A bridge section flow field fast prediction method based on geometric guide implicit mapping

Abstract

This invention discloses a rapid prediction method for bridge cross-section flow fields based on geometry-guided implicit mapping, belonging to the field of bridge wind resistance technology. The method first constructs a symbolic distance function based on the bridge cross-section geometry to implicitly represent the fluid and structural domains. Then, it samples physical nodes and fuses physical parameters to construct input features including geometric and boundary conditions. Furthermore, the method projects unstructured physical nodes onto a structured implicit feature space. Within this space, a multi-scale feature aggregation and multi-branch operator coupling structure is used to model the global trend of the flow field, correct local details, and establish long-range spatial dependencies. Finally, the decoder outputs the predicted flow field results for the bridge cross-section. The entire process incorporates a composite loss function that includes data errors and physical constraints for model training. This invention can achieve high-precision and rapid prediction of flow fields in complex bridge cross-sections while ensuring physical consistency.

Description

Technical Field

[0001] This invention belongs to the field of bridge wind resistance technology, and specifically relates to a method for rapid prediction of bridge cross-section flow field based on geometrically guided implicit mapping. Background Technology

[0002] In the design of modern long-span bridges, accurately assessing steady-state fluid flow over complex geometries is a core aspect of wind-resistant bridge design. The variability of bridge cross-sectional geometry can lead to strong nonlocal interactions and multi-scale flow structures (such as boundary layer separation and wake formation). While traditional numerical solvers are mathematically rigorous, they face bottlenecks such as long computation cycles and high costs when iteratively solving these coupled multi-scale physical phenomena across dense computational grids, making it difficult to meet the demands of rapid iteration in engineering.

[0003] In recent years, data-driven deep learning alternative models have been increasingly applied to flow field prediction. However, early convolutional neural networks heavily relied on uniform Cartesian grids, making it difficult to adapt to irregular bridge cross-sectional boundaries; while graph neural networks can handle unstructured grids, they are prone to feature oversmoothing when capturing long-distance dependencies in large-scale flow fields; and existing methods such as Fourier neural operators often introduce discretization errors when dealing with fluid domains with complex geometric boundaries or sharp edges.

[0004] For wind field prediction in bridge engineering with complex geometries, such as split box girders and variable cross-section bridge towers, existing deep learning methods still face problems such as poor geometric adaptability, loss of local eddy flow details, and insufficient physical consistency. How to ensure accurate reconstruction of local details while maintaining computational efficiency of the macroscopic flow field is a technical challenge that urgently needs to be solved in the field of bridge wind resistance calculation. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a rapid prediction method for the flow field of bridge cross sections based on geometrically guided implicit mapping. The aim is to achieve rapid and accurate prediction of the flow field and aerodynamic forces of complex bridge cross sections by constructing a geometrically constrained driven spatial mapping mechanism and a multi-scale flow field evolution structure.

[0006] To achieve the above objectives, the present invention provides a method for rapid prediction of flow field in bridge cross sections based on geometrically guided implicit mapping, comprising the following steps:

[0007] Step 1: Geometric Modeling of Bridge Section and Construction of Symbolic Distance Function: Obtain the geometric contour data of the bridge section and construct a two-dimensional physical computation domain; perform implicit geometric modeling of the continuous physical space through the symbolic distance function (SDF) to distinguish between fluid regions and solid structure regions; generate a discrete set of physical computation nodes within the fluid region.

[0008] Step 2: Physical Node Sampling and Construction of Physical Parameter Features: Node sampling is performed within the physical computation domain in Step 1 to obtain a discrete set of physical nodes; physical control parameters for bridge flow field analysis are set, and the physical control parameters are concatenated with the physical node coordinates and their sign distance function values ​​from Step 1 to construct physical input node features that include geometric and fluid boundary conditions;

[0009] Step 3: Establish a geometrically guided mapping from the physical domain to the implicit structured feature space: Construct a dimension-compressed implicit structured feature space, and map the irregularly distributed physical computing nodes and their features to this structured implicit feature space through a nonlinear mapping model based on the spatial attention mechanism; at the same time, convert the value of the symbolic distance function in Step 1 into a geometric mask matrix to participate in the weight calculation of the spatial attention mechanism, and physically truncate and shield invalid nodes inside the structure.

