maximum convergence focuses on key extreme responses. Combining the two can simultaneously consider both the continuous shape of the entire vehicle and key local structures. In implementation, if it is desired to further enhance the difference in contribution of different nodes to the overall representation, an attention-based global fusion method can be introduced to make the contribution of important nodes to the overall representation greater. The corresponding attention convergence relationship can be written as:

[0064] in, Indicates the first The attention weight of each node in the global fusion process ranges from 0 to 1. The specific value is set according to the specific situation and will not be elaborated here. This represents the attention score calculated from node features; Represents an exponential function; This represents the global fusion result after attention weighting. The principle reflected in this formula is to give a greater weight to nodes that are more critical to the aerodynamic shape of the entire vehicle in the overall expression, thereby improving the sensitivity of the overall expression to key geometric regions.

[0065] Output organization processing is performed on the overall representation to generate a global feature vector characterizing the aerodynamic shape of the entire vehicle. Output organization processing refers to organizing the dimensions, order, and numerical form of the overall representation to meet the requirements of subsequent network inputs. The global feature vector is a fixed-length vector ultimately used to characterize the aerodynamic shape of a single vehicle sample. It is the result of the combined effects of the aforementioned hierarchical alignment, feature concatenation, embedding, and global fusion processing. This vector retains local surface geometry information, regional contour relationship information, and overall vehicle semantic structure information; therefore, it can be considered a unified semantic encoding of the vehicle's aerodynamic shape. If the overall representation is first linearly integrated and then output as a fixed-length vector, its expression can be written as:

[0066] in, This represents the final generated global feature vector; This indicates the output organization mapping function; This represents the output mapping matrix, used to project the overall representation onto the target dimension space; This represents the overall expression after global fusion. This represents the output bias vector. The principle reflected in this formula is to organize the overall expression derived from multiple convergence results into a global feature vector of uniform length and semantics, so that it can be directly used by the subsequent bi-branch prediction structure. In implementation, the output organization processing also incorporates a numerical normalization step to keep the numerical range of each dimension of the global feature vector stable, preventing any one dimension from unreasonably dominating the generation of subsequent drag coefficient and flow field prediction results due to excessively large values.

[0067] S140. Construct a dual-branch prediction structure based on global feature vectors to output drag coefficient prediction results and flow field prediction results through the dual-branch prediction structure.

[0068] Specifically, the global feature vector is determined as the unified input to the dual-branch prediction structure, and parallel branches for drag coefficient prediction and flow field prediction are constructed based on this unified input. The global feature vector is a fixed-length feature vector formed after hierarchical alignment, feature concatenation, embedding, and global fusion processing. It simultaneously encodes local surface geometry, regional contour relationships, and overall vehicle semantic structure information; therefore, it is essentially a unified high-dimensional representation of the vehicle's aerodynamic shape. The unified input means that, when constructing the dual-branch prediction structure, instead of designing separate inputs for the drag coefficient prediction and flow field prediction tasks, the same global feature vector is used as the common input source for both branches, ensuring consistency in semantic starting point. The dual-branch prediction structure involves setting up two parallel prediction paths with different functions but the same input source after the same input. One path is dedicated to outputting the drag coefficient prediction result, and the other is dedicated to outputting the flow field prediction result. Parallelism means that the two branches exist simultaneously in structure and can propagate forward synchronously during computation, but their parameters can be updated independently to adapt to the different feature transformation requirements of different tasks. If the global feature vector is denoted as... The input organization of the bi-branch prediction structure can be expressed as:

[0069] in, This represents the initial input features for the drag coefficient prediction branch; This represents the initial input features of the flow field prediction branch; This represents the global feature vector. The principle reflected in this formula is that although the two branches undertake different prediction tasks, they both start from the same vehicle-level semantic representation. Therefore, they can share the aerodynamic shape information of the whole vehicle contained in the same vehicle body point cloud representation. In implementation, the global feature vector is first written into a unified input buffer, and then sent to the drag coefficient prediction branch and the flow field prediction branch respectively, so that the two start synchronously in time and unfold in parallel in structure.

[0070] Based on the global feature vector, continuous mapping processing is performed in the drag coefficient prediction branch to progressively transform the aerodynamic shape features of the vehicle in the global feature vector, generating the corresponding drag coefficient prediction result. The drag coefficient prediction branch refers to the computational path in the dual-branch prediction structure specifically used to establish the mapping relationship between the vehicle's aerodynamic shape and drag coefficient. Continuous mapping processing involves setting up multiple sequentially connected mapping units along this branch, using the output of the previous layer as the input of the next layer, and progressively completing information filtering, semantic reorganization, and dimensional transformation in each layer. The vehicle's aerodynamic shape features refer to the comprehensive semantic information related to the vehicle's airflow drag in the global feature vector, such as the frontal windward surface, roof transition curve, rear tapering profile, side panel organization, and the disturbance shape of additional components. Progressive transformation means not directly jumping from the high-dimensional global feature vector to the final drag coefficient prediction result, but first compressing the complex geometric semantics into intermediate representations that increasingly approximate the scalar regression target through multiple feature transformations. Several fully connected mapping layers and nonlinear activation layers can be set in the drag coefficient prediction branch. The input of the layer is Then the output of this layer can be represented as:

[0071] in, The first branch of the drag coefficient prediction is represented. The output features of the layer; This represents a nonlinear activation function used to enhance the nonlinear fitting ability of feature representation; it is used as a correction linear unit function. The first branch of the drag coefficient prediction is represented. The layer weight matrix is ​​used to perform linear combination of features and dimensional transformation; The first branch of the drag coefficient prediction is represented. Layer bias vector; The first branch of the drag coefficient prediction is represented. The output features of the layer. The principle reflected in this formula is that with each layer of continuous mapping, the high-dimensional aerodynamic shape features of the vehicle in the original global feature vector are recombined and compressed, strengthening the representations strongly correlated with the drag coefficient, while gradually weakening redundant representations weakly correlated with the current regression target. After the last layer of continuous mapping, the predicted drag coefficient for a single sample can be obtained, and its expression can be written as:

[0072] in, This indicates the predicted drag coefficient. This indicates the output weight of the last layer in the drag coefficient prediction branch; This represents the intermediate feature of the penultimate layer output of the drag coefficient prediction branch; This indicates the output bias of the last layer in the drag coefficient prediction branch; This represents the total number of layers in the drag coefficient prediction branch. The principle reflected in this formula is to map the intermediate representations after multiple compressed layers into a single scalar, thereby obtaining the drag coefficient prediction result for the current vehicle sample. In practice, to improve training stability, normalization units and inactivation suppression units can be added to the intermediate layers, ensuring that the continuous mapping process retains the discriminative nature of the vehicle's aerodynamic shape characteristics while reducing the risk of overfitting.

