A physical field prediction method and device, computer equipment and storage medium

Abstract

The application provides a physical field prediction method and device, computer equipment and a storage medium, comprising: firstly obtaining the geometric information and external condition information of an object to be evaluated, sampling the geometric information to obtain the position information and adjacent relationship information of each sampling point, and generating geometric context features. The geometric context features and the external condition information are jointly input into a backbone network model to predict a basic physical field. Then, based on the basic physical field, difference or aggregation is performed in the neighborhood of the sampling points to generate local proxy features. A residual local adapter is constructed, and the above-mentioned multi-class features and adjacent relationship information are input into the residual local adapter to output a local residual correction amount. Finally, the basic physical field and the correction amount are superimposed to obtain a corrected target physical field. By using the above method, the overall accuracy and local fineness of the physical field prediction are improved while ensuring the reasoning efficiency.

Description

Technical Field

[0001] This application relates to the field of intelligent prediction of industrial physical fields, and more specifically, to a physical field prediction method, apparatus, computer equipment, and storage medium. Background Technology

[0002] In industrial sectors such as automotive, aerospace, energy and power, and electronic heat dissipation, physics simulation is a core supporting link for product performance evaluation and structural optimization. Traditional numerical simulation methods obtain the distribution of physical quantities across the entire field by discretely solving the physical partial differential control equations. Although they have high computational accuracy, the solution cycle for a single example is long and the computational resources are consumed in large quantities, making it difficult to support the engineering requirements of rapid iteration of multiple schemes and batch parametric analysis. The industry urgently needs more efficient physics prediction technology to shorten the R&D cycle and reduce simulation costs.

[0003] Currently, data-driven physics prediction technology, represented by global neural operators, is the mainstream solution in this field. Typical examples include Fourier neural operators, geometric perception neural operators, and grid graph neural networks. These models possess function space mapping capabilities and can learn the end-to-end mapping relationship between geometric shape, operating conditions, and physics distribution based on a large number of high-fidelity simulation samples. During the inference phase, they can output the full-field physics prediction results in a very short time, improving computational efficiency by more than two orders of magnitude compared to traditional numerical simulation.

[0004] This type of global neural operator model has a core technical flaw: the model training process takes minimizing the average prediction error across the entire field as the optimization objective, and the optimization weights are tilted towards the large-scale uniform field region, which has a higher proportion. This results in a significant lack of prediction accuracy in key local high-gradient regions such as the boundary layer, flow separation zone, stress concentration zone, and heat source zone. The details of local field changes are prone to excessive smoothing. These regions are often the key parts that determine the core performance and safety margin of the product. Local prediction deviations will directly reduce the engineering reference value of the simulation results and cannot meet the application requirements of high-precision industrial design. Summary of the Invention

[0005] In view of this, the purpose of this application is to provide a physical field prediction method, apparatus, computer equipment and storage medium that improves the overall accuracy and local precision of physical field prediction while ensuring inference efficiency.

[0006] In a first aspect, embodiments of this application provide a physical field prediction method, the method comprising: Obtain geometric and external condition information of the object to be evaluated; Based on the geometric information, sampling is performed to obtain the position information and adjacency relationship information of each sampling point, and geometric context features are generated based on the position information and adjacency relationship information. Using the geometric context features and the external condition information as input, the basic physical field is predicted through the backbone network model. Based on the fundamental physical field, differential or aggregated features are generated within the neighborhood of each sampling point to produce local proxy features. Construct a residual local adapter, input the basic physical field, the geometric context features, the local proxy features, and the adjacency relationship information into the residual local adapter, and output the local residual correction amount; The corrected target physical field is obtained by superimposing the basic physical field with the local residual correction.

[0007] Optionally, the generation of geometric context features includes: Based on the geometric information, sampling is performed in the surface region, near-boundary region, or volume region of the object to be evaluated to obtain a set of sampling points. The coordinates of each sampling point in the set of sampling points in space are used as the location information; The adjacency information is constructed based on the spatial adjacency or grid connection relationship between each sampling point; Based on the location information and adjacency information, calculate at least one of the wall distance, normal vector, and curvature of each sampling point; The location information, the adjacency information, and at least one of the calculated wall distance, normal vector, and curvature are combined to form the geometric context feature.

[0008] Optionally, the external condition information includes at least one of operating parameters, material properties, and boundary conditions; the external condition information serves as the condition input to the backbone network model and participates in the prediction of the basic physical field together with the geometric context features.

[0009] Optionally, the step of using the geometric context features and the external condition information as input to predict the fundamental physical field through the backbone network model includes: The geometric context features are used as the main input to the backbone network model, and the external condition information is used as the condition input to the backbone network model. The backbone network model is used to jointly map the geometric context features and the external condition information, and output the predicted values ​​of the basic physical field of the object to be evaluated at each sampling point.

[0010] Optionally, the construction of the residual local adapter, which inputs the fundamental physics field, the geometric context features, the local proxy features, and the adjacency information into the residual local adapter and outputs a local residual correction, includes: A residual local adapter based on local neighborhood aggregation is constructed, wherein the residual local adapter is used to aggregate information in the local neighborhood of each sampling point; The basic physical field, geometric context features, and local proxy features of the central sampling point, as well as the neighborhood features of each neighboring point of the central sampling point, are jointly input into the residual local adapter; the neighborhood features include the basic physical field, geometric context features, and local proxy features of the neighboring points, as well as the edge features between the central sampling point and the neighboring points. The residual local adapter is used to perform message passing or aggregation on the neighborhood features to update the residual representation at the central sampling point. The dimension of the local residual correction output by the residual local adapter is the same as the dimension of the basic physical field, and a local residual correction is output at each sampling point.

[0011] Optionally, the method further includes: Calculate derived performance indices based on the modified target physics field; Obtain the reference physics field information and reference derived performance indicators of the object to be evaluated; The physical field loss is calculated based on the difference between the corrected target physical field and the reference physical field information; The gradient loss is calculated based on the difference between the local gradient of the modified target physical field and the local gradient of the reference physical field information; The performance loss is calculated based on the difference between the derived performance metric and the reference derived performance metric; Calculate the regularization term loss based on the local residual correction amount; The total loss is obtained by weighted summing of the physical field loss, the gradient loss, the performance loss, and the regularization term loss. The parameters of the backbone network model and the residual local adapter are adjusted based on the total loss.

[0012] Optionally, the method further includes a few-sample rapid adaptation step: Obtain reference physical field information for newly added objects to be evaluated, wherein the number of samples in the reference physical field information is less than the number of reference samples used to train the backbone network model. Freeze the parameters of the backbone network model; Geometric context features are generated by sampling based on the geometric information of the newly added object to be evaluated; Using the geometric context features as input, the basic physical field is predicted through the frozen backbone network model; The local residual correction amount is output through the residual local adapter, and the basic physical field is superimposed with the local residual correction amount to obtain the corrected target physical field; Based on the difference between the corrected target physics field and the reference physics field information, only at least one of the parameters of the residual local adapter, the learnable residual scale parameter, and the derived performance index prediction head is updated, while the parameters of the backbone network model remain frozen.

[0013] Secondly, embodiments of this application provide a physical field prediction device, the device comprising: The acquisition module is used to acquire geometric information and external condition information of the object to be evaluated. The sampling module is used to sample based on the geometric information to obtain the position information and adjacency information of each sampling point, and generate geometric context features based on the position information and adjacency information. The backbone prediction module is used to predict the fundamental physical field through the backbone network model, taking the geometric context features and the external condition information as input. The local proxy construction module is used to perform differential or aggregation within the neighborhood of each sampling point based on the basic physical field to generate local proxy features; The residual adaptation module is used to construct a residual local adapter, inputting the basic physical field, the geometric context features, the local proxy features and the adjacency relationship information into the residual local adapter, and outputting the local residual correction amount; The correction module is used to superimpose the basic physical field with the local residual correction amount to obtain the corrected target physical field.

[0014] Optionally, the sampling module is specifically used to generate geometric context features, including: Based on the geometric information, sampling is performed in the surface region, near-boundary region, or volume region of the object to be evaluated to obtain a set of sampling points. The coordinates of each sampling point in the set of sampling points in space are used as the location information; The adjacency information is constructed based on the spatial adjacency or grid connection relationship between each sampling point; Based on the location information and adjacency information, calculate at least one of the wall distance, normal vector, and curvature of each sampling point; The location information, the adjacency information, and at least one of the calculated wall distance, normal vector, and curvature are combined to form the geometric context feature.

[0015] Optionally, the external condition information includes at least one of operating parameters, material properties, and boundary conditions; the backbone prediction module is specifically used to use the external condition information as a condition input to the backbone network model, and participate in the prediction of the basic physical field together with the geometric context features.

