Method for physical field simulation of three-dimensional geometric structure, model training method and device

Abstract

This disclosure provides a method, model training method, and apparatus for simulating the physical field of three-dimensional geometric structures, relating to the fields of data processing and simulation technology, and deep learning technology in the field of artificial intelligence. The specific implementation scheme is as follows: based on the physical data of the three-dimensional geometric structure, the geometric features and physical quantity features of the three-dimensional geometric structure are obtained; the geometric features and physical quantity features of the three-dimensional geometric structure are fused to obtain fused features; local neighborhood information is aggregated through a graph neural network, and the fused features are mapped to a latent feature space to obtain latent features; physical field simulation operations are performed based on the latent features to obtain the physical field simulation results of the three-dimensional geometric structure. This disclosure can improve the simulation accuracy and efficiency of physical fields.

Description

Technical Field

[0001] This disclosure relates to the field of computer technology, particularly to the field of data processing and simulation technology and deep learning technology in the field of artificial intelligence, and especially to physical field simulation methods, model training methods and devices for three-dimensional geometric structures, which can be applied to application scenarios such as industrial design optimization, real-time simulation, and digital twins. Background Technology

[0002] In related technologies, physical field analysis is mainly achieved through numerical simulation methods (such as the finite element method (FEM) and the finite volume method (FVM). The core idea is "discretization," which discretizes the continuous physical field into a finite number of points (grids) in space and time, and then uses a computer to solve a set of large algebraic equations to obtain an approximate solution. However, for the physical field analysis of complex three-dimensional geometric structures, numerical simulation methods in related technologies suffer from high data processing costs and long solution times. Currently, there is a lack of effective means for simulating the physical fields of three-dimensional geometric structures. Summary of the Invention

[0003] This disclosure provides a physical field simulation method, model training method, and apparatus for three-dimensional geometric structures, which can solve the problems of high data processing costs and long solution times in related technologies.

[0004] In a first aspect, embodiments of this disclosure provide a physical field simulation method for a three-dimensional geometric structure, including:

[0005] Based on the physical data of the three-dimensional geometric structure, the geometric features and physical quantity features of the three-dimensional geometric structure are obtained; The geometric features and physical quantity features of the three-dimensional geometric structure are fused to obtain the fused features; By aggregating local neighborhood information through a graph neural network, the fused features are mapped to a latent feature space to obtain latent features; Based on the potential features, a physical field simulation operation is performed to obtain the physical field simulation results of the three-dimensional geometric structure.

[0006] Secondly, embodiments of this disclosure provide a method for training a physics field simulation model, including: Based on the physical data of the three-dimensional geometric structure sample, obtain the geometric features and physical quantity features of the three-dimensional geometric structure sample; The geometric features and physical quantity features of the three-dimensional geometric structure sample are input into the physical field simulation model; the physical field simulation model is used to fuse the geometric features and physical quantity features to obtain fused features, and to aggregate local neighborhood information through a graph neural network, map the fused features to a latent feature space to obtain latent features, and to perform physical field simulation operations based on the latent features to obtain the physical field simulation results of the three-dimensional geometric structure. Based on the physical field simulation results, true values ​​of the physical field, and surface normal vectors output by the physical field simulation model, a model loss value is generated. The physical field simulation model is trained based on the model loss value.

[0007] Thirdly, embodiments of this disclosure provide a physical field simulation device for a three-dimensional geometric structure, comprising: The feature extraction module is used to obtain the geometric features and physical quantity features of the three-dimensional geometric structure based on the physical data of the three-dimensional geometric structure. The feature fusion module is used to fuse the geometric features and physical quantity features of the three-dimensional geometric structure to obtain fused features; The encoding module is used to aggregate local neighborhood information through a graph neural network and map the fused features to a latent feature space to obtain latent features; The decoding module is used to perform physical field simulation operations based on the potential features to obtain the physical field simulation results of the three-dimensional geometric structure.

[0008] Fourthly, embodiments of this disclosure provide a training apparatus for a physics field simulation model, comprising: The feature extraction module is used to obtain the geometric features and physical quantity features of the three-dimensional geometric structure sample based on the physical data of the three-dimensional geometric structure sample; The input module is used to input the geometric features and physical quantity features of the three-dimensional geometric structure sample into the physical field simulation model; the physical field simulation model is used to fuse the geometric features and physical quantity features to obtain fused features, and to aggregate local neighborhood information through a graph neural network, map the fused features to a latent feature space to obtain latent features, and to perform physical field simulation operations based on the latent features to obtain the physical field simulation results of the three-dimensional geometric structure; The loss generation module is used to generate model loss values ​​based on the physical field simulation results, physical field truth values, and surface normal vectors output by the physical field simulation model. The training module is used to train the physical field simulation model based on the model loss value.

[0009] Fifthly, embodiments of this disclosure provide an electronic device, including: At least one processor; and A memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor to enable the at least one processor to perform the methods described in the first and second aspects above.

[0010] In a sixth aspect, embodiments of this disclosure provide a non-transitory computer-readable storage medium storing computer instructions, wherein the computer instructions are used to cause the computer to perform the methods described in the first and second aspects above.

[0011] In a seventh aspect, embodiments of this disclosure provide a computer program product, including a computer program, wherein the computer program, when executed by a processor, implements the steps of the methods described in the first and second aspects.

[0012] According to the technical solution disclosed herein, by introducing statistical geometric features and physical flux features based on graph neighborhood as additional input channels, the impact of geometric irregularities in unstructured grids on the simulation accuracy of the model can be resolved. This can enhance the model's ability to perceive key physical regions of the flow field (such as shock waves and separation zones), thereby improving the simulation accuracy and efficiency of the physical field. It can also solve the problems of high data processing costs and long solution times in traditional physical field analysis methods in related technologies.

[0013] It should be understood that the description in this section is not intended to identify key or essential features of the embodiments of this disclosure, nor is it intended to limit the scope of this disclosure. Other features of this disclosure will become readily apparent from the following description. Attached Figure Description

[0014] The accompanying drawings are provided to better understand this solution and do not constitute a limitation of this disclosure. Wherein: Figure 1 This is a flowchart of the physical field simulation method for three-dimensional geometric structures provided in the embodiments of this disclosure; Figure 2 This is a flowchart of the physical field simulation method for three-dimensional geometric structures provided in the embodiments of this disclosure; Figure 3 This is a flowchart of the physical field simulation method for three-dimensional geometric structures provided in the embodiments of this disclosure; Figure 4 This is a flowchart of the training method for the physical field simulation model provided in the embodiments of this disclosure; Figure 5 This is a block diagram of a physical field simulation device for three-dimensional geometric structures provided in the embodiments of this disclosure; Figure 6 This is a block diagram of a physical field simulation device for three-dimensional geometric structures provided in the embodiments of this disclosure; Figure 7 This is a block diagram of a training device for a physics simulation model provided in an embodiment of this disclosure; Figure 8 This is a block diagram of an electronic device according to an embodiment of the present disclosure. Detailed Implementation

[0015] The exemplary embodiments of this disclosure are described below with reference to the accompanying drawings, including various details of the embodiments to aid understanding, and should be considered merely exemplary. Therefore, those skilled in the art will recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of this disclosure. Similarly, for clarity and brevity, descriptions of well-known functions and structures are omitted in the following description.

