Large-scale grid intelligent generation method based on operator learning and related equipment

Abstract

The invention provides an operator learning-based large-scale grid intelligent generation method and related equipment, and is applied to the technical field of grid generation. The method is applied to a double-branch shared backbone network architecture, and the double-branch shared backbone network architecture is composed of a shared backbone network, a first branch network and a second branch network. According to the method, global features of computational domain coordinates are extracted through a shared backbone network, meanwhile, transverse and longitudinal distribution characteristics of boundary coordinates are learned through a double-branch network, multi-dimensional feature coupling is achieved through operator learning of multivariate mapping, and finally a physical domain grid is generated through coordinate mapping. On the premise of ensuring accurate capture of boundary features, efficient and high-quality grid generation is realized through sharing feature multiplexing and multivariable decoupling processing, and generalization to different geometric shapes can be realized, so that collaborative optimization of complex geometric adaptability, multivariable coupling capability and calculation efficiency is achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of grid generation, and in particular to a large-scale grid intelligent generation method based on operator learning and related equipment. Background Art

[0002] In the fields of scientific computing and engineering simulation, structured mesh generation is the core foundation of numerical analysis, and its quality directly affects computational accuracy and resource efficiency. However, when faced with complex geometries, the contradiction between quality and efficiency of traditional methods is becoming increasingly prominent.

[0003] Traditional mesh generation methods mainly include fast generation techniques based on transfinite interpolation and high-quality generation techniques that rely on solving partial differential equations. Although the former can quickly construct meshes, it is difficult to accurately capture complex geometric features. Although the latter can ensure mesh quality, it has a bottleneck of low computational efficiency. To overcome the limitations of traditional methods, physical information-driven methods have significantly improved generation efficiency by integrating physical constraints with machine learning algorithms. However, their models are heavily dependent on the geometric distribution characteristics of training data, resulting in repeated training when faced with new topological structures, making it difficult to meet the needs of real-time dynamic adjustment. Operator learning methods developed in recent years have shown potential by establishing a mapping relationship between input parameters and output meshes. However, existing technologies mainly focus on single-variable mapping scenarios and cannot effectively handle complex mapping relationships of multiple variables such as geometric parameters in mesh generation, which restricts their practical engineering application value.

[0004] Therefore, how to resolve the contradiction between mesh quality and generation efficiency and develop a mesh generation method that takes into account efficient generation, strong generalization ability and supports multi-variable coupling has become a technical problem that technical personnel in this field urgently need to solve. Summary of the Invention

[0005] In view of the above problems, the present invention provides a large-scale grid intelligent generation method based on operator learning and related equipment that overcomes the above problems or at least partially solves the above problems. The technical solution is as follows:

[0006] A large-scale grid intelligent generation method based on operator learning is applied to a dual-branch shared backbone network architecture, wherein the dual-branch shared backbone network architecture comprises a shared backbone network, a first branch network, and a second branch network. The method comprises:

[0007] Obtaining a computational domain coordinate set of a target geometric shape, wherein the computational domain coordinate set includes computational domain coordinates of grid points extracted from a square uniform grid mapped on the computational domain by the target geometric shape;

[0008] Obtaining a first boundary function and a second boundary function of the target geometric shape, wherein the first boundary function is composed of abscissas of boundary points of the target geometric shape collected from a physical domain, and the second boundary function is composed of ordinates of the boundary points;

[0009] Using the first branch network to perform feature extraction on the horizontal coordinate of each boundary point in the first boundary function to obtain a first boundary feature vector of the target geometric shape;

[0010] Using the second branch network to perform feature extraction on the ordinate of each boundary point in the second boundary function to obtain a second boundary feature vector of the target geometric shape;

[0011] Using the shared backbone network to perform feature extraction on the computational domain coordinates of each grid point in the computational domain coordinate set to obtain a high-dimensional shared feature vector of the target geometric shape;

[0012] Based on an operator learning algorithm, the high-dimensional shared feature vector is respectively fused with the first boundary feature vector and the second boundary feature vector to obtain the physical domain coordinates of the grid points corresponding to the computational domain coordinates of the grid points in the physical domain;

[0013] The physical domain coordinates of each of the grid points are used to generate a physical domain grid of the target geometric shape.

[0014] Optionally, obtaining the first boundary function and the second boundary function of the target geometric shape includes:

[0015] Using a subsampling strategy, collecting position coordinates of a preset number of boundary points of the target geometric shape in the physical domain by fixing the sensor position;

[0016] The position coordinates of each of the boundary points are converted into a first boundary function and a second boundary function represented by a finite-dimensional vector.

[0017] Optionally, the method further includes:

[0018] Defining a joint loss function, wherein the joint loss function is equal to a weighted sum of an internal loss term and a boundary loss term;

[0019] Based on the joint loss function, the network parameters of the dual-branch shared backbone network architecture are optimized to minimize the value of the joint loss function and realize nonlinear mapping from boundary conditions to grid nodes.

[0020] Optionally, the using the first branch network to perform feature extraction on the horizontal coordinate of each boundary point in the first boundary function to obtain a first boundary feature vector of the target geometric shape includes:

[0021] Inputting the first boundary function into the multi-layer fully connected network of the first branch network, performing dimensionality reduction on the horizontal coordinate of each boundary point in the first boundary function to extract features, and obtaining a first dimensionality reduction feature representation of the first boundary function;

[0022] The first dimensionality reduction feature representation is input into the branch layer of the first branch network, and feature extraction is performed on the first dimensionality reduction feature representation to obtain a first boundary feature vector of the target geometric shape.

[0023] Optionally, the using the second branch network to perform feature extraction on the ordinate of each boundary point in the second boundary function to obtain a second boundary feature vector of the target geometric shape includes:

[0024] Inputting the second boundary function into the multi-layer fully connected network of the second branch network, performing dimensionality reduction on the ordinate of each boundary point in the second boundary function to extract features, and obtaining a second dimensionality reduction feature representation of the second boundary function;

[0025] The second dimensionality reduction feature representation is input into the branch layer of the second branch network, and feature extraction is performed on the second dimensionality reduction feature representation to obtain a second boundary feature vector of the target geometric shape.

[0026] Optionally, the using the shared backbone network to perform feature extraction on the computational domain coordinates of each grid point in the computational domain coordinate set to obtain a high-dimensional shared feature vector of the target geometric shape includes:

[0027] Inputting the computational domain coordinate set into the dimensionality-increasing layer of the shared backbone network, expanding the computational domain coordinates of each grid point in the computational domain coordinate set into a high-dimensional space, and obtaining a high-dimensional shared feature representation of the computational domain coordinate set;

[0028] The high-dimensional feature representation is input into the backbone layer of the shared backbone network, and feature extraction is performed on the high-dimensional shared feature representation to obtain a high-dimensional shared feature vector of the target geometric shape.

