A complex curved surface physical field prediction method, device, equipment and storage medium

Abstract

This application provides a method, apparatus, device, and storage medium for predicting the physical field of complex curved surfaces. The method involves decomposing the target curved surface into multiple surface patches and constructing overlapping regions between adjacent patches. For each patch, a parametric mapping to a unified two-dimensional reference domain is constructed, and geometric distortion information is calculated. A mesh is generated in the reference domain, and the mesh's three-dimensional coordinates, distortion information, and operating conditions are encoded as input tensors. The local predicted physical field of each patch is output through neural operator inference. The local field is then written back to the target curved surface via inverse mapping to obtain the surface write-back field for each patch. In the overlapping regions, a weighted fusion weight is constructed based on the distortion information, and all write-back fields are fused to obtain a globally continuous predicted physical field. Using this method, the prediction accuracy, global continuity, and prediction efficiency of the physical field of complex curved surfaces can be improved.

Description

Technical Field

[0001] This application relates to the field of physical field prediction technology, and more specifically, to a method, apparatus, device, and storage medium for predicting physical fields on complex curved surfaces. Background Technology

[0002] In industrial sectors such as automotive and aerospace, predicting the physical fields (e.g., surface pressure fields and shear stress fields) of complex curved surfaces is a core aspect of shape optimization design. While traditional computational fluid dynamics (CFD) simulation methods can obtain high-precision physical field results, they suffer from high computational costs and long cycles, making it difficult to meet the efficiency requirements of large-scale iterative shape optimization in industrial design. Data-driven neural operator methods, with their efficient reasoning capabilities, have become an important research direction to replace traditional CFD methods, providing a new technical path for the rapid prediction of physical fields of complex curved surfaces.

[0003] The current mainstream neural operator physics prediction method usually adopts the technical path of "surface parameterization-reference domain inference-result write-back": first, the three-dimensional complex surface is transformed into a two-dimensional regular reference domain through parameterization mapping, then the physics prediction is completed on the reference domain using neural operators, and finally the prediction results are written back to the original surface to achieve the adaptation of irregular surface to regular computation domain.

[0004] However, these existing methods have significant drawbacks: angular and area distortions inevitably occur during the parametric mapping process, which destroy the local geometric features of the surface. Existing methods do not incorporate parametric distortion information into the model prediction process, causing the model to be unable to perceive the impact of distortion on the physical field distribution. As a result, the error of the prediction results increases significantly in areas with severe distortion, making it difficult to meet the prediction accuracy requirements of industrial applications. Summary of the Invention

[0005] In view of this, the purpose of this application is to provide a method, apparatus, device and storage medium for predicting complex surface physical fields, which can improve the prediction accuracy, global continuity and prediction efficiency of complex surface physical fields.

[0006] In a first aspect, embodiments of this application provide a method for predicting the physical field of a complex curved surface, the method comprising: The input target surface is decomposed into multiple surface patch pieces, and overlapping regions are constructed between adjacent surface patch pieces. For each surface atlas patch, construct a parametric mapping from the surface atlas patch to a unified two-dimensional reference domain, and calculate the geometric distortion information of the parametric mapping; Grid points are generated on the unified two-dimensional reference domain. The three-dimensional coordinates of the grid points, the geometric distortion information, and the working condition information are encoded into an input tensor. Neural operators are used to infer on the unified two-dimensional reference domain to output the local predicted physics field of each surface patch. By inverse mapping of the parameterized mapping, the local predicted physical field is written back from the grid points to the corresponding position of the target surface, thus obtaining the surface write-back field of each surface patch. Within the overlapping region, a weighted fusion weight is constructed based on the geometric distortion information, and the weighted fusion weight is used to fuse the surface write-back fields of all surface atlas patches to obtain a globally continuous predicted physics field.

[0007] Optionally, the step of decomposing the input target surface into multiple surface patch pieces and constructing overlapping regions between adjacent surface patch pieces includes: Perform geometric preprocessing on the input target surface to obtain the preprocessed surface; Extract geometric features from the preprocessed surface; Based on the geometric features, the discrete units of the surface are clustered using a graph neural network or attention mechanism model to obtain the soft partitioning results of the surface. The soft partitioning results are converted into surface atlas patches with clear boundaries, and the adjacency relationship between the surface atlas patches is established. Based on the adjacency relationship, an overlapping region is constructed between adjacent surface patch.

[0008] Optionally, constructing a parametric mapping from the surface atlas patch to a unified two-dimensional reference domain for each surface atlas patch, and calculating the geometric distortion information of the parametric mapping, includes: For each surface atlas patch, a mapping from that surface atlas patch to a unified two-dimensional reference domain is constructed to obtain the parametric mapping; The determinant of the Jacobian matrix of the parameterized mapping is constrained to be greater than zero, and the angular distortion and area distortion of the parameterized mapping are controlled. Based on the parameterized mapping, calculate the geometric distortion information of the parameterized mapping; The geometric distortion information is used to determine whether the parametric distortion of each surface patch exceeds the threshold. If it exceeds the threshold, the surface patch is reparametrically mapped or the mapping boundary is adjusted until the distortion meets the requirements.

[0009] Optionally, the step of writing back the local predicted physics field from the grid points to the corresponding positions on the target surface through the inverse mapping of the parameterized mapping, to obtain the surface write-back field for each surface patch, includes: For any target point on the target surface, the parameter coordinates of the target point in the unified two-dimensional reference domain are determined by the inverse mapping; Among the grid points, determine multiple grid points adjacent to the parameter coordinates; The predicted physical field value of the target point is calculated using bilinear interpolation or higher-order interpolation methods based on the local predicted physical field values ​​at adjacent grid points. The calculated predicted physical field value is assigned to the target point. The above operation is performed on all target points within the coverage area of ​​the surface atlas patch to obtain the surface write-back field of each surface atlas patch.

[0010] Optionally, constructing a weighted fusion weight based on the geometric distortion information within the overlapping region includes: For each target point within the overlapping region, determine all surface patch maps covering that target point; For each surface patch covering the target point, obtain the distance from the target point to the boundary of the surface patch, and the distortion degree index corresponding to the surface patch in the geometric distortion information; Based on the distance and the distortion index, a weighted fusion weight is constructed for each covered surface patch at the target point; wherein, the smaller the distortion index and the larger the distance, the larger the constructed weighted fusion weight.

[0011] Optionally, the step of fusing the surface write-back fields of all surface atlas patches using the weighted fusion weights to obtain a globally continuous predicted physics field includes: For each target point on the target surface, determine all surface atlas patches covering the target point, and obtain the surface write-back field value and corresponding weighted fusion weight of each covered surface atlas patch at the target point; The obtained surface write-back field values ​​are weighted and summed or weighted and averaged, and the calculation result is used as the fusion prediction value of the target point; For target points that are only covered by a single surface atlas patch, the surface write-back field value of that surface atlas patch is directly used as the fusion prediction value; Gradient uniformity correction or smoothing correction is performed on the fused global prediction values ​​to obtain a globally continuous predicted physics field and output it.

[0012] Optionally, the method further includes the step of training a neural operator: The input target surface, working conditions, and corresponding physical field true data are used to construct training samples; Define a multi-objective loss function, which includes: data term error between the predicted physical field and the true value, consistency error of predicted values ​​of adjacent surface plot patches in the overlapping region, and gradient jump error at the boundary of adjacent surface plot patches; The neural operator is optimized using the multi-objective loss function until the loss converges.