[0016] This disclosure is not exhaustive, but merely illustrative of some embodiments, and is not intended to limit the scope of protection of this disclosure. Unless otherwise specified, each step in a particular embodiment can be implemented as an independent embodiment, and the steps can be arbitrarily combined. For example, a solution after removing some steps in a particular embodiment can also be implemented as an independent embodiment, and the order of the steps in a particular embodiment can be arbitrarily interchanged. Furthermore, the optional implementation methods in a particular embodiment can be arbitrarily combined; moreover, the embodiments can be arbitrarily combined, for example, some or all steps of different embodiments can be arbitrarily combined, and a particular embodiment can be arbitrarily combined with the optional implementation methods of other embodiments. In all embodiments of this disclosure, unless otherwise specified or logically conflicting, the terminology and / or descriptions between the embodiments are consistent and can be mutually referenced. Technical features in different embodiments can be combined to form new embodiments based on their inherent logical relationships.

[0017] The terminology used in the embodiments of this disclosure is for the purpose of describing particular embodiments only and is not intended to limit the scope of this disclosure.

[0018] This disclosure relates to the fields of artificial intelligence technology, such as deep learning.

[0019] Artificial Intelligence (AI) is a new technological science that studies, develops, and applies theories, methods, technologies, and application systems to simulate, extend, and expand human intelligence.

[0020] Deep learning learns the inherent patterns and hierarchical representations of sample data. The information gained during this learning process greatly aids in interpreting data such as text, images, and sound. The ultimate goal of deep learning is to enable machines to possess analytical and learning capabilities similar to humans, allowing them to recognize data such as text, images, and sound.

[0021] It should be noted that the collection, storage, use, processing, transmission, provision, and disclosure of user personal information involved in the technical solution disclosed herein all comply with the provisions of relevant laws and regulations and do not violate public order and good morals.

[0022] It should also be noted that the information (including but not limited to user device information, user personal information, etc.), data (including but not limited to data used for analysis, data stored, data displayed, etc.) and signals involved in this disclosure are all authorized by the user or fully authorized by all parties, and the collection, use and processing of related data must comply with the relevant laws, regulations and standards of the relevant countries and regions.

[0023] The physical field simulation method, model training method, and apparatus for three-dimensional geometric structures according to embodiments of the present disclosure are described below with reference to the accompanying drawings.

[0024] It should be noted that the execution subject of the physical field simulation method for three-dimensional geometric structures in this embodiment of the present disclosure can be a physical field simulation device for three-dimensional geometric structures. This device can be implemented by software and / or hardware, and can be configured in an electronic device, which may include, but is not limited to, a terminal, a server, etc.

[0025] It is worth noting that the physical field simulation method for three-dimensional geometric structures in this disclosure embodiment can be implemented by an autonomous agent based on a large model, which can perform accurate simulation of the physical field based on a given three-dimensional geometric structure file or physical data.

[0026] It should be noted that the technical solutions of this disclosure can be widely applied in the following fields: (1) Aerospace Engineering Aerodynamic shape optimization: Real-time simulation of the aerodynamic performance of different wing and fuselage shapes, supporting interactive design optimization; Flow field visualization: Quickly generate flow field distributions around complex aircraft to assist in aerodynamic analysis; Multi-condition simulation: Quickly evaluate aerodynamic characteristics at different angles of attack and Mach numbers.

[0027] (2) Automotive Engineering Drag optimization: Simulate the pressure distribution and flow field structure around the vehicle body to optimize the vehicle body shape to reduce drag; Engine compartment thermal management: Simulate the temperature field distribution inside the engine compartment to optimize heat dissipation design; Wind noise simulation: Simulates flow field separation at locations such as rearview mirrors and A-pillars to assess wind noise levels.

[0028] (3) Energy and Power Engineering Wind turbine aerodynamic analysis: Simulate the three-dimensional flow field around the wind turbine blades to optimize the blade design; Heat exchanger design: Simulate the flow and heat transfer inside the heat exchanger to improve heat exchange efficiency; Nuclear power plant safety analysis: rapid assessment of fluid behavior under accident conditions.

[0029] (4) Building and Environmental Engineering Building wind environment: Simulate the wind field distribution around the building complex and assess pedestrian wind comfort; Indoor ventilation design: Simulate indoor airflow organization to optimize HVAC system design; Pollutant diffusion: Simulates atmospheric pollutant diffusion at the city scale to support environmental assessment.

[0030] It is worth noting that the physics simulation scheme for the three-dimensional geometric structure provided in this disclosure can be applied to the following products or projects: Intelligent CFD (Computational Fluid Dynamics) simulation platform: replaces traditional numerical solvers, achieving second-level flow field simulation; Industrial design and optimization system: supports real-time aerodynamic shape optimization and heat dissipation structure design; Digital Twin System: Provides a high-efficiency physics simulation engine for digital twins; Large Model for Scientific Computing: Embedded as a foundational module in the large model of scientific computing.

[0031] Figure 1 This is a flowchart of a physical field simulation method for three-dimensional geometric structures provided in this disclosure. Figure 1 As shown, the physical field simulation method for this three-dimensional geometric structure may include, but is not limited to, the following steps.

[0032] In step 101, the geometric features and physical quantity features of the three-dimensional geometric structure are obtained based on the physical data of the three-dimensional geometric structure.

[0033] It is worth noting that the three-dimensional geometric structure used in the physical field simulation method provided in this disclosure varies depending on the field and application scenario. For example, when applying this technical solution to aerospace engineering for aerodynamic shape optimization, the three-dimensional geometric structure can be the three-dimensional geometric structure of an aircraft. As another example, when applying this technical solution to automotive engineering for wind resistance optimization, the three-dimensional geometric structure can be the three-dimensional geometric structure of a car body; if applied to engine compartment thermal management in automotive engineering, the three-dimensional geometric structure can be the three-dimensional geometric structure of a car engine. The examples given above are merely illustrative to facilitate understanding of the three-dimensional geometric structure by those skilled in the art and should not be construed as limiting this disclosure. In other words, the three-dimensional geometric structure can also be the object of study for analyzing physical fields in other fields or application scenarios, which will not be elaborated further here.

[0034] In some embodiments, the physical data of a three-dimensional geometric structure may refer to the three-dimensional data of the object surface of the three-dimensional geometric structure. Optionally, the physical data may include, but is not limited to, the point cloud coordinates of the surface of the three-dimensional geometric structure, and may also include surface normal vectors. In some possible embodiments, the physical data of the three-dimensional geometric structure may be physical data obtained by analyzing the physical model of the three-dimensional geometric structure (such as a CAD (Computer-Aided Design) model), but is not limited thereto. For example, the physical data of the three-dimensional geometric structure may also be physical data directly input by the user. This disclosure does not specifically limit or elaborate on this.