[0010] Step 4: Multi-scale feature extraction and spatial aggregation: In the implicit structured feature space constructed in Step 3, the spatial features of the target node in different scale neighborhoods are extracted by the multi-scale spatial feature aggregation module, and the aggregation ratio of each scale feature is adaptively allocated by attention weight to generate a fused feature representation, so as to simultaneously capture the local sharp edges of the bridge section and the global flow topology.

[0011] Step 5: Flow field multi-branch evolution calculation: Input the aggregated features from Step 4 into the multi-branch operator coupling structure for nonlinear physical state update, and perform parallel calculation and fuse flow physical information at three scales: global flow trend, local detail correction, and spatial correlation establishment; for the process of nonlinear physical state update, a composite loss function including data error and prior physical constraints is used to optimize network parameters.

[0012] Step 6: Output the predicted flow field results of the bridge section: Use the decoder to backmap the evolved implicit features back to the macroscopic physical calculation node, reconstruct and output the steady-state velocity field distribution of the bridge section, and complete the flow field assessment.

[0013] Furthermore, in step one, the calculated symbolic distance function can distinguish between fluid and solid regions: when a node is located in a fluid domain, the symbolic distance function is positive, and its value is the shortest Euclidean distance from the node to the solid boundary; when a node is located inside a structural entity, the symbolic distance function is negative.

[0014] Furthermore, in step two, the physical control parameters include Reynolds number, incoming wind speed, and wind angle of attack.

[0015] Furthermore, in step three, a geometrically guided mapping is established from the physical domain to the implicitly structured feature space. The specific nonlinear mapping calculation model is as follows: Target implicitly structured feature space nodes. Features From the physical nodes within its spatial neighborhood Features It is aggregated, and the expression for aggregation is:

[0016]

[0017] In the formula, the superscript For different scales; Implicit node The corresponding physical neighborhood set; , For the feedforward neural network mapping function;

[0018] Among them, attention weight The expression is:

[0019]

[0020]

[0021] In the formula, To query the matrix Bond matrix The calculated initial spatial correlation score; For implicit nodes Its spatial neighborhood set any physical node inside Initial spatial correlation score between them; The dimension of a single feature vector.

[0022] Furthermore, in step four, the implementation method of the multi-scale spatial feature aggregation module is as follows: First, in the implicit structured feature space, with the target node... Centered on a central point, multiple neighborhood sets with different discrete radii are defined. This allows for the division of spatial neighborhoods at different scales. Then, for each different scale Extract spatial feature subsets within the neighborhood of that scale respectively. Finally, the features at each scale are weighted and fused using an adaptive dynamic weight allocation mechanism. The expression for the fusion calculation is as follows:

[0023]

[0024] In the formula, This represents the feature representation after multi-scale fusion. coordinates Corresponding to different scales The dynamic allocation of weights; the dynamic allocation of weights By studying a set of learnable functions Real-time calculation, the expression for which it is calculated is:

[0025]

[0026] Furthermore, in step five, parallel computing is employed to fuse the flow physics information at three scales, as detailed below:

[0027] 1) Global flow trend calculation: The spatial signal is converted to the frequency domain by Fourier transform. A frequency domain filtering strategy that truncates high-frequency components and retains low-frequency components is adopted to separate and evolve the continuous macroscopic background flow and large-scale wake structure in the flow field.

[0028] 2) Local detail correction: Using local convolutional network branches, high-precision compensation is performed for local high-frequency features and discontinuous changes lost during frequency domain truncation;

[0029] 3) Establishing spatial correlation: Using spatial attention mechanisms to handle the spatial dependence of long-distance flow fields.