[0013] Secondly, embodiments of this application provide a device for predicting the physical field of complex curved surfaces, the device comprising: The overlapping region construction module is used to decompose the input target surface into multiple surface patches and construct overlapping regions between adjacent surface patches. The geometric distortion information calculation module is used to construct a parametric mapping from the surface atlas patch to a unified two-dimensional reference domain for each surface atlas patch, and to calculate the geometric distortion information of the parametric mapping. The local predicted physics output module is used to generate grid points on the unified two-dimensional reference domain, encode at least the three-dimensional coordinates of the grid points, the geometric distortion information, and the information of the working conditions into an input tensor, use neural operators to infer on the unified two-dimensional reference domain, and output the local predicted physics for each surface patch. The surface write-back field determination module is used to write back the local predicted physical field from the grid points to the corresponding positions of the target surface through the inverse mapping of the parameterized mapping, so as to obtain the surface write-back field of each surface atlas patch. The global predicted physics field determination module is used to construct a weighted fusion weight based on the geometric distortion information within the overlapping region, and to fuse the surface write-back fields of all surface atlas patches using the weighted fusion weight to obtain a globally continuous predicted physics field.

[0014] Optionally, the step of decomposing the input target surface into multiple surface patch pieces and constructing overlapping regions between adjacent surface patch pieces includes: Perform geometric preprocessing on the input target surface to obtain the preprocessed surface; Extract geometric features from the preprocessed surface; Based on the geometric features, the discrete units of the surface are clustered using a graph neural network or attention mechanism model to obtain the soft partitioning results of the surface. The soft partitioning results are converted into surface atlas patches with clear boundaries, and the adjacency relationship between the surface atlas patches is established. Based on the adjacency relationship, an overlapping region is constructed between adjacent surface patch.

[0015] Optionally, constructing a parametric mapping from the surface atlas patch to a unified two-dimensional reference domain for each surface atlas patch, and calculating the geometric distortion information of the parametric mapping, includes: For each surface atlas patch, a mapping from that surface atlas patch to a unified two-dimensional reference domain is constructed to obtain the parametric mapping; The determinant of the Jacobian matrix of the parameterized mapping is constrained to be greater than zero, and the angular distortion and area distortion of the parameterized mapping are controlled. Based on the parameterized mapping, calculate the geometric distortion information of the parameterized mapping; The geometric distortion information is used to determine whether the parametric distortion of each surface patch exceeds the threshold. If it exceeds the threshold, the surface patch is reparametrically mapped or the mapping boundary is adjusted until the distortion meets the requirements.

[0016] Optionally, the step of writing back the local predicted physics field from the grid points to the corresponding positions on the target surface through the inverse mapping of the parameterized mapping, to obtain the surface write-back field for each surface patch, includes: For any target point on the target surface, the parameter coordinates of the target point in the unified two-dimensional reference domain are determined by the inverse mapping; Among the grid points, determine multiple grid points adjacent to the parameter coordinates; The predicted physical field value of the target point is calculated using bilinear interpolation or higher-order interpolation methods based on the local predicted physical field values ​​at adjacent grid points. The calculated predicted physical field value is assigned to the target point. The above operation is performed on all target points within the coverage area of ​​the surface atlas patch to obtain the surface write-back field of each surface atlas patch.

[0017] Optionally, constructing a weighted fusion weight based on the geometric distortion information within the overlapping region includes: For each target point within the overlapping region, determine all surface patch maps covering that target point; For each surface patch covering the target point, obtain the distance from the target point to the boundary of the surface patch, and the distortion degree index corresponding to the surface patch in the geometric distortion information; Based on the distance and the distortion index, a weighted fusion weight is constructed for each covered surface patch at the target point; wherein, the smaller the distortion index and the larger the distance, the larger the constructed weighted fusion weight.

[0018] Optionally, the step of fusing the surface write-back fields of all surface atlas patches using the weighted fusion weights to obtain a globally continuous predicted physics field includes: For each target point on the target surface, determine all surface atlas patches covering the target point, and obtain the surface write-back field value and corresponding weighted fusion weight of each covered surface atlas patch at the target point; The obtained surface write-back field values ​​are weighted and summed or weighted and averaged, and the calculation result is used as the fusion prediction value of the target point; For target points that are only covered by a single surface atlas patch, the surface write-back field value of that surface atlas patch is directly used as the fusion prediction value; Gradient uniformity correction or smoothing correction is performed on the fused global prediction values ​​to obtain a globally continuous predicted physics field and output it.

[0019] Optionally, the device further includes a neural operator training module for: The input target surface, working conditions, and corresponding physical field true data are used to construct training samples; Define a multi-objective loss function, which includes: data term error between the predicted physical field and the true value, consistency error of predicted values ​​of adjacent surface plot patches in the overlapping region, and gradient jump error at the boundary of adjacent surface plot patches; The neural operator is optimized using the multi-objective loss function until the loss converges.

[0020] Thirdly, embodiments of this application provide a computer device, including: a processor, a memory, and a bus. The memory stores machine-readable instructions executable by the processor. When the computer device is running, the processor communicates with the memory via the bus. When the machine-readable instructions are executed by the processor, they perform the steps of the complex surface physics field prediction method described in any of the optional embodiments of the first aspect above.

[0021] Fourthly, embodiments of this application provide a computer-readable storage medium storing a computer program, which, when executed by a processor, performs the steps of the complex surface physics prediction method described in any of the optional embodiments of the first aspect.

[0022] The technical solution provided in this application includes, but is not limited to, the following beneficial effects: Decomposing the input target surface into multiple surface patches and constructing overlapping regions between adjacent surface patches can reduce the geometric complexity of a single surface patch, providing a foundation for the construction of subsequent low-distortion parameterized mappings. At the same time, the overlapping regions between adjacent patches provide a transition interval for the smooth fusion of multi-patch prediction results, avoiding numerical jumps in the global physics field at patch boundaries.

[0023] For each surface atlas patch, a parametric mapping from the surface atlas patch to a unified two-dimensional reference domain is constructed, and the geometric distortion information of the parametric mapping is calculated. This allows for optimization of the quality of the parametric mapping based on the geometric characteristics of different patches, effectively controlling the degree of parametric distortion in a single patch. At the same time, the calculated geometric distortion information provides a reliable basis for subsequent distortion-aware model prediction and the construction of weighted fusion weights.

[0024] Grid points are generated on the unified two-dimensional reference domain. The three-dimensional coordinates of the grid points, the geometric distortion information, and the operating conditions are encoded into an input tensor. A neural operator is used to infer on the unified two-dimensional reference domain, and the local predicted physics field of each surface patch is output. This can adapt to the processing requirements of the neural operator for regular computation domains. At the same time, the geometric distortion information is incorporated into the input tensor, so that the neural operator inference process can perceive the influence of parameterized distortion on the physics field distribution, effectively improving the accuracy of the local predicted physics field of each patch.

[0025] By inverse mapping of the parameterized mapping, the local predicted physical field is written back from the grid points to the corresponding positions of the target surface, resulting in the surface write-back field of each surface patch. This ensures that the prediction results in the reference domain correspond precisely to the geometric positions of the original surface, and obtains a single-patch surface write-back field that matches the discrete points of the surface one by one, providing accurate basic data for subsequent global fusion.

[0026] Within the overlapping region, a weighted fusion weight is constructed based on the geometric distortion information, and the surface write-back fields of all surface atlas patches are fused using the weighted fusion weight to obtain a globally continuous predicted physics field. This allows the prediction results of low-distortion patches to receive higher weights and suppresses the error propagation of high-distortion patches. At the same time, the weighted fusion of the overlapping region eliminates the stitching artifacts at the patch boundaries, resulting in a globally continuous predicted physics field that meets the requirements of engineering applications for the continuity of the physics field.