[0035] In embodiments of this disclosure, geometric features can be extracted from the physical data of a three-dimensional geometric structure. These geometric features may include, but are not limited to, point cloud coordinates (point cloud coordinates of the surface of the three-dimensional geometric structure) and normal vectors (normal vectors of the surface of the three-dimensional geometric structure). The physical data of the three-dimensional geometric structure can be used to extract statistical geometric features and physical flux features based on graph neighborhoods, thereby obtaining the physical quantity features of the three-dimensional geometric structure. By introducing statistical geometric features and physical flux features based on graph neighborhoods as additional input channels, this disclosure can address the impact of geometric irregularities in unstructured meshes on the simulation accuracy of the model and enhance the model's ability to perceive key physical regions of the flow field (such as shock waves and separation zones).

[0036] In step 102, the geometric features and physical quantity features of the three-dimensional geometric structure are fused to obtain fused features.

[0037] In some possible embodiments, the fusion operation can be feature stitching. For example, the geometric features and physical quantity features of a three-dimensional geometric structure can be stitched together, and the resulting feature can be used as the fused feature.

[0038] In some possible implementations, a nonlinear recovery network (Recovery MLP) can be used for adaptive feature fusion. As an example, the formula for this nonlinear recovery network can be expressed as follows: f_enhanced = MLP(Concat(f_raw, f_geo)), where f_raw is the geometric feature (e.g., point cloud coordinates, normal vector, etc.), f_geo is the physical quantity feature, and Concat is the concatenation function; MLP is a multilayer perceptron, which can be used to map the concatenated heterogeneous features back to the latent space dimension and automatically learn the weight contribution of geometric features to the physical field simulation.

[0039] To eliminate the influence of dimensions between features and for ease of data processing, the geometric and physical features of the 3D geometric structure can be normally normalized separately before merging them. For example, training set statistics can be used to normalize the geometric and physical features. For instance, taking point cloud coordinates as an example, training set statistics can be used to scale the point cloud coordinates to the range [-1, 1] or a specific physical domain. As another example, taking normal vectors as an example, the normal vectors can be standardized. This involves determining the global mean and standard deviation of the normal vectors of the 3D geometric structure, and then using these global mean and standard deviation to standardize the normal vectors of each physical point (or query point) on the surface of the 3D geometric structure. The formula for this standardization can be expressed as: x_norm = (x - mean) / std, where x_norm is the normal vector obtained after normalizing the normal vector x, mean is the global mean of the normal vectors, and std is the standard deviation. For example, physical quantity characteristics can also be standardized, and the processing method is similar to that of normal vector standardization, which will not be elaborated here.

[0040] In step 103, local neighborhood information is aggregated through a graph neural network, and the fused features are mapped to the latent feature space to obtain latent features.

[0041] In some possible embodiments, an encoder can be used to encode the fused features, facilitating their mapping to a latent feature space to obtain latent features. For example, the fused features can be input into an encoder, which, based on the constructed latent feature space and graph structure, aggregates local neighborhood information through a graph neural network to map the fused features to the latent feature space, thus obtaining latent features.

[0042] In one possible implementation, the aforementioned latent feature space and graph structure can be constructed as follows: (1) Latent Token Generation: Generate a regular grid of points within the physical domain as latent space query points for the physics simulation model. For example, a three-dimensional grid can be generated using a multi-grid creation function (such as torch.meshgrid) and scaled to a scale consistent with physical coordinates; (2) Multi-scale Graph Connection: Construct a bipartite graph between physical nodes and latent tokens. Based on the set neighborhood radius and multi-scale scales, determine the edge index of the encoder and decoder to achieve information aggregation and distribution from the physical space to the latent space.

[0043] In step 104, a physical field simulation operation is performed based on the latent features to obtain the physical field simulation results of the three-dimensional geometric structure.

[0044] In some possible embodiments, latent features can be interpolated back to physical surface nodes. Optionally, latent features (i.e., features on points in the latent feature space) can be aggregated to corresponding physical surface nodes based on the nearest neighbor relationship between physical points and the latent feature space. This aggregation method can be a weighted summation. For example, the features on points in the latent feature space can be weighted and summed with the features (geometric features) of the corresponding physical surface nodes to interpolate the latent features back to the physical surface nodes, thus completing the decoding of the latent features and obtaining the physical field simulation results. Since the features used for physical field simulation are normalized, the physical field simulation results obtained after decoding are also normalized physical field simulation results. The physical field simulation results can be denormalized to obtain the final physical field simulation results of the three-dimensional geometric structure.

[0045] Optionally, in some possible embodiments, the physical field simulation method for three-dimensional geometric structures involved in this disclosure can be implemented using a physical field simulation model. For example, the geometric features and physical quantity features of the three-dimensional geometric structure can be used as model inputs to the physical field simulation model. The physical field simulation model can fuse the geometric features and physical quantity features of the three-dimensional geometric structure to obtain fused features, and aggregate local neighborhood information through a graph neural network to map the fused features to a latent feature space to obtain latent features. Based on the latent features, physical field simulation operations can be performed, thereby outputting the physical field simulation results of the three-dimensional geometric structure.

[0046] In the above embodiments, geometric features and physical quantity features can be extracted from the physical data of the three-dimensional geometric structure, and then fused. Local neighborhood information is aggregated through a graph neural network, and the fused features are mapped to a latent feature space to obtain latent features. Based on these latent features, physical field simulation operations can be performed to obtain the physical field simulation results for the three-dimensional geometric structure. This disclosure, by introducing statistical geometric features and physical flux features based on graph neighborhoods as additional input channels, can address the impact of geometric irregularities in unstructured meshes on the model simulation accuracy. It can enhance the model's perception of key physical regions of the flow field (such as shock waves and separation zones), thereby improving the model simulation accuracy and efficiency of the physical field. This addresses the problems of high data processing costs and long solution times inherent in traditional physical field analysis methods in related technologies.

[0047] Optionally, in some possible embodiments, such as Figure 2 As shown, the optional implementation methods for obtaining the physical quantity characteristics of a three-dimensional geometric structure based on its physical data may include, but are not limited to, the following steps.

[0048] In step 201, a local graph structure is constructed based on the physical data of the three-dimensional geometric structure; statistical geometric features are extracted based on the local graph structure.

[0049] In some possible embodiments, for physical data of a three-dimensional geometric structure, a local graph structure is constructed based on radius search or the K-nearest neighbor algorithm, and statistical geometric features are extracted from this local graph structure. In embodiments of this disclosure, these statistical geometric features may include, but are not limited to: neighborhood distribution statistics, local PCA (Principal Component Analysis) features, and normal statistics for roughness and curvature.

[0050] For example, this neighborhood distribution statistical feature can be used to characterize the sparsity and uniformity of the local mesh, correcting simulation biases caused by non-uniform sampling. This neighborhood distribution statistical feature may include, but is not limited to: average neighborhood distance (e.g., represented by D_avg), distance variance (e.g., represented by D_var), and centroid offset (e.g., represented by Delta).

[0051] As an example, the formula for average neighborhood distance is as follows: D_avg = (1 / k) SUM(norm(x_j- x_i)) is a function that sums up points, k is the number of neighboring points, norm represents the Euclidean distance, x_i and x_j represent two points in the neighborhood, and norm(x_j - x_i) represents the Euclidean distance from point x_i to point x_j in the neighborhood.