[0073] Based on global feature vectors, flow field representation mapping is performed in the flow field prediction branch to implicitly learn the flow-related geometric features in the global feature vectors, generating corresponding flow field prediction results. The flow field prediction branch refers to the computational path in the dual-branch prediction structure specifically used to establish the mapping relationship between the vehicle's aerodynamic shape and the flow field velocity and pressure distributions. Flow field representation mapping refers to projecting the geometric semantics related to airflow behavior in the global feature vectors onto the flow field representation space through multi-layer feature transformations. This allows the model to directly learn the implicit correspondence between the vehicle geometry and the flow field distribution without explicitly solving the fluid control equations point by point. Flow-related geometric features refer to geometric patterns that significantly affect external air adhesion, separation, acceleration, deceleration, and pressure redistribution, such as the front edge curvature, roof arch amplitude, rear end contraction, side panel transitions, and the local disturbance contours of additional components. Implicit representation learning refers to a model that does not directly write out the explicit physical solution process for each flow field sampling point. Instead, it uses a trainable mapping function to compress the aerodynamic features of the entire vehicle into a latent representation that can generate the flow field distribution, and then recovers the flow field prediction result from this latent representation. If the flow field prediction branch... The input of the layer is Then its feature transformation process can be expressed as:

[0074] in, Indicates the flow field prediction branch. The output features of the layer; This represents the nonlinear mapping function in the flow field prediction branch, used to enhance the ability to express complex flow field relationships; Indicates the flow field prediction branch. Layer weight matrix; Indicates the flow field prediction branch. Layer bias vector; Indicates the flow field prediction branch. The input features of each layer. The principle reflected in this formula is that the flow field prediction branch extracts flow-related geometric features from the global feature vector layer by layer along independent paths, gradually evolving them into a potential representation that can generate the flow field distribution. If the final output requires both the flow field velocity distribution and the flow field pressure distribution, the last layer's potential representation can be mapped to the joint flow field prediction result, and the expression can be written as:

[0075] in, This indicates the flow field prediction results; This represents the output weight matrix of the last layer in the flow field prediction branch; This represents the potential representation of the penultimate layer of the flow field prediction branch; This represents the output bias vector of the last layer in the flow field prediction branch; This represents the total number of branches in the flow field prediction. If the flow field prediction results are split into velocity distribution and pressure distribution, it can be further written as:

[0076] in, This indicates the results of the joint flow field prediction; This indicates the predicted velocity distribution of the flow field; This represents the predicted flow field pressure distribution. The principle reflected in this formula is to organize the flow field prediction task into a multi-output regression task, allowing the model to simultaneously learn the relationship between the velocity field, pressure field, and the vehicle's aerodynamic shape within the same flow field prediction branch. In implementation, if it is necessary to subsequently map the flow field prediction results back to vehicle surface sampling points, an output dimension matching the number of surface sampling points can be pre-designed in the output layer of the flow field prediction branch. This ensures that each surface sampling location can correspond to the flow field velocity component and flow field pressure value, thus providing direct input for subsequent physical constraint construction.

[0077] S150. Based on the predicted drag coefficient and the labeled drag coefficient data, data fitting constraints are constructed. At the same time, physical constraints are constructed based on the flow field prediction results. The data fitting constraints and physical constraints are fused to form a unified training objective. The feature extraction parameters corresponding to the dynamic graph structure and the prediction parameters corresponding to the bi-branch prediction structure are updated through backpropagation so that the initial model can meet the unified training objective while fitting the data distribution.

[0078] Specifically, a sample-level correspondence is established based on the predicted drag coefficient results and the labeled drag coefficient data. A unified metric is then applied to the deviation between the predicted and labeled drag coefficient data to form data fitting constraints. The sample-level correspondence refers to the relationship between the predicted and labeled drag coefficients within each training batch. Each target vehicle sample corresponds to a unique drag coefficient prediction result and a unique drag coefficient label, ensuring no sample misalignment, duplicate binding, or label drift. Unified metric processing refers to quantifying the drag coefficient deviation of all training samples using the same error calculation method, thereby obtaining comparable, cumulative, and differentiable data fitting constraints. The drag coefficient prediction result is a scalar result output by the drag coefficient prediction branch after performing continuous mapping processing on the global feature vector; the drag coefficient label data is a supervisory label formed from wind tunnel test results or computational fluid dynamics simulation results after working condition consistency verification. To ensure that the deviation of all samples within a batch is uniformly reflected, mean squared error is used as the data fitting constraint, and its expression is:

[0079] in, This represents the loss value corresponding to the data fitting constraints; This indicates the number of samples in the current training batch; Indicates the first The predicted drag coefficient of each sample; Indicates the first The formula reflects the principle of squared amplification of the prediction deviation for each sample, followed by averaging over the entire batch. This ensures that samples with larger deviations are subject to stronger constraints during training, thereby driving the model to continuously bring the predicted drag coefficient closer to the true labeled value. In implementation, if the drag coefficient labeled data has already undergone standardization, then... and All calculations are performed within a unified numerical space, which avoids instability in data fitting constraints caused by differences in the original numerical ranges of different samples.

[0080] Based on the mapping relationship between the flow field prediction results and the corresponding spatial location of the vehicle body geometry, the continuous change state of the flow field, the momentum change state of the flow field, and the flow attachment state of the vehicle body wall are extracted. Continuity constraints, momentum conservation constraints, and wall no-slip constraints are then constructed to form physical constraints. The flow field prediction results refer to the velocity and pressure distributions obtained after the flow field prediction branch performs flow field expression mapping processing based on global feature vectors. The mapping relationship between the vehicle body geometry and the corresponding spatial location means that these velocity and pressure distributions have been aligned according to the vehicle body point cloud representation or preset sampling points on the vehicle body surface, ensuring that each flow field value corresponds to a specific spatial location. The continuous change state of the flow field means that the spatial change of the velocity field cannot produce unfounded volume accumulation or volume loss. The momentum change state of the flow field means that the relationship between velocity, pressure, and viscosity must satisfy the laws of fluid dynamics conservation. The flow attachment state of the vehicle body wall means that the fluid velocity near the vehicle body wall must obey the wall boundary conditions. The continuity constraint corresponds to the zero divergence condition for incompressible fluids, and its expression can be written as:

[0081] in, Indicates continuous residuals; , , These represent the flow field velocities at... , , Components in the three coordinate directions; , , Represents the spatial coordinates in the vehicle body coordinate system; This represents the loss value corresponding to the continuity constraint; This indicates the number of flow field sampling points involved in the continuity constraint calculation; Indicates the first The formula reflects the principle that if the velocity field meets the continuity requirement of incompressible fluid, the inflow and outflow of fluid per unit volume should remain in balance, and therefore the sum of the three-directional velocity change rates should approach zero; if it does not approach zero, it indicates that there is non-physical volume expansion or contraction in the flow field prediction results.