[0027] In summary, the method of this application achieves high-precision, globally continuous prediction of complex surface physical fields through a closed-loop process of surface decomposition, low-distortion parameterization, distortion-aware neural operator inference, accurate write-back, and weighted fusion, balancing prediction efficiency with the accuracy requirements of engineering applications.

[0028] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0029] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0030] Figure 1 A flowchart of a method for predicting physical fields on complex surfaces provided in Embodiment 1 of this application is shown; Figure 2 A flowchart of an overlapping region construction method provided in Embodiment 1 of this application is shown; Figure 3 A flowchart of a geometric distortion information calculation method provided in Embodiment 1 of this application is shown; Figure 4 A flowchart of a method for determining a surface write-back field provided in Embodiment 1 of this application is shown; Figure 5 A flowchart of a weighted fusion weight construction method provided in Embodiment 1 of this application is shown; Figure 6 A flowchart of a method for determining a predicted physical field provided in Embodiment 1 of this application is shown; Figure 7 A flowchart of a neural operator training method provided in Embodiment 1 of this application is shown; Figure 8 This paper presents a schematic diagram of the overall process of a method for predicting physical fields on complex curved surfaces provided in Embodiment 1 of this application. Figure 9 This paper shows a schematic diagram of the structure of a complex curved surface physics field prediction device provided in Embodiment 2 of this application; Figure 10 A schematic diagram of the structure of a computer device provided in Embodiment 3 of this application is shown. Detailed Implementation

[0031] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application 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. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely represents selected embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0032] Example 1 To facilitate understanding of this application, the following is combined with... Figure 1 The flowchart of the method for predicting physical fields on complex surfaces provided in Embodiment 1 of this application illustrates Embodiment 1 in detail.

[0033] See Figure 1 As shown, Figure 1 A flowchart of a method for predicting the physical field of a complex curved surface provided in Embodiment 1 of this application is shown, wherein the method includes steps S101 to S105: S101: Decompose the input target surface into multiple surface patches (patch, surface patch block), and construct overlapping regions between adjacent surface patches.

[0034] Specifically, the target surface (Manifold, manifold / target surface) is the result of triangular mesh, point cloud reconstructed surface, or CAD surface discretization. Before decomposition, standardized geometric preprocessing is performed: degenerate triangular patches with an area close to 0 and isolated unconnected patches are accurately removed to avoid numerical singularities during parameterization; the normal directions of all vertices of the surface are unified to prevent geometric feature calculation errors caused by normal confusion; topological defects such as small cracks and holes on the surface are repaired to ensure the overall connectivity of the surface; and boundary loops and sharp edges with curvature abrupt changes on the surface are accurately detected to provide key geometric boundary basis for subsequent partitioning.

[0035] Multi-dimensional geometric features are extracted from the preprocessed surface: vertex 3D coordinates, unit normal vector, mean curvature, Gaussian curvature, and normal rate of change. These features comprehensively characterize the local curvature, orientation changes, and geometric abrupt changes of the surface, serving as the core input of the partitioning model. Subsequently, a learning-based partitioning model (graph neural network clustering / attention mechanism partitioning model) is adopted, using a grid as the graph structure and geometric features as node attributes to automatically cluster the discrete units of the surface and output soft partitioning results.

[0036] The soft partitioning result is the probability distribution of each discrete unit belonging to different patches. Then, through connected component extraction and graph clustering algorithms, the probability distribution is transformed into a set of geometrically connected and clearly defined hard partition patches. (Patch Set, a collection of surface atlas blocks), and simultaneously construct a patch adjacency graph to record the correspondence between each pair of adjacent patches; the generated patches strictly satisfy the topological approximation of a disk shape, simple geometric structure, and no narrow and elongated high distortion shape; an overlapping region is constructed between adjacent patches, with a fixed width of 8% of the average patch diameter, to provide a smooth transition interval for subsequent global weighted fusion.

[0037] S102: For each surface atlas patch, construct a parametric mapping from the surface atlas patch to a unified two-dimensional reference domain, and calculate the geometric distortion information of the parametric mapping.

[0038] Specifically, for each patch, a parametric mapping is constructed using quasi-conformal / low-distortion parameterization methods (LSCM (Least Squares Conformal Mapping), ARAP (As-Rigid-As-Possible Mapping), and harmonic mapping). ;in For the first Parametric mapping of a surface atlas patch. For the first A surface atlas patch. To unify the two-dimensional reference domain, it is uniformly set as a unit square. Alternatively, a unit disk can be used to ensure that all patches are mapped to a reference domain of the same size, adapting to batch processing by neural operators; the reference domain coordinates are denoted as... , complex form This is used for subsequent Beltrami coefficient calculations.

[0039] Define the inverse parametric representation from the reference domain to the surface:

[0040] in: Reference domain The coordinate points are mapped onto a three-dimensional coordinate vector on the surface; : Parameterized mapping The inverse mapping is used for writing back the prediction results; The three coordinate components of a three-dimensional rectangular coordinate system on a curved surface; : Two-dimensional regularization parameters for a unified two-dimensional reference domain; : Reference domain complex parameters, by definition.

[0041] Calculating the Jacobian matrix based on parameterized mapping Characterizes the local stretching and rotation properties of the mapping: in: : No. A Jacobian matrix with dimensions of 3 rows and 2 columns; : For reference domain parameters The first-order partial derivative; : For reference domain parameters The first-order partial derivative.

[0042] Derive the first fundamental form (metric tensor) from the Jacobian matrix. Describes the local metric properties of a surface:

[0043]

[0044]

[0045]

[0046] in: : No. Each metric tensor is a 2×2 symmetric matrix; : The transpose of the Jacobian matrix; The three independent components of a metric tensor; : Vector inner product operation in three-dimensional Euclidean space.

[0047] Calculating the area factor from the metric tensor This enables the conversion between the reference domain and the surface area element.

[0048] in: : No. An area factor, representing the area element of the reference domain. To the surface area element The scaling ratio; Matrix determinant operations; Cross product operation of vectors in three-dimensional space; L2 norm (modulus) operation on vectors; : A tiny area element on the original surface.

[0049] Define singular value condition number Quantify the degree of area distortion:

[0050] in: : No. The condition number of the metric tensor is such that a larger value indicates a more severe area distortion. The largest singular value of the Jacobian matrix; : The smallest singular value of the Jacobian matrix.

[0051] Define Beltrami coefficient Quantitative distortion level:

[0052] in: : No. Each Beltrami coefficient satisfies Time mapping is non-reflective, direction-preserving, and approximate angle-preserving; For complex parameters The first-order partial derivative; For complex conjugate parameters The first-order partial derivative.

[0053] Strictly constrain distortion during parameterization: forced Ensure that the mapping is locally bijective and without flipping or overlapping; control Suppress angular distortion; limit Upper limit, reduce area distortion; final output This information serves as complete geometric distortion information and is used for subsequent distortion compensation.

[0054] S103: Generate grid points on the unified two-dimensional reference domain, encode at least the three-dimensional coordinates of the grid points, the geometric distortion information, and the information of the working conditions into an input tensor, use neural operators to infer on the unified two-dimensional reference domain, and output the local predicted physics field of each surface patch.