[0030] Furthermore, in step five, the fusion method of the multi-branch operator coupling structure is parallel feature addition fusion with residual connections, and feature conflict avoidance and recalibration are performed through layer normalization and feedforward neural network; for a given input feature Intermediate features after multi-branch fusion The calculation expression is:

[0031]

[0032] In the formula, For layer normalization operation; For spatial attention branch operators; and These are global frequency domain branching operators formed by the Fast Fourier Transform and its inverse transform, respectively. It is a learnable complex weight matrix; For local convolutional network branch operators;

[0033] Then, intermediate features The final coupling features are obtained through a nonlinear mapping along the channel dimension. Its calculation expression is:

[0034]

[0035] In the formula, It is a feedforward neural network used to perform nonlinear interactions and recalibration between channels of the features after the summation of multiple branches, so as to avoid conflicts caused by differences in the feature distribution extracted by different branches.

[0036] Furthermore, in step five, during the nonlinear physical state update, a composite loss function incorporating data error and prior physical constraints is used to optimize network parameters; the composite loss function The loss includes data error loss, spatial gradient consistency loss, and divergence loss, expressed as follows:

[0037]

[0038]

[0039]

[0040]

[0041] In the formula, The mean absolute error between the predicted and actual values; For spatial gradient consistency loss, For divergence loss, the mass conservation law of incompressible fluids must be satisfied. ; , , These are preset weight hyperparameters; Predict flow field velocities for the model; The actual reference flow field velocity; This represents the total number of discrete physical nodes participating in the loss function calculation within the fluid computation domain.

[0042] The divergence loss is used to force the flow field to satisfy the mass conservation law of incompressible fluids; combined with the symbolic distance function mask, the spatial gradient consistency loss and divergence loss only apply to the fluid domain nodes.

[0043] This invention also provides a rapid prediction system for bridge cross-section flow field based on geometry-guided implicit mapping, including a geometric modeling module, a node feature construction module, a geometry-guided mapping module, a multi-scale feature extraction module, a flow field evolution calculation module, and a result output module. The system is used to execute the rapid prediction method for bridge cross-section flow field based on geometry-guided implicit mapping described above, ultimately achieving high-precision and rapid prediction of the steady-state velocity field under complex bridge cross-section geometry conditions.

[0044] The geometric modeling module is used to acquire the geometric contour data of the bridge cross section, construct a two-dimensional physical computing domain, complete implicit geometric modeling through the signed distance function to distinguish between fluid regions and solid structure regions, and generate a discrete set of physical computing nodes within the fluid region.

[0045] The node feature construction module is used to sample nodes in a two-dimensional physical computing domain to obtain a discrete set of physical nodes, set physical control parameters including Reynolds number, incoming wind speed and wind angle of attack, and concatenate the physical control parameters with physical node coordinates and symbolic distance function values ​​to construct physical input node features including geometric and fluid boundary conditions.

[0046] The geometric guided mapping module is used to construct a dimension-compressed implicit structured feature space. Through a nonlinear mapping model based on spatial attention mechanism, it maps irregularly distributed physical computing nodes and their features to the implicit structured feature space. At the same time, it converts the symbolic distance function value into a geometric mask matrix to participate in the weight calculation of the spatial attention mechanism, and physically truncates and masks invalid nodes inside the structure.

[0047] The multi-scale feature extraction module is used to extract spatial features of the target node in different scale neighborhoods in the implicit structured feature space through the multi-scale spatial feature aggregation module, and to generate a fused feature representation by adaptively allocating the aggregation ratio of features at each scale through attention weights.

[0048] The flow field evolution calculation module is used to input the fused features into the multi-branch operator coupling structure for nonlinear physical state update, calculate and fuse global flow trend, local detail correction and spatial correlation to establish flow physical information at three scales in parallel, and use a composite loss function that includes data error and prior physical constraints to optimize network parameters.

[0049] The result output module is used to reverse map the evolved implicit features back to the macroscopic physical calculation node through the decoder, reconstruct and output the steady-state velocity field distribution of the bridge section.

[0050] The present invention also provides an electronic device, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement a method for rapid prediction of bridge cross-section flow field based on geometrically guided implicit mapping as described above.