[0082] The momentum conservation constraint is used to ensure that the flow field prediction results conform to the equilibrium relationship under the combined effects of inertial, pressure, and viscous terms during spatial variations. Momentum equation residuals can be established separately for each of the three coordinate directions. Taking direction as an example, its residual can be written as:

[0083] Correspondingly, direction and The momentum residual in the direction can be written as: Therefore, the loss value corresponding to the momentum conservation constraint can be written as: in, , , They represent , , Momentum residual in the direction; Air density is generally expressed using known values ​​under test or simulation conditions. Indicates the flow field pressure; The aerodynamic viscosity is a known value; This represents the loss value corresponding to the momentum conservation constraint; , , They represent the first The momentum residuals at each flow field sampling point in three coordinate directions. The principle reflected in this set of formulas is that the velocity change of a fluid in space is not arbitrary, but must be consistent with the pressure gradient and viscous diffusion. Therefore, if the flow field prediction deviates from the actual mechanical equilibrium, the momentum residuals will increase significantly.

[0084] Wall slip-free constraints are used to limit the velocity state of the flow field prediction results at the vehicle body wall, making it conform to the basic adhesion laws when a fluid comes into contact with a solid boundary. Let the set of sampling points on the vehicle body wall be denoted as... Then the loss value for the wall without slip constraints can be written as:

[0085] in, This represents the loss value corresponding to the absence of slip constraints on the wall. Indicates the number of sampling points on the vehicle body wall; , , They represent the first The formula represents the components of the flow field velocity in three coordinate directions at each sampling point on the vehicle body wall. The principle reflected in this formula is that, under ideal adhesion conditions, the fluid velocity near the vehicle body wall should approach zero. Therefore, the smaller the sum of squares of the velocities at the wall sampling points, the more the flow field prediction conforms to the boundary physical laws. In practice, these three types of constraints do not exist in isolation but together constitute the physical constraints. Specifically, automatic differentiation techniques can be used to transform the continuity condition, momentum conservation condition, and no-slip boundary condition of the incompressible Navier-Stokes equations (NS equations) into calculable physical losses. Simultaneously, a multi-scale loss function, weighted and fused with data fitting loss and physical constraint loss, is constructed to constrain the model training process, ensuring the physical rationality and interpretability of the drag coefficient prediction results.

[0086] Data fitting constraints and physical constraints are fused to form a unified training objective. This unified training objective reflects both the sample fit of the drag coefficient prediction results and the physical consistency of the flow field prediction results. The unified training objective refers to the overall objective function actually involved in parameter optimization during model training. It considers both factors simultaneously, rather than simply whether the drag coefficient prediction results are close to the labeled values ​​or whether the flow field prediction results satisfy physical laws. Sample fit refers to the level of approximation of the drag coefficient prediction results to the labeled drag coefficient data; physical consistency refers to the level of satisfaction of the flow field prediction results with the requirements of continuity, momentum conservation, and wall sliplessness. The three types of physical constraints are first combined into a total physical constraint, and then weighted and fused with the data fitting constraints. The total physical constraint can be written as:

[0087] in, This represents the loss value corresponding to the total physical constraints; Represents the weighting coefficients of continuity constraints; The weighting coefficients representing the momentum conservation constraint; This represents the weighting coefficient for walls without slip constraints. , , These represent the loss values ​​corresponding to the continuity constraint, momentum conservation constraint, and wall no-slip constraint, respectively. The weighting coefficients mentioned above range from 0 to 1, and the specific values ​​are set according to the specific circumstances, which will not be elaborated here. The principle reflected in this formula is that the importance of different physical constraints in training can be weighted and balanced according to the data distribution, sampling scale, and training stage, thereby avoiding any one type of physical constraint being too strong or too weak. Furthermore, the unified training objective can be written as:

[0088] in, This indicates a unified training objective; The weighting coefficients represent the data fitting constraints; These represent the weighting coefficients of the physical constraints. The two weighting coefficients above range from 0 to 1, and the specific values ​​are set according to the specific situation, which will not be elaborated here. This represents the loss value corresponding to the data fitting constraints; This represents the loss value corresponding to the total physical constraints. Generally, it is required... and Both are non-negative numbers, and can be set as normalized weights that sum to 1, or dynamically adjusted according to the training phase. The principle reflected in this formula is that the training objective should simultaneously drive two things: first, to gradually bring the predicted drag coefficient closer to the true labeled value; and second, to gradually bring the predicted flow field closer to a physically acceptable state. In implementation, if the goal is for the model to quickly establish basic data fitting ability in the early stages of training, the weights can be appropriately increased. If, during the later stages of training, it is desired to further enhance the physical plausibility of the model, then the [specific parameters] can be appropriately increased. The data fitting loss and the physical constraint loss are weighted and summed using weighting coefficients to form the total loss function for model training, which is used to balance the requirements of prediction accuracy and physical consistency.

[0089] Backpropagation is performed based on a unified training objective. Bias information generated by data fitting constraints and bias information generated by physical constraints are jointly fed back to the bi-branch prediction structure and the dynamic graph structure to obtain the backpropagation results. Backpropagation refers to the process of calculating gradients layer by layer in the reverse direction of the network's forward computation path, starting from the unified training objective, and then passing these gradients back to the bi-branch prediction structure and the dynamic graph structure. Bias information refers to the numerical representation of the unified training objective's sensitivity to parameters at each layer, essentially manifested as the partial derivatives of the loss function with respect to the parameters. In the bi-branch prediction structure, the drag coefficient prediction branch directly receives bias information from data fitting constraints, while the flow field prediction branch simultaneously receives bias information from physical constraints and its internal flow field representation mapping. Since both branches share the same global feature vector, which originates from the feature extraction process of the dynamic graph structure, this bias information will eventually continue to be fed back to the dynamic graph structure, subjecting the parameters corresponding to neighborhood search, edge convolution operations, and multi-scale geometric feature representation to training constraints as well. If all trainable parameters are uniformly denoted as... Then the gradient required for backpropagation can be written as:

[0090] in, This represents the gradient result of a unified training objective with respect to all trainable parameters; Represents the parameter set Calculating the gradient; This indicates a unified training objective; This represents the set of all trainable parameters in the model. If we further break down the parameter set, it can be written as:

[0091] in, This represents the set of feature extraction parameters corresponding to the dynamic graph structure, mainly including the mapping parameters in the convolution operation of each layer's edges; This represents the set of prediction parameters corresponding to the drag coefficient prediction branch. This represents the set of prediction parameters corresponding to the flow field prediction branch. The corresponding gradient components can then be written as:

[0092] in, , , These represent the gradient results of the unified training objective with respect to the dynamic graph structure, drag coefficient prediction branch, and flow field prediction branch, respectively. The principle reflected in these formulas is that the unified training objective does not only act on the final output layer, but is propagated forward through a chained approach to all trainable layers, enabling the entire model, from the output to the feature extraction end, to adjust synchronously based on bias information. All trainable parameters of the model are updated through gradient backpropagation, including the convolutional EdgeConv layer and the two-branch MLP layer.