[0052] As an example, the formula for distance variance (D_var) is as follows: D_var = Mean(d 2 ) - (Mean(d)) 2 Where Mean is the mean function, and d is the distance from a neighboring point to the center point. This feature is truncated to a non-negative value and can be used to measure the dispersion of the grid distribution.

[0053] As an example, the centroid offset (Delta) is expressed as follows: Delta = Centroid(N(x)) –x, representing the deviation vector between the neighborhood geometric center N(x) and the centroid of the query point x. For example, the neighborhood geometric center N(x) can be the geometric centroid of all points in the neighborhood (such as the average position). Using the physical data of the three-dimensional geometry, the average neighborhood distance, distance variance, and centroid offset can be determined using their respective formulas. Thus, the determined average neighborhood distance, distance variance, and centroid offset can be used as statistical features of the neighborhood distribution.

[0054] For example, this local geometry PCA feature can extract the anisotropy of the local geometry by performing eigenvalue decomposition on the covariance matrix of the neighborhood coordinates. As an example, the coordinate covariance matrix Cov_coord can be constructed, and its eigenvalues ​​lambda_1, lambda_2, and lambda_3 can be solved. Using these eigenvalues ​​as input features can identify geometric structures such as planes, edges, or sharp corners (e.g., when one eigenvalue is much larger than the other two, it indicates a linear structure).

[0055] For example, this normal roughness and curvature feature can utilize the statistical properties of normal vectors to characterize small changes (such as roughness) or drastic changes (such as geometrical abrupt changes) on a surface. As an example, this normal roughness and curvature feature may include mean normal, normal covariance feature (Normal PCA), etc. Here, the mean normal can refer to the average of the normal vectors of all points in the neighborhood. The eigenvalues ​​of the covariance matrix of the normal vector differences can be used as the normal covariance feature by determining the covariance matrix of the normal vector differences and its eigenvalues. This normal covariance feature has rotation invariance and can effectively characterize the local curvature complexity and geometric noise of the surface.

[0056] In step 202, data processing is performed based on the geometric features of the local graph structure and the global flow field condition features to obtain physical flux proxy features.

[0057] In some possible embodiments, the geometric features of the local graph structure and the global flow field condition features can be summed by dot product to obtain the convective flux proxy features of the local graph structure; the geometric features of the local graph structure and the global flow field condition features can be summed by dot product and the absolute value can be taken, and the absolute value can be averaged to obtain the numerical dissipation proxy features of the local graph structure; the flux proxy features and the numerical dissipation proxy features can be fused to obtain the physical flux proxy features.

[0058] Optionally, the aforementioned global flow field condition features can be determined based on the global flow field condition information provided by the user. For example, taking the global flow field condition feature as the wind speed vector (e.g., represented by V_wind), the geometric features of the local graph structure (normal vector n_j) and the global flow field condition features (e.g., the wind speed vector) can be coupled to obtain the convective flux proxy feature and the numerical dissipation proxy feature.

[0059] As an example, the formula for the convective flux proxy feature is as follows: F_flux = Sum(dot(n_j , V_wind)), where dot is the dot product function. The physical meaning of this formula is that the sign of the dot product directly indicates the windward and leeward sides. This feature helps the model distinguish between positive and negative pressure zones at the geometric level.

[0060] As an example, the formula for the numerical dissipative surrogate feature (Lax-Friedrichs Flux Proxy) is as follows: F_lf = Mean(abs(dot(n_j, V_wind))), where abs is the absolute value function. The physical meaning of this formula is: a statistical measure based on the absolute value of wave velocity. This feature simulates the dissipative term in the Lax-Friedrichs numerical scheme and is crucial for capturing shock waves and high-gradient flow field regions.

[0061] The flow rate proxy feature and the numerical dissipation proxy feature can be obtained by using the data processing formulas for the flow rate proxy feature and the numerical dissipation proxy feature, respectively. The flow rate proxy feature and the numerical dissipation proxy feature are then concatenated, and the concatenated feature is used as the physical flow rate proxy feature.

[0062] In step 203, the physical quantity characteristics of the three-dimensional geometric structure are obtained based on statistical geometric features and physical flux proxy features.

[0063] In some possible embodiments, statistical geometric features and physical flux surrogate features can be concatenated, and the concatenated features can be used as physical quantity features of the three-dimensional geometric structure.

[0064] In the above embodiments, the introduction of PCA geometric features enhances the topological awareness of the flow field, enabling the physical field simulation model to distinguish regions of dramatic geometric changes in three-dimensional structures (such as the leading and trailing edges of an airfoil), significantly reducing pressure simulation errors in these regions. Physical flux surrogate features endow the model with "flow direction awareness," allowing it to geometrically distinguish between windward shock waves and leeward separated flows without the need for an additional flow field solver. Neighborhood distribution statistical features (mean and variance) enable the model to adapt to non-uniform, sparse, or low-quality meshes, improving its generalization ability under different mesh densities. By introducing numerical dissipation surrogate features, the shock wave capture mechanism in the CFD solver is simulated, resulting in sharper and more accurate simulated shock wave locations.

[0065] Figure 3 This is a flowchart of a physical field simulation method for three-dimensional geometric structures provided in this disclosure. Figure 3 As shown, the physical field simulation method for this three-dimensional geometric structure may include, but is not limited to, the following steps.

[0066] In step 301, the geometric features and physical quantity features of the three-dimensional geometric structure are obtained based on the physical data of the three-dimensional geometric structure.

[0067] In the embodiments of this disclosure, step 301 can be implemented in any of the ways described in the various embodiments of this disclosure. This disclosure does not limit this and will not elaborate further.

[0068] In step 302, the geometric features and physical quantity features of the three-dimensional geometric structure are fused to obtain fused features.

[0069] To eliminate the influence of dimensions between features and for ease of data processing, the geometric and physical features of the 3D geometric structure can be normally normalized separately before merging them. For example, training set statistics can be used to normalize the geometric and physical features.

[0070] In the embodiments of this disclosure, step 302 can be implemented in any of the ways described in the various embodiments of this disclosure. This disclosure does not limit this and will not elaborate further.

[0071] In step 303, local neighborhood information is aggregated through a graph neural network, and the fused features are mapped to the latent feature space to obtain latent features.

[0072] In the embodiments of this disclosure, step 303 can be implemented in any of the ways described in the various embodiments of this disclosure. This disclosure does not limit this and will not elaborate further.

[0073] In step 304, the latent features are enhanced based on a hybrid architecture of three-dimensional axial attention and fully self-attention.

[0074] In the embodiments of this disclosure, during the encoding stage, local neighborhood information is aggregated using a graph neural network to map the fused features to a latent feature space. After obtaining the latent features, these latent features can be enhanced using a hybrid architecture based on 3D axial attention and fully self-attention. To balance long-range dependency capture with local detail modeling, as an example, this hybrid architecture can adopt a hybrid mode configured as "aaaaffaaaa", i.e.: Shallow layers (Layer 1-4): Four layers of 3D axial-attention modules are stacked consecutively to quickly process local 3D structures; Middle layer (Layer 5-6): Insert two standard full self-attention modules to achieve full fusion of global contextual information; Deep layers (Layer 7-10): Stack four more 3D axial attention modules to refine high-level semantic features.