[0029] Optionally, the operator learning algorithm is used to perform feature fusion on the high-dimensional shared feature vector with the first boundary feature vector and the second boundary feature vector to obtain the physical domain coordinates of the grid points corresponding to the computational domain coordinates of the grid points in the physical domain, including:

[0030] The high-dimensional shared feature vector, the first boundary feature vector, and the second boundary feature vector are input into the formula:

[0031]

[0032]

[0033] Obtain the physical domain coordinates of the grid points corresponding to the computational domain coordinates of each grid point in the physical domain, wherein: Number The physical domain abscissa of the physical domain coordinate of the grid point; Number The physical domain ordinate of the physical domain coordinate of the grid point; is the operator corresponding to the first branch network; is the operator corresponding to the second branch network; is the first boundary function; is the second boundary function; For and number The computational domain abscissa corresponding to the physical domain abscissa of the physical domain coordinate of the grid point; For and number The computational domain ordinate corresponding to the physical domain ordinate of the physical domain coordinate of the grid point; is the first boundary eigenvector; is the second boundary eigenvector; is the high-dimensional shared feature vector; The first branch network output Weight coefficients; The second branch network output Weight coefficients; The first Features, used for linear combination with the weights of branch network output; is the bias term corresponding to the first branch network; is the bias term corresponding to the second branch network.

[0034] A large-scale grid intelligent generation device based on operator learning is applied to a dual-branch shared backbone network architecture. The dual-branch shared backbone network architecture consists of a shared backbone network, a first branch network, and a second branch network. The device includes: a computational domain coordinate set acquisition unit, a boundary function acquisition unit, a first boundary feature vector acquisition unit, a second boundary feature vector acquisition unit, a high-dimensional shared feature vector acquisition unit, a feature fusion unit, and a grid generation unit.

[0035] The calculation domain coordinate set obtaining unit is used to obtain a calculation domain coordinate set of a target geometric shape, wherein the calculation domain coordinate set includes calculation domain coordinates of grid points extracted from a square uniform grid mapped on the calculation domain by the target geometric shape;

[0036] The boundary function obtaining unit is configured to obtain a first boundary function and a second boundary function of the target geometric shape, wherein the first boundary function is composed of abscissas of boundary points of the target geometric shape collected from a physical domain, and the second boundary function is composed of ordinates of the boundary points;

[0037] The first boundary feature vector obtaining unit is configured to use the first branch network to perform feature extraction on the horizontal coordinate of each boundary point in the first boundary function to obtain a first boundary feature vector of the target geometric shape;

[0038] The second boundary feature vector obtaining unit is configured to use the second branch network to perform feature extraction on the ordinate of each boundary point in the second boundary function to obtain a second boundary feature vector of the target geometric shape;

[0039] The high-dimensional shared feature vector obtaining unit is configured to use the shared backbone network to perform feature extraction on the computational domain coordinates of each grid point in the computational domain coordinate set to obtain a high-dimensional shared feature vector of the target geometric shape;

[0040] The feature fusion unit is configured to perform feature fusion on the high-dimensional shared feature vector with the first boundary feature vector and the second boundary feature vector based on an operator learning algorithm to obtain the physical domain coordinates of the grid points corresponding to the computational domain coordinates of the grid points in the physical domain;

[0041] The grid generation unit is used to generate a physical domain grid of the target geometric shape using the physical domain coordinates of each grid point.

[0042] A computer-readable storage medium stores a program, which, when executed by a processor, implements the large-scale grid intelligent generation method based on operator learning.

[0043] An electronic device comprising at least one processor, and at least one memory and a bus connected to the processor; wherein the processor and the memory communicate with each other via the bus; and the processor is used to call program instructions in the memory to execute the large-scale grid intelligent generation method based on operator learning.

[0044] By means of the above technical solution, the large-scale grid intelligent generation method based on operator learning and related equipment provided by the present invention are applied to a dual-branch shared backbone network architecture, which is composed of a shared backbone network, a first branch network and a second branch network. The method includes: obtaining a calculation domain coordinate set of a target geometric shape, wherein the calculation domain coordinate set includes the calculation domain coordinates of grid points extracted from a square uniform grid mapped on the calculation domain by the target geometric shape; obtaining a first boundary function and a second boundary function of the target geometric shape, wherein the first boundary function is composed of the horizontal coordinates of the boundary points of the target geometric shape collected from the physical domain, and the second boundary function is composed of the vertical coordinates of the boundary points; using the first branch network to generate a target geometric shape; obtaining ... The horizontal coordinates of each boundary point in the first boundary function are feature extracted to obtain the first boundary feature vector of the target geometric shape; the vertical coordinates of each boundary point in the second boundary function are feature extracted using the second branch network to obtain the second boundary feature vector of the target geometric shape; the computational domain coordinates of each grid point in the computational domain coordinate set are feature extracted using the shared backbone network to obtain the high-dimensional shared feature vector of the target geometric shape; based on the operator learning algorithm, the high-dimensional shared feature vector is feature fused with the first boundary feature vector and the second boundary feature vector respectively to obtain the physical domain coordinates of the grid points corresponding to the computational domain coordinates of each grid point in the physical domain; and the physical domain coordinates of each grid point are used to generate the physical domain grid of the target geometric shape. The present invention extracts the global features of the computational domain coordinates through a shared backbone network, and adopts a dual-branch network to respectively learn the horizontal and vertical distribution characteristics of the boundary coordinates, and uses operator learning of multivariable mapping to realize multi-dimensional feature coupling. Finally, the physical domain grid is generated through coordinate mapping. Under the premise of ensuring the accurate capture of boundary features, efficient and high-quality grid generation is achieved through shared feature reuse and multivariable decoupling processing, and it can be generalized to different geometric shapes, thereby achieving the coordinated optimization of complex geometric adaptability, multivariable coupling capability and computational efficiency.