[0016] Optionally, the backbone prediction module is specifically used for: The geometric context features are used as the main input to the backbone network model, and the external condition information is used as the condition input to the backbone network model. The backbone network model is used to jointly map the geometric context features and the external condition information, and output the predicted values ​​of the basic physical field of the object to be evaluated at each sampling point.

[0017] Optionally, the residual adaptation module is specifically used for: A residual local adapter based on local neighborhood aggregation is constructed, wherein the residual local adapter is used to aggregate information in the local neighborhood of each sampling point; The basic physical field, geometric context features, and local proxy features of the central sampling point, as well as the neighborhood features of each neighboring point of the central sampling point, are jointly input into the residual local adapter; the neighborhood features include the basic physical field, geometric context features, and local proxy features of the neighboring points, as well as the edge features between the central sampling point and the neighboring points. The residual local adapter is used to perform message passing or aggregation on the neighborhood features to update the residual representation at the central sampling point. The dimension of the local residual correction output by the residual local adapter is the same as the dimension of the basic physical field, and a local residual correction is output at each sampling point.

[0018] Optionally, the apparatus further includes a model training module, the model training module being used for: Calculate derived performance indices based on the modified target physics field; Obtain the reference physics field information and reference derived performance indicators of the object to be evaluated; The physical field loss is calculated based on the difference between the corrected target physical field and the reference physical field information; The gradient loss is calculated based on the difference between the local gradient of the modified target physical field and the local gradient of the reference physical field information; The performance loss is calculated based on the difference between the derived performance metric and the reference derived performance metric; Calculate the regularization term loss based on the local residual correction amount; The total loss is obtained by weighted summing of the physical field loss, the gradient loss, the performance loss, and the regularization term loss. The parameters of the backbone network model and the residual local adapter are adjusted based on the total loss.

[0019] Optionally, the device further includes a few-shot adaptation module, which is used to perform a few-shot fast adaptation step: Obtain reference physical field information for newly added objects to be evaluated, wherein the number of samples in the reference physical field information is less than the number of reference samples used to train the backbone network model. Freeze the parameters of the backbone network model; Geometric context features are generated by sampling based on the geometric information of the newly added object to be evaluated; Using the geometric context features as input, the basic physical field is predicted through the frozen backbone network model; The local residual correction amount is output through the residual local adapter, and the basic physical field is superimposed with the local residual correction amount to obtain the corrected target physical field; Based on the difference between the corrected target physics field and the reference physics field information, only at least one of the parameters of the residual local adapter, the learnable residual scale parameter, and the derived performance index prediction head is updated, while the parameters of the backbone network model remain frozen.

[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 physical 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 that, when executed by a processor, performs the steps of the physical field 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: It can acquire geometric and external condition information of the object to be evaluated, and can uniformly accept multi-format geometric expressions and various types of working conditions, materials, and boundary conditions. It fully covers all input elements required for physical field prediction, ensures the completeness and standardization of input data, and provides a unified and standardized data source for subsequent full-process prediction, adapting to the prediction input needs of different engineering fields and different physical field types.

[0023] Sampling based on geometric information and generating geometric context features can transform the original geometric shape into a structured feature representation that can be processed by neural networks. At the same time, the spatial topological relationship between sampling points is preserved through adjacency information. The sampling process can adjust the sampling density of different regions as needed, fully characterizing the geometric details of key regions while controlling the overall data scale, providing a consistent geometric feature benchmark for subsequent global physical field mapping and local correction.

[0024] By inputting geometric context features and external condition information into the backbone network model to predict the fundamental physical field, the model can effectively capture the large-scale distribution patterns and long-range physical correlations of the physical field by relying on the global mapping capability of the backbone network. The output fundamental physical field has good global physical consistency and cross-sample generalization ability. The joint input of external conditions enables a single model to support prediction under multiple working conditions and multiple material scenarios, thereby improving the model's scenario adaptability.

[0025] Based on the fundamental physical field, local proxy features are generated through neighborhood difference or aggregation. The degree of field change in each region can be quickly characterized with only a small amount of local computation. Without the need to strictly solve the residuals of the governing equations, it can accurately locate key local regions with large prediction errors and high impact on performance. This provides clear directional guidance for the subsequent local correction process, allowing the correction operation to focus on key regions and effectively control the computational cost of local correction.

[0026] By constructing a local residual adapter and outputting the local residual correction, the local structured error left by the global backbone model can be specifically corrected through an independent lightweight module. Without adjusting the main structure and parameters of the global backbone network, the prediction bias in high gradient regions and boundary regions can be specifically compensated. The adapter only focuses on the calculation of local residuals, with a small number of parameters and fast inference speed, and will not significantly increase the computational burden of the overall prediction.

[0027] The corrected target physical field is obtained by superimposing the basic physical field with the local residual correction. By adopting the fusion method of residual connection, the local correction is added on the basis of fully preserving the main structure of the physical field of the global backbone prediction. This not only improves the prediction accuracy of key areas, but also avoids the local correction from destroying the rationality and physical consistency of the physical distribution of the whole field, thus achieving an organic unity between global prediction reliability and local prediction accuracy.

[0028] In summary, this application employs a layered and progressive prediction process. It uses a global backbone to ensure the rationality and efficiency of the overall prediction of the physical field, uses local proxies to guide the precise location and correction of the correction area, and uses lightweight residuals to compensate for the shortcomings in local accuracy. Without significantly increasing the computational cost, it effectively solves the problem of insufficient prediction accuracy in local high-gradient regions of existing global neural operator models. It can simultaneously meet the multiple requirements of industrial scenarios for the efficiency, global consistency, and local accuracy of physical field prediction.

[0029] 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

[0030] 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.

[0031] Figure 1 A flowchart of a physical field prediction method provided in Embodiment 1 of this application is shown; Figure 2 A flowchart of a geometric context feature generation method provided in Embodiment 1 of this application is shown; Figure 3 A flowchart of a basic physical field prediction method provided in Embodiment 1 of this application is shown; Figure 4 A flowchart of a local proxy feature construction method provided in Embodiment 1 of this application is shown; Figure 5 A flowchart of a local residual correction output method provided in Embodiment 1 of this application is shown; Figure 6 A flowchart of a modified target physics field determination method provided in Embodiment 1 of this application is shown; Figure 7 A flowchart of a parameter adjustment method provided in Embodiment 1 of this application is shown; Figure 8 The flowchart of a fast adaptation method with few samples provided in Embodiment 1 of this application is shown; Figure 9 This illustration shows a schematic diagram of an embodiment of automobile surface pressure field prediction provided in Embodiment 1 of this application; Figure 10 This paper shows a schematic diagram of the structure of a physical field prediction device provided in Embodiment 2 of this application; Figure 11 A schematic diagram of the structure of a computer device provided in Embodiment 3 of this application is shown. Detailed Implementation

[0032] 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.

[0033] Example 1 To facilitate understanding of this application, the following is combined with... Figure 1 The flowchart of the physical field prediction method provided in Embodiment 1 of this application illustrates Embodiment 1 in detail.

[0034] See Figure 1 As shown, Figure 1 A flowchart of a physical field prediction method provided in Embodiment 1 of this application is shown, wherein the method includes steps S101 to S106: S101: Obtain the geometric information and external condition information of the object to be evaluated.

[0035] Specifically, the geometric information of the object to be evaluated can be expressed in various forms, such as CAD (Computer Aided Design) models, STL (Standard Tessellation Language), OBJ (Wavefront Object), STEP (Standard for the Exchange of Product model data), IGES (Initial Graphics Exchange Specification), surface triangular meshes, volume meshes, regular meshes, point clouds, or implicit geometric fields, covering the shape description requirements of various complex engineering objects such as automobiles, rail vehicles, aircraft, drones, wind turbine blades, mechanical structural components, heat exchange structures, and electronic heat dissipation structures.

[0036] Specifically, the content acquired in step S101 may also include surface sampling points, near-boundary sampling points, local high-gradient region sampling points, and volume sampling point data, as well as working conditions or boundary conditions such as fluid velocity, pressure boundary, temperature boundary, load, constraints, material properties, contact conditions, heat source, electromagnetic excitation, and time step. It may also include engineering parameters such as reference area, geometric dimensions, local attachment positions, distance from the ground or wall, thickness, material partitions, and control surface angles.

[0037] Specifically, step S101 can also obtain historical high-fidelity simulation results and optional experimental test data. The historical high-fidelity simulation results include pressure, velocity, temperature, heat flow, stress, displacement, concentration, electromagnetic field, residual convergence information and derived performance indicators. The optional experimental test data includes wind tunnel test, bench test, road test or sensor calibration data.

[0038] Specifically, external condition information includes three categories: operating parameters, material properties, and boundary conditions. These can cover various engineering input conditions such as inflow velocity, pressure boundary, temperature boundary, load constraints, material parameters, contact conditions, heat source excitation, moving part status, and environmental parameters, corresponding to different physical field prediction scenario requirements.