[0055] Specifically, in the unified reference domain A regular uniform grid is generated with a uniform grid size (e.g., 512×512) to ensure that the dimensions of the input tensors for all patches are consistent. Then, geometric conditional encoding is performed to fuse geometric information, distortion information, and working condition information into the input tensor, completely abandoning the unreasonable assumption that "the reference domain is a flat Euclidean domain".

[0056] The input tensor channels include: 3D coordinates (3 channels), unit normal vector (3 channels), mean curvature and Gaussian curvature (2 channels), Jacobian matrix components, metric tensor components, area factor, condition number, Beltrami coefficient modulus (distortion information channel), and operating conditions (incoming flow velocity, Reynolds number, yaw angle, 1 channel). All channel data are aligned point-by-point on the reference domain grid points to fully characterize the surface geometry and distortion properties.

[0057] The neural operators selected are either FNO (Fourier Neural Operator) or UNO (U-shaped Neural Operator), and a shared backbone network structure is adopted. At the same time, patch type encoding is introduced for conditional modulation to adapt to the geometric distortion differences of different patches. It supports GPU parallel batch inference, which greatly improves the prediction efficiency of multiple patches.

[0058] The neural operator outputs a locally predicted physical field, with the core being the surface pressure coefficient. The formula is defined as follows:

[0059] in: Surface pressure coefficient, representing the core output of the locally predicted physical field; : Static pressure value of curved surface; : Static pressure of the far-field incoming flow; : Incoming air density; Far-field incoming flow velocity; It can also output a local shear stress field to meet the needs of multiphysics prediction.

[0060] S104: By inverse mapping of the parameterized mapping, the local predicted physical field is written back from the grid points to the corresponding position of the target surface to obtain the surface write-back field of each surface patch.

[0061] Specifically, call the inverse mapping of the parameterized mapping. This inverse mapping is guaranteed to be invertible based on parametric bijectivity and is unambiguous; it accurately maps the local predicted physics field at the regular grid points of the reference domain back to the original surface. Corresponding points on Establish a one-to-one correspondence between the reference domain predicted values ​​and the actual positions of the surface.

[0062] During the write-back process, the interpolation method is adapted as follows: bilinear interpolation is used in areas with normal curvature to balance computational efficiency and mapping accuracy; high-curvature and high-gradient areas (such as corners and edges) are interpolated with higher order to reduce interpolation errors; the interpolation calculation is applied to the vertices, face centers or sampling points of the surface to ensure that the write-back results fit the surface discrete accuracy.

[0063] Traversing the first Each patch covers all discrete points on the surface. The inverse mapping, interpolation, and assignment operations are performed point by point, and the final output is a surface write-back field that fully covers the geometry of the patch, providing single-patch prediction results for subsequent global fusion.

[0064] S105: Within the overlapping area, a weighted fusion weight is constructed based on the geometric distortion information, and the weighted fusion weight is used to fuse the surface write-back fields of all surface atlas patches to obtain a globally continuous predicted physical field.

[0065] Specifically, an anisotropic PoU (Partition of Unity) weighted fusion strategy is adopted, and the fusion weight is jointly determined by three core factors: patch boundary distance, local distortion degree, and geometric continuity of adjacent patches. The weight design follows the principle of "low distortion priority and central region priority", with patches with smaller distortion and farther away from the boundary having greater weight.

[0066] The fusion weights have three key characteristics: the sum of the weights is always 1 (unit decomposition), the weights decay smoothly from the center of the patch to the boundary, and the weights are adaptively adjusted according to the degree of distortion (anisotropy). The weight allocation suppresses the error propagation of high-distortion patches and amplifies the reliable prediction results of low-distortion patches.

[0067] After fusion, the global physics field reaches an approximation at the patch boundary. It is continuous and effectively eliminates splicing artifacts; the fusion result can be directly used to calculate global physical quantities through surface integrals, including drag coefficient, pressure drag component, and surface load resultant force, which can be directly adapted to the iterative needs of industrial shape design in automobiles, aerospace and other industries.

[0068] In an optional implementation, see Figure 2 As shown, Figure 2The flowchart illustrates a method for constructing overlapping regions according to Embodiment 1 of this application, wherein the step of decomposing the input target surface into multiple surface patch pieces and constructing overlapping regions between adjacent surface patch pieces includes steps S201 to S205: S201: Perform geometric preprocessing on the input target surface to obtain the preprocessed surface.

[0069] Specifically, the preprocessing performs refined and standardized operations: degenerate triangles with an area close to 0 and isolated, unconnected faces are screened and removed one by one to avoid numerical anomalies during subsequent parameterization and partitioning; the normal direction of all vertices of the surface is unified to eliminate the problem of reversed normals; topological defects such as tiny cracks and holes on the surface are repaired to ensure that the surface is connected and unbroken; and the boundary loops and sharp edges with abrupt curvature changes on the surface are accurately identified and marked to provide clear geometric boundary references for partitioning.

[0070] S202: Extract geometric features from the preprocessed surface.

[0071] Specifically, the geometric features of the surface in all dimensions are extracted: the three-dimensional rectangular coordinates of the vertex, the unit normal vector, the mean curvature, the Gaussian curvature, and the rate of change of the normal. These features respectively characterize the surface position, orientation, local curvature degree, and the degree of curvature change, comprehensively covering the geometric characteristics of the surface and providing complete input for the partitioned model.

[0072] S203: Based on the geometric features, cluster the discrete units of the surface using a graph neural network or attention mechanism model to obtain the soft partitioning results of the surface.

[0073] Specifically, a graph neural network model is constructed using the surface mesh as the graph structure and geometric features as node attributes; or an attention mechanism model is adopted to automatically focus on key areas such as abrupt changes in surface curvature and boundaries; the model performs probabilistic clustering on the discrete units of the surface and outputs soft partitioning results, that is, the probability distribution of each discrete unit belonging to different patches, avoiding hard partitioning boundaries that abruptly cut off the geometric continuity of the surface.

[0074] S204: Convert the soft partitioning result into a surface atlas patch with clear boundaries, and establish the adjacency relationship between the surface atlas patches.

[0075] Specifically, connected component extraction and graph clustering algorithms are used to transform the probability distribution of soft partitions into geometrically connected and clearly defined hard partition patches. Each patch ensures a simple geometric structure and a topologically approximately disk-shaped structure. A patch adjacency graph is constructed to accurately record the correspondence and adjacent boundary range of each pair of adjacent patches, providing a topological association basis for subsequent overlapping region construction, parameterization, and fusion.

[0076] S205: Based on the adjacency relationship, construct overlapping regions between adjacent surface patch patches.

[0077] Specifically, adjacent patch pairs are determined based on the patch adjacency graph. At the boundary of each pair of adjacent patches, the intersection-expanded overlapping region is constructed. The width of the overlapping region is strictly set to 8% of the average diameter of the patch to ensure a smooth transition between adjacent patches. The overlapping region provides an effective transition interval for subsequent PoU weighted fusion, avoiding numerical jumps in the global physics field at the patch boundary.

[0078] In an optional implementation, see Figure 3 As shown, Figure 3 The flowchart illustrates a geometric distortion information calculation method provided in Embodiment 1 of this application. The method involves constructing a parametric mapping from each surface patch to a unified two-dimensional reference domain, and calculating the geometric distortion information of the parametric mapping, including steps S301-S304: S301: For each surface atlas patch, construct a mapping from the surface atlas patch to a unified two-dimensional reference domain to obtain a parametric mapping.