[0093] The prediction parameters of the bi-branch prediction structure and the feature extraction parameters of the dynamic graph structure are updated synchronously based on the backpropagation results to ensure that the initial model meets a unified training objective while fitting the data distribution. Synchronous updating means that in each training iteration, the trainable parameters of the drag coefficient prediction branch, the flow field prediction branch, and the dynamic graph structure are updated based on the gradient results of the same unified training objective, rather than updating only a portion of them. Prediction parameters refer to the weights and biases of each layer within the bi-branch prediction structure; feature extraction parameters refer to the mapping parameters used in the edge convolution operations of each layer within the dynamic graph structure. The initial model refers to the complete prediction model whose training is not yet complete and whose parameters are still in a state of optimization. Parameter updates can be performed using an optimizer based on first-order gradients. Expressed using the most basic gradient descent, the update relationship can be written as:

[0094] in, Indicates the first The parameter set at the next iteration; Indicates the first The parameter set after the next iteration; Indicates the first The learning rate used in this iteration; Indicates the first The gradient result of the unified training objective with respect to the parameter set in the next iteration. The principle reflected in this formula is that the parameters move in the direction that reduces the unified training objective, thus making the drag coefficient prediction and flow field prediction results output in the next round of forward inference closer to the target state than in the current round. If we expand the update relationship of the three parameter subsets separately, it can be written as:

[0095] in, , , They represent the first The parameter sets of the dynamic graph structure, drag coefficient prediction branch, and flow field prediction branch in the next iteration; , , These represent the updated parameter sets; , , These represent the corresponding parameter subsets at the th... Learning rate in the next iteration; , , These represent the gradient results for the corresponding parameter subsets. The principle reflected in this set of formulas is that although the three parts can use the same learning rate or different learning rates as needed, they are all constrained by the same unified training objective, thus the update direction has a consistent global optimization orientation. In implementation, the Adam or AdamW optimizer will be used instead of simple gradient descent to obtain a more stable convergence process. After continuous iteration, the initial model can, on the one hand, continuously reduce data fitting constraints, thereby better fitting the drag coefficient labeled data; on the other hand, it can continuously reduce physical constraints, so that the flow field prediction results and drag coefficient prediction results gradually meet the requirements of the unified training objective.

[0096] S160. Based on the training set, validation set, and test set, the training process of the initial model is optimized by combining the learning rate scheduling strategy, regularization constraints, and early stopping mechanism of the validation set to determine the optimal model parameters. Based on the optimal model parameters and the initial model, the vehicle drag coefficient prediction model that integrates convolution and physical information is constructed.

[0097] Specifically, multiple training iterations are performed on the initial model based on the training set. Each training sample sequentially undergoes the feature extraction process corresponding to the dynamic graph structure, global fusion processing, and inference calculation of the dual-branch prediction structure. The feature extraction parameters and prediction parameters corresponding to the initial model are continuously updated based on a unified training objective. The training set refers to the subset of data that is partitioned from the effective sample set during the preliminary data preparation stage and is specifically used to drive parameter learning. The initial model refers to the vehicle drag coefficient prediction model that integrates convolution and physical information and has not yet been fully trained, and whose internal feature extraction parameters and prediction parameters are still in an unoptimized state. Multiple training iterations refer to repeatedly executing multiple training rounds around the training set, with each training round containing multiple training batches. In implementation, training batches are first extracted from the training set according to a preset batch size. Then, each training sample in each batch is sequentially fed into the feature extraction process corresponding to the dynamic graph structure, completing neighborhood search, dynamic graph structure construction, multi-layer edge convolution operations, and multi-scale geometric feature generation. Subsequently, global fusion processing is performed to obtain a global feature vector representing the aerodynamic shape of the entire vehicle. This global feature vector is then input into a dual-branch prediction structure, which outputs the drag coefficient prediction result and the flow field prediction result, respectively. Finally, the total loss of the current training batch is calculated based on a unified training objective, and the parameters are updated once. If the total number of training set samples is... Batch size is Then the number of batches in each training round can be expressed as:

[0098] in This indicates the number of training batches included in each training round; This represents the total number of samples in the training set; Indicates the number of samples contained in a single training batch; This represents the floor function. The principle behind this formula is that the entire training set is divided into fixed batch sizes, and training is performed batch by batch, thereby increasing the parameter update frequency while controlling memory usage and computational overhead. The training set is used for model parameter updates, and the parameters of the convolutional EdgeConv layer and the two-branch MLP layer are updated through backpropagation.

[0099] During multiple training iterations, a learning rate scheduling strategy is used to dynamically control the parameter update rhythm, allowing the initial model to gradually transition from a fast convergence phase to a stable convergence phase. The learning rate refers to the step size coefficient along the gradient direction during parameter updates; the learning rate scheduling strategy refers to the rule that dynamically changes the learning rate as the training progresses; the fast convergence phase requires a larger step size in the early training stage when the parameters are not yet close to the optimum value region to rapidly reduce the loss; the stable convergence phase requires a smaller step size in the later training stage when the parameters are close to the optimum value region to prevent oscillations. In implementation, the learning rate can be updated after each training epoch or each training batch, based on the current epoch index, the current loss trend, or a preset scheduling function. The scheme using cosine annealing learning rate scheduling to dynamically adjust the learning rate can be expressed as:

[0100] in Indicates the first The training iteration or the The learning rate corresponding to each training round; This represents the lower bound of the learning rate, used to ensure that the ability to make small updates is still retained in later stages; This represents the upper limit of the learning rate, corresponding to the initial learning rate at the beginning of training. Indicates the current training progress index; This represents the total number of iterations or rounds within a complete scheduling cycle; Represents pi; This represents the cosine function. The principle reflected in this formula is that the learning rate is kept at a high level in the early stages of training, then gradually decreases along a smooth curve, eventually approaching the lower limit, allowing parameter updates to smoothly transition from large-step search to small-step fine-tuning. In implementation, the learning rate scheduling strategy can also be linked to the performance of the validation set; that is, when the performance improvement of the validation set stagnates, the learning rate can be reduced in advance to further enhance the later convergence stability. The learning rate is dynamically adjusted through cosine annealing learning rate scheduling to cooperate with the optimizer in completing parameter updates.