[0045] The above description is only an overview of the technical solution of the present invention. In order to more clearly understand the technical means of the present invention, it can be implemented in accordance with the contents of the specification. In order to make the above and other purposes, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are specifically listed below. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Various other advantages and benefits will become apparent to those skilled in the art upon reading the detailed description of the preferred embodiment below. The accompanying drawings are for illustration purposes only and are not to be considered as limiting the present invention. The same reference symbols are used throughout the drawings to represent the same components. In the drawings:

[0047] Figure 1A schematic diagram showing a flow chart of an implementation of a large-scale grid intelligent generation method based on operator learning provided by an embodiment of the present invention;

[0048] Figure 2 A schematic diagram showing a flow chart of another implementation of a large-scale grid intelligent generation method based on operator learning provided by an embodiment of the present invention;

[0049] Figure 3 A schematic diagram showing a flow chart of another implementation of a large-scale grid intelligent generation method based on operator learning provided by an embodiment of the present invention;

[0050] Figure 4 A schematic diagram showing a flow chart of another implementation of a large-scale grid intelligent generation method based on operator learning provided by an embodiment of the present invention;

[0051] Figure 5 A schematic diagram showing a flow chart of another implementation of a large-scale grid intelligent generation method based on operator learning provided by an embodiment of the present invention;

[0052] Figure 6 A schematic diagram showing a flow chart of another implementation of a large-scale grid intelligent generation method based on operator learning provided by an embodiment of the present invention;

[0053] Figure 7 A schematic diagram of a grid generation logic based on a dual-branch shared backbone network architecture provided by an embodiment of the present invention is shown;

[0054] Figure 8 A schematic diagram of the structure of a large-scale grid intelligent generation device based on operator learning provided by an embodiment of the present invention is shown;

[0055] Figure 9 A schematic structural diagram of an electronic device provided by an embodiment of the present invention is shown. DETAILED DESCRIPTION

[0056] Exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present invention are shown in the accompanying drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present invention and to fully convey the scope of the present invention to those skilled in the art.

[0057] In scientific computing and engineering simulation, structured mesh generation is a prerequisite and foundation for numerical analysis and solving complex physical problems. High-quality meshes not only improve computational accuracy but also significantly reduce computing resource consumption. However, with increasing computational demands, traditional mesh generation methods face numerous challenges, especially when dealing with complex geometries.

[0058] Traditional mesh generation methods primarily include transfinite interpolation and differential equation methods. Transfinite interpolation methods are widely used due to their rapid generation speed, but they can easily produce low-quality meshes when faced with complex geometries. This is because these methods provide insufficiently detailed descriptions of the geometry during the generation process, which compromises the smoothness and uniformity of the mesh. On the other hand, while differential equation methods can generate high-quality meshes, they are computationally expensive and inefficient. These methods typically require significant computational resources, and when dealing with large-scale problems, computational time increases exponentially, limiting their application.

[0059] To address the shortcomings of traditional methods, physics-based mesh generation methods have emerged. These methods improve mesh generation efficiency by leveraging physical information and machine learning techniques. However, physics-based methods often require retraining the model to handle new geometries, resulting in insufficient generalization. This limitation makes these methods unsuitable for real-time or large-scale applications, especially in scenarios where frequent geometric adjustments are required.

[0060] In recent years, operator learning methods have gained increasing attention as an emerging technology. These methods solve complex tasks by learning operator mapping relationships, offering considerable flexibility and adaptability. However, existing operator learning methods primarily target single-variable mapping problems and face challenges with multivariable mapping when applied to mesh generation. Therefore, extending operator learning methods to multivariable mapping to meet the demands of mesh generation has become a pressing issue.

[0061] In summary, although traditional mesh generation methods and emerging physical information-driven methods have played an important role in their respective fields, they both have shortcomings in processing complex geometries and meeting real-time performance.

[0062] Based on this, in an embodiment of the present invention, a large-scale intelligent grid generation method based on operator learning is provided. First, the method proposes a dual-branch shared backbone neural network architecture. Through the neural network architecture, it can significantly improve the generation efficiency while generating high-quality grids, solving the trade-off problem between efficiency and grid quality in traditional methods. Secondly, the method converts the grid generation task into an operator learning problem of multi-variable mapping, solving the problem that existing operator learning methods can only handle single-variable mappings, and enables it to be applied to grid generation tasks. At the same time, combined with an efficient neural network structure, it can adapt to the geometric shapes and requirements of diverse grid generation tasks without retraining, solving the problem that physical information-driven methods need to be retrained when faced with new geometric shapes, and achieving efficient and high-quality grid generation, thereby promoting the development of scientific computing and engineering simulation.

[0063] The large-scale grid intelligent generation method based on operator learning provided by an embodiment of the present invention is applied to a dual-branch shared backbone network architecture, which consists of a shared backbone network, a first branch network and a second branch network.

[0064] The dual-branch shared trunk network architecture is a deep learning model structure consisting of a shared trunk network (Trunk Network) and two independent branch networks (Branch-x Network and Branch-y Network). The input of the dual-branch shared trunk network architecture is the computational domain coordinates and two boundary functions, and the output is the corresponding physical domain coordinates.

[0065] The shared backbone network is used to extract features from the computational domain coordinates and capture the coupling relationships between different coordinates. This network effectively integrates high-dimensional feature information from the computational domain, supporting subsequent boundary feature fusion and improving the overall efficiency and accuracy of mesh generation.

[0066] The first branch network processes the horizontal coordinate (x-coordinate) of the target geometric shape's boundary. By extracting features from the horizontal coordinate data extracted from the physical domain, the first branch network generates a first boundary feature vector. This ensures that the horizontal coordinate features are effectively captured and integrated during mesh generation, providing support for meshing the overall geometric shape.

[0067] The second branch network processes the y-coordinate of the target geometry's boundary. Similar to the first branch network, the second branch performs feature extraction on the extracted y-coordinate data to generate a second boundary feature vector. This second branch network ensures that the y-coordinate features are effectively captured and integrated during mesh generation, supporting meshing of the overall geometry.

[0068] like Figure 1 As shown, a flowchart of an implementation of a large-scale grid intelligent generation method based on operator learning provided by an embodiment of the present invention is provided. The method may include:

[0069] S100 . Obtain a calculation domain coordinate set of a target geometric shape, wherein the calculation domain coordinate set includes calculation domain coordinates of grid points extracted from a square uniform grid mapped on the calculation domain by the target geometric shape.

[0070] In scientific computing and engineering simulation, a target geometry is a specific physical structure or shape that needs to be analyzed and simulated. The target geometry can be two-dimensional or three-dimensional and typically represents the geometric features of a real-world object, such as a building, mechanical component, or other engineering structure.

[0071] The computational domain coordinate set is the set of discretized coordinate points within the computational domain of the target geometric shape involved in the numerical calculation process. Embodiments of the present invention can extract all grid points or randomly sample some grid points from the square uniform grid mapped onto the computational domain of the target geometric shape, and obtain the computational domain coordinates of the corresponding grid points, thereby forming a computational domain coordinate set for subsequent numerical analysis and simulation calculations.

[0072] In structured grid methods, the computational domain refers to a parameterized, regularized mathematical space. A square uniform grid refers to the grid structure that maps the target geometric shape onto the computational domain. It's important to note that different geometric shapes are mapped to square uniform grids within the computational domain. The grid densities of the square uniform grids mapped to different geometric shapes can be the same or different.