[0051] The present invention also provides a computer program product, which, when executed by a processor, implements a method for rapid prediction of bridge cross-section flow field based on geometrically guided implicit mapping as described above.

[0052] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which is executed by a processor to implement a method for rapid prediction of bridge cross-section flow field based on geometrically guided implicit mapping as described above.

[0053] Advantages and benefits of this invention: This invention enables high-precision and rapid prediction of flow fields in complex bridge cross-sections while ensuring physical consistency. It adapts to irregular bridge cross-section boundaries through geometrically guided implicit mapping, combined with multi-scale feature extraction, simultaneously capturing local sharp edge details and global flow field topology, avoiding the loss of local eddy details. Based on a multi-branch operator coupling structure, it parallelly fuses multi-scale flow physics information, coupled with a composite loss function containing physical prior constraints, strictly adhering to the laws of fluid physics to ensure physical consistency. Compared to traditional numerical solvers, it significantly improves computational efficiency, adapts to the rapid iteration requirements of engineering projects, and solves problems such as poor geometric adaptability, over-smoothing of features, and discretization errors in existing deep learning methods. Attached Figure Description

[0054] Figure 1 This is a flowchart of the bridge cross-section flow field prediction method of the present invention;

[0055] Figure 2 This is a schematic diagram of SDF modeling of a fluid domain in a double box girder section according to an embodiment of the present invention;

[0056] Figure 3 A schematic diagram of SDF modeling of a fluid domain at a two-column cross section in an embodiment of the present invention;

[0057] Figure 4 This is a hidden layer feature of a double box girder section after multi-scale fusion in an embodiment of the present invention;

[0058] Figure 5 This is a hidden layer feature of a two-column cross section after multi-scale fusion in an embodiment of the present invention;

[0059] Figure 6 This is a comparison diagram of the predicted flow field and the CFD benchmark solution for a certain double box girder section in an embodiment of the present invention. );

[0060] Figure 7 This is a comparison diagram of the predicted flow field and the CFD benchmark solution for a certain two-column cross section in an embodiment of the present invention. ). Detailed Implementation

[0061] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. The specific embodiments described herein are merely illustrative and are not intended to limit the invention.

[0062] Example 1

[0063] like Figure 1 As shown, this embodiment provides a method for rapid prediction of the flow field of a bridge section based on geometrically guided implicit mapping. Using a double-box girder in bridge wind engineering as an example, the Reynolds number of the dataset in this example is... The specific steps are as follows:

[0064] Step 1: Geometric Modeling of Bridge Section and Construction of Symbolic Distance Function: Obtain the geometric profile of the double box girder section using the CAD design file. Define the computational domain, where the physical point cloud size is... Calculate its signed distance function. The calculation formula is as follows: Let... , i.e., point to solid boundary any point above The shortest Euclidean distance.

[0065]

[0066] If any point Located in the fluid domain, then If the point is positive; Located inside the box girder structure, The value is negative, thus strictly defining the aerodynamic boundary of the double box girder.

[0067] Step 2: Physical Node Sampling and Construction of Physical Parameter Features: This involves combining the Reynolds number, incoming wind speed, and the two-dimensional coordinates of each physical node. The values ​​are concatenated and merged to form the initial input feature vector.

[0068] Step 3: Establish a geometrically guided mapping from the physical domain to the implicitly structured feature space: A set of mesh points is constructed at the bottom layer. A uniform, low-dimensional implicitly structured feature space is used to project the discrete physical input features into this space, employing a nonlinear mapping encoder based on a spatial attention mechanism. The specific algorithm and mathematical model are as follows:

[0069] For any target node in the implicitly structured feature space The aggregated hidden features are set as The calculation process for feature extraction is shown in the following formula:

[0070]

[0071] In the formula, the superscript For different scales; For implicit nodes The corresponding physical neighborhood set; For physical nodes Input features; and All of these are mapping functions for feedforward neural networks.

[0072] Among them, core parameters The calculation formula is as follows:

[0073]

[0074]

[0075] In the formula, To query the matrix Bond matrix The calculated initial spatial correlation score; For implicit nodes Its spatial neighborhood set any physical node inside Initial spatial correlation score between them; The dimension of a single feature vector.