[0079] Specifically, harmonic mapping and Tutte mapping are first used to quickly generate initial parameterized mappings and initially establish a one-to-one correspondence between the patch and the unified reference domain. Then, a quasi-conformal optimization algorithm is used to iteratively adjust the mappings to adapt to the local curvature distribution of the patch, gradually reducing the mapping distortion and laying the foundation for low-distortion parameterization.

[0080] S302: Constrain the determinant of the Jacobian matrix of the parameterized mapping to be greater than zero, and control the angular distortion and area distortion of the parameterized mapping.

[0081] Specifically, mandatory constraints This ensures that the parametric mapping is locally bijective, without reflections or overlaps, and strictly maintains the original topological structure of the surface; through constraints Effectively control mapping angle distortion and ensure approximate angle preservation; through constraints The upper limit suppresses distortion of the mapped area and avoids excessive stretching or compression in certain areas.

[0082] S303: Calculate the geometric distortion information of the parameterized mapping based on the parameterized mapping.

[0083] Specifically, complete geometric distortion information is calculated point by point: Jacobian matrix, metric tensor, area factor, metric tensor condition number, and Beltrami coefficient modulus; all distortion information is calculated synchronously on the regular grid points of the reference domain, with no missing data; the calculation results are directly used as the distortion compensation channel for the input tensor of the neural operator, realizing explicit distortion modeling.

[0084] S304: Use the geometric distortion information to determine whether the parametric distortion of each surface atlas patch exceeds the threshold. If it exceeds the threshold, reparametrically map or adjust the mapping boundary of the surface atlas patch until the distortion meets the requirements.

[0085] Specifically, set a strict distortion threshold: The distortion information of each patch is checked one by one. For patches that exceed the threshold, a re-anchoring operation is performed: the position of the patch boundary anchor point is adjusted, the mapping boundary constraint is optimized, and the "parameterization-distortion calculation-threshold judgment" process is repeated until the distortion index of all patches meets the standard.

[0086] In an optional implementation, see Figure 4 As shown, Figure 4 The flowchart illustrates a method for determining a surface write-back field according to Embodiment 1 of this application. The method involves writing back the local predicted physical field from the grid points to the corresponding positions on the target surface using the inverse mapping of the parameterized mapping, thereby obtaining the surface write-back field for each surface patch. This includes steps S401-S404. S401: For any target point on the target surface, determine the parameter coordinates of the target point in the unified two-dimensional reference domain through the inverse mapping.

[0087] Specifically, for the original surface any discrete point on Call the inverse mapping Based on the bijective invertibility of the parametric mapping, the point is uniquely determined in the reference domain. Parameter coordinates on The coordinate error during the mapping process is controlled within the accuracy range of the reference domain grid to ensure accurate positional correspondence.

[0088] S402: Among the grid points, determine a plurality of grid points adjacent to the parameter coordinates.

[0089] Specifically, the reference domain is a uniform regular grid, and the target parameter coordinates are... The nearest neighboring grid points are selected as the basic sampling points for interpolation calculation; the selection of sampling points takes into account both interpolation efficiency and local fitting accuracy, and adapts to the characteristics of regular grid distribution.

[0090] S403: Using bilinear interpolation or higher-order interpolation methods, calculate the predicted physical field value of the target point based on the local predicted physical field values ​​at adjacent grid points.

[0091] Specifically, bilinear interpolation is preferred for regions with normal curvature because it is fast and accurate enough to meet the needs of industrial applications. Higher-order interpolation is used for regions with high curvature and high gradient (corners, edges, and abrupt curvature changes) to reduce interpolation errors and improve the accuracy of local physical field prediction. The interpolation calculation is strictly based on the predicted values ​​of adjacent grid points to ensure the reliability of the results.

[0092] S404: Assign the calculated predicted physical field value to the target point, and perform the above operation on all target points within the coverage area of ​​the surface atlas patch to obtain the surface write-back field of each surface atlas patch.

[0093] Specifically, traversing the first Each patch covers all discrete points (vertices, face centers, and sampling points) on the surface, completing the entire process of "inverse mapping - adjacent grid point selection - interpolation calculation - assignment" point by point; finally, it outputs a continuously distributed surface write-back field that fully covers the geometric range of the patch, ensuring that the prediction results of a single patch are complete and without omissions or biases.

[0094] In an optional implementation, see Figure 5 As shown, Figure 5 The flowchart illustrates a weighted fusion weight construction method provided in Embodiment 1 of this application, wherein the step of constructing weighted fusion weights based on the geometric distortion information within the overlapping region includes steps S501-S503: S501: For each target point within the overlapping region, determine all surface patch maps covering that target point.

[0095] Specifically, based on the pre-built patch adjacency graph and surface space index structure, spatial inclusion determination is performed on each discrete target point in the overlapping area. First, candidate covering patches are quickly filtered by the axial bounding box of the patch to exclude patches with no intersection. Then, the ray method is used to accurately determine whether the target point is within the geometric projection range of the patch.

[0096] The overlapping region is the boundary extension region of adjacent patches. A single target point is only covered by 2 to 3 geometrically adjacent patches. Through a dual judgment mechanism, all patches covering the target point are accurately identified, with no omissions or over-selections, ensuring that the multi-source prediction results can be fully involved in the fusion.

[0097] S502: For each surface patch covering the target point, obtain the distance from the target point to the boundary of the surface patch, and the distortion degree index corresponding to the surface patch in the geometric distortion information.

[0098] Specifically, the boundary distance is calculated using the shortest distance in three-dimensional Euclidean space: traverse all boundary edges and vertices of the patch, calculate the perpendicular distance from the target point to the boundary edge and the straight-line distance to the boundary vertex, and take the minimum value as the distance from the target point to the patch boundary. This distance is normalized to the interval [0,1] to quantify the center / edge position of the target point within the patch.

[0099] The distortion level index is selected using a dual-index selection method, prioritizing the Beltrami coefficient modulus. When there are no valid Beltrami coefficients, the condition number of the metric tensor should be used. Both types of indicators are directly retrieved from geometric distortion information and normalized to the maximum and minimum values. The smaller the indicator value, the lower the parameterized distortion of the patch and the higher the reliability of the prediction result.

[0100] S503: Based on the distance and the distortion index, construct a weighted fusion weight for each covered surface patch at the target point; wherein, the smaller the distortion index and the larger the distance, the larger the constructed weighted fusion weight.

[0101] Specifically, the weight construction strictly follows the principle of "low distortion priority and central region priority", and adopts a product-type anisotropic weight formula: basic weight = normalized boundary distance × (1 - normalized distortion index); the basic weight of all patches covering target points is normalized, and the final weighted fusion weight = basic weight of a single patch / sum of basic weights of all covered patches; this construction method gives greater weight to patches with smaller distortion index and farther distance from the boundary, and the sum of weights of all covered patches is always 1, which satisfies the unit decomposition characteristic and ensures the physical consistency and numerical stability of the fusion result.

[0102] In an optional implementation, see Figure 6 As shown, Figure 6 The flowchart of a method for determining a predicted physics field provided in Embodiment 1 of this application is shown. The step of fusing the surface write-back fields of all surface atlas patches using the weighted fusion weights to obtain a globally continuous predicted physics field includes steps S601-S604: S601: For each target point on the target surface, determine all surface patch that covers the target point, and obtain the surface write-back field value and corresponding weighted fusion weight of each covered surface patch at the target point.