[0073] The computational domain coordinates of a grid point are the coordinate values of a grid point extracted from the uniform square grid that maps the target geometry onto the computational domain. These coordinates represent the location of the grid point within the computational domain and serve as fundamental data for numerical calculations and simulation analysis. The computational domain coordinates of each grid point reflect the local characteristics of the target geometry and its distribution within the overall computational domain.

[0074] S110 , obtaining a first boundary function and a second boundary function of the target geometric shape, wherein the first boundary function is composed of the horizontal coordinates of the boundary points of the target geometric shape collected from the physical domain, and the second boundary function is composed of the vertical coordinates of the boundary points.

[0075] The first boundary function refers to a mathematical expression or function composed of the horizontal coordinates (x-coordinates) of the boundary points of the target geometric shape, which is used to describe the characteristics and morphology of the boundary of the target geometric shape in the horizontal direction, so as to accurately reflect the boundary conditions in the numerical calculation.

[0076] Among them, the second boundary function refers to a mathematical expression or function composed of the longitudinal coordinates (y coordinates) of the boundary points of the target geometric shape, which is used to describe the characteristics and morphology of the boundary of the target geometric shape in the longitudinal direction, so as to accurately reflect the boundary conditions in numerical calculations.

[0077] The boundary points refer to the specific coordinate points that constitute the boundary of the target geometric shape and are obtained by collecting in the physical domain.

[0078] Specifically, embodiments of the present invention can collect multiple boundary points evenly or on demand along the boundary of a target geometric shape. For example, embodiments of the present invention can collect boundary points at equal intervals or based on the geometric characteristics of the boundary. Subsequently, all the horizontal coordinates (x-coordinates) of the collected boundary points are input into a function model to form a first boundary function. Similarly, all the vertical coordinates (y-coordinates) of the collected boundary points are input into a corresponding function model to form a second boundary function.

[0079] S120 , using the first branch network to perform feature extraction on the horizontal coordinates of each boundary point in the first boundary function to obtain a first boundary feature vector of the target geometric shape.

[0080] The first boundary feature vector is a high-dimensional vector obtained by extracting features from the horizontal coordinates of each boundary point in the first boundary function through the first branch network. The first boundary feature vector integrates the multidimensional feature information of the horizontal coordinates of the boundary points and can effectively capture the horizontal characteristics and morphology of the target geometry.

[0081] Specifically, the embodiment of the present invention can perform deep learning processing on the input boundary point horizontal coordinate data through the first branch network to identify and learn key features related to the target geometry. Furthermore, the embodiment of the present invention can perform layer-by-layer analysis on the input boundary point horizontal coordinate data through multiple neural network layers in the first branch network to extract information such as boundary shape, curvature changes, and local features, and then integrate the extracted features into a high-dimensional feature vector, that is, the first boundary feature vector used to describe the horizontal feature representation of the target geometry.

[0082] S130 , using the second branch network to perform feature extraction on the ordinate of each boundary point in the second boundary function to obtain a second boundary feature vector of the target geometric shape.

[0083] The second boundary feature vector is a high-dimensional vector obtained by extracting features from the vertical coordinates of each boundary point in the second boundary function through the second branch network. The second boundary feature vector integrates the multidimensional feature information of the vertical coordinates of the boundary points and can effectively capture the vertical characteristics and morphology of the target geometry.

[0084] Specifically, the embodiment of the present invention can perform deep learning processing on the input boundary point vertical coordinate data through the second branch network to identify and learn key features related to the target geometry. Furthermore, the embodiment of the present invention can perform layer-by-layer analysis on the input boundary point vertical coordinate data through multiple neural network layers in the second branch network to extract information such as boundary shape, curvature changes, and local features, and then integrate the extracted features into a high-dimensional feature vector, that is, a second boundary feature vector used to describe the vertical characteristics of the target geometry.

[0085] S140 , using a shared backbone network to perform feature extraction on the computational domain coordinates of each grid point in the computational domain coordinate set, to obtain a high-dimensional shared feature vector of the target geometric shape.

[0086] The high-dimensional shared feature vector is a high-dimensional representation generated by extracting features from the grid point coordinates in the computational domain coordinate set using a shared backbone network. This high-dimensional shared feature vector is used to share the fundamental features of the target geometry with the branch network, improving computational efficiency and reducing redundancy.

[0087] Specifically, embodiments of the present invention utilize a shared backbone network to perform in-depth analysis of input grid point computational domain coordinate data, identifying and extracting meaningful features related to the target geometry. Furthermore, embodiments of the present invention utilize multiple neural network layers within the shared backbone network to extract features from the spatial relationships and structural characteristics between the computational domain coordinates of each grid point in the computational domain coordinate set. These processed features are then integrated into a high-dimensional shared feature vector, providing reliable foundational features for subsequent mesh generation tasks.

[0088] S150 , based on the operator learning algorithm, perform feature fusion on the high-dimensional shared feature vector with the first boundary feature vector and the second boundary feature vector respectively, to obtain the physical domain coordinates of the grid points corresponding to the computational domain coordinates of each grid point in the physical domain.

[0089] Operator learning algorithms are machine learning methods used to learn mappings from one function space to another using input-output data pairs. Specifically, they analyze the relationship between input functions and corresponding output functions to create an operator that effectively transforms the input function into the corresponding output function, thereby facilitating the capture of more complex structural connections between inputs and outputs. Existing operator learning algorithms can only handle single-variable mapping problems, but mesh generation tasks involve multivariable mappings and cannot be directly applied.

[0090] The physical domain coordinates of the grid points refer to the actual position coordinates in the physical space obtained by mapping the computational domain coordinates of each grid point in the computational domain.

[0091] Specifically, the present invention uses an operator learning algorithm to analyze and process the input high-dimensional shared feature vectors and boundary feature vectors, identifying features closely related to the actual location of each grid point in the physical domain. This process effectively captures complex spatial relationships and feature interactions, providing rich information for subsequent feature fusion.

[0092] The embodiments of the present invention can use operator learning algorithms to identify key features related to the positions of grid points in the physical domain from high-dimensional shared feature vectors and boundary feature vectors, so as to capture the complex relationships that affect the physical coordinates of the grid points through in-depth analysis of the spatial distribution and boundary conditions of the grid points, and then learn the interactions and mutual influences between these features through operator learning algorithms, thereby effectively converting high-dimensional input information into corresponding physical domain coordinates, which helps to achieve more accurate grid generation.

[0093] The embodiments of the present invention utilize an operator learning algorithm to treat the multivariate mapping problem as a feature learning problem. The operator learning algorithm adaptively integrates the boundary feature vectors output by the branch network and uses the learned operators to establish a nonlinear mapping relationship between the input feature vectors and the output physical domain coordinates, effectively addressing the limitations of traditional operator learning algorithms in multidimensional data mapping.