[0076] Step 4: Multi-scale feature extraction and spatial aggregation: Define the scale set (in This value (the normalized Euclidean distance of the flow field) corresponds to small, medium, and large spatial search radii, respectively, to construct a multi-scale neighborhood. A dynamic adaptive allocation formula is used when performing multi-scale feature aggregation:

[0077]

[0078] In the formula, This represents the feature representation after multi-scale fusion. coordinates Corresponding to different scales The dynamic allocation of weights; the dynamic allocation of weights By studying a set of learnable functions Real-time calculation, the expression for which it is calculated is:

[0079]

[0080] This enables precise extraction of geometric features from the blunt and sharp corners of box girders, as well as the extraction of large-scale macroscopic flow regime information from the wake or uniform flow region. Features at different scales are then weighted and fused using a spatial attention mechanism. Figure 4 The hidden layer characteristics of the double box girder section after multi-scale fusion are shown and passed to the next step.

[0081] Step 5: Flow Field Multi-Branch Evolution Calculation: In implicit space, three modules are coupled for calculation: a global low-frequency evolution branch (FNO), a local high-frequency correction branch (CNN), and a long-range spatial attention branch. In the nonlinear physical state update, the coupling process of the three branches strictly follows the principles of residual addition and channel recalibration. The features input to the coupling module are... First, perform parallel addition and fusion:

[0082]

[0083] In the formula, For layer normalization operation; For spatial attention branch operators; and These are global frequency domain branching operators formed by the Fast Fourier Transform and its inverse transform, respectively. It is a learnable complex weight matrix; This is a branch operator for local convolutional networks; where the first term is the original feature truncation; the second term introduces the attention space correlation features normalized by the layer; and the third term is the Fourier transform... Apply weights in the frequency domain The filtered global background flow features; the fourth item is the high-frequency shearing layer feature compensated by the local convolutional network. After the above features are added in parallel, the intermediate features are... The final coupling features are obtained through a nonlinear mapping along the channel dimension. Its calculation expression is:

[0084]

[0085] In the formula, It is a feedforward neural network; using layer normalization Smoothing out variance abrupt changes caused by different feature scales, and then passing it through a feedforward neural network. The feature channels after addition are nonlinearly redistributed and mixed to avoid conflicts caused by differences in feature distribution extracted from different branches.

[0086] Meanwhile, this deduction process is constrained by a loss function introduced by prior physical formulas. The composite loss function L is specifically:

[0087]

[0088] in, The mean absolute error between the predicted and actual values; Spatial gradient consistency loss is used to constrain local gradients such as wall shear stress. To mitigate divergence loss, the flow field is forced to satisfy the mass conservation law for incompressible fluids. For this example of a double box girder, , , Combined with the SDF mask, the above physical gradient and divergence penalty only apply to fluid domain nodes, ensuring that the model strictly conforms to physical laws.

[0089]

[0090]

[0091]

[0092] In the formula, Predict flow field velocities for the model; The actual reference flow field velocity; This represents the total number of discrete physical nodes participating in the loss function calculation within the fluid computation domain.

[0093] Step 6: Output the predicted flow field results of the bridge section: Use the decoder to backmap the evolved implicit features back to the macroscopic physical calculation node, reconstruct and output the steady-state velocity field distribution of the bridge section. Figure 6 The results show a comparison between the predicted flow field of the double box girder and the actual values. The relative error of the results is 1.883%, and the flow field conditions are in high agreement with the actual values.

[0094] In this embodiment, a deep learning model is trained and inferred end-to-end on a single NVIDIA RTX A6000 GPU, using FP32 precision. During the training phase, the optimizer employs the Adam algorithm, with an initial learning rate set to [value missing]. Furthermore, a cosine annealing learning rate decay strategy is employed to ensure convergence stability.