[0101] During multiple training iterations, regularization constraints are used to limit the parameter size and feature response of the initial model to suppress overfitting and enhance the model's generalization ability. Regularization constraints are complexity control mechanisms added to the unified training objective to suppress excessively large model parameters or overly strong feature activation. Parameter size refers to the overall size and distribution amplitude of the weight parameters in the model; feature response refers to the activation intensity of intermediate layer features on the input samples. Overfitting refers to the phenomenon where the model performs well on the training set but degrades on the validation and test sets; generalization ability refers to the model's ability to maintain stable performance when faced with new samples not used in training. In implementation, both parameter regularization and random deactivation can be used simultaneously. Parameter regularization corresponds to weight norm penalty, incorporating the case of excessively large model parameters into the loss function for suppression. If L2 regularization is used, its regularization term can be written as:

[0102] in This represents the loss term corresponding to the regularization constraint. This represents the regularization coefficient, used to control the strength of the parameter penalty; This indicates the number of weight matrices involved in regularization in the model; Indicates the first Weight matrices; Indicates the first The sum of squares of all elements in a weight matrix. This formula reflects the principle that applying additional penalties to excessively large weights makes the model more inclined to choose smooth and stable parameter solutions. Random deactivation, on the other hand, randomly masks the outputs of some neurons during the training phase to prevent feature pathways from becoming overly dependent on certain fixed responses. If the output features of a certain layer are denoted as... Then the output after random deactivation can be written as:

[0103] in This represents the feature output after random deactivation; This represents a random mask vector, where each element is randomly selected according to a preset retention probability. This represents element-wise multiplication; This represents the original feature output. The principle reflected in this formula is that some feature responses are randomly shut down during each forward propagation, preventing the model from relying on a fixed local path to complete the prediction, thereby improving overall robustness. Dropout layers and L2 regularization are added to the network layers, and a parameter norm penalty term is added to the total loss to suppress overfitting.

[0104] The model performance corresponding to the current parameter state is evaluated based on the validation set, and an early stopping mechanism is executed according to the performance trend of the validation set to terminate the training process when a preset stopping condition is met. The validation set refers to a subset of data independently partitioned from the effective sample set and specifically used for performance evaluation and model selection during training. The current parameter state refers to the instantaneous values ​​of all parameters within the dynamic graph structure and the bi-branch prediction structure after a certain training epoch. The early stopping mechanism actively terminates the training process when the validation set performance no longer improves within several consecutive epochs to prevent overfitting from continued training. In implementation, after each training epoch, the current parameter state is frozen, gradient updates are not performed, and the validation set samples are input into the model along the same forward path to obtain the corresponding drag coefficient prediction results and flow field prediction results, and the evaluation index on the validation set is calculated. If the main evaluation index on the validation set is labeled as... ,in Indicates the first If there are several training epochs, early stopping can be determined based on the count of consecutive epochs where there is no improvement. If a minimization metric is used, such as validation error, the optimal validation metric can be defined as:

[0105] in This represents the best validation metric obtained up to the current training process. Indicates the first Validation metrics for each training round; This indicates the number of training rounds that have been completed so far. Let the tolerance rounds be... Then when continuous The early stopping mechanism is triggered when the current validation metric is not better than the historical best validation metric in a given training epoch. This decision relationship can be written as:

[0106] in Indicates whether the early stopping mechanism of the validation set has been triggered; A function representing the number of consecutive rounds without improvement; This indicates the preset tolerance number of iterations. The principle reflected in this formula is that when the model's performance on the validation set has not improved for a long time, continuing training may only make the model fit the training set better, thus impairing its generalization ability. Therefore, training should be terminated promptly. After each iteration, the wind resistance prediction error is calculated on the validation set. If the error does not decrease for several consecutive iterations, training is stopped and the optimal model parameters are saved.

[0107] After training terminates, the parameter states whose validation set performance meets preset conditions are selected from the training epochs as the optimal model parameters. These optimal model parameters are then loaded into the initial model to complete the construction of the vehicle drag coefficient prediction model that integrates convolutional and physical information. Optimal model parameters refer to the parameter states that have the best validation set performance or meet preset comprehensive conditions throughout all training epochs. Loading refers to writing the saved weight matrix, bias vector, and other trainable parameters back to their corresponding positions in the initial model. Completing model construction means transforming the initial model, which was still in the training iteration process, into a formal model with fixed parameters that can be used for subsequent inference. In practice, after each training epoch, if the current validation set metric is better than the historical best metric, the current parameter state is immediately saved. When early stopping is triggered or the maximum number of training epochs is reached, the optimal set of parameter states is selected from all saved records as the optimal model parameters. If the first... The parameter states for each training epoch are denoted as follows: Then the optimal model parameters can be expressed as:

[0108] in Indicates the optimal model parameters; Indicates the first The parameter states corresponding to each training round; Indicates the first Performance metrics of the validation set corresponding to each training round; This represents the parameter state that optimizes the validation set performance metrics. The principle behind this formula is that instead of directly using the parameters from the end of the last training session, it selects the parameter state that best performs on the validation set throughout the entire training history, thus maximizing both training sufficiency and generalization ability. In implementation, it will... The feature extraction module, drag coefficient prediction branch, and flow field prediction branch corresponding to the dynamic graph structure are written respectively, so that the entire initial model is finalized into the final vehicle drag coefficient prediction model.

[0109] Independent performance evaluations were performed on the constructed vehicle drag coefficient prediction model based on the test set to verify the generalization ability of the model corresponding to the optimal model parameters. The test set refers to a subset of data independently retained during the sample partitioning phase; it neither participates in parameter updates driven by the training set nor in model selection driven by the validation set. Independent performance evaluation refers to objectively measuring the model's performance on unknown samples by performing forward inference without any parameter adjustments after the model parameters are completely fixed. Generalization ability refers to the model's ability to maintain accurate drag coefficient predictions and reasonable flow field predictions even when faced with unseen target vehicle samples. During implementation, each target vehicle sample from the test set was input into the constructed vehicle drag coefficient prediction model to obtain the drag coefficient prediction results. These results were then compared with the corresponding drag coefficient labeled data, and indices such as mean absolute error, root mean square error, and coefficient of determination were calculated. Their expressions can be written as follows:

[0110] in Mean absolute error is used to reflect the average absolute deviation between the prediction result and the actual label. This represents the root mean square error, used to highlight the impact of large prediction bias on overall performance. The coefficient of determination is used to reflect the model's ability to explain the actual trend of drag coefficient changes. Indicates the total number of samples in the test set; Indicates the first The predicted drag coefficient of each test sample; Indicates the first The drag coefficient labeled data for each test sample; This represents the average value of all labeled drag coefficient data in the test set. The principle reflected in this set of formulas is to comprehensively evaluate the final model's performance on the test set from three perspectives: average deviation, deviation fluctuation, and trend fitting ability. If these indicators on the test set meet the preset requirements, it indicates that the model corresponding to the optimal model parameters has good generalization ability.