[0039] S102: Based on the geometric information, sampling is performed to obtain the position information and adjacency relationship information of each sampling point, and geometric context features are generated according to the position information and adjacency relationship information.

[0040] Specifically, before sampling, the three-dimensional geometry of the target needs to be aligned to a unified coordinate system and normalized in scale to obtain the main scale direction, lateral direction, height direction and incoming flow direction, so as to ensure that the objects to be evaluated of different sizes and different postures have a consistent spatial reference benchmark.

[0041] Specifically, the sampling process can differentiate the sampling points according to the physical field distribution characteristics, covering different spatial ranges such as surface points, near-wall points, wake points, and external flow field points. The sampling density can be increased for key physical areas such as the boundary layer, separation zone, stress concentration zone, and near the heat source, while the sampling density can be reduced for far-field and uniform field areas, thus controlling the overall computational load while ensuring the prediction accuracy of key areas.

[0042] Specifically, adjacency information is used to characterize the spatial topological connections between sampling points. In regular grid scenarios, the original grid adjacency relationship can be used, while in unstructured grid or point cloud scenarios, the k-nearest neighbor, radius neighborhood, or original grid cell connection relationship can be used to construct the adjacency topology, providing basic support for subsequent local feature calculation and neighborhood aggregation.

[0043] S103: Using the geometric context features and the external condition information as input, the basic physical field is predicted through the backbone network model.

[0044] Specifically, the backbone network model is a global neural operator backbone model, which can be any of the following: Fourier Neural Operator, Graph Neural Operator, Geometry-Informed Neural Operator, MeshGraphNet (Mesh Graph Network), Graph Transformer (Transformer, Transform Attention Neural Network), point cloud neural operator, voxel-based or regular mesh-based neural operator, or neural operator based on implicit geometric field. It has the ability to map function space and can learn the end-to-end global mapping relationship between geometry and physical field.

[0045] Specifically, external condition information can be encoded as a global condition vector, which is then injected into the multi-layer structure of the backbone network through methods such as condition injection, feature concatenation, and global modulation. This enables the same backbone model to support physical field prediction under different working conditions, materials, and boundary conditions, thereby improving the model's versatility across multiple scenarios.

[0046] Specifically, external condition information is also input into the residual local adapter, so that the local residual correction can adapt to the local physical field change law under different working conditions and different boundary conditions, and ensure the correction accuracy in multi-working-condition scenarios.

[0047] Specifically, for any sampling location or grid cell i, the output of the global neural operator backbone model can be expressed as the following formula:

[0048] in, The first output of the backbone model The predicted values ​​of the underlying physical fields at each sampling point may include pressure, velocity, temperature, heat flow, stress, strain, displacement, concentration, electromagnetic field or other physical variables; For the mapping function of the global neural operator backbone model; The set of input target geometry, working conditions, material properties, and boundary conditions; For the first Spatial coordinates of each sampling point; For the first Geometric context features of each sampling point.

[0049] Specifically, the backbone model is responsible for capturing the global large-scale structure of the target physical field, such as overall pressure recovery, wake morphology, temperature distribution trend, global stress transfer path, large-scale displacement field or other long-range physical correlations, and outputting preliminary prediction results of the basic physical field covering the entire sampling area.

[0050] S104: Based on the fundamental physical field, perform differential or aggregate analysis within the neighborhood of each sampling point to generate local proxy features.

[0051] Specifically, local proxy features are not necessarily equivalent to strictly controlling the residuals of the equations. Their core function is to indicate which local regions of the model may have large prediction errors or contribute significantly to the derived performance indicators, thus assisting the subsequent adapter in locating high-gradient and high-contribution regions that need to be corrected.

[0052] Specifically, the calculation method of local proxy features is adapted to the form of input data. In regular grid scenarios, local proxy features can be obtained by finite difference, Sobel gradient, Laplacian operator or multi-scale smooth gradient; in surface grid, unstructured grid or point cloud scenarios, local proxy features can be obtained by edge neighborhood difference, finite volume neighborhood, graph Laplacian, local least squares gradient or grid connection relationship.

[0053] S105: Construct a residual local adapter, input the basic physical field, the geometric context features, the local proxy features and the adjacency relationship information into the residual local adapter, and output the local residual correction amount.

[0054] Specifically, the Residual Local Adapter (ReLA) module is designed as a lightweight, low-parameter structure that focuses solely on correcting local structured errors left over from the global backbone model. It does not replace the overall prediction capability of the global backbone model. It can perform lightweight corrections on structured errors near the boundary, in high-gradient regions, stress concentration areas, heat source regions, wake regions, or local peripheral perturbation regions without completely replacing the global backbone model.

[0055] Specifically, for a mesh node, patch, volume element, or sampling point i, the output of the residual local adapter can be expressed as the following formula:

[0056] in, For the first Local residual correction at each sampling point; For the mapping function of the ReLA residual local adapter, This is the set of trainable parameters for the adapter; For the first Spatial coordinates of each sampling point; For the first Geometric context features of each sampling point; The first output of the backbone model Predicted values ​​of the fundamental physical fields at each sampling point; For the first Local proxy features at each sampling point; For the first The local neighborhood set of each sampling point; For the first The sampling point and its neighborhood Neighborhood edge features between sampling points; Encode global operating parameters, material properties, or boundary conditions.

[0057] Specifically, neighborhood edge features It can include one or more of the following: relative position, distance, normal angle, area / volume weight, boundary type, and material interface type, to characterize the association attributes between neighborhood sampling points and support local neighborhood aggregation calculation.

[0058] Specifically, the residual local adapter can select the corresponding network structure according to the form of the input data. In the regular grid implementation, depthwise separable convolution, local convolution, or window attention can be used; in the unstructured grid implementation, graph convolution, message passing network, local graph attention, finite volume neighborhood aggregation, or point cloud local operators can be used.

[0059] S106: The basic physical field is superimposed with the local residual correction amount to obtain the corrected target physical field.

[0060] Specifically, the two are superimposed using a residual connection method. While fully preserving the main structure of the global backbone prediction of the physical field, the correction amount of the local region is added to avoid the local correction from destroying the overall rationality and physical consistency of the global physical field.

[0061] Specifically, the corrected target physical field can be expressed as the following formula:

[0062] in, For the first Corrected target physical field values ​​at each sampling point; The first output of the backbone model Predicted values ​​of the fundamental physical fields at each sampling point; It is a learnable residual scaling parameter used to control the overall magnitude of local corrections; For the first Local residual correction at each sampling point.

[0063] Specifically, the learnable residual scale parameter can be set independently for different physical quantities, or it can share the same parameter. The optimal correction magnitude can be automatically learned through training, avoiding the correction amount output by the lightweight adapter from covering or destroying the flow structure and physical laws already learned by the global backbone model.

[0064] In an optional implementation, see Figure 2 As shown, Figure 2 The flowchart of a geometric context feature generation method provided in Embodiment 1 of this application is shown, wherein the generation of geometric context features includes steps S201 to S205: S201: Based on the geometric information, sampling is performed in the surface area, near-boundary area, or volume region of the object to be evaluated to obtain a set of sampling points.

[0065] Specifically, surface region sampling can be based on surface triangular mesh for uniform sampling or curvature adaptive sampling, near boundary region sampling can be extended inward and outward along the surface normal to generate near wall sampling points, and volume domain sampling can cover different spatial regions such as the wake region, separation sensitive region, and far field of the external flow field to form a set of sampling points combining multiple regions.

[0066] Specifically, taking the scenario of predicting vehicle drag as an example, the set of sampling points may include sampling points on the vehicle body surface, key sampling points in the rear area and near-wall area, as well as volume flow field sampling points near the vehicle body, the rear wake area and the far field area, covering the core areas of interest in aerodynamic field prediction.

[0067] S202: Use the coordinates of each sampling point in the sampling point set in space as the location information.

[0068] Specifically, the spatial coordinates of the sampling points are three-dimensional Cartesian coordinates. Before sampling, it is necessary to complete the alignment of the unified coordinate system and scale normalization. For example, in the car scene, the incoming flow direction is aligned with the x-axis, and the car body coordinates are normalized to a unified car length scale to ensure the consistency of the spatial distribution of different sample inputs.

[0069] S203: Construct the adjacency relationship information based on the spatial adjacency relationship or grid connection relationship between each sampling point.

[0070] Specifically, for native mesh input, the connection relationship of mesh cells can be directly reused to construct adjacency relationships; for point cloud or discrete sampling point input, the neighboring point set of each sampling point can be matched through k-nearest neighbor search and radius neighborhood search to construct the corresponding adjacency topology relationship.

[0071] Specifically, the adjacency information not only includes the adjacency index of the sampling points, but also generates corresponding neighborhood edge features, such as relative position vectors, Euclidean distance, normal angle, area weight, volume weight, etc., providing complete topological attribute support for subsequent local neighborhood aggregation calculations.