[0095] Example 2

[0096] For the application scenario of bluff body sections under multi-body interference in bridge wind engineering, such as square piers and bridge towers, the actual engineering effect of the above-mentioned rapid flow field prediction technology is verified. The specific steps are as follows:

[0097] Step 1: Bridge Cross-Section Geometric Modeling and Signed Distance Function Construction: Obtain the cross-sectional profiles of the tandem columns using CAD. Set the Reynolds number. The feature size ratio between the windward square column and the downstream square column is 0.6, and the physical point cloud size is... Each node has a corresponding physical computation domain. The symbolic distance function (SDF) for each node is then calculated. For example... Figure 3 As shown, an SDF implicit geometric model that distinguishes between the fluid domain and the biaxial column solid boundary was successfully constructed.

[0098] Step 2, Physical Node Sampling and Physical Parameter Feature Construction: Discrete physical nodes are sampled within the dual computational domain, and the macroscopic physical parameters at this time are ( ), node two-dimensional coordinates and Figure 3 The SDF values ​​calculated in the process are concatenated to generate input features for describing the boundary conditions of the flow field of the tandem square columns.

[0099] Step 3: Establish a geometrically guided mapping from the physical domain to the implicitly structured feature space: Project the unstructured two-column flow field nodes onto a low-dimensional implicitly structured feature space, the size of which is... In this process, the SDF negative value mask is strictly applied to block invalid participation of nodes inside both pillars and cut off the transmission of non-physical information across the pillar entities.

[0100] Step 4: Multi-scale Feature Extraction and Spatial Aggregation: For the unique right-angled sharp edges and inter-column gaps of the two columns, the multi-scale aggregation module adaptively allocates the receptive field and extracts... Euclidean distance after normalization of the flow field domain Small-scale windows are used to accurately capture the fluid separation point features on the surface of the square column, while large-scale windows are used to extract the evolution features of the gap between the two columns and the downstream wake. Figure 5 The hidden layer features of the two pillars after multi-scale fusion are displayed and passed to the next step.

[0101] Step 5: Multi-branch evolution calculation of the flow field: The input features undergo multi-branch evolution in the implicit space: the global frequency domain branch is responsible for analyzing the macroscopic shedding trend of the downstream square column wake; the local convolution branch focuses on compensating for the gradient changes of the extremely high shear layer at the stagnation point and corners of both square columns; at the same time, a composite loss function containing the law of mass conservation is applied for physical consistency constraints. For this example of two square columns, , , .

[0102] Step Six: Output the predicted flow field results for the bridge cross-section: After inverse mapping by the decoder, the steady-state wind field distribution of both column cross-sections is directly output. For example... Figure 7 As shown, the method of the present invention can accurately reconstruct the complex vortex interaction between the two columns in series and the flow field in the wake region. The prediction results are highly consistent with the traditional CFD benchmark solution, with a relative error of 2.384%.

Claims

1. A method for rapid prediction of flow field in bridge cross sections based on geometrically guided implicit mapping, characterized in that, Includes the following steps: Step 1: Geometric Modeling of Bridge Cross-Section and Construction of Symbolic Distance Function: Obtain the geometric contour data of the bridge cross-section and construct a two-dimensional physical computation domain; perform implicit geometric modeling of the continuous physical space using the symbolic distance function to distinguish between fluid regions and solid structure regions; generate a discrete set of physical computation nodes within the fluid region; Step 2: Physical Node Sampling and Physical Parameter Feature Construction: Node sampling is performed within the physical computation domain in Step 1 to obtain a discrete set of physical nodes; physical control parameters for bridge flow field analysis are set, and the physical control parameters are concatenated with the physical node coordinates and their sign distance function values ​​from Step 1 to construct physical input node features that include geometric and fluid boundary conditions; Step 3: Establish a geometrically guided mapping from the physical domain to the implicit structured feature space: Construct a dimension-compressed implicit structured feature space, and map the irregularly distributed physical computing nodes and their features to this structured implicit feature space through a nonlinear mapping model based on the spatial attention mechanism. At the same time, the value of the symbolic distance function in step one is converted into a geometric mask matrix to participate in the weight calculation of the spatial attention mechanism, physically truncating and shielding invalid nodes inside the structure; Step 4: Multi-scale feature extraction and spatial aggregation: In the implicit structured feature space constructed in Step 3, the spatial features of the target node in different scale neighborhoods are extracted through the multi-scale spatial feature aggregation module, and the aggregation ratio of each scale feature is adaptively allocated through attention weights to generate a fused feature representation. Step 5: Flow field multi-branch evolution calculation: Input the aggregated features from Step 4 into the multi-branch operator coupling structure for nonlinear physical state update, and perform parallel calculation and fuse flow physical information at three scales: global flow trend, local detail correction, and spatial correlation establishment; for the process of nonlinear physical state update, a composite loss function including data error and prior physical constraints is used to optimize network parameters. Step 6: Output the predicted flow field results of the bridge section: Use the decoder to backmap the evolved implicit features back to the macroscopic physical calculation node, reconstruct and output the steady-state velocity field distribution of the bridge section, and complete the flow field assessment.