[0111] This application also provides a device for constructing a vehicle drag coefficient prediction model that integrates convolutional and physical information, referring to... Figure 2 , Figure 2This is a schematic diagram of the vehicle drag coefficient prediction model construction device that integrates convolutional and physical information provided in this application embodiment. The device is a server, which includes an acquisition module 21 and a processing module 22. The acquisition module 21 is used to acquire the three-dimensional geometric data of the target vehicle and construct a vehicle body point cloud representation. It also acquires the drag coefficient annotation data and flow field physical data corresponding to the target vehicle, and performs unified normalization processing on the vehicle body point cloud representation, drag coefficient annotation data, and flow field physical data to generate training sets, validation sets, and test sets. The processing module 22 is used to perform neighborhood search on each node according to the vehicle body point cloud representation to construct a set of neighboring nodes, and construct a dynamic graph structure based on the set of neighboring nodes. At the same time, it performs multi-layer edge convolution operation on the dynamic graph structure, performs feature mapping and feature aggregation on the relative geometric relationship between nodes and neighboring nodes to form a multi-scale geometric feature expression. The processing module 22 is also used to perform global fusion processing on the multi-scale geometric feature expression. The processing module 22 is used to generate a global feature vector; it is also used to construct a dual-branch prediction structure based on the global feature vector, so as to output the drag coefficient prediction result and the flow field prediction result through the dual-branch prediction structure; the processing module 22 is also used to construct data fitting constraints based on the drag coefficient prediction result and the drag coefficient labeled data, and construct physical constraints based on the flow field prediction result, and perform fusion processing on the data fitting constraints and physical constraints to form a unified training objective, and update the feature extraction parameters corresponding to the dynamic graph structure and the prediction parameters corresponding to the dual-branch prediction structure through backpropagation, so that the initial model can meet the unified training objective while fitting the data distribution; the processing module 22 is also used to optimize the training process of the initial model based on the training set, validation set and test set, combined with the learning rate scheduling strategy, regularization constraints and validation set early stopping mechanism, to determine the optimal model parameters, so as to complete the construction of the vehicle drag coefficient prediction model that integrates convolution and physical information according to the optimal model parameters and the initial model.

[0112] It should be noted that the above embodiments of the apparatus are only illustrated by the division of the above functional modules. In practical applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the device can be divided into different functional modules to complete all or part of the functions described above. In addition, the apparatus and method embodiments provided in the above embodiments belong to the same concept, and the specific implementation process can be found in the method embodiments, which will not be repeated here.

[0113] This application also provides an electronic device, with reference to... Figure 3 , Figure 3 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. The electronic device may include: at least one processor 31, at least one network interface 34, a user interface 33, a memory 35, and at least one communication bus 32.

[0114] The communication bus 32 is used to enable communication between these components.

[0115] The user interface 33 may include a display screen and a camera. Optionally, the user interface 33 may also include a standard wired interface and a wireless interface.

[0116] The network interface 34 may optionally include a standard wired interface or a wireless interface (such as a Wi-Fi interface).

[0117] The processor 31 may include one or more processing cores. The processor 31 connects to various parts of the server via various interfaces and lines, executing instructions, programs, code sets, or instruction sets stored in the memory 35, and calling data stored in the memory 35 to perform various server functions and process data. Optionally, the processor 31 may be implemented using at least one hardware form of Digital Signal Processing (DSP), Field-Programmable Gate Array (FPGA), or Programmable Logic Array (PLA). The processor 31 may integrate one or a combination of several of the following: Central Processing Unit (CPU), Graphics Processing Unit (GPU), and modem. The CPU primarily handles the operating system, user interface, and applications; the GPU is responsible for rendering and drawing the content to be displayed on the screen; and the modem handles wireless communication. It is understood that the modem may also not be integrated into the processor 31 and may be implemented as a separate chip.

[0118] The memory 35 may include random access memory (RAM) or read-only memory. Optionally, the memory 35 may include a non-transitory computer-readable storage medium. The memory 35 can be used to store instructions, programs, code, code sets, or instruction sets. The memory 35 may include a program storage area and a data storage area, wherein the program storage area may store instructions for implementing an operating system, instructions for at least one function (such as touch function, sound playback function, image playback function, etc.), instructions for implementing the above-described method embodiments, etc.; the data storage area may store data involved in the above-described method embodiments, etc. Optionally, the memory 35 may also be at least one storage device located remotely from the aforementioned processor 31. Figure 3 As shown, the memory 35, which serves as a computer storage medium, may include an operating system, a network communication module, a user interface module, and an application program for constructing a vehicle drag coefficient prediction model that integrates convolutional and physical information.

[0119] exist Figure 3 In the electronic device shown, the user interface 33 is mainly used to provide an input interface for the user and obtain the user input data; while the processor 31 can be used to call the application program stored in the memory 35 that stores the method for constructing a car drag coefficient prediction model by fusing convolution and physical information. When executed by one or more processors, the electronic device executes one or more methods as described in the above embodiments.

[0120] This application also provides a non-transitory computer-readable storage medium storing instructions. When executed by one or more processors, these instructions cause an electronic device to perform one or more of the methods described in the above embodiments.

[0121] In the above embodiments, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0122] In the several embodiments provided in this application, it should be understood that the disclosed apparatus can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the shown or discussed mutual couplings or direct couplings or communication connections may be through some service interfaces; indirect couplings or communication connections between apparatuses or units may be electrical or other forms.

[0123] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0124] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0125] 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 device (CMD). Based on this understanding, the technical solution of this application, 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 memory and includes several instructions to cause a computer 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 application. The aforementioned memory includes various media capable of storing program code, such as USB flash drives, portable hard drives, magnetic disks, or optical disks.