[0072] S204: Based on the location information and adjacency information, calculate at least one of the wall distance, normal vector and curvature of each sampling point.

[0073] Specifically, the wall distance can be a signed or unsigned distance, representing the shortest distance from the sampling point to the target surface; the normal vector is the normal vector of the nearest surface point, which can distinguish between internal and external directions; the curvature can be the principal curvature, average curvature, or discrete curvature, representing the degree of local bending of the surface.

[0074] Specifically, the calculation of geometric features can be completed offline by the CAD / mesh preprocessing module, or it can be calculated in real time on demand during the training and inference stages, balancing computational efficiency and deployment flexibility.

[0075] S205: Combine the location information, the adjacency relationship information, and at least one of the calculated wall distance, normal vector, and curvature into the geometric context feature.

[0076] Specifically, geometric context features can also supplement mesh quality features such as local surface area, element volume, mesh aspect ratio, and skewness; directional features such as the angle with the incoming flow direction or normal projection; distance features to key regions such as the leading edge, trailing edge, bottom, attachments, and curvature change zones; and regional label features such as whether it is located near the wall, in the wake region, in the separation sensitive region, or in the far field of the external flow field, comprehensively characterizing the geometric and spatial attributes of the sampling points.

[0077] Specifically, taking the scenario of predicting vehicle drag as an example, the geometric context features of surface points can also be used to calculate the projection of the normal in the drag direction for subsequent pressure-drag integration; the geometric context features of wake region points can also be used to calculate their downstream distance relative to the rear section of the vehicle for wake loss proxy calculation.

[0078] In an optional implementation, the external condition information includes at least one of operating parameters, material properties, and boundary conditions; the external condition information serves as a conditional input to the backbone network model and participates in the prediction of the fundamental physical field together with the geometric context features.

[0079] Specifically, operating parameters, material properties, and boundary conditions can be converted into fixed-dimensional feature vectors through numerical normalization, one-hot encoding, or category embedding, and then mapped to a unified-dimensional global condition vector through a global encoding network. The global condition vector can be fused with the first-layer geometric context features through feature concatenation, or it can be applied to the operator features of each layer of the backbone network through affine transformation and gating modulation. This enables global control of the global physical field mapping process by operating conditions, materials, and boundary information, allowing a single backbone model to cover the prediction needs of multiple operating conditions and multiple materials.

[0080] In an optional implementation, see Figure 3 As shown, Figure 3 The flowchart of a local proxy feature construction method provided in Embodiment 1 of this application is shown, wherein the step of generating local proxy features by performing differential or aggregation within the neighborhood of each sampling point based on the basic physical field includes steps S301-S302: S301: Based on the geometric context features and the fundamental physical field, perform differential or aggregate calculations within the neighborhood of each sampling point to generate proxy information for indicating the degree of local field change; the proxy information includes at least one of field gradient magnitude information, local energy information, and regional attribute indication information.

[0081] Specifically, differential calculations can employ methods such as finite difference, neighborhood difference, and graph Laplacian operator, while aggregate calculations can employ methods such as multi-scale neighborhood smoothing and local least squares fitting to characterize the degree of drastic change in the local physical field at different spatial scales, including local changes in the neighborhood at small, medium, and large scales.

[0082] Specifically, the field gradient magnitude information may include one or more of the following: pressure gradient magnitude, velocity gradient magnitude, temperature gradient magnitude, stress gradient magnitude, and displacement gradient magnitude, corresponding to different physical field prediction scenarios; the local energy information may include one or more of the following: strain energy density, vorticity, divergence, Tu Laplace energy, and local energy proxy; the regional attribute indication information may include the regional identifiers of the boundary layer, wake region, contact region, material interface region, heat source region, or constraint region.

[0083] S302: The local proxy feature is formed by at least one of the field gradient magnitude information, the local energy information, and the regional attribute indication information; the local proxy feature is used to indicate the degree of field change in the local region where each sampling point is located, or to indicate the sensitivity of the local region where each sampling point is located to derived performance indicators.

[0084] Specifically, local proxy features can also supplement fluid scene features such as the angle between the local velocity direction and the incoming flow direction, the tangential component of the near-wall velocity, and the wall shear proxy amount, as well as performance-sensitive features such as the drag contribution projection of the surface normal and the pressure direction, the load direction projection, and the local performance contribution proxy, further guiding the residual local adapter to focus on local areas that have a significant impact on the final engineering performance.

[0085] Specifically, taking the scenario of predicting vehicle drag as an example, local proxy features may include pressure gradient proxy obtained from the pressure difference between adjacent patches of the surface mesh, velocity gradient proxy obtained from the velocity difference in the neighborhood of the volume domain, wake region proxy in the rear region, boundary layer proxy constructed from the wall distance and velocity tangential changes, and local drag contribution proxy constructed from the surface normal and pressure direction projection, which are used to prompt the adapter to focus on correcting the sensitive areas of the drag coefficient.

[0086] In one specific embodiment, for predicting the pressure field on a vehicle surface, the surface pressure field is represented by a pressure coefficient. The local neighborhood of each surface sampling point is then considered. We define 16 nearest neighbor sampling points determined based on Euclidean distance, and perform scale normalization on the coordinates of these sampling points and the predicted values ​​of the base pressure coefficient. For the ... For each sampling point, the pressure change surcharge value is calculated as follows: :

[0087] in, The superscript represents the predicted base pressure coefficient for the corresponding sampling points after scale normalization. This indicates that the corresponding variable has undergone scale normalization. This represents the number of neighboring sampling points; For the scale-normalized first The spatial coordinates of the sampling point and the first sampling point Spatial coordinates of each sampling point; It is the Euclidean norm (L2 norm); For numerical smoothing terms, take This is used to avoid the denominator being zero and to ensure calculation stability; To normalize the distance weights, the average distance between the current sampling point and its neighboring sampling points is taken, which can be expressed as:

[0088] in, The bandwidth parameter is the Gaussian weight, and it is the average distance between the current sampling point and the 16 nearest neighbor sampling points. The pressure change is proxied. The local proxy features are concatenated with the normalized coordinates, normal vectors, curvature, surface unit areas, and region attribute identifiers of the sampling points to obtain the local proxy features. For volume velocity fields, structural stress fields, or temperature fields, the aforementioned pressure coefficient differences can be replaced with the differences in the corresponding physical quantities. In the effect evaluation of this embodiment, sampling points whose reference physical field gradient amplitude is in the top 20% of each test sample are defined as high gradient regions, and the overall field error and high gradient region error are calculated separately.

[0089] In an optional implementation, see Figure 4 As shown, Figure 4 The flowchart of a local residual correction output method provided in Embodiment 1 of this application is shown, wherein the step of predicting the fundamental physical field through the backbone network model using the geometric context features and the external condition information as input includes steps S401-S402: S401: Use the geometric context features as the main input of the backbone network model, and use the external condition information as the condition input of the backbone network model.

[0090] Specifically, geometric context features are input into the input layer of the backbone network in the form of point-by-point features, fully preserving the spatial coordinates and adjacency topology of the sampling points; external condition information is mapped into a global condition vector by a fully connected coding network and then injected into the neural operator modules of each layer of the backbone network. Condition modulation is performed during the feature transformation process of each layer to ensure that the external condition information can participate in the full-process mapping calculation of the global physical field.

[0091] S402: By jointly mapping the geometric context features and the external condition information through the backbone network model, the predicted values ​​of the basic physical field of the object to be evaluated at each sampling point are output.

[0092] Specifically, the backbone network sequentially performs global spatial transformation and long-range information aggregation on the input features through multiple layers of neural operator blocks. Each layer modulates the feature distribution by combining the global condition vector, gradually mapping the geometric spatial features to the physical field distribution features. After iterative calculations of all operator layers, the output layer maps the high-level features to the basic physical field values ​​corresponding to each sampling point through linear transformation, forming a basic physical field prediction result covering the entire sampling area.

[0093] In an optional implementation, see Figure 5 As shown, Figure 5 The flowchart illustrates a method for outputting local residual correction quantities according to Embodiment 1 of this application. The method involves constructing a local residual adapter, inputting the fundamental physical field, the geometric context features, the local proxy features, and the adjacency relationship information into the local residual adapter, and outputting the local residual correction quantity. This includes steps S501-S503: S501: Construct a residual local adapter based on local neighborhood aggregation, wherein the residual local adapter is used to aggregate information in the local neighborhood of each sampling point.

[0094] Specifically, residual local adapters can be implemented in various ways, including regular grid convolution adapters, depthwise separable convolution adapters, graph message passing adapters, local window attention adapters, point cloud neighborhood adapters, finite volume neighborhood adapters, low-rank adapters, and multi-expert ReLA adapters. The appropriate adapter can be selected flexibly based on the input data format and task requirements.