[0094] S160 , using the physical domain coordinates of each grid point to generate a physical domain grid of the target geometric shape.

[0095] The physical domain is the actual physical area. The physical domain mesh is the grid structure that represents the target geometry in the physical domain. The physical domain coordinates of the grid points in the physical domain mesh define the position and shape of the target geometry in space.

[0096] Specifically, embodiments of the present invention may use physical domain coordinates to determine the specific location of each grid point in the physical domain, and then connect these grid points according to the arrangement and connection rules of the grid points to generate a physical domain grid of the target geometric shape.

[0097] The large-scale grid intelligent generation method based on operator learning provided by the present invention is applied to a dual-branch shared backbone network architecture, which is composed of a shared backbone network, a first branch network, and a second branch network. The method comprises: obtaining a computational domain coordinate set of a target geometric shape, wherein the computational domain coordinate set comprises computational domain coordinates of grid points extracted from a computational domain grid of the target geometric shape; obtaining a first boundary function and a second boundary function of the target geometric shape, wherein the first boundary function is composed of the horizontal coordinates of the boundary points of the target geometric shape collected from the physical domain, and the second boundary function is composed of the vertical coordinates of the boundary points; using the first branch network to perform computational operations on each boundary point in the first boundary function. The horizontal coordinate of the target geometry is extracted to obtain the first boundary feature vector of the target geometry; the second branch network is used to extract the vertical coordinate of each boundary point in the second boundary function to obtain the second boundary feature vector of the target geometry; the shared backbone network is used to extract the computational domain coordinates of each grid point in the computational domain coordinate set to obtain the high-dimensional shared feature vector of the target geometry; based on the operator learning algorithm, the high-dimensional shared feature vector is respectively fused with the first boundary feature vector and the second boundary feature vector to obtain the physical domain coordinates of the grid points corresponding to the computational domain coordinates of each grid point in the physical domain; the physical domain coordinates of each grid point are used to generate the physical domain grid of the target geometry. The present invention extracts the global features of the computational domain coordinates through a shared backbone network, and at the same time adopts a dual-branch network to learn the horizontal and vertical distribution characteristics of the boundary coordinates respectively, and uses the operator learning of multivariate mapping to realize multi-dimensional feature coupling, and finally generates the physical domain grid through coordinate mapping. Under the premise of ensuring the accurate capture of boundary features, efficient and high-quality grid generation is achieved through shared feature reuse and multivariate decoupling processing, and can be generalized to different geometric shapes, thereby achieving the coordinated optimization of complex geometric adaptability, multivariate coupling capability and computational efficiency.

[0098] Optional, based on Figure 1 The method shown, such as Figure 2 As shown, a flow chart of another implementation of a large-scale grid intelligent generation method based on operator learning provided by an embodiment of the present invention is shown, where step S110 may include:

[0099] S200 , using a subsampling strategy, collecting position coordinates of a preset number of boundary points of a target geometric shape in a physical domain by fixing a sensor position.

[0100] Among them, the sub-sampling strategy refers to the process of collecting boundary points of the target geometric shape by selecting a part of the boundary points instead of using all the boundary points to solve the infinite-dimensional problem of boundary conditions and improve computational efficiency.

[0101] When using a subsampling strategy, embodiments of the present invention first determine the boundary characteristics of the target geometry and the key areas requiring acquisition. Then, at a fixed sensor location, the coordinates of boundary points are selectively acquired according to a preset quantity and distribution strategy. The coordinates of these boundary points represent the physical characteristics of the target geometry. Through appropriate selection and distribution, they effectively capture important information about the geometry, providing efficient and accurate foundational data for subsequent branch network data analysis and numerical simulation.

[0102] S210 , converting the position coordinates of each boundary point into a first boundary function and a second boundary function represented by a finite-dimensional vector.

[0103] For example: Assume that the position coordinates of each boundary point collected are "( , ),( , ),…,( , )", then the first boundary function can be converted to "[ , ,…, ]", the second boundary function can be "[ , ,…, ]”.

[0104] By employing a subsampling strategy, the embodiments of the present invention collect the coordinates of a predetermined number of boundary points of the target geometry in the physical domain using a fixed sensor position. This solves the infinite-dimensional problem of boundary conditions, reducing computational complexity and storage requirements while ensuring the key features and information of the collected boundary information. Furthermore, converting the coordinates of these boundary points into first and second boundary functions represented by finite-dimensional vectors facilitates the mathematical representation of complex geometric features, making subsequent numerical calculations and simulations more efficient and accurate.

[0105] Optional, based on Figure 1 The method shown, such as Figure 3 As shown, a flow chart of another implementation of a large-scale grid intelligent generation method based on operator learning provided by an embodiment of the present invention is provided. The method may further include:

[0106] S300. Define a joint loss function, where the joint loss function is equal to the weighted sum of the internal loss term and the boundary loss term.

[0107] Among them, the joint loss function is a comprehensive objective function used to train and optimize the network parameters of the dual-branch shared backbone network architecture. Multiple loss terms are combined by weighted summation of each loss term, so that multiple constraint targets can be considered simultaneously during the optimization process, thereby guiding the dual-branch shared backbone network architecture to output more accurate results.

[0108] Among them, the internal loss term is a loss function used to ensure that the generated mesh nodes are reasonably distributed within the physical domain.

[0109] Among them, the boundary loss term is a loss function used to ensure that the generated grid nodes meet the boundary conditions.

[0110] S310. Based on the joint loss function, optimize the network parameters of the dual-branch shared backbone network architecture to minimize the value of the joint loss function and realize nonlinear mapping from boundary conditions to grid nodes.

[0111] The network parameters are learnable variables in the dual-branch shared-backbone network architecture. They determine the structure and performance of the neural network and are adjusted during training using optimization algorithms (such as gradient descent) to minimize the value of the joint loss function, thereby making the dual-branch shared-backbone network architecture output closer to the target.

[0112] By defining a joint loss function, the embodiments of the present invention can effectively and simultaneously consider the performance of the dual-branch shared backbone network architecture in both internal feature learning and boundary conditions, ensuring the accuracy and stability of the output results of the dual-branch shared backbone network architecture. By optimizing the network parameters of the dual-branch shared backbone network architecture based on this joint loss function to minimize the value of the loss function, a nonlinear mapping from boundary conditions to mesh nodes can be achieved, thereby improving the dual-branch shared backbone network architecture's ability to capture complex geometric shapes and enhancing the generalization performance of mesh generation.