[0126] The foregoing description is merely an exemplary embodiment of this disclosure and should not be construed as limiting the scope of this disclosure. Any equivalent changes and modifications made in accordance with the teachings of this disclosure shall still fall within the scope of this disclosure. Those skilled in the art will readily conceive of other embodiments of this disclosure upon considering the specification and the disclosure of practical truth. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not described in this disclosure. The specification and embodiments are considered exemplary only, and the scope and spirit of this disclosure are defined by the claims.

Claims

1. A method for constructing a vehicle drag coefficient prediction model that integrates convolution and physical information, characterized in that, The method includes: The three-dimensional geometric data of the target vehicle is acquired and a point cloud representation of the vehicle body is constructed. At the same time, the drag coefficient annotation data and flow field physical data corresponding to the target vehicle are acquired. The vehicle body point cloud representation, the drag coefficient annotation data and the flow field physical data are subjected to uniform normalization processing to generate training set, validation set and test set. Based on the vehicle body point cloud representation, a neighborhood search is performed on each node to construct a neighborhood node set, and a dynamic graph structure is constructed based on the neighborhood node set. At the same time, multi-layer edge convolution operation is performed on the dynamic graph structure to perform feature mapping and feature aggregation on the relative geometric relationship between the node and the neighborhood node to form a multi-scale geometric feature representation. A global fusion process is performed on the multi-scale geometric feature representation to generate a global feature vector; A dual-branch prediction structure is constructed based on the global feature vector to output the drag coefficient prediction result and the flow field prediction result through the dual-branch prediction structure; Data fitting constraints are constructed based on the predicted drag coefficient and the labeled drag coefficient data. At the same time, physical constraints are constructed based on the predicted flow field. The data fitting constraints and the physical constraints are fused to form a unified training objective. The feature extraction parameters corresponding to the dynamic graph structure and the prediction parameters corresponding to the bi-branch prediction structure are updated through backpropagation so that the initial model can satisfy the unified training objective while fitting the data distribution. Based on the training set, the validation set, and the test set, the training process of the initial model is optimized by combining the learning rate scheduling strategy, regularization constraints, and early stopping mechanism of the validation set to determine the optimal model parameters. Based on the optimal model parameters and the initial model, the construction of a vehicle drag coefficient prediction model that integrates convolution and physical information is completed. The process involves acquiring the three-dimensional geometric data of the target vehicle and constructing a point cloud representation of the vehicle body. Simultaneously, it acquires the drag coefficient annotation data and flow field physical data corresponding to the target vehicle. A unified normalization process is then performed on the vehicle body point cloud representation, the drag coefficient annotation data, and the flow field physical data to generate training, validation, and test sets. Specifically, this includes: The three-dimensional geometric data is subjected to format conversion and surface sampling processing to uniformly convert the three-dimensional geometric data into a vehicle body point cloud representation with a preset number of points and spatial distribution density. The vehicle body point cloud representation is then subjected to outlier removal and duplicate point merging processing to maintain the integrity of the vehicle body geometric structure features. The drag coefficient annotation data is subjected to a working condition consistency check to ensure that the drag coefficient annotation data remains consistent in terms of incoming flow conditions, reference area and calculation standards, and a one-to-one mapping relationship is established between the drag coefficient annotation data and the corresponding vehicle body point cloud representation. Spatial registration processing is performed on the flow field physical data to map the flow field velocity distribution and flow field pressure distribution to a spatial coordinate system consistent with the vehicle body point cloud representation, and the flow field physical data is aligned to the surface sampling points corresponding to the vehicle body point cloud representation according to a preset sampling method; The vehicle body point cloud representation, the drag coefficient labeled data, and the flow field physical data are subjected to unified normalization processing to eliminate the numerical scale differences between different data and form a unified data representation. The data that has undergone unified normalization is subjected to integrity verification to select a valid sample set that simultaneously contains vehicle body point cloud representation, drag coefficient labeled data and flow field physical data; The effective sample set is subjected to sample shuffling and isolation partitioning to generate the training set, the validation set, and the test set; The process involves constructing data fitting constraints based on the predicted drag coefficient and the labeled drag coefficient data, and simultaneously constructing physical constraints based on the flow field prediction results. These data fitting constraints and physical constraints are then fused to form a unified training objective. Backpropagation is used to update the feature extraction parameters corresponding to the dynamic graph structure and the prediction parameters corresponding to the bi-branch prediction structure, ensuring that the initial model satisfies the unified training objective while fitting the data distribution. Specifically, this includes: A sample-level correspondence is established based on the predicted drag coefficient and the labeled drag coefficient data, and a unified measurement process is performed on the deviation between the predicted drag coefficient and the labeled drag coefficient data to form data fitting constraints. Based on the mapping relationship between the flow field prediction results and the corresponding spatial position of the vehicle body geometry, the continuous change state of the flow field, the change state of the flow field momentum, and the flow attachment state of the vehicle body wall are extracted, and continuity constraints, momentum conservation constraints, and wall no-slip constraints are constructed respectively to form physical constraints. The data fitting constraints and the physical constraints are fused to form the unified training objective, which is used to simultaneously reflect the sample fitting degree of the drag coefficient prediction results and the physical consistency degree of the flow field prediction results. Backpropagation is performed based on the unified training objective, and the bias information generated by the data fitting constraints and the bias information generated by the physical constraints are jointly fed back to the dual-branch prediction structure and the dynamic graph structure to obtain the backpropagation result; Based on the backpropagation results, the prediction parameters corresponding to the bi-branch prediction structure and the feature extraction parameters corresponding to the dynamic graph structure are updated synchronously so that the initial model satisfies the unified training objective while fitting the data distribution.

2. The method for constructing a vehicle drag coefficient prediction model that integrates convolution and physical information according to claim 1, characterized in that, The process involves performing a neighborhood search for each node based on the vehicle body point cloud representation to construct a neighborhood node set, then building a dynamic graph structure based on the neighborhood node set. Simultaneously, multi-layer edge convolution operations are performed on the dynamic graph structure to map and aggregate features of the relative geometric relationships between nodes and their neighbors, forming a multi-scale geometric feature representation. Specifically, this includes: Each node in the vehicle body point cloud representation is uniformly numbered, and a neighborhood search is performed on each node based on a preset neighborhood determination method to generate a set of neighboring nodes corresponding to the node, and to establish the adjacency relationship between the node and the neighboring nodes. A dynamic graph structure is constructed based on the adjacency relationship, with each node as the central node, the set of neighboring nodes as the local association unit, and the association relationship between the node and the neighboring node is represented by the node connection edge; Edge convolution is performed on the dynamic graph structure to extract node features and relative geometric relationships for each central node and its corresponding set of neighboring nodes. Feature mapping is then performed on the node features and the relative geometric relationships to generate corresponding edge feature representations. The edge feature representation is subjected to feature aggregation processing to form the node feature update result of each central node at the current level, and the dynamic graph structure is updated based on the node feature update result so that the relationship between nodes is dynamically adjusted as the node features change. Based on the updated dynamic graph structure, multi-layer edge convolution operations are repeatedly performed to extract local surface geometric features, regional contour geometric features, and whole vehicle semantic geometric features from the vehicle body point cloud representation layer by layer. The local surface geometric features, regional contour geometric features, and vehicle semantic geometric features output from the convolution operations of each layer are integrated and processed to form the multi-scale geometric feature representation.