[0095] Specifically, the residual local adapter is designed as a small parameter module with a much smaller number of parameters than the global neural operator backbone model. This allows it to be updated with only a small number of high-fidelity simulations or experimental samples when a new geometric family or new working condition is added, avoiding the need to retrain the entire global backbone model and reducing adaptation costs.

[0096] S502: Input the basic physical field, geometric context features, local proxy features of the central sampling point, and the neighborhood features of each neighboring point of the central sampling point into the residual local adapter; the neighborhood features include the basic physical field of the neighboring points, the geometric context features of the neighboring points, the local proxy features of the neighboring points, and the edge features between the central sampling point and the neighboring points.

[0097] Specifically, firstly, the basic physical field, geometric context features, and local proxy features of the central sampling point and each neighboring sampling point are mapped to the feature dimensions and unified to the hidden feature dimensions of the adapter; then, the feature differences between the central sampling point and the neighboring sampling points and the neighboring edge features are concatenated to form the initial neighboring edge message, which provides the input basis for subsequent neighborhood information aggregation.

[0098] S503: The residual local adapter performs message passing or aggregation on the neighborhood features to update the residual representation at the central sampling point.

[0099] Specifically, during the message passing process, a message vector corresponding to each adjacent edge is first generated based on edge features and neighborhood point features. Then, all neighborhood edge messages of the same central sampling point are aggregated into neighborhood aggregate features through mean aggregation, weighted aggregation, or attention aggregation. Subsequently, the neighborhood aggregate features are fused with the features of the central sampling point itself, and the updated residual representation of the central sampling point is obtained after calculation by the node update network. After multiple layers of message passing iterations, the residual representation of the central sampling point can integrate the physical field and geometric information of multi-order neighborhoods to accurately capture local error patterns.

[0100] The dimension of the local residual correction output by the residual local adapter is the same as the dimension of the basic physical field, and a local residual correction is output at each sampling point.

[0101] Specifically, the point-to-point and dimensionally consistent correction method ensures that the basic physical field and the residual correction amount correspond one-to-one in spatial location and physical quantity channel, without the need for additional spatial interpolation or dimensional transformation. This not only ensures the physical consistency of residual superposition but also reduces the computational complexity of the adapter, ensuring that inference efficiency is not significantly affected.

[0102] In one specific embodiment, the residual local adapter employs a three-layer graph message passing structure. The initial node features of the i-th sampling point... It is obtained by concatenating the predicted values ​​of the fundamental physics field, geometric context features, local proxy features, and external conditional codes:

[0103] In the formula, This indicates a concatenation operation along the feature channel dimensions; The first output of the backbone model Predicted values ​​of the fundamental physical fields at each sampling point; For the first Geometric context features of each sampling point; For the first Local proxy features of each sampling point; It is a global external conditional encoding vector, which is repeated point by point at each sampling point before participating in feature concatenation.

[0104] For the Layer message passing (superscript) Indicates the first (Layered message passing) First, side messages are generated based on the features of the central sampling point, the features of neighboring sampling points, and the features of neighboring edges. Then, side messages of the same central sampling point are aggregated, and the features of the central sampling point are updated. Specifically, this is represented as follows:

[0105] Among them, superscript Indicates the first Layered message passing; For the first Sampling points in the layer and The edge message vector between them; For the first Layer edge messages generate multilayer perceptron networks; For the first The node features of the center sampling point and neighboring sampling points in the layer output; Sampling points and Neighborhood edge features between them; For the first Layer center sampling point The results of neighborhood message aggregation; For the central sampling point All neighborhood edge messages are averaged and aggregated. For the first Center sampling point of layer output Update node characteristics; For the first The nodes of the layer update the multilayer perceptron network. In this example configuration, the residual scale parameter... The trainable vector corresponding to the physical quantity channel is initialized to 0.1. The number of parameters in the global neural operator backbone model is approximately 15.2M, and the number of parameters in the residual local adapter is approximately 0.9M, accounting for about 5.9% of the backbone model parameters.

[0106] Specifically, taking the scenario of predicting automotive wind resistance as an example, the residual local adapter can output corresponding residual correction amounts for the pressure field and velocity field respectively. The correction formula can be expressed as:

[0107] in, The first Corrected pressure, x-direction velocity, and y-direction velocity values ​​at each sampling point; The outputs of the backbone model are respectively Basic predicted values ​​of pressure, x-direction velocity, and y-direction velocity at each sampling point; These are the learnable residual scale parameters corresponding to pressure, x-direction velocity, and y-direction velocity, respectively. These three parameters can be shared or set separately. The first The local residual correction amount of pressure, x-direction velocity, and y-direction velocity at each sampling point.

[0108] See Figure 6 As shown, Figure 6 The flowchart of a method for determining a modified target physical field according to Embodiment 1 of this application is shown, wherein the step of superimposing the basic physical field with the local residual correction amount to obtain the modified target physical field includes steps S601~S602: S601: Obtain learnable residual scaling parameters.

[0109] Specifically, the residual scaling parameter is a trainable scalar or vector parameter. During the initialization phase, it can be set to a small initial value to ensure that the prediction of the global backbone model dominates in the early stage of training. As training progresses, it gradually learns the optimal correction magnitude, balancing the weights of global prediction and local correction.

[0110] Specifically, for multi-physical quantity prediction scenarios, independent residual scale parameters can be set for each physical quantity, so that the correction magnitude of different physical quantities can be optimized independently to adapt to the differences in error magnitude of different physical quantities.

[0111] S602: Multiply the local residual correction by the residual scale parameter, and then add it point by point to the basic physical field to obtain the corrected target physical field.

[0112] Specifically, the point-by-point additive residual connection structure can retain the basic physical field information of the global backbone prediction and supplement the correction amount in the local region; by limiting the local correction magnitude through residual scale parameters and residual regularization terms, the perturbation of the large-scale field distribution already learned by the residual local adapter can be reduced.

[0113] Specifically, the corrected complete target physics field can be uniformly expressed as the following formula:

[0114] in, The corrected overall target physics field; The global fundamental physics field output by the global backbone model; For learnable residual scaling parameters; This is the global local residual correction value output by the ReLA residual local adapter. The values ​​in parentheses are all the input items of the adapter.

[0115] In an optional implementation, see Figure 7 As shown, Figure 7 A flowchart of a parameter adjustment method provided in Embodiment 1 of this application is shown, wherein the method further includes steps S701 to S707: S701: Calculate derived performance indices based on the modified target physical field.

[0116] Specifically, the derived performance indicators are obtained from the modified physical field through physical calculations, and may include calculation forms such as surface integral, volume integral, maximum value statistics, average value statistics, force / torque integral, heat flux integral, or energy integral, corresponding to the engineering performance requirements of different scenarios.

[0117] Specifically, taking the static stress field prediction scenario of mechanical structural components as an example, its input information, local proxy features, and output results have a clear corresponding mapping relationship: the geometric information on the input side can adopt a solid model in STEP format or a tetrahedral mesh, covering geometric details such as structural component wall thickness, stiffener layout, chamfer dimensions, and material interfaces; external condition information includes structural condition parameters such as concentrated loads, fixed constraints, elastic modulus, Poisson's ratio, and contact pair settings. The corresponding geometric context features, in addition to sampling point coordinates and adjacency relationships, also include features such as local curvature, wall thickness distribution, distance to the load application area and constraint boundaries, and material interface identification, providing complete geometric spatial attribute input for the global backbone network.

[0118] After the global backbone network outputs the basic equivalent stress field and displacement field, local proxy features are generated through neighborhood difference and local aggregation calculations. Specifically, these features include the equivalent stress gradient magnitude, local strain energy density proxy, stress concentration area attribute indication, and characterization of the intensity of field changes near the load / constraint boundary. These features are used to prompt the residual local adapter to pay attention to high stress-sensitive areas such as rounded transition areas, stiffener joints, and load application points, and to specifically correct the prediction bias of the global backbone at local stress concentration points.

[0119] After the local residual correction is output by the residual local adapter and superimposed, the corrected equivalent stress field and displacement field are obtained. Based on the corrected field, derived performance indicators such as maximum equivalent stress, displacement of key measuring points, and stress amplitude of fatigue hazard points can be further calculated. The output results can directly support structural strength verification and lightweight optimization design.

[0120] Specifically, taking the prediction of the drag coefficient of a car as an example, the drag coefficient... It can be obtained by integrating the pressure resistance and frictional resistance of the target's surface, and the continuous form formula is as follows:

[0121] in, The drag coefficient is calculated using physical integration. air density; The incoming flow velocity; For reference, the windward area; The corrected surface pressure in continuous form; For the continuous form, this is the component of the surface normal in the direction of resistance; The wall shear stress is in continuous form; This represents the component of wall shear in the direction of resistance. The integral domain is the continuous surface of the object. It is a surface integral element.