[0075] It should be noted that the above-described 3D axial attention mechanism can be understood as follows: 3D attention is decomposed into data processing along three orthogonal axes: depth, height, and width. For example, for latent features, attention processing is first performed on the depth axis (Depth-Axis). This involves spatially rearranging the feature map and performing attention processing along the depth axis D. That is, after normalizing the 3D feature map Z, attention processing (AxialAttn) is performed on the normalized feature map along the depth axis D to obtain a feature, which is then superimposed on the original 3D feature map Z to obtain Z_d, expressed as: Z_d = Z + AxialAttn_D( Norm(Z) ). Then, attention processing is performed on the height axis (Height-Axis), that is, based on the output of the depth axis attention processing, attention processing is performed along the height axis H, expressed as: Z_h = Z_d + AxialAttn_H( Norm(Z_d) ). Finally, attention processing is performed along the width axis (W), i.e., based on the output of the height axis attention processing, attention processing is performed along the width axis W, expressed as: Z_out = Z_h + AxialAttn_W( Norm(Z_h) ). This three-dimensional axial attention mechanism can be used to enhance latent features.

[0076] Optionally, when enhancing latent features using the three-dimensional axial attention mechanism, for any axis (taking the axis length L as an example), the specific data processing unit (AxialAttn unit) can adopt grouped-query attention (GQA) combined with QK normalization. The specific steps are as follows: (1) Projection and grouping (GQA mechanism): The input features are linearly mapped to obtain the query matrix Q, the key matrix K, and the value matrix V. The formula is expressed as: Q = X·W_Q, K = X·W_K, V = X·W_V, where the number of heads of Q is num_heads, and the number of heads of K and V is num_kv_heads. When num_kv_heads < num_heads, the number of heads of K and V can be extended to be consistent with Q through the repeat interleave strategy to reduce the video memory occupancy of the key-value cache (KV Cache) and accelerate inference.

[0077] (2) QK normalization: In some embodiments, before determining the attention scores based on the three-dimensional axial attention mechanism, layer normalization can be performed on the query matrix Q and the key matrix K. To improve the stability of large model training, before determining the attention scores, layer normalization (Layer Normalization) can be performed on the query matrix Q and the key matrix K. The formula is expressed as: Q_norm = LayerNorm(Q), K_norm = LayerNorm(K).

[0078] (3) 3D rotational position encoding (RoPE 3D): In some embodiments, when performing attention processing based on the three-dimensional axial attention mechanism, rotational position encoding can be injected into the query matrix Q and the key matrix K according to the absolute position of the current dimensional axis in the three-dimensional grid to retain relative position information. This can capture the geometric relationships in three-dimensional space better than traditional absolute position encoding.

[0079] Optionally, the present disclosure can use the 3D rotational position encoding technology to extend the position encoding from one-dimensional space to three-dimensional space. The 3D rotational position encoding technology will be introduced below: Let the position in the three-dimensional grid be: p = (x, y, z), where: x represents the coordinate in the width direction, y represents the coordinate in the height direction, and z represents the coordinate in the depth direction. Let the total number of feature dimensions be D, which is divided into three subspaces: D = Dx + Dy + Dz, where: Dx is the feature dimension corresponding to the x direction, Dy is the feature dimension corresponding to the y direction, and Dz is the feature dimension corresponding to the z direction. Respectively determine the corresponding one-dimensional RoPE frequency vectors based on the three coordinates: θx ∈ R {Dx} , θy ∈ R {Dy}, θz∈R {Dz} Where θx is generated from coordinate x, θy from coordinate y, and θz from coordinate z. As an example, taking θx as an example, θx can be determined by the following formula: θx k =10000 -2k / Dx k=0,1,2,… θx k Let be the k-th frequency vector. Concatenate the frequency vectors in the x, y, and z directions to construct a combined frequency tensor: Θ = Concat(θz, θy, θx), where Θ ∈ R. {D} Concat represents the vector concatenation operation.

[0080] Let q∈C {D} Let k ∈ C be the query vector. {D} Let q and k be the key vectors, and treat them as complex field vectors (usually, two adjacent real dimensions are combined into one complex dimension). Perform element-wise rotation on each element: q' = q⊙exp(iΘ), k' = k⊙exp(iΘ), where: ⊙ represents the Hadamard product (element-wise multiplication), i is the imaginary unit, satisfying i² = -1, and exp(iΘ) represents the data processing on each element of Θ to obtain the complex exponent.

[0081] When performing attention processing based on a three-dimensional axial attention mechanism, the query matrix Q and the key matrix K can be rotated and encoded according to the absolute position of the current dimensional axis in the three-dimensional mesh using the aforementioned 3D rotational position encoding technique. By applying the rotational encoding to the three orthogonal directions of x, y, and z, positional relationships in three-dimensional space are modeled, while preserving the relative positional characteristics and rotational isometry of RoPE. Thus, this disclosure decouples the positional information of the height, width, and depth dimensions through channel segmentation, allowing the model to independently perceive the relative distances in different dimensions. It reuses the mature one-dimensional RoPE operator, requiring only one frequency concatenation and complex multiplication, without additional data processing resource overhead, thereby improving data processing efficiency. It retains the long-range decay characteristics of RoPE, and the attention weight between any two points depends only on the relative distance in each dimension.

[0082] (4) Attention processing and output: Determine the Scaled Dot-Product Attention, expressed by the formula: Score = (Q_rot·K_rot) T= ) / sqrt(d_k), AttnMap = Softmax(Score), Output = AttnMap·V. For example, the attention score Score can be determined using the query matrix (represented by Q_rot) and the key matrix (represented by K_rot) after 3D rotation position encoding. Then, the attention score is normalized to obtain the attention weight. The attention weight is weighted with the value matrix V, and finally, the attention processing result for the current axis is obtained through the output projection layer W_O.

[0083] It is worth noting that the complexity of the standard 3D Self-Attention mechanism is O((HWD)). 2 This disclosure employs three-dimensional axial attention, which reduces the complexity to O(HWD·(H + W + D)). When H=W=D=n, the complexity can be reduced from O(n 6 Reduced to O(n) 4 This significantly reduces the amount of computation.

[0084] In step 305, a physical field simulation operation is performed based on the enhanced latent features to obtain the physical field simulation results of the three-dimensional geometric structure.

[0085] In the embodiments of this disclosure, step 305 can be implemented in any of the ways described in the various embodiments of this disclosure. This disclosure does not limit this and will not elaborate further.

[0086] In the above embodiments, high-resolution 3D voxel data far exceeding GPU memory limitations can be processed through orthogonal axis decomposition and GQA mechanisms. The introduction of QK Norm technology effectively prevents gradient instability caused by attention score overflow during large-scale 3D data training. 3D RoPE rotational position encoding, compared to traditional learnable position encoding, better captures relative distance relationships in 3D space, enabling precise position awareness. By introducing a hybrid architecture design of 3D axial attention and fully self-attention, the inference speed (mostly linear complexity axial layers) is maintained while the intermediate fully attention layer solves the problem of "limited receptive field" in pure axial networks.