3. The method for constructing a vehicle drag coefficient prediction model that integrates convolution and physical information according to claim 1, characterized in that, The step of performing global fusion processing on the multi-scale geometric feature representation to generate a global feature vector specifically includes: The node features of each node at different levels in the multi-scale geometric feature representation are uniformly organized, and the node features are subjected to hierarchical alignment processing to establish the correspondence of the same node at different levels. The node features that have completed the hierarchical alignment process are subjected to feature splicing to form composite node features containing multi-layer information, so that the composite node features simultaneously represent the local surface geometric features of the vehicle body, the regional contour geometric features, and the semantic geometric features of the whole vehicle. Embedding processing is performed on the composite node features to suppress irrelevant disturbances and enhance highly relevant node features that are related to the overall vehicle aerodynamic shape; Global fusion processing is performed on the highly relevant node features of each node to unify and aggregate node features across the entire vehicle, so that local surface geometric information, regional contour relationship information and vehicle semantic structure information can be expressed as a whole. The overall representation is processed to generate a global feature vector characterizing the aerodynamic shape of the vehicle.

4. The method for constructing a vehicle drag coefficient prediction model that integrates convolution and physical information according to claim 1, characterized in that, The construction of a dual-branch prediction structure based on the global feature vector, to output drag coefficient prediction results and flow field prediction results through the dual-branch prediction structure, specifically includes: The global feature vector is determined as the unified input of the dual-branch prediction structure, and the drag coefficient prediction branch and the flow field prediction branch are constructed in parallel based on the unified input. Based on the global feature vector, by performing continuous mapping processing in the drag coefficient prediction branch, the aerodynamic shape features of the whole vehicle in the global feature vector are transformed step by step to generate the corresponding drag coefficient prediction result. Based on the global feature vector, flow field representation mapping is performed in the flow field prediction branch to implicitly learn the flow-related geometric features in the global feature vector and generate the corresponding flow field prediction results.

5. The method for constructing a vehicle drag coefficient prediction model that integrates convolutional and physical information according to claim 1, characterized in that, The process of optimizing the initial model training process based on the training set, the validation set, and the test set, combined with a learning rate scheduling strategy, regularization constraints, and a validation set early stopping mechanism, determines the optimal model parameters. Based on these optimal model parameters and the initial model, a vehicle drag coefficient prediction model fusing convolutional and physical information is constructed. Specifically, this includes: Based on the training set, the initial model is subjected to multiple rounds of training iterations, so that each training sample sequentially goes through the feature extraction process corresponding to the dynamic graph structure, global fusion processing, and inference calculation of the dual-branch prediction structure, and the feature extraction parameters and prediction parameters corresponding to the initial model are continuously updated based on the unified training objective. During multiple training iterations, the learning rate scheduling strategy is combined with dynamic control of the parameter update rhythm so that the initial model gradually transitions from the fast convergence stage to the stable convergence stage. During multiple training iterations, the parameter size and feature response of the initial model are limited by the regularization constraints to suppress overfitting and enhance the model's generalization ability. The model performance corresponding to the current parameter state is evaluated based on the validation set, and the early stopping mechanism of the validation set is executed according to the performance change trend of the validation set, so as to terminate the training process when the preset stopping conditions are met. After training is terminated, the parameter states whose performance on the validation set meets the preset conditions are selected from the training rounds as the optimal model parameters, and the optimal model parameters are loaded into the initial model to complete the construction of the vehicle drag coefficient prediction model that integrates convolution and physical information. Independent performance evaluations were performed on the constructed vehicle drag coefficient prediction model based on the test set to verify the generalization ability of the model corresponding to the optimal model parameters.

6. A device for constructing a vehicle drag coefficient prediction model that integrates convolution and physical information, characterized in that, The apparatus is used to execute the method for constructing a vehicle drag coefficient prediction model that fuses convolutional and physical information as described in any one of claims 1 to 5. The apparatus includes an acquisition module and a processing module, wherein... The acquisition module is used to acquire the three-dimensional geometric data of the target vehicle and construct the vehicle body point cloud representation. At the same time, it acquires the drag coefficient annotation data and flow field physical data corresponding to the target vehicle, and performs unified normalization processing on the vehicle body point cloud representation, the drag coefficient annotation data and the flow field physical data to generate training set, validation set and test set. The processing module is used to perform neighborhood search for each node based on the vehicle body point cloud representation to construct a neighborhood node set, construct a dynamic graph structure based on the neighborhood node set, and perform multi-layer edge convolution operation on the dynamic graph structure to perform feature mapping and feature aggregation on the relative geometric relationship between the node and the neighborhood node to form a multi-scale geometric feature expression. The processing module is further configured to perform global fusion processing on the multi-scale geometric feature representation to generate a global feature vector; The processing module is also used to construct a dual-branch prediction structure based on the global feature vector, so as to output the drag coefficient prediction result and the flow field prediction result through the dual-branch prediction structure; The processing module is also used to construct data fitting constraints based on the wind resistance coefficient prediction results and the wind resistance coefficient labeled data, and construct physical constraints based on the flow field prediction results. The data fitting constraints and the physical constraints are then fused to form a unified training objective. The feature extraction parameters corresponding to the dynamic graph structure and the prediction parameters corresponding to the bi-branch prediction structure are updated through backpropagation so that the initial model satisfies the unified training objective while fitting the data distribution. The processing module is further configured to optimize the training process of the initial model based on the training set, the validation set, and the test set, combined with a learning rate scheduling strategy, regularization constraints, and a validation set early stopping mechanism, to determine the optimal model parameters, so as to complete the construction of a vehicle drag coefficient prediction model that integrates convolution and physical information based on the optimal model parameters and the initial model.

7. An electronic device, characterized in that, The electronic device includes a processor, a memory, a user interface, and a network interface. The memory is used to store instructions. The user interface and the network interface are both used to communicate with other devices. The processor is used to execute the instructions stored in the memory to cause the electronic device to perform the method as described in any one of claims 1 to 5.

8. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium stores instructions that, when executed, perform the method as described in any one of claims 1 to 5.

Images