[0113] Optional, based on Figure 1 The method shown, such as Figure 4 As shown, a flow chart of another implementation of a large-scale grid intelligent generation method based on operator learning provided by an embodiment of the present invention is shown, and step S120 may include:

[0114] S400: Input the first boundary function into the multi-layer fully connected network of the first branch network, perform dimensionality reduction on the horizontal coordinates of each boundary point in the first boundary function and extract features to obtain a first dimensionality reduction feature representation of the first boundary function.

[0115] The multi-layer fully connected network (Adjust-Layer) is a neural network structure in which each neuron in each layer is connected to all neurons in the previous layer. The multi-layer fully connected network of the first branch network is used to map the high-dimensional first boundary function to a low-dimensional first dimensionality reduction feature representation.

[0116] S410: Input the first dimensionality reduction feature representation into a branch layer of a first branch network, perform feature extraction on the first dimensionality reduction feature representation, and obtain a first boundary feature vector of the target geometric shape.

[0117] The branch layer is also a neural network structure, where each neuron in each layer is connected to all neurons in the previous layer. The branch layer (Branch-x-Layer) of the first branch network is used to extract features from the first dimensionality-reduced feature representation to obtain the first boundary feature vector of the target geometric shape.

[0118] The embodiment of the present invention helps to simplify complex lateral boundary information, reduce computational costs, and improve the efficiency of subsequent feature extraction by extracting features through dimensionality reduction. The obtained first dimensionality reduction feature representation is then input into the branch layer for further feature extraction, which can focus more on the learning of key lateral features, thereby generating a more accurate first boundary feature vector of the target geometric shape.

[0119] Optional, based on Figure 1 The method shown, such as Figure 5 As shown, a flow chart of another implementation of a large-scale grid intelligent generation method based on operator learning provided by an embodiment of the present invention is shown, and step S130 may include:

[0120] S500: Input the second boundary function into the multi-layer fully connected network of the second branch network, perform dimensionality reduction on the ordinate of each boundary point in the second boundary function and extract features to obtain a second dimensionality reduction feature representation of the second boundary function.

[0121] The multi-layer fully connected network of the second branch network is used to map the high-dimensional second boundary function into a low-dimensional second dimensionality reduction feature representation.

[0122] S510: Input the second dimensionality reduction feature representation into the branch layer of the second branch network, perform feature extraction on the second dimensionality reduction feature representation, and obtain a second boundary feature vector of the target geometric shape.

[0123] The branch layer (Branch-y-Layer) of the second branch network is used to extract features from the second dimensionality reduction feature representation to obtain a second boundary feature vector of the target geometric shape.

[0124] The embodiment of the present invention helps to simplify complex longitudinal boundary information, reduce computational costs, and improve the efficiency of subsequent feature extraction by extracting features through dimensionality reduction. The obtained second dimensionality reduction feature representation is then input into the branch layer for further feature extraction, which can focus more on the learning of key longitudinal features, thereby generating a more accurate second boundary feature vector of the target geometric shape.

[0125] Optionally, the activation function of the multi-layer fully connected network in the branch network and each neural network layer in the branch layer can be:

[0126]

[0127] in, It is The weight matrix of the layer; It is The bias term of the layer.

[0128] The present invention uses activation functions to introduce nonlinear features in branch networks, enhancing their ability to learn complex data patterns. Using the hyperbolic tangent function as the activation function not only improves the network's gradient propagation during training, but also mitigates the vanishing gradient problem and improves model stability and convergence speed.

[0129] Optional, based on Figure 1 The method shown, such as Figure 6 As shown, a flow chart of another implementation of a large-scale grid intelligent generation method based on operator learning provided by an embodiment of the present invention is shown, and step S140 may include:

[0130] S600: Input the computational domain coordinate set into the dimensionality-increasing layer of the shared backbone network, expand the computational domain coordinates of each grid point in the computational domain coordinate set to a high-dimensional space, and obtain a high-dimensional shared feature representation of the computational domain coordinate set.

[0131] Among them, the lift-layer is a neural network layer that transforms the computational domain coordinates of each grid point in the computational domain coordinate set and expands them to a high-dimensional space.

[0132] Among them, the high-dimensional shared feature representation is the feature expression obtained after the computational domain coordinates of each grid point in the computational domain coordinate set are processed by the dimensionality increase layer.

[0133] S610: Input the high-dimensional feature representation into the backbone layer of the shared backbone network, perform feature extraction on the high-dimensional shared feature representation, and obtain a high-dimensional shared feature vector of the target geometric shape.

[0134] Among them, the trunk layer is a neural network layer that performs in-depth feature extraction and learning on the high-dimensional shared feature representation generated by the dimensionality increase layer.

[0135] Among them, the high-dimensional shared feature vector is the vector representation result output from the backbone layer.

[0136] The embodiment of the present invention can effectively expand the low-dimensional grid point coordinates to high-dimensional space through the dimensionality-raising layer of the shared backbone network, thereby capturing more complex and rich feature information in the data. This high-dimensional shared feature representation can not only preserve the spatial relationship of the original coordinates, but also enhance the shared backbone network's ability to understand geometric shapes. Next, the high-dimensional feature representation is input into the backbone layer for in-depth feature extraction, which will further refine the high-dimensional shared feature vector of the target geometric shape, thereby enabling the shared backbone network to identify and learn more abstract features in the high-dimensional feature space, promoting the capture and understanding of complex geometric shapes, and significantly improving the efficiency of the grid generation task.

[0137] Optional, in the above Figure 1 On the basis of one or more corresponding embodiments, in another optional embodiment provided by the embodiment of the present invention, step S150 may specifically include:

[0138] Input the high-dimensional shared eigenvector, the first boundary eigenvector, and the second boundary eigenvector into the formula:

[0139]

[0140]

[0141] Obtain the physical domain coordinates of the grid points corresponding to the computational domain coordinates of each grid point in the physical domain, where: Number The physical domain abscissa of the physical domain coordinates of the grid point; Number The physical domain ordinate of the physical domain coordinate of the grid point; is the operator corresponding to the first branch network; is the operator corresponding to the second branch network; is the first boundary function; is the second boundary function; For and number The computational domain abscissa corresponding to the physical domain abscissa of the physical domain coordinate of the grid point; For and number The computational domain ordinate corresponds to the physical domain ordinate of the grid point physical domain coordinate; is the first boundary eigenvector; is the second boundary eigenvector; is a high-dimensional shared feature vector; The output of the first branch network Weight coefficients; The output of the second branch network Weight coefficients; The first extracted from the shared backbone network Features, used for linear combination with the weights of branch network output; is the bias term corresponding to the first branch network; is the bias term corresponding to the second branch network.