[0087] Optionally, the physics simulation method for the three-dimensional geometric structure involved in the embodiments of this disclosure can be implemented using a physics simulation model, which can be pre-trained using training data. See also Figure 4 This is a flowchart of a training method for a physics simulation model provided in an embodiment of this disclosure. For example... Figure 4 As shown, the training method for this physical field simulation model may include, but is not limited to, the following steps.

[0088] In step 401, the geometric features and physical quantity features of the three-dimensional geometric structure sample are obtained based on the physical data of the three-dimensional geometric structure sample.

[0089] In some embodiments, the physical data of a three-dimensional geometric sample may refer to the three-dimensional data of the object surface of the three-dimensional geometric sample. Optionally, the physical data may include, but is not limited to, the point cloud coordinates of the surface of the three-dimensional geometric sample, and may also include surface normal vectors. In some possible embodiments, the physical data of a three-dimensional geometric sample may be physical data obtained by analyzing the physical model of the three-dimensional geometric sample (such as a CAD (Computer-Aided Design) model), but is not limited thereto. For example, the physical data of the three-dimensional geometric sample may also be physical data directly input by the user. This disclosure does not specifically limit or elaborate on this.

[0090] In embodiments of this disclosure, geometric features can be extracted from the physical data of a three-dimensional geometric structure sample. These geometric features may include, but are not limited to, point cloud coordinates (point cloud coordinates of the surface of the three-dimensional geometric structure sample) and normal vectors (normal vectors of the surface of the three-dimensional geometric structure sample). The physical data of the three-dimensional geometric structure sample can be used to extract statistical geometric features and physical flux features based on graph neighborhood, thereby obtaining the physical quantity features of the three-dimensional geometric structure sample. By introducing statistical geometric features and physical flux features based on graph neighborhood as additional input channels, this disclosure can address the impact of geometric irregularities in unstructured meshes on the model's simulation accuracy and enhance the model's ability to perceive key physical regions of the flow field (such as shock waves and separation zones).

[0091] In step 402, the geometric features and physical quantity features of the three-dimensional geometric structure sample are input into the physical field simulation model.

[0092] In the embodiments of this disclosure, the physical field simulation model can be used to fuse geometric features and physical quantity features to obtain fused features, aggregate local neighborhood information through a graph neural network, map the fused features to a latent feature space to obtain latent features, and perform physical field simulation operations based on the latent features to obtain the physical field simulation results of the three-dimensional geometric structure. Optional implementation methods can be found in the relevant steps described in the embodiments of the physical field simulation method for the three-dimensional geometric structure above, and will not be repeated here.

[0093] Optionally, in some embodiments, the physics simulation model can be a neural operator framework for solving partial differential equations in the geometric domain, such as the GAOT 3D model. Exemplarily, the physics simulation model may include a feature fusion module, an encoder, an attention module, and a decoder. The feature fusion module can be used to fuse geometric features and physical quantity features to obtain fused features. The encoder can be used to aggregate local neighborhood information through a graph neural network, mapping the fused features to a latent feature space to obtain latent features. The attention module can be used to enhance the latent features based on a hybrid architecture of 3D axial attention and fully self-attention. The decoder can be used to perform physics simulation operations based on the latent features to obtain physics simulation results for the 3D geometric structure.

[0094] In step 403, the model loss value is generated based on the physical field simulation results, the true value of the physical field, and the surface normal vector output by the physical field simulation model.

[0095] For example, a loss function can be used to generate a model loss value based on the physical field simulation results, the true values ​​of the physical fields, and the surface normal vectors output by the physical field simulation model. As an example, this loss function is constructed based on data supervision loss and physical regularization loss. For instance, the loss function L can be defined as a weighted sum of the data supervision loss (L_data) and the physical regularization loss (L_reg): L = L_data + λ_reg L_reg, where λ_reg is the weight of the physical regularization loss (also called the normal regularization loss).

[0096] The data supervision loss (L_data) can be determined by using mean squared error (MSE) or L1 loss to determine the difference between the simulated physical field value u_pred and the true physical field value u_gt. The physical regularization loss L_reg is determined by introducing physical constraints for vector physical fields (such as wall shear stress), forcing the simulated vector to conform to the surface geometry, determining the dot product of the simulated vector and the surface normal vector, and constraining the tangential characteristics of the flow field by minimizing the square of this dot product: L_reg = mean((u_pred·normal)). 2 ), where: normal is the surface normal vector, and here we take the physical field simulation value as the physical field vector simulation value as an example.

[0097] In this step, a predefined loss function can be used to determine the data supervision loss based on the physical field simulation results and the true value of the physical field, and the physical regularization loss can be determined based on the simulation vector and the surface normal vector. The data supervision loss and the physical regularization loss are then weighted and summed to obtain the model loss value.

[0098] In step 404, the physical field simulation model is trained based on the model loss value.

[0099] In the embodiments of this disclosure, given the model loss value, a gradient is determined based on the model loss value, and the parameters of the physics simulation model are adjusted according to this gradient so that the upper loss value is reduced to the target loss value. During the model training phase, the AdamW optimizer can be used, with weight decay configured. The learning rate scheduling during the model training phase can employ a mixed scheduler strategy, namely: including an initial warmup phase, a subsequent cosine annealing phase, and a final exponential decay phase, and supporting automatic mixed precision (AMP, bfloat16) training to improve efficiency.

[0100] In the above embodiments, by introducing statistical geometric features and physical flux features based on graph neighborhood as additional input channels, the impact of geometric irregularities in unstructured grids on the model simulation accuracy can be resolved. This can enhance the model's ability to perceive key physical regions of the flow field (such as shock waves and separation zones), thereby improving the model simulation accuracy and efficiency of the physical field. It can also solve the problems of high data processing costs and long solution times in traditional physical field analysis methods in related technologies.

[0101] Figure 5 This is a block diagram of a physics field simulation device for a three-dimensional geometric structure provided in an embodiment of this disclosure. Figure 5 As shown, the physical field simulation device for the three-dimensional geometric structure may include: a feature extraction module 501, a feature fusion module 502, an encoding module 503, and a decoding module 504.

[0102] The feature extraction module 501 is used to obtain the geometric features and physical quantity features of the three-dimensional geometric structure based on the physical data of the three-dimensional geometric structure.

[0103] The feature fusion module 502 is used to fuse the geometric features and physical quantity features of the three-dimensional geometric structure to obtain fused features.

[0104] The encoding module 503 is used to aggregate local neighborhood information through a graph neural network, map the fused features to the latent feature space, and obtain latent features.

[0105] The decoding module 504 is used to perform physical field simulation operations based on latent features to obtain physical field simulation results of three-dimensional geometric structures.

[0106] In some embodiments, the feature extraction module 501 is used to: construct a local graph structure based on the physical data of the three-dimensional geometric structure; extract statistical geometric features based on the local graph structure; obtain physical flux surrogate features based on the geometric features of the local graph structure and the global flow field condition features; and obtain physical quantity features of the three-dimensional geometric structure based on the statistical geometric features and the physical flux surrogate features.