[0122] Specifically, the formula for calculating the drag coefficient in discrete summation form can be broken down into two parts: pressure drag and friction drag, as shown in the following formula:

[0123] Specifically, among them This represents the drag coefficient component corresponding to pressure resistance. This represents the drag coefficient component corresponding to frictional resistance; The total drag coefficient is obtained by integration; air density; The incoming flow velocity; For reference, the windward area; For the first Corrected pressure at each surface sampling point; For the first The component of the surface normal in the direction of resistance at each surface sampling point; For the first The component of wall shear in the resistance direction at each surface sampling point; For the first The area of ​​the unit corresponding to each surface sampling point; It is the discrete set of all surface sampling points.

[0124] Specifically, when high-precision wall shear tags, structural local stress tags, or heat flow tags are lacking, derived performance indicators can be calculated using integral surrogate, local gradient surrogate, and neural network prediction heads. Taking the drag coefficient as an example, the joint prediction formula is as follows:

[0125] Specifically, among them The drag coefficient is the final output derived performance index. For the prediction of derived performance indicators The set of trainable parameters for the prediction head; This indicates weighted pooling, attention pooling, or physical region pooling operations on features of surfaces, volumes, wake regions, load concentration regions, or heat source regions. The corrected overall target physics field; It is the set of geometric context features for the entire field; For the set of local proxy features across the entire field; Encode global operating condition parameters; This is the integral surrogate value of the drag coefficient.

[0126] Specifically, the final derived performance index can also be obtained by weighted fusion of physical integrals and neural network prediction heads, as shown in the following formula:

[0127] in, This represents the final output drag coefficient. The weights used for fusion can be either fixed weights or learnable weights; The drag coefficient is obtained by correcting the physical field integral; The drag coefficient is predicted by the head output through a neural network.

[0128] S702: Obtain the reference physics field information and reference derived performance index of the object to be evaluated.

[0129] Specifically, the reference physics information and reference derived performance indicators are derived from high-fidelity numerical simulations or experimental test data. As supervision labels for model training, they cover the real benchmark values ​​of the corresponding physics and derived performance indicators. For example, the pressure field, velocity field and drag coefficient of CFD (Computational Fluid Dynamics) simulation in fluid scenarios, and the stress field, displacement field and maximum stress of finite element simulation in structural scenarios.

[0130] S703: Calculate the physical field loss based on the difference between the corrected target physical field and the reference physical field information.

[0131] Specifically, the physical field loss can be calculated using regression loss functions such as mean square error and mean absolute error, which calculate the deviation between the predicted physical field and the reference physical field within the entire sampling area, thereby constraining the overall prediction accuracy of the physical field.

[0132] Specifically, the physical field loss can be supplemented with gradient loss, key region weighted loss, and other sub-items. The gradient loss is used to constrain the local gradient accuracy of the physical field, while the key region weighted loss is used to assign higher weights to high gradient and high sensitivity regions such as the wake region, boundary layer, stress concentration region, and heat source region, thereby further improving the prediction accuracy of key regions.

[0133] S704: Calculate the gradient loss based on the difference between the local gradient of the corrected target physical field and the local gradient of the reference physical field information.

[0134] Specifically, the gradient loss adopts the neighborhood difference method consistent with the local proxy feature, calculates the local gradient magnitude and gradient direction of the predicted physical field and the reference physical field at each sampling point, and then calculates the mean square error of the difference in gradient values. The gradient loss can constrain the local change trend and spatial distribution of the physical field, avoid the problem of excessive smoothing or local abrupt distortion in the predicted field, and further improve the field distribution restoration degree in high gradient regions.

[0135] S705: Calculate the performance loss based on the difference between the derived performance index and the reference derived performance index.

[0136] Specifically, performance loss can be calculated using mean absolute percentage error or mean square error. Before calculation, the derived performance indicators are normalized to eliminate the difference in magnitude between different indicators. Performance loss directly constrains the model's prediction accuracy for core engineering indicators, avoiding situations where the average error of the entire physical field is small, but the deviation of key performance indicators is large, making the model output more in line with the actual needs of engineering design.

[0137] S706: Calculate the regularization term loss based on the local residual correction amount.

[0138] Specifically, the regularization loss uses the L2 norm or L1 norm to calculate the sum of the magnitudes of the local residual corrections at all sampling points, penalizing the overall magnitude of the corrections. The regularization loss is used to limit the correction magnitude of the residual adapter, avoiding excessive local corrections that could disrupt the large-scale physical laws learned by the global backbone model, and ensuring that the corrected physical field always has global physical consistency and rationality.

[0139] S707: The physical field loss, the performance loss, and the regularization term loss are weighted and summed to obtain the total loss.

[0140] Specifically, the complete formula for calculating the total loss is as follows:

[0141] in, Total loss; For the target physical field error loss; The corrected target physics field for prediction; The weighting system for the physical field loss; For reference physics field labels (such as high-fidelity CFD simulation results); This is to account for the loss of derived performance index error. The weighting coefficient for performance index loss; The predicted drag coefficient of the vehicle (derived performance index). For reference, refer to the drag coefficient label; This is the loss due to local gradient error. These are the weighting coefficients for the gradient loss; Weighted loss for key areas; The weighting coefficients for the loss in the key areas; This is the loss of the regularization term for the residual correction; The weighting coefficients for the regularization loss; This represents the local residual correction amount for the entire field.

[0142] Specifically, the weighting coefficients of each loss can be adjusted according to the needs of the specific task to balance the relationship between the accuracy of the physical field distribution, the accuracy of the performance index and the stability of model training, so as to achieve multi-objective joint optimization.

[0143] S708: Adjust the parameters of the backbone network model and the residual local adapter according to the total loss.

[0144] Specifically, during the full training phase, all parameters of the backbone network and the adapter can be updated simultaneously. The total loss is optimized through backpropagation and gradient descent algorithms, enabling the model to learn the correlation between the target physical field distribution and derived performance indicators, thereby improving the overall prediction accuracy and physical interpretability.

[0145] Specifically, training strategies can be flexibly selected based on data conditions and training stages, including full joint training, training the backbone first and then the adapter, freezing the backbone and training the adapter, alternating training, meta-learning initialization, incremental adaptation of enterprise product families, and other strategies to adapt to different training scenarios and data scales.

[0146] Specifically, full joint training refers to training all parameters of the global backbone and ReLA adapter simultaneously, suitable for initial large-scale dataset training scenarios; training the backbone first and then the adapter refers to completing the convergence training of the global backbone model first, and then connecting the adapter for fine-tuning, suitable for modular iterative development; freezing the backbone and training the adapter refers to fixing the global backbone parameters and only updating the adapter and prediction head parameters, suitable for few-sample adaptation scenarios; alternating training refers to alternating the updating of backbone and adapter parameters to balance global and local learning effects; meta-learning initialization refers to generating initial parameters for the adapter to adapt to different geometric families through meta-learning, further improving the efficiency of few-sample adaptation; incremental adaptation of enterprise product families refers to incrementally adapting new product series based on existing product family models through adapters, accumulating enterprise general model assets.

[0147] In one specific embodiment, a dataset was constructed using 240 sets of automotive geometry-condition samples, with 180 sets used for training, 30 sets for validation, and 30 sets for testing. The reference surface pressure coefficient field for each sample was obtained by dimensionlessly transforming the surface static pressure obtained from steady-state incompressible RANS numerical simulations according to the incoming flow pressure. The k-ωSST model was used for turbulence, with inlet velocities ranging from 20 m / s to 40 m / s. Each sample had 32,768 sampling points uniformly sampled on the outer surface of the vehicle, and adjacency relationships were constructed using 16 nearest neighbors. This embodiment uses a geometry-aware neural operator containing 4 global operator blocks and a hidden feature dimension of 128 as the backbone network. In the first training phase, the backbone network was trained for 300 epochs using the AdamW optimizer with an initial learning rate of 1×10⁻⁶. -3 The second training phase involves freezing the backbone network and training the residual local adapter and residual scaling parameters for 150 epochs with an initial learning rate of 5 × 10⁻⁶.-4 Optionally, then use 1×10 -4 The learning rate was jointly fine-tuned for 30 rounds. The batch size was 2, and the weight decay coefficient was 1×10⁻⁶. -5 The learning rate is adjusted using cosine annealing. In the total loss, the physics loss has a weighting. Set to 1.0 for gradient loss weights. Set the weight to 0.2, and assign a weight to the derived performance metric loss. Set the weight to 0.1 for the weighted loss in the key area. Take 0.5 as the weight of the residual regularization term. Take 1×10 -4 In this embodiment, the weighted loss for the key region is calculated for the top 20% of sampling points with the gradient magnitude of the reference surface pressure coefficient field. The reference derived performance index is the drag coefficient of the entire vehicle obtained from numerical simulation. The model predicts the drag coefficient using the aforementioned derived performance index prediction head, based on the corrected surface pressure coefficient field, geometric context features, local proxy features, and external condition encoding. Before training, the spatial coordinates, external conditions, and physical field labels are standardized, and the inference output is then de-standardized using the same statistics.