[0142] In order to facilitate understanding of the overall technical solution of the embodiment of the present invention, Figure 7 To explain: Figure 7 The figure shows a schematic diagram of the grid generation logic based on the dual-branch shared backbone network architecture provided by an embodiment of the present invention. First, prepare the input data, including the calculation domain coordinates ( ), represents the position of the grid point in the computational domain, is the horizontal coordinate of the point in the computational domain, and is the ordinate of the point in the computational domain, and the boundary function and , corresponding to the x-coordinate and y-coordinate of the boundary points respectively. In order to cope with the infinite dimensionality of the boundary conditions, a subsampling strategy is adopted to select m points from the boundary "( , ),( , ),…,( , )", converting them into finite-dimensional vectors: =[ , ,…, ]and =[ , ,…, ].

[0143] Next, the first branch network receives the boundary function The x-coordinate of [ , ,…, ] is used as input, and firstly, the dimension reduction feature extraction is performed through the multi-layer fully connected network (Adjust Layer), and then the features are further extracted in the branch layer (Branch-x-Layer) and finally output as the first boundary feature vector. The boundary function is received by the second branch network The y coordinate of [ , ,…, ] as input, firstly, dimension reduction feature extraction is performed through a multi-layer fully connected network (Adjust Layer), and then features are further extracted in the branch layer (Branch-y-Layer) and finally output as the extracted second boundary feature vector.

[0144] At the same time, the shared backbone network receives the computational domain coordinates ( ) as input, and the coordinates are expanded to a high-dimensional space through a lift-layer to capture linear and nonlinear features. The expansion formula is:

[0145]

[0146] Next, the trunk layer further extracts high-dimensional features through a multi-layer neural network and outputs a high-dimensional shared feature vector of the computational domain coordinates.

[0147] Then, feature fusion combines the features extracted by the first and second branch networks with the features extracted by the shared backbone network through the dot product operation to generate the grid coordinates of the physical domain ( ).

[0148] Joint loss function for training and optimizing a dual-branch shared backbone network architecture according to an embodiment of the present invention for:

[0149]

[0150] in, is the internal loss item; is the boundary loss term; and is a weight coefficient used to balance the effects of internal loss and boundary loss.

[0151] The formula for the internal loss term is:

[0152]

[0153] in, represents the internal grid points of the computational domain, , is the output value of the neural network is the operator corresponding to the first branch network, is the operator corresponding to the second branch network; is the tag value.

[0154] The formula for the boundary loss term is:

[0155]

[0156] in, Represents the boundary grid points of the computational domain.

[0157] The core means of the large-scale intelligent grid generation method based on operator learning provided by the embodiment of the present invention include: 1. Converting the grid generation task into a multivariate mapping problem to overcome the limitation of existing operator learning methods that only handle single-variable mapping; 2. Adopting a dual-branch shared backbone architecture to process x and y coordinates separately while ensuring the coupling relationship between them; 3. Implementing a subsampling strategy to obtain a finite-dimensional representation of boundary points by fixing the sensor position, thereby improving computational efficiency; 4. Possessing strong generalization capabilities, it can adapt between different geometric shapes without retraining, thereby improving practicality. This method effectively resolves the contradiction between efficiency and quality of traditional methods, significantly improving the efficiency of generating high-quality grids; at the same time, it solves the generalization problem of physical information-driven methods that require retraining when facing new geometric shapes; and through operator learning of multivariate mapping, it overcomes the limitations of existing methods and makes them suitable for grid generation tasks.

[0158] Although the operations are depicted in a particular order, this should not be understood as requiring that the operations be performed in the particular order shown or in a sequential order.Multitasking and parallel processing may be advantageous under certain circumstances.

[0159] It should be understood that the various steps described in the method embodiments of the present invention may be performed in different orders and / or in parallel. In addition, the method embodiments may include additional steps and / or omit the steps shown. The scope of the present invention is not limited in this respect.

[0160] Corresponding to the above method embodiment, the embodiment of the present invention also provides a large-scale grid intelligent generation device based on operator learning, which is applied to a dual-branch shared backbone network architecture. The dual-branch shared backbone network architecture consists of a shared backbone network, a first branch network and a second branch network. The structure of the device is as follows: Figure 8 As shown, it may include: a computational domain coordinate set obtaining unit 10, a boundary function obtaining unit 20, a first boundary feature vector obtaining unit 30, a second boundary feature vector obtaining unit 40, a high-dimensional shared feature vector obtaining unit 50, a feature fusion unit 60 and a grid generating unit 70.

[0161] The calculation domain coordinate set obtaining unit 10 is used to obtain a calculation domain coordinate set of a target geometric shape, wherein the calculation domain coordinate set includes calculation domain coordinates of grid points extracted from a square uniform grid mapped on the calculation domain by the target geometric shape.

[0162] The boundary function obtaining unit 20 is used to obtain a first boundary function and a second boundary function of the target geometric shape, wherein the first boundary function is composed of the horizontal coordinates of the boundary points of the target geometric shape collected from the physical domain, and the second boundary function is composed of the vertical coordinates of the boundary points.

[0163] The first boundary feature vector obtaining unit 30 is configured to use the first branch network to perform feature extraction on the horizontal coordinates of each boundary point in the first boundary function to obtain a first boundary feature vector of the target geometric shape.

[0164] The second boundary feature vector obtaining unit 40 is configured to use a second branch network to perform feature extraction on the ordinate of each boundary point in the second boundary function to obtain a second boundary feature vector of the target geometric shape.

[0165] The high-dimensional shared feature vector obtaining unit 50 is used to extract features from the computational domain coordinates of each grid point in the computational domain coordinate set using a shared backbone network to obtain a high-dimensional shared feature vector of the target geometric shape.

[0166] The feature fusion unit 60 is used to perform feature fusion on the high-dimensional shared feature vector with the first boundary feature vector and the second boundary feature vector based on the operator learning algorithm to obtain the physical domain coordinates of the grid points corresponding to the computational domain coordinates of each grid point in the physical domain.

[0167] The grid generation unit 70 is used to generate a physical domain grid of the target geometric shape using the physical domain coordinates of each grid point.

[0168] Optionally, the boundary function acquisition unit 20 is specifically used to use a subsampling strategy to collect the position coordinates of a preset number of boundary points of the target geometric shape in the physical domain by fixing the sensor position; and convert the position coordinates of each boundary point into a first boundary function and a second boundary function represented by a finite-dimensional vector.

[0169] Optionally, the device may further include: a network parameter optimization unit.

[0170] The network parameter optimization unit is used to define a joint loss function, where the joint loss function is equal to the weighted sum of the internal loss term and the boundary loss term; based on the joint loss function, the network parameters of the dual-branch shared backbone network architecture are optimized to minimize the value of the joint loss function and realize the nonlinear mapping from boundary conditions to grid nodes.