[0103] Specifically, the process traverses all discrete points of the original surface in the order of the surface vertex index, and accurately distinguishes between overlapping areas (multiple patch coverage) and non-overlapping areas (single patch coverage) using a spatial inclusion determination algorithm. For each target point, the surface write-back field prediction values ​​of all covering patches and the weighted fusion weights calculated by S503 are retrieved synchronously from the pre-allocated memory cache. A point-to-point aligned data storage structure is adopted to ensure that the field values ​​and weights correspond one-to-one, thus preparing complete and misaligned input data for subsequent weighted fusion.

[0104] S602: Perform a weighted summation or weighted average on the obtained surface write-back field values, and use the calculation result as the fusion prediction value of the target point.

[0105] Specifically, for target points covered by multiple patches in the overlapping area, a weighted summation formula is used to calculate the fused prediction value: ,in The number of patches to cover the target points. For the first The weighted fusion weight of each patch For the first The surface write-back field value of each patch at the target point. This is the final fused prediction value; this calculation method can effectively suppress the error propagation of high-distortion patches, amplify the reliable prediction contribution of low-distortion patches, preserve the local features of the physical field during the fusion process, and improve the overall accuracy of the global prediction results.

[0106] S603: For target points that are only covered by a single surface atlas patch, the surface write-back field value of that surface atlas patch is directly used as the fusion prediction value.

[0107] Specifically, target points in non-overlapping regions belong to only a single patch, without interference from multiple patch prediction values. The field value written back from a single patch already meets the prediction accuracy requirements. The surface write-back field value of the patch at the target point is directly read and assigned as the fused prediction value, eliminating the need for weighted calculations, reducing redundant computations, and ensuring the continuity, consistency, and accuracy of the physical field values ​​in non-overlapping regions.

[0108] S604: Perform gradient uniformity correction or smoothing correction on the global prediction values ​​obtained after fusion to obtain a globally continuous predicted physics field and output it.

[0109] Specifically, gradient uniformity correction employs a least-squares optimization algorithm to construct a gradient loss function at the patch boundary, minimizing the gradient jump difference between adjacent patch predictions, thus achieving approximation of the global physics field at the patch boundary. The order is continuous; the smoothing correction adopts the Gaussian filtering algorithm, sets a 3×3 Gaussian kernel, and takes the standard deviation as the average grid side length of the surface. The global prediction value is low-pass filtered to smooth out small numerical fluctuations and splicing artifacts.

[0110] After calibration, the continuity and smoothness of the global physical field are verified, and the global continuous physical field data is finally output to support subsequent surface integral calculations of key industrial indicators such as drag coefficient, pressure drag, and surface load resultant force.

[0111] In an optional implementation, see Figure 7 As shown, Figure 7 A flowchart of a neural operator training method provided in Embodiment 1 of this application is shown, wherein the method further includes steps S701-S703 for training the neural operator: S701: Construct training samples from the input target surface, working conditions, and corresponding physical field ground truth data.

[0112] Specifically, the ground truth data uses CFD (Computational Fluid Dynamics) numerical solutions, with ANSYS Fluent as the solution tool. The turbulence model used is RNG k-ε (Renormalization Group k-ε Turbulence Model), which outputs ground truth values ​​for surface pressure field, shear stress field, and drag coefficient. The operating conditions cover different incoming flow velocities, Reynolds numbers, and yaw angles. The target surfaces include industrial surfaces with different shapes, curvatures, and topologies (vehicle bodies, wheel hubs, blades, etc.). The samples are divided into training, validation, and test sets according to proportions to ensure the model's generalization ability.

[0113] S702: Define a multi-objective loss function, which includes: the data term error between the predicted physical field and the true value, the consistency error of the predicted values ​​of adjacent surface patches in the overlapping region, and the gradient jump error at the boundary of adjacent surface patches.

[0114] Specifically, the complete multi-objective loss function formula is as follows:

[0115] in: Total loss function, used for model parameter optimization; Data item error measures the point-to-point error between the predicted physical field and the true value. : Consistency error in overlapping areas, ensuring smooth connection of prediction results between adjacent patches; : Boundary gradient jump error, reduce patch boundary gradient discontinuity; The residual term of PDE (Partial Differential Equation) introduces physical equation constraints to enhance the physical consistency of prediction results. : Global integral constraint term, fitting error of global physical quantities such as drag coefficient; : Preset weight coefficients for each loss term to balance the impact of different loss terms on model optimization.

[0116] S703: Optimize the parameters of the neural operator using the multi-objective loss function until the loss converges.

[0117] Specifically, the Adam or SGD optimization algorithm is selected, and training set samples are input in batches to iteratively update the FNO / UNO network parameters. During the training process, the training set loss and validation set loss are monitored simultaneously to avoid model overfitting. When the training set loss and validation set loss decrease steadily for several consecutive rounds and tend to stabilize, the loss is determined to be converged, training is stopped, and the optimal model parameters are saved. After training, the model can achieve inference at the second level, which is suitable for large-scale industrial shape design iteration scenarios.

[0118] The above details the specific implementation details of each optional implementation step of the method in this application. To present the overall implementation logic and complete technical chain of the complex surface physics field prediction method of this application more clearly and intuitively, the following section, in conjunction with the appendix, provides further details. Figure 8 Provide a unified explanation of the overall process.

[0119] See Figure 8 As shown, Figure 8 The diagram illustrates the overall flow of a complex surface physics prediction method provided in Embodiment 1 of this application. This flow achieves high-precision physics prediction through a closed-loop process of "surface decomposition - parameterization - neural operator inference - global fusion". The specific steps are explained below: S1: Surface mesh and working conditions. As the input step of the process, it obtains the discrete mesh model of the target surface and the corresponding working conditions, providing basic data support for all subsequent processing steps.

[0120] S2: Atlas generation: geometry preprocessing, patch collection The input surface undergoes standardized geometric preprocessing. Then, the surface is decomposed into multiple topologically approximate disk-shaped surface map blocks using a learning-based partitioning method, forming a set of surface map blocks. At the same time, the adjacency relationship between adjacent surface map blocks is established and overlapping regions are constructed.

[0121] S3: Calculate the quasi-conformal mapping With inverse mapping Check and optimize parameterization quality, and reprocess unqualified patches. For each surface atlas block, construct a quasi-conformal parametric mapping and its inverse mapping (i.e., in the figure). ,in , For reference domain coordinates, (For the three-dimensional coordinates of the surface); calculate distortion information such as the Jacobian matrix, metric tensor, and Beltrami coefficients; check the parameterization quality; if the distortion of the surface atlas block exceeds the preset threshold, re-parameterize the mapping or adjust the mapping boundary until the distortion meets the requirements.

[0122] S4: Reference Field Generate a regular mesh, compute the Jacobian, and measure the tensor. , , , …Combining the input tensor with the working conditions, a regular uniform grid is generated on a unified two-dimensional reference domain; based on parametric mapping, complete geometric distortion information such as the Jacobian matrix, metric tensor, area factor, condition number, Beltrami coefficient modulus, etc. are calculated; the three-dimensional coordinates, normal vectors, curvature information, distortion information and working conditions of the grid points are encoded into the input tensor to realize geometric conditional encoding and provide input for neural operator inference.

[0123] S5: Reference Domain Neural operator inference: Input tensors are fed into FNO / UNO networks to obtain local predictions and prediction uncertainties. The constructed input tensors are then fed into Fourier neural operators or U-shaped neural operator networks to perform parallel inference on the reference domain. The local predicted physics field and prediction uncertainty of each surface map block are output, providing single-surface map block prediction results for subsequent write-back and global fusion.