[0148] In an optional implementation, see Figure 8 As shown, Figure 8 The flowchart of a few-sample fast adaptation method provided in Embodiment 1 of this application is shown, wherein the method further includes few-sample fast adaptation steps S801~S806: S801: Obtain reference physical field information for the newly added object to be evaluated, wherein the number of samples of the reference physical field information is less than the number of reference samples used to train the backbone network model.

[0149] Specifically, the newly added objects to be evaluated may correspond to a completely new family of geometries, an uncovered operating range, a new material system, or special boundary conditions. The number of reference samples is usually only 5% to 20% of the training sample size of the backbone network. They may come from a small number of supplementary high-fidelity numerical simulation calculation results or from sparse measured data obtained from test benches, wind tunnels, etc., to adapt to the local physical field error characteristics under the new scenario.

[0150] S802: Freeze the parameters of the backbone network model.

[0151] Specifically, freezing the backbone network parameters can fully preserve the general physical laws and global field prediction capabilities that the model has learned, avoid catastrophic forgetting of the global model due to a small number of new samples, and make full use of the training assets and knowledge accumulation of existing large models.

[0152] Specifically, the freezing range can be flexibly adjusted according to adaptation needs. Typically, all global neural operator backbone parameters are frozen, and only the residual local adapter and residual scaling parameters are retained as updatable parameters to maximize the reuse capability of existing models.

[0153] S803: Sample and generate geometric context features based on the geometric information of the newly added object to be evaluated.

[0154] Specifically, the geometric preprocessing, sampling, and feature construction processes for newly added objects are completely consistent with the processing processes of the original model, ensuring that the distribution of input features matches the learning distribution of the backbone network, and guaranteeing the reliability and consistency of the prediction of the basic physical field.

[0155] S804: Using the geometric context features as input, predict the fundamental physical field through the frozen backbone network model.

[0156] Specifically, the frozen backbone model outputs the basic physics prediction results for the newly added objects. These results retain the general global physics structure and only have structured prediction errors in the local structural regions specific to the newly added objects, providing a reliable baseline for subsequent local corrections.

[0157] S805: Output the local residual correction amount through the residual local adapter, and superimpose the basic physical field with the local residual correction amount to obtain the corrected target physical field.

[0158] Specifically, the residual local adapter is responsible for learning the local physical field error patterns unique to the new object, such as the local separation, wake, or pressure recovery errors unique to the new vehicle model, and provides targeted compensation for the local prediction bias of the backbone model without changing the main structure and parameters of the global model.

[0159] S806: Based on the difference between the corrected target physical field and the reference physical field information, only at least one of the parameters of the residual local adapter, the learnable residual scale parameter, and the derived performance index prediction head is updated, while the parameters of the backbone network model remain frozen.

[0160] Specifically, the adaptation training phase can use a smaller learning rate and fewer training rounds. The loss function can be a combination of physics loss, regularization loss and performance loss, depending on the adaptation requirements. There is no need to fully execute the multi-objective optimization process of full training. Since only the adapter and prediction head with a small number of parameters are updated, a small number of samples can converge quickly. While retaining the global backbone general prediction capability, it can quickly adapt to the local prediction accuracy requirements of new scenarios.

[0161] See Figure 9 As shown, Figure 9This diagram illustrates an embodiment of vehicle surface pressure field prediction provided in Embodiment 1 of this application, comprising two parts: the left and right sides. The left side diagram, labeled with vehicle geometry, displays the three-dimensional geometric model of the passenger vehicle's outer surface to be evaluated, serving as the input geometric information for the physical field prediction method based on residual local adaptation neural operators in this application. The right side diagram, labeled with surface pressure field, is represented in this embodiment as a surface pressure coefficient field. It shows the corrected predicted surface pressure coefficient field after calculating the left-side vehicle geometry using the method of this application. The pressure distribution differences in different areas, such as the high-pressure area at the front of the vehicle and the pressure transition area on the side of the vehicle, are visually presented using color mapping. This result can be used for subsequent calculation of derived performance indicators such as drag coefficient and aerodynamic performance evaluation.

[0162] To verify the impact of local proxy features and residual local adapters on the overall error of the physics field and the error in local high-gradient regions, a comparative experiment was set up under the same training set, test set, input features, and backbone network conditions. The overall relative L2 error was used to measure the prediction error of the surface pressure coefficient field at all sampling points, and the relative L2 error in high-gradient regions was used to measure the error of the top 20% of sampling points with the gradient magnitude of the reference surface pressure coefficient field. The derived performance index used was the relative error of the overall vehicle drag coefficient output by the aforementioned derived performance index predictor.

[0163] See Table 1 for comparison results of different prediction models:

[0164] Table 1 As shown in Table 1, compared to the scheme using only the global backbone model, the complete scheme of this application reduces the overall relative L2 error by approximately 26.6%, the relative L2 error in high-gradient regions by approximately 39.4%, and the relative error of the drag coefficient by approximately 43.8%. The residual local adapter increases the number of model parameters by approximately 5.9% and the single-sample inference time by approximately 12.2%. These results indicate that local neighborhood residual correction improves the prediction accuracy in locally highly variable regions with relatively small additional computational overhead.

[0165] See Table 2 for the ablation experiment results of local proxy, edge features, and loss terms:

[0166] Table 2 Table 2 shows that after removing local proxy features, the increase in error in high-gradient regions is greater than the increase in overall field error, indicating that local proxy features formed by local differences and geometric properties of the fundamental physical field can provide positioning information for high-variable regions for the residual local adapter. Removing neighborhood edge features or gradient loss also increases the error in local regions. Removing derived performance index loss mainly leads to an increase in drag coefficient error. These results illustrate the synergistic relationship between local proxy features, neighborhood edge features, local gradient constraints, and derived performance index constraints.

[0167] Furthermore, to verify the rapid adaptation effect with fewer samples, in addition to the above 240 sets of data, a newly added family of vehicle geometries that did not participate in the backbone network training was selected, and 8 sets of reference surface pressure coefficient field samples were used for adaptation. The results were tested on the other 24 sets of samples, and the results are shown in the table below.

[0168] See Table 3 for the few-sample fitting results of the newly added geometric families:

[0169] Table 3 As shown in Table 3, when the backbone network is frozen and the ReLA and residual scale parameters are updated, the number of trainable parameters is about 5.6% of that of full model fine-tuning, the adaptation time is shortened by about 81.0%, and the prediction error of the whole field and high gradient region is close to that of full model fine-tuning. This shows that the residual local adapter can adapt the local error pattern of the newly added geometric family with fewer trainable parameters while retaining the global mapping capability of the backbone network.

[0170] Example 2 See Figure 10 As shown, Figure 10 This illustration shows a schematic diagram of a physical field prediction device provided in Embodiment 2 of this application, which includes: The acquisition module 1001 is used to acquire the geometric information and external condition information of the object to be evaluated. The sampling module 1002 is used to sample based on the geometric information to obtain the position information and adjacency relationship information of each sampling point, and generate geometric context features based on the position information and adjacency relationship information; The backbone prediction module 1003 is used to predict the basic physical field through the backbone network model by taking the geometric context features and the external condition information as input. The local proxy construction module 1004 is used to perform differential or aggregation within the neighborhood of each sampling point based on the basic physical field to generate local proxy features; The residual adaptation module 1005 is used to construct a residual local adapter, inputting the basic physical field, the geometric context features, the local proxy features and the adjacency relationship information into the residual local adapter, and outputting the local residual correction amount; The correction module 1006 is used to superimpose the basic physical field with the local residual correction amount to obtain the corrected target physical field.

[0171] In an optional implementation, the sampling module is specifically used to generate geometric context features, including: Based on the geometric information, sampling is performed in the surface region, near-boundary region, or volume region of the object to be evaluated to obtain a set of sampling points. The coordinates of each sampling point in the set of sampling points in space are used as the location information; The adjacency information is constructed based on the spatial adjacency or grid connection relationship between each sampling point; Based on the location information and adjacency information, calculate at least one of the wall distance, normal vector, and curvature of each sampling point; The location information, the adjacency information, and at least one of the calculated wall distance, normal vector, and curvature are combined to form the geometric context feature.

[0172] In an optional implementation, the external condition information includes at least one of operating parameters, material properties, and boundary conditions; the backbone prediction module is specifically used to use the external condition information as a condition input to the backbone network model, and participate in the prediction of the basic physical field together with the geometric context features.