2. The method for rapid prediction of bridge cross-section flow field based on geometrically guided implicit mapping according to claim 1, characterized in that, In step one, the calculated symbolic distance function can distinguish between fluid and solid regions: when the node is located in the fluid domain, the symbolic distance function value is positive, and its size is the shortest Euclidean distance from the node to the solid boundary; when the node is located inside the structural entity, the symbolic distance function value is negative.

3. The method for rapid prediction of bridge cross-section flow field based on geometrically guided implicit mapping according to claim 1, characterized in that, In step two, the physical control parameters include Reynolds number, incoming wind speed, and wind angle of attack.

4. The method for rapid prediction of bridge cross-section flow field based on geometrically guided implicit mapping according to claim 1, characterized in that, In step three, a geometrically guided mapping is established from the physical domain to the implicitly structured feature space. The specific nonlinear mapping calculation model is as follows: Target implicitly structured feature space nodes Features From the physical nodes within its spatial neighborhood Features It is aggregated, and the expression for aggregation is: In the formula, the superscript For different scales; For implicit nodes The corresponding physical neighborhood set; For physical nodes Input features; , For the feedforward neural network mapping function; Among them, attention weight The expression is: In the formula, To query the matrix Bond matrix The calculated initial spatial correlation score; For implicit nodes Its spatial neighborhood set any physical node inside Initial spatial correlation score between them; The dimension of a single feature vector.

5. The method for rapid prediction of bridge cross-section flow field based on geometrically guided implicit mapping according to claim 4, characterized in that, In step four, the implementation method of the multi-scale spatial feature aggregation module is as follows: First, in the implicit structured feature space, with the target node... Centered on a central point, multiple neighborhood sets with different discrete radii are defined. This allows for the division of spatial neighborhoods at different scales. Then, for each different scale Extract spatial feature subsets within the neighborhood of that scale respectively. Finally, the features at each scale are weighted and fused using an adaptive dynamic weight allocation mechanism. The expression for the fusion calculation is as follows: In the formula, This represents the feature representation after multi-scale fusion. coordinates Corresponding to different scales The dynamic allocation of weights; the dynamic allocation of weights By studying a set of learnable functions Real-time calculation, the expression for which it is calculated is:

6. The method for rapid prediction of bridge cross-section flow field based on geometrically guided implicit mapping according to claim 5, characterized in that, In step five, the fusion method of the multi-branch operator coupling structure is to perform parallel feature addition fusion with residual connections, and to avoid feature conflicts and recalibrate through layer normalization and feedforward neural networks; for a given input feature Intermediate features after multi-branch fusion The calculation expression is: In the formula, For layer normalization operation; For spatial attention branch operators; and These are global frequency domain branching operators formed by the Fast Fourier Transform and its inverse transform, respectively. It is a learnable complex weight matrix; For local convolutional network branch operators; Then, intermediate features The final coupling features are obtained through a nonlinear mapping along the channel dimension. Its calculation expression is: In the formula, It is a feedforward neural network used to perform nonlinear interactions and recalibration between channels of the features after the summation of multiple branches, so as to avoid conflicts caused by differences in the feature distribution extracted by different branches.