[0107] In some embodiments, the feature extraction module 501 is used to: perform dot product summation on the geometric features of the local graph structure and the global flow field condition features to obtain the convective flux proxy features of the local graph structure; perform dot product summation on the geometric features of the local graph structure and the global flow field condition features and take the absolute value, and then average the obtained absolute value to obtain the numerical dissipation proxy features of the local graph structure; and fuse the flux proxy features and the numerical dissipation proxy features to obtain the physical flux proxy features.

[0108] Optionally, in some embodiments, such as Figure 6 As shown, the physics simulation device for the three-dimensional geometric structure may further include a feature enhancement module 605. This feature enhancement module 605 can be used to enhance latent features based on a hybrid architecture of three-dimensional axial attention and fully self-attention; wherein, during attention processing based on the three-dimensional axial attention mechanism, rotational position encoding is injected into the query matrix Q and the key matrix K according to the absolute position of the current dimension axis in the three-dimensional mesh. Figure 6 601-604 and Figure 5 The 501-504 series have the same function and structure.

[0109] In some embodiments, the feature enhancement module 605 is further configured to: perform layer normalization on the query matrix Q and the key matrix K before determining the attention score based on the three-dimensional axial attention mechanism.

[0110] In some embodiments, the decoding module is used to: interpolate potential features to physical surface nodes based on the nearest neighbor relationship between physical points and potential feature space points to obtain normalized physical quantity simulation results; and perform inverse normalization processing on the normalized physical quantity simulation results to obtain physical field simulation results of three-dimensional geometric structures.

[0111] Regarding the apparatus in the above embodiments, the specific manner in which each module performs its operation has been described in detail in the embodiments related to the method, and will not be elaborated upon here.

[0112] Figure 7 This is a block diagram of a training device for a physics simulation model provided in an embodiment of this disclosure. Figure 7As shown, the training device for the physical field simulation model may include: a feature extraction module 701, an input module 702, a loss generation module 703, and a training module 704.

[0113] The feature extraction module 701 is used to obtain the geometric features and physical quantity features of the three-dimensional geometric structure sample based on the physical data of the three-dimensional geometric structure sample.

[0114] The input module 702 is used to input the geometric features and physical quantity features of the three-dimensional geometric structure sample into the physical field simulation model. The physical field simulation model is used to fuse the geometric features and physical quantity features to obtain fused features, and to aggregate local neighborhood information through a graph neural network, map the fused features to the latent feature space to obtain latent features, and to perform physical field simulation operations based on the latent features to obtain the physical field simulation results of the three-dimensional geometric structure.

[0115] The loss generation module 703 is used to generate model loss values ​​based on the physical field simulation results, physical field truth values, and surface normal vectors output by the physical field simulation model.

[0116] Training module 704 is used to train the physics simulation model based on the model loss value.

[0117] Regarding the training device for the physics simulation model in the above embodiments, the specific methods by which each module performs its operations have been described in detail in the embodiments related to the method, and will not be elaborated upon here.

[0118] According to embodiments of this disclosure, this disclosure also provides an electronic device and a readable storage medium.

[0119] like Figure 8 The diagram shown is a block diagram of an electronic device according to an embodiment of the present disclosure. The electronic device is intended to represent various forms of digital computers, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The electronic device may also represent various forms of mobile devices, such as personal digital processors, cellular phones, smartphones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely illustrative and are not intended to limit the implementation of the present disclosure described and / or claimed herein.

[0120] like Figure 8As shown, the electronic device includes one or more processors 801, a memory 802, and interfaces for connecting the components, including high-speed interfaces and low-speed interfaces. The components are interconnected via different buses and can be mounted on a common motherboard or otherwise as required. The processors can process instructions executed within the electronic device, including instructions stored in or on memory to display graphical information of a GUI on an external input / output device (such as a display device coupled to the interface). In other embodiments, multiple processors and / or multiple buses can be used with multiple memories and multiple memory modules, if desired. Similarly, multiple electronic devices can be connected, each providing some of the necessary operations (e.g., as a server array, a group of blade servers, or a multiprocessor system). Figure 8 Take the 801 processor as an example.

[0121] The memory 802 is the non-transitory computer-readable storage medium provided in this disclosure. The memory stores instructions executable by at least one processor to cause the at least one processor to perform the physics simulation method or physics simulation model training method for three-dimensional geometric structures provided in this disclosure. The non-transitory computer-readable storage medium of this disclosure stores computer instructions for causing a computer to perform the physics simulation method or physics simulation model training method for three-dimensional geometric structures provided in this disclosure.

[0122] Memory 802, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs, non-transitory computer-executable programs, and modules, such as the program instructions / modules corresponding to the physical field simulation method for three-dimensional geometric structures in the embodiments of this disclosure (e.g., attached...). Figure 5 The feature extraction module 501, feature fusion module 502, encoding module 503, and decoding module 504 shown, or, as indicated, are attached. Figure 6 The feature extraction module 601, feature fusion module 602, encoding module 603, decoding module 604, and feature enhancement module 605 shown, or the program instructions / modules corresponding to the training method of the physical field simulation model in the embodiments of this disclosure (e.g., attached...). Figure 7 The feature extraction module 701, input module 702, loss calculation module 703, and training module 704 are shown. The processor 801 executes various server functions and data processing by running non-transient software programs, instructions, and modules stored in the memory 802, thereby realizing the physical field simulation method or physical field simulation model training method for the three-dimensional geometric structure in the above method embodiments.

[0123] The memory 802 may include a program storage area and a data storage area. The program storage area may store the operating system and applications required for at least one function; the data storage area may store data created based on the use of the electronic device. Furthermore, the memory 802 may include high-speed random access memory and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, the memory 802 may optionally include memory remotely located relative to the processor 801, and these remote memories can be connected to the electronic device via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0124] The electronic device may also include an input device 803 and an output device 804. The processor 801, memory 802, input device 803, and output device 804 can be connected via a bus or other means. Figure 8 Taking the example of a connection between China and Israel via a bus.

[0125] Input device 803 can receive input numerical or character information, and generate key signal inputs related to user settings and function control of the electronic device, such as touch screens, keypads, mice, trackpads, touchpads, joysticks, one or more mouse buttons, trackballs, joysticks, etc. Output device 804 may include display devices, auxiliary lighting devices (e.g., LEDs), and haptic feedback devices (e.g., vibration motors). The display device may include, but is not limited to, liquid crystal displays (LCDs), light-emitting diode (LED) displays, and plasma displays. In some embodiments, the display device may be a touch screen.

[0126] Various implementations of the systems and techniques described herein can be implemented in digital electronic circuit systems, integrated circuit systems, application-specific integrated circuits (ASICs), computer hardware, firmware, software, and / or combinations thereof. These various implementations may include: implementations in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which may be a dedicated or general-purpose programmable processor, capable of receiving data and instructions from a storage system, at least one input device, and at least one output device, and transmitting data and instructions to the storage system, the at least one input device, and the at least one output device.