[0173] In an optional implementation, the backbone prediction module is specifically used for: The geometric context features are used as the main input to the backbone network model, and the external condition information is used as the condition input to the backbone network model. The backbone network model is used to jointly map the geometric context features and the external condition information, and output the predicted values ​​of the basic physical field of the object to be evaluated at each sampling point.

[0174] In an optional implementation, the residual adaptation module is specifically used for: A residual local adapter based on local neighborhood aggregation is constructed, wherein the residual local adapter is used to aggregate information in the local neighborhood of each sampling point; The basic physical field, geometric context features, and local proxy features of the central sampling point, as well as the neighborhood features of each neighboring point of the central sampling point, are jointly input into the residual local adapter; the neighborhood features include the basic physical field, geometric context features, and local proxy features of the neighboring points, as well as the edge features between the central sampling point and the neighboring points. The residual local adapter is used to perform message passing or aggregation on the neighborhood features to update the residual representation at the central sampling point. The dimension of the local residual correction output by the residual local adapter is the same as the dimension of the basic physical field, and a local residual correction is output at each sampling point.

[0175] In an optional implementation, the apparatus further includes a model training module, the model training module being used for: Calculate derived performance indices based on the modified target physics field; Obtain the reference physics field information and reference derived performance indicators of the object to be evaluated; The physical field loss is calculated based on the difference between the corrected target physical field and the reference physical field information; The gradient loss is calculated based on the difference between the local gradient of the modified target physical field and the local gradient of the reference physical field information; The performance loss is calculated based on the difference between the derived performance metric and the reference derived performance metric; Calculate the regularization term loss based on the local residual correction amount; The total loss is obtained by weighted summing of the physical field loss, the gradient loss, the performance loss, and the regularization term loss. The parameters of the backbone network model and the residual local adapter are adjusted based on the total loss.

[0176] In an optional implementation, the apparatus further includes a few-shot adaptation module for performing a few-shot fast adaptation step: Obtain reference physical field information for newly added objects to be evaluated, wherein the number of samples in the reference physical field information is less than the number of reference samples used to train the backbone network model. Freeze the parameters of the backbone network model; Geometric context features are generated by sampling based on the geometric information of the newly added object to be evaluated; Using the geometric context features as input, the basic physical field is predicted through the frozen backbone network model; The local residual correction amount is output through the residual local adapter, and the basic physical field is superimposed with the local residual correction amount to obtain the corrected target physical field; Based on the difference between the corrected target physics field and the reference physics field information, only at least one of the parameters of the residual local adapter, the learnable residual scale parameter, and the derived performance index prediction head is updated, while the parameters of the backbone network model remain frozen.

[0177] Example 3 Based on the same application concept, see [link / reference] Figure 11 As shown, Figure 11 This illustration shows a structural schematic diagram of a computer device provided in Embodiment 3 of this application, wherein, as shown... Figure 11 As shown, the computer device 1100 provided in Embodiment 3 of this application includes: The computer device 1100 includes a processor 1101, a memory 1102, and a bus 1103. The memory 1102 stores machine-readable instructions that can be executed by the processor 1101. When the computer device 1100 is running, the processor 1101 and the memory 1102 communicate through the bus 1103. The machine-readable instructions are executed by the processor 1101 to perform the steps of the physical field prediction method shown in Embodiment 1 above.

[0178] Example 4 Based on the same concept, embodiments of this application also provide a computer-readable storage medium storing a computer program, which, when executed by a processor, performs the steps of the physical field prediction method described in any of the above embodiments.

[0179] 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.

[0180] The computer program product for predicting physical fields 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.

[0181] The 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.

[0182] 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.

[0183] 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.

[0184] 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.

[0185] 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.

[0186] 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.

[0187] 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 scope of protection 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 scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for predicting physical fields, characterized in that, include: Obtain geometric and external condition information of the object to be evaluated; Based on the geometric information, sampling is performed to obtain the position information and adjacency relationship information of each sampling point, and geometric context features are generated based on the position information and adjacency relationship information. Using the geometric context features and the external condition information as input, the basic physical field is predicted through a backbone network model; Based on the underlying physical field, differential or aggregated features are generated within the neighborhood of each sampling point to produce local proxy features. Construct a residual local adapter, input the basic physical field, the geometric context features, the local proxy features, and the adjacency relationship information into the residual local adapter, and output the local residual correction amount; The corrected target physical field is obtained by superimposing the basic physical field with the local residual correction.

2. The method according to claim 1, characterized in that, The generated geometric context features include: Based on the geometric information, sampling is performed in the surface region, near-boundary region, or volume region of the object to be evaluated to obtain a set of sampling points. The coordinates of each sampling point in the set of sampling points in space are used as the location information; The adjacency information is constructed based on the spatial adjacency or grid connection relationship between each sampling point; Based on the location information and adjacency information, calculate at least one of the wall distance, normal vector, and curvature of each sampling point; The location information, the adjacency information, and at least one of the calculated wall distance, normal vector, and curvature are combined to form the geometric context feature.

3. The method according to claim 1, characterized in that, The external condition information includes at least one of operating parameters, material properties, and boundary conditions; the external condition information serves as the condition input of the backbone network model and, together with the geometric context features, participates in the prediction of the fundamental physical field.

4. The method according to claim 1, characterized in that, The process of predicting the fundamental physical field using the geometric context features and external condition information as input through the backbone network model includes: The geometric context features are used as the main input to the backbone network model, and the external condition information is used as the condition input to the backbone network model. The backbone network model is used to jointly map the geometric context features and the external condition information, and output the predicted values ​​of the basic physical field of the object to be evaluated at each sampling point.

5. The method according to claim 1, characterized in that, The construction of the residual local adapter involves inputting the fundamental physics field, the geometric context features, the local proxy features, and the adjacency relationship information into the residual local adapter, and outputting a local residual correction amount, including: A residual local adapter based on local neighborhood aggregation is constructed, wherein the residual local adapter is used to aggregate information in the local neighborhood of each sampling point; The basic physical field, geometric context features, and local proxy features of the central sampling point, as well as the neighborhood features of each neighboring point of the central sampling point, are jointly input into the residual local adapter; the neighborhood features include the basic physical field, geometric context features, and local proxy features of the neighboring points, as well as the edge features between the central sampling point and the neighboring points. The residual local adapter is used to perform message passing or aggregation on the neighborhood features to update the residual representation at the central sampling point. The dimension of the local residual correction output by the residual local adapter is the same as the dimension of the basic physical field, and a local residual correction is output at each sampling point.

6. The method according to claim 5, characterized in that, The method further includes: Calculate derived performance indices based on the modified target physics field; Obtain the reference physics field information and reference derived performance indicators of the object to be evaluated; The physical field loss is calculated based on the difference between the corrected target physical field and the reference physical field information; The gradient loss is calculated based on the difference between the local gradient of the modified target physical field and the local gradient of the reference physical field information; The performance loss is calculated based on the difference between the derived performance metric and the reference derived performance metric; Calculate the regularization term loss based on the local residual correction amount; The total loss is obtained by weighted summing of the physical field loss, the gradient loss, the performance loss, and the regularization term loss. The parameters of the backbone network model and the residual local adapter are adjusted based on the total loss.

7. The method according to claim 5, characterized in that, The method also includes a rapid adaptation step with few samples: Obtain reference physical field information for newly added objects to be evaluated, wherein the number of samples in the reference physical field information is less than the number of reference samples used to train the backbone network model. Freeze the parameters of the backbone network model; Geometric context features are generated by sampling based on the geometric information of the newly added object to be evaluated; Using the geometric context features as input, the basic physical field is predicted through the frozen backbone network model; The local residual correction amount is output through the residual local adapter, and the basic physical field is superimposed with the local residual correction amount to obtain the corrected target physical field; Based on the difference between the corrected target physics field and the reference physics field information, only at least one of the parameters of the residual local adapter, the learnable residual scale parameter, and the derived performance index prediction head is updated, while the parameters of the backbone network model remain frozen.

8. A physical field prediction device, characterized in that, include: The acquisition module is used to acquire geometric information and external condition information of the object to be evaluated. The sampling module is used to sample based on the geometric information to obtain the position information and adjacency information of each sampling point, and generate geometric context features based on the position information and adjacency information. The backbone prediction module is used to predict the fundamental physical field through a backbone network model, taking the geometric context features and the external condition information as input. The local proxy construction module is used to perform differential or aggregation within the neighborhood of each sampling point based on the basic physical field to generate local proxy features; The residual adaptation module is used to construct a residual local adapter, inputting the basic physical field, the geometric context features, the local proxy features and the adjacency relationship information into the residual local adapter, and outputting the local residual correction amount; The correction module is used to superimpose the basic physical field with the local residual correction amount to obtain the corrected target physical 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 physical field 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 physical field prediction method as described in any one of claims 1 to 7.

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