[0124] S6 & 7: Write-back to surface points + global fusion: Anisotropic PoU weighted fusion (boundary distance, geometric distortion, prediction uncertainty) is performed in the overlapping region to obtain a global continuous field. First, through parametric inverse mapping, the local predicted physics field of the reference domain grid points is written back to the corresponding position of the target surface to obtain the surface write-back field of each surface atlas block. Then, in the overlapping region of adjacent surface atlas blocks, anisotropic unit decomposition weighted fusion weights are constructed by combining the distance from the target point to the boundary of the surface atlas block, the degree of geometric distortion, and the prediction uncertainty. The surface write-back fields of all surface atlas blocks are fused to obtain a globally continuous predicted physics field, effectively suppressing stitching artifacts.

[0125] S8: Output Results: Outputs global physical field (such as pressure cloud map), uncertainty map, high-risk area marker, global integral quantity (such as drag coefficient). Based on the fused global continuous field, it outputs results in various forms, including global physical field visualization (such as pressure cloud map), prediction uncertainty map, high-risk area marker, and global integral physical quantity such as drag coefficient, adapting to the multi-dimensional needs of automotive, aerospace and other industrial shape design iterations.

[0126] Example 2 See Figure 9 As shown, Figure 9 A schematic diagram of a complex curved surface physics field prediction device provided in Embodiment 2 of this application is shown, wherein the device includes: The overlapping region construction module 901 is used to decompose the input target surface into multiple surface patches and construct overlapping regions between adjacent surface patches. The geometric distortion information calculation module 902 is used to construct a parametric mapping from the surface atlas patch to a unified two-dimensional reference domain for each surface atlas patch, and to calculate the geometric distortion information of the parametric mapping. The local predicted physics output module 903 is used to generate grid points on the unified two-dimensional reference domain, encode at least the three-dimensional coordinates of the grid points, the geometric distortion information and the working condition information into an input tensor, use neural operators to infer on the unified two-dimensional reference domain, and output the local predicted physics field of each surface patch. The surface write-back field determination module 904 is used to write back the local predicted physical field from the grid points to the corresponding positions of the target surface through the inverse mapping of the parameterized mapping, so as to obtain the surface write-back field of each surface atlas patch. The global prediction physics field determination module 905 is used to construct a weighted fusion weight based on the geometric distortion information within the overlapping area, and to fuse the surface write-back fields of all surface atlas patches using the weighted fusion weight to obtain a globally continuous prediction physics field.

[0127] In an optional implementation, the step of decomposing the input target surface into multiple surface patch pieces and constructing overlapping regions between adjacent surface patch pieces includes: Perform geometric preprocessing on the input target surface to obtain the preprocessed surface; Extract geometric features from the preprocessed surface; Based on the geometric features, the discrete units of the surface are clustered using a graph neural network or attention mechanism model to obtain the soft partitioning results of the surface. The soft partitioning results are converted into surface atlas patches with clear boundaries, and the adjacency relationship between the surface atlas patches is established. Based on the adjacency relationship, an overlapping region is constructed between adjacent surface patch.

[0128] In an optional implementation, constructing a parametric mapping from the surface atlas patch to a unified two-dimensional reference domain for each surface atlas patch, and calculating the geometric distortion information of the parametric mapping, includes: For each surface atlas patch, a mapping from that surface atlas patch to a unified two-dimensional reference domain is constructed to obtain the parametric mapping; The determinant of the Jacobian matrix of the parameterized mapping is constrained to be greater than zero, and the angular distortion and area distortion of the parameterized mapping are controlled. Based on the parameterized mapping, calculate the geometric distortion information of the parameterized mapping; The geometric distortion information is used to determine whether the parametric distortion of each surface patch exceeds the threshold. If it exceeds the threshold, the surface patch is reparametrically mapped or the mapping boundary is adjusted until the distortion meets the requirements.

[0129] In an optional implementation, the step of writing back the local predicted physics field from the grid points to the corresponding positions on the target surface through the inverse mapping of the parameterized mapping, to obtain the surface write-back field for each surface patch, includes: For any target point on the target surface, the parameter coordinates of the target point in the unified two-dimensional reference domain are determined by the inverse mapping; Among the grid points, determine multiple grid points adjacent to the parameter coordinates; The predicted physical field value of the target point is calculated using bilinear interpolation or higher-order interpolation methods based on the local predicted physical field values ​​at adjacent grid points. The calculated predicted physical field value is assigned to the target point. The above operation is performed on all target points within the coverage area of ​​the surface atlas patch to obtain the surface write-back field of each surface atlas patch.

[0130] In an optional implementation, constructing a weighted fusion weight based on the geometric distortion information within the overlapping region includes: For each target point within the overlapping region, determine all surface patch maps covering that target point; For each surface patch covering the target point, obtain the distance from the target point to the boundary of the surface patch, and the distortion degree index corresponding to the surface patch in the geometric distortion information; Based on the distance and the distortion index, a weighted fusion weight is constructed for each covered surface patch at the target point; wherein, the smaller the distortion index and the larger the distance, the larger the constructed weighted fusion weight.

[0131] In an optional implementation, the step of fusing the surface write-back fields of all surface atlas patches using the weighted fusion weights to obtain a globally continuous predicted physics field includes: For each target point on the target surface, determine all surface atlas patches covering the target point, and obtain the surface write-back field value and corresponding weighted fusion weight of each covered surface atlas patch at the target point; The obtained surface write-back field values ​​are weighted and summed or weighted and averaged, and the calculation result is used as the fusion prediction value of the target point; For target points that are only covered by a single surface atlas patch, the surface write-back field value of that surface atlas patch is directly used as the fusion prediction value; Gradient uniformity correction or smoothing correction is performed on the fused global prediction values ​​to obtain a globally continuous predicted physics field and output it.

[0132] In an optional implementation, the device further includes a neural operator training module for: The input target surface, working conditions, and corresponding physical field true data are used to construct training samples; Define a multi-objective loss function, which includes: data term error between the predicted physical field and the true value, consistency error of predicted values ​​of adjacent surface plot patches in the overlapping region, and gradient jump error at the boundary of adjacent surface plot patches; The neural operator is optimized using the multi-objective loss function until the loss converges.

[0133] Example 3 Based on the same application concept, see [link / reference] Figure 10 As shown, Figure 10 This illustration shows a structural schematic diagram of a computer device provided in Embodiment 3 of this application, wherein, as shown... Figure 10 As shown, the computer device 1000 provided in Embodiment 3 of this application includes: The computer device 1000 includes a processor 1001, a memory 1002, and a bus 1003. The memory 1002 stores machine-readable instructions that can be executed by the processor 1001. When the computer device 1000 is running, the processor 1001 and the memory 1002 communicate through the bus 1003. When the machine-readable instructions are executed by the processor 1001, they perform the steps of the complex surface physics field prediction method shown in Embodiment 1 above.

[0134] Example 4 Based on the same concept, this application also provides a computer-readable storage medium storing a computer program, which, when run by a processor, performs the steps of the complex surface physics field prediction method described in any of the above embodiments.

[0135] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the system and apparatus described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0136] The computer program product for predicting the physical field of complex curved surfaces provided in this application includes a computer-readable storage medium storing program code. The instructions included in the program code can be used to execute the methods described in the preceding method embodiments. For specific implementation details, please refer to the method embodiments, which will not be repeated here.