7. The method for rapid prediction of bridge cross-section flow field based on geometrically guided implicit mapping according to claim 6, characterized in that, In step five, during the nonlinear physical state update, a composite loss function incorporating data error and prior physical constraints is used to optimize network parameters; the composite loss function... The loss includes data error loss, spatial gradient consistency loss, and divergence loss, expressed as follows: In the formula, The mean absolute error between the predicted and actual values; For spatial gradient consistency loss, This is for divergence loss; to satisfy the mass conservation law for incompressible fluids. ; , , These are preset weight hyperparameters; Predict flow field velocities for the model; The actual reference flow field velocity; This represents the total number of discrete physical nodes participating in the loss function calculation within the fluid computation domain. The divergence loss is used to force the flow field to satisfy the mass conservation law of incompressible fluids; combined with the symbolic distance function mask, the spatial gradient consistency loss and divergence loss only apply to the fluid domain nodes.

8. The method for rapid prediction of bridge cross-section flow field based on geometrically guided implicit mapping according to claim 1, characterized in that, In step five, parallel computing and the fusion of flow physics information at three scales are employed as follows: 1) Global flow trend calculation: The spatial signal is converted to the frequency domain by Fourier transform. A frequency domain filtering strategy that truncates high-frequency components and retains low-frequency components is adopted to separate and evolve the continuous macroscopic background flow and large-scale wake structure in the flow field. 2) Local detail correction: Using local convolutional network branches, high-precision compensation is performed for local high-frequency features and discontinuous changes lost during frequency domain truncation; 3) Establishing spatial correlation: Using spatial attention mechanisms to handle the spatial dependence of long-distance flow fields.

9. A rapid prediction system for the flow field of a bridge cross section based on geometrically guided implicit mapping, characterized in that, The system includes a geometric modeling module, a node feature construction module, a geometric guided mapping module, a multi-scale feature extraction module, a flow field evolution calculation module, and a result output module. The system is used to execute a method for rapid prediction of bridge cross-section flow field based on geometric guided implicit mapping as described in any one of claims 1-8, and ultimately achieves high-precision and rapid prediction of steady-state velocity field under complex bridge cross-section geometry conditions. The geometric modeling module is used to acquire the geometric contour data of the bridge cross section, construct a two-dimensional physical computing domain, complete implicit geometric modeling through the signed distance function to distinguish between fluid regions and solid structure regions, and generate a discrete set of physical computing nodes within the fluid region. The node feature construction module is used to sample nodes in a two-dimensional physical computing domain to obtain a discrete set of physical nodes, set physical control parameters including Reynolds number, incoming wind speed and wind angle of attack, and concatenate the physical control parameters with physical node coordinates and symbolic distance function values ​​to construct physical input node features including geometric and fluid boundary conditions. The geometric guided mapping module is used to construct a dimension-compressed implicit structured feature space. Through a nonlinear mapping model based on spatial attention mechanism, it maps irregularly distributed physical computing nodes and their features to the implicit structured feature space. At the same time, it converts the symbolic distance function value into a geometric mask matrix to participate in the weight calculation of the spatial attention mechanism, and physically truncates and masks invalid nodes inside the structure. The multi-scale feature extraction module is used to extract spatial features of the target node in different scale neighborhoods in the implicit structured feature space through the multi-scale spatial feature aggregation module, and to generate a fused feature representation by adaptively allocating the aggregation ratio of features at each scale through attention weights. The flow field evolution calculation module is used to input the fused features into the multi-branch operator coupling structure for nonlinear physical state update, calculate and fuse global flow trend, local detail correction and spatial correlation to establish flow physical information at three scales in parallel, and use a composite loss function that includes data error and prior physical constraints to optimize network parameters. The result output module is used to reverse map the evolved implicit features back to the macroscopic physical calculation node through the decoder, reconstruct and output the steady-state velocity field distribution of the bridge section.

10. An electronic device, characterized in that, include: The system includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, it implements the method for rapid prediction of bridge cross-section flow field based on geometrically guided implicit mapping as described in any one of claims 1-8.

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