[0127] These computational programs (also referred to as programs, software, software applications, or code) include machine instructions for a programmable processor and can be implemented using high-level procedural and / or object-oriented programming languages, and / or assembly / machine languages. As used herein, the terms “machine-readable medium” and “computer-readable medium” refer to any computer program product, device, and / or apparatus (e.g., disk, optical disk, memory, programmable logic device (PLD)) used to provide machine instructions and / or data to a programmable processor, including machine-readable media that receive machine instructions as machine-readable signals. The term “machine-readable signal” refers to any signal used to provide machine instructions and / or data to a programmable processor.

[0128] To provide interaction with a user, the systems and techniques described herein can be implemented on a computer having: a display device for displaying information to the user (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor); and a keyboard and pointing device (e.g., a mouse or trackball) through which the user provides input to the computer. Other types of devices can also be used to provide interaction with the user; for example, feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including sound input, voice input, or tactile input).

[0129] The systems and technologies described herein can be implemented in computing systems that include backend components (e.g., as data servers), or middleware components (e.g., application servers), or frontend components (e.g., user computers with graphical user interfaces or web browsers through which users can interact with implementations of the systems and technologies described herein), or any combination of such backend, middleware, or frontend components. The components of the system can be interconnected via digital data communication of any form or medium (e.g., communication networks). Examples of communication networks include local area networks (LANs), wide area networks (WANs), the Internet, and blockchain networks.

[0130] Computer systems can include clients and servers. Clients and servers are generally geographically separated and typically interact via communication networks. The client-server relationship is created by computer programs running on the respective computers and having a client-server relationship with each other. A server can be a cloud server, also known as a cloud computing server or cloud host, a hosting product within the cloud computing service system that addresses the shortcomings of traditional physical hosts and VPS (Virtual Private Server) services, such as high management difficulty and weak business scalability. Servers can also be servers for distributed systems or servers incorporating blockchain technology.

[0131] It should be understood that the various forms of processes shown above can be used to rearrange, add, or delete steps. For example, the steps described in this application can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this disclosure can be achieved, and this is not limited herein.

[0132] The specific embodiments described above do not constitute a limitation on the scope of protection of this disclosure. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this disclosure should be included within the scope of protection of this disclosure.

Claims

1. A physical field simulation method for a three-dimensional geometric structure, comprising: Based on the physical data of the three-dimensional geometric structure, the geometric features and physical quantity features of the three-dimensional geometric structure are obtained; The geometric features and physical quantity features of the three-dimensional geometric structure are fused to obtain the fused features; By aggregating local neighborhood information through a graph neural network, the fused features are mapped to a latent feature space to obtain latent features; Based on the potential features, a physical field simulation operation is performed to obtain the physical field simulation results of the three-dimensional geometric structure.

2. The method according to claim 1, wherein, Based on the physical data of the three-dimensional geometric structure, the physical quantity characteristics of the three-dimensional geometric structure are obtained, including: Based on the physical data of the three-dimensional geometric structure, a local graph structure is constructed; Statistical geometric features are extracted based on the local graph structure; Data processing is performed based on the geometric features of the local graph structure and the global flow field condition features to obtain physical flux proxy features; Based on the statistical geometric features and the physical flux proxy features, the physical quantity features of the three-dimensional geometric structure are obtained.

3. The method according to claim 2, wherein, The step of processing data based on the geometric features of the local graph structure and the global flow field condition features to obtain physical flux proxy features includes: The geometric features of the local graph structure and the global flow field condition features are summed by dot product to obtain the convective flux proxy features of the local graph structure. The geometric features of the local graph structure and the global flow field condition features are multiplied by a dot product and the absolute value is taken. The absolute values ​​are then averaged to obtain the numerical dissipation surrogate features of the local graph structure. The physical flux proxy feature is obtained by fusing the flux proxy feature and the numerical dissipation proxy feature.

4. The method according to any one of claims 1-3, further comprising: The latent features are enhanced using a hybrid architecture based on 3D axial attention and fully self-attention. Specifically, when performing attention processing based on the 3D axial attention mechanism, rotational position encoding is injected into the query matrix Q and the key matrix K according to the absolute position of the current dimension axis in the 3D mesh.

5. The method according to claim 4, further comprising: Before determining the attention score based on the three-dimensional axial attention mechanism, the query matrix Q and the key matrix K are subjected to layer normalization.

6. The method according to claim 1, wherein, The physical field simulation operation based on the latent features, to obtain the physical field simulation results of the three-dimensional geometric structure, includes: Based on the nearest neighbor relationship between physical points and potential feature spatial points, the potential features are interpolated to physical surface nodes to obtain normalized physical quantity simulation results. The normalized physical quantity simulation results are denormalized to obtain the physical field simulation results of the three-dimensional geometric structure.

7. A training method for a physics field simulation model, comprising: Based on the physical data of the three-dimensional geometric structure sample, obtain the geometric features and physical quantity features of the three-dimensional geometric structure sample; The geometric features and physical quantity features of the three-dimensional geometric structure sample are input into the physical field simulation model; the physical field simulation model is used to fuse the geometric features and physical quantity features to obtain fused features, and to aggregate local neighborhood information through a graph neural network, map the fused features to a latent feature space to obtain latent features, and to perform physical field simulation operations based on the latent features to obtain the physical field simulation results of the three-dimensional geometric structure. Based on the physical field simulation results, true values ​​of the physical field, and surface normal vectors output by the physical field simulation model, a model loss value is generated. The physical field simulation model is trained based on the model loss value.

8. A physical field simulation device with a three-dimensional geometric structure, comprising: The feature extraction module is used to obtain the geometric features and physical quantity features of the three-dimensional geometric structure based on the physical data of the three-dimensional geometric structure. The feature fusion module is used to fuse the geometric features and physical quantity features of the three-dimensional geometric structure to obtain fused features; The encoding module is used to aggregate local neighborhood information through a graph neural network and map the fused features to a latent feature space to obtain latent features; The decoding module is used to perform physical field simulation operations based on the potential features to obtain the physical field simulation results of the three-dimensional geometric structure.

9. A training device for a physics field simulation model, comprising: The feature extraction module is used to obtain the geometric features and physical quantity features of the three-dimensional geometric structure sample based on the physical data of the three-dimensional geometric structure sample; The input module is used to input the geometric features and physical quantity features of the three-dimensional geometric structure sample into the physical field simulation model; the physical field simulation model is used to fuse the geometric features and physical quantity features to obtain fused features, and to aggregate local neighborhood information through a graph neural network, map the fused features to a latent feature space to obtain latent features, and to perform physical field simulation operations based on the latent features to obtain the physical field simulation results of the three-dimensional geometric structure; The loss generation module is used to generate model loss values ​​based on the physical field simulation results, physical field truth values, and surface normal vectors output by the physical field simulation model. The training module is used to train the physical field simulation model based on the model loss value.

10. An electronic device, comprising: At least one processor; as well as A memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor to enable the at least one processor to perform the method of any one of claims 1-6 and 7.

11. A non-transitory computer-readable storage medium storing computer instructions, wherein, The computer instructions are used to cause the computer to perform the method according to any one of claims 1-6 and 7.

12. A computer program product comprising a computer program, wherein, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 11-6 and 7.

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