[0137] The complex curved surface physics field prediction device provided in this application embodiment can be specific hardware on a device or software or firmware installed on the device. The implementation principle and technical effects of the device provided in this application embodiment are the same as those in the foregoing method embodiments. For the sake of brevity, any parts not mentioned in the device embodiment can be referred to the corresponding content in the foregoing method embodiments. Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can all be referred to the corresponding processes in the above method embodiments, and will not be repeated here.

[0138] In the embodiments provided in this application, it should be understood that the disclosed apparatus and methods can be implemented in other ways. The apparatus embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. Furthermore, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Additionally, the displayed or discussed mutual couplings, direct couplings, or communication connections may be through some communication interfaces; indirect couplings or communication connections between devices or units may be electrical, mechanical, or other forms.

[0139] 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.

[0140] In addition, the functional units in the embodiments provided in 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.

[0141] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause 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 described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0142] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. In addition, the terms "first", "second", "third", etc. are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0143] Finally, it should be noted that the above-described embodiments are merely specific implementations of this application, used to illustrate the technical solutions of this application, and not to limit them. The protection scope of this application is not limited thereto. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments, or make equivalent substitutions for some of the technical features, within the scope of the technology disclosed in this application; and these modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application. All should be covered within the protection scope of this application. Therefore, the protection scope of this application should be determined by the protection scope of the claims.

Claims

1. A method for predicting physical fields on complex curved surfaces, characterized in that, The method includes: The input target surface is decomposed into multiple surface patch pieces, and overlapping regions are constructed between adjacent surface patch pieces. For each surface atlas patch, construct a parametric mapping from the surface atlas patch to a unified two-dimensional reference domain, and calculate the geometric distortion information of the parametric mapping; Grid points are generated on the unified two-dimensional reference domain. The three-dimensional coordinates of the grid points, the geometric distortion information, and the working condition information are encoded into an input tensor. Neural operators are used to infer on the unified two-dimensional reference domain to output the local predicted physics field of each surface patch. By inverse mapping of the parameterized mapping, the local predicted physical field is written back from the grid points to the corresponding position of the target surface, thus obtaining the surface write-back field of each surface patch. Within the overlapping region, a weighted fusion weight is constructed based on the geometric distortion information, and the weighted fusion weight is used to fuse the surface write-back fields of all surface atlas patches to obtain a globally continuous predicted physics field.

2. The method according to claim 1, characterized in that, The step of decomposing the input target surface into multiple surface patch pieces and constructing overlapping regions between adjacent surface patch pieces includes: Perform geometric preprocessing on the input target surface to obtain the preprocessed surface; Extract geometric features from the preprocessed surface; Based on the geometric features, the discrete units of the surface are clustered using a graph neural network or attention mechanism model to obtain the soft partitioning results of the surface. The soft partitioning results are converted into surface atlas patches with clear boundaries, and the adjacency relationship between the surface atlas patches is established. Based on the adjacency relationship, an overlapping region is constructed between adjacent surface patch.

3. The method according to claim 1, characterized in that, The step of constructing a parametric mapping from each surface atlas patch to a unified two-dimensional reference domain, and calculating the geometric distortion information of the parametric mapping, includes: For each surface atlas patch, a mapping from that surface atlas patch to a unified two-dimensional reference domain is constructed to obtain the parametric mapping; The determinant of the Jacobian matrix of the parameterized mapping is constrained to be greater than zero, and the angular distortion and area distortion of the parameterized mapping are controlled. Based on the parameterized mapping, calculate the geometric distortion information of the parameterized mapping; The geometric distortion information is used to determine whether the parametric distortion of each surface patch exceeds the threshold. If it exceeds the threshold, the surface patch is reparametrically mapped or the mapping boundary is adjusted until the distortion meets the requirements.

4. The method according to claim 1, characterized in that, The inverse mapping of the parameterized mapping, which writes the local predicted physics field back from the grid points to the corresponding positions on the target surface, yields the surface write-back field for each surface patch, including: For any target point on the target surface, the parameter coordinates of the target point in the unified two-dimensional reference domain are determined by the inverse mapping; Among the grid points, determine multiple grid points adjacent to the parameter coordinates; The predicted physical field value of the target point is calculated using bilinear interpolation or higher-order interpolation methods based on the local predicted physical field values ​​at adjacent grid points. The calculated predicted physical field value is assigned to the target point. The above operation is performed on all target points within the coverage area of ​​the surface atlas patch to obtain the surface write-back field of each surface atlas patch.

5. The method according to claim 1, characterized in that, The step of constructing a weighted fusion weight based on the geometric distortion information within the overlapping region includes: For each target point within the overlapping region, determine all surface patch maps covering that target point; For each surface patch covering the target point, obtain the distance from the target point to the boundary of the surface patch, and the distortion degree index corresponding to the surface patch in the geometric distortion information; Based on the distance and the distortion index, a weighted fusion weight is constructed for each covered surface patch at the target point; wherein, the smaller the distortion index and the larger the distance, the larger the constructed weighted fusion weight.

6. The method according to claim 1, characterized in that, The process of fusing the surface write-back fields of all surface atlas patches using the weighted fusion weights to obtain a globally continuous predicted physics field includes: For each target point on the target surface, determine all surface atlas patches covering the target point, and obtain the surface write-back field value and corresponding weighted fusion weight of each covered surface atlas patch at the target point; The obtained surface write-back field values ​​are weighted and summed or weighted and averaged, and the calculation result is used as the fusion prediction value of the target point; For target points that are only covered by a single surface atlas patch, the surface write-back field value of that surface atlas patch is directly used as the fusion prediction value; Gradient uniformity correction or smoothing correction is performed on the fused global prediction values ​​to obtain a globally continuous predicted physics field and output it.

7. The method according to claim 1, characterized in that, The method also includes the step of training a neural operator: The input target surface, working conditions, and corresponding physical field true data are used to construct training samples; Define a multi-objective loss function, which includes: data term error between the predicted physical field and the true value, consistency error of predicted values ​​of adjacent surface plot patches in the overlapping region, and gradient jump error at the boundary of adjacent surface plot patches; The neural operator is optimized using the multi-objective loss function until the loss converges.

8. A device for predicting physical fields on complex curved surfaces, characterized in that, The device includes: The overlapping region construction module is used to decompose the input target surface into multiple surface patches and construct overlapping regions between adjacent surface patches. The geometric distortion information calculation module is used to construct a parametric mapping from the surface atlas patch to a unified two-dimensional reference domain for each surface atlas patch, and to calculate the geometric distortion information of the parametric mapping. The local predicted physics output module is used to generate grid points on the unified two-dimensional reference domain, encode at least the three-dimensional coordinates of the grid points, the geometric distortion information, and the information of the working conditions into an input tensor, use neural operators to infer on the unified two-dimensional reference domain, and output the local predicted physics for each surface patch. The surface write-back field determination module is used to write back the local predicted physical field from the grid points to the corresponding positions of the target surface through the inverse mapping of the parameterized mapping, so as to obtain the surface write-back field of each surface atlas patch. The global predicted physics field determination module is used to construct a weighted fusion weight based on the geometric distortion information within the overlapping region, and to fuse the surface write-back fields of all surface atlas patches using the weighted fusion weight to obtain a globally continuous predicted physics field.

9. A computer device, characterized in that, include: The computer device includes a processor, a memory, and a bus. The memory stores machine-readable instructions executable by the processor. When the computer device is running, the processor communicates with the memory via the bus. When the machine-readable instructions are executed by the processor, they perform the steps of the complex surface physics prediction method as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, performs the steps of the complex surface physics prediction method as described in any one of claims 1 to 7.

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