[0171] Optionally, the first boundary feature vector obtaining unit 30 is specifically used to input the first boundary function into the multi-layer fully connected network of the first branch network, perform dimensionality reduction and feature extraction on the horizontal coordinates of each boundary point in the first boundary function, and obtain the first dimensionality reduction feature representation of the first boundary function; input the first dimensionality reduction feature representation into the branch layer of the first branch network, perform feature extraction on the first dimensionality reduction feature representation, and obtain the first boundary feature vector of the target geometric shape.

[0172] Optionally, the second boundary feature vector obtaining unit 40 is specifically used to input the second boundary function into the multi-layer fully connected network of the second branch network, perform dimensionality reduction and feature extraction on the vertical coordinates of each boundary point in the second boundary function, and obtain a second dimensionality reduction feature representation of the second boundary function; input the second dimensionality reduction feature representation into the branch layer of the second branch network, perform feature extraction on the second dimensionality reduction feature representation, and obtain a second boundary feature vector of the target geometric shape.

[0173] Optionally, the high-dimensional shared feature vector obtaining unit 50 is specifically used to input the computational domain coordinate set into the dimensionality increasing layer of the shared backbone network, expand the computational domain coordinates of each grid point in the computational domain coordinate set to the high-dimensional space, and obtain a high-dimensional shared feature representation of the computational domain coordinate set; input the high-dimensional feature representation into the backbone layer of the shared backbone network, perform feature extraction on the high-dimensional shared feature representation, and obtain a high-dimensional shared feature vector of the target geometric shape.

[0174] Optionally, the feature fusion unit 60 is specifically configured to input the high-dimensional shared feature vector, the first boundary feature vector, and the second boundary feature vector into the formula:

[0175]

[0176]

[0177] Obtain the physical domain coordinates of the grid points corresponding to the computational domain coordinates of each grid point in the physical domain, where: Number The physical domain abscissa of the physical domain coordinates of the grid point; Number The physical domain ordinate of the physical domain coordinate of the grid point; is the operator corresponding to the first branch network; is the operator corresponding to the second branch network; is the first boundary function; is the second boundary function; For and number The computational domain abscissa corresponding to the physical domain abscissa of the grid point physical domain coordinate; For and number The computational domain ordinate corresponds to the physical domain ordinate of the grid point physical domain coordinate; is the first boundary eigenvector; is the second boundary eigenvector; is a high-dimensional shared feature vector; The output of the first branch network Weight coefficients; The output of the second branch network Weight coefficients; The first extracted from the shared backbone network Features, used for linear combination with the weights of branch network output; is the bias term corresponding to the first branch network; is the bias term corresponding to the second branch network.

[0178] The large-scale grid intelligent generation device based on operator learning provided by the present invention is applied to a dual-branch shared backbone network architecture, which is composed of a shared backbone network, a first branch network and a second branch network. The device is used to: obtain a calculation domain coordinate set of a target geometric shape, wherein the calculation domain coordinate set includes the calculation domain coordinates of grid points extracted from the calculation domain grid of the target geometric shape; obtain a first boundary function and a second boundary function of the target geometric shape, wherein the first boundary function is composed of the horizontal coordinates of the boundary points of the target geometric shape collected from the physical domain, and the second boundary function is composed of the vertical coordinates of the boundary points; use the first branch network to calculate the coordinates of each boundary point in the first boundary function The horizontal coordinate of the target geometry is extracted to obtain the first boundary feature vector of the target geometry; the second branch network is used to extract the vertical coordinate of each boundary point in the second boundary function to obtain the second boundary feature vector of the target geometry; the shared backbone network is used to extract the computational domain coordinates of each grid point in the computational domain coordinate set to obtain the high-dimensional shared feature vector of the target geometry; based on the operator learning algorithm, the high-dimensional shared feature vector is respectively fused with the first boundary feature vector and the second boundary feature vector to obtain the physical domain coordinates of the grid points corresponding to the computational domain coordinates of each grid point in the physical domain; the physical domain coordinates of each grid point are used to generate the physical domain grid of the target geometry. The present invention extracts the global features of the computational domain coordinates through a shared backbone network, and at the same time adopts a dual-branch network to learn the horizontal and vertical distribution characteristics of the boundary coordinates respectively, and uses the operator learning of multivariate mapping to realize multi-dimensional feature coupling, and finally generates the physical domain grid through coordinate mapping. Under the premise of ensuring the accurate capture of boundary features, efficient and high-quality grid generation is achieved through shared feature reuse and multivariate decoupling processing, and can be generalized to different geometric shapes, thereby achieving the coordinated optimization of complex geometric adaptability, multivariate coupling capability and computational efficiency.

[0179] Regarding the apparatus in the above embodiment, the specific manner in which each unit performs operations has been described in detail in the embodiment of the method, and will not be elaborated on here.

[0180] The large-scale grid intelligent generation device based on operator learning includes a processor and a memory. The above-mentioned calculation domain coordinate set acquisition unit 10, boundary function acquisition unit 20, first boundary feature vector acquisition unit 30, second boundary feature vector acquisition unit 40, high-dimensional shared feature vector acquisition unit 50, feature fusion unit 60 and grid generation unit 70 are all stored in the memory as program units, and the processor executes the above-mentioned program units stored in the memory to realize corresponding functions.

[0181] The processor contains a kernel, which retrieves the corresponding program unit from memory. One or more kernels can be set. By adjusting the kernel parameters, a shared backbone network is used to extract the global features of the computational domain coordinates. A dual-branch network is used to learn the horizontal and vertical distribution characteristics of the boundary coordinates, respectively. Multi-variable mapping operator learning is used to achieve multi-dimensional feature coupling. Ultimately, the physical domain mesh is generated through coordinate mapping. While ensuring accurate capture of boundary features, shared feature reuse and multi-variable decoupling processing enable efficient, high-quality mesh generation. This mesh can be generalized to different geometric shapes, achieving a coordinated optimization of complex geometric adaptability, multi-variable coupling capabilities, and computational efficiency.

[0182] An embodiment of the present invention provides a computer-readable storage medium having a program stored thereon. When the program is executed by a processor, the method for intelligently generating large-scale grids based on operator learning is implemented.

[0183] An embodiment of the present invention provides a processor, which is used to run a program, wherein the program executes the large-scale grid intelligent generation method based on operator learning when running.

[0184] like Figure 9 As shown, an embodiment of the present invention provides an electronic device 1000, which includes at least one processor 1001, at least one memory 1002 connected to the processor 1001, and a bus 1003. The processor 1001 and the memory 1002 communicate with each other via the bus 1003. The processor 1001 is configured to call program instructions in the memory 1002 to execute the above-described large-scale intelligent grid generation method based on operator learning. The electronic device herein may be a server, a PC, a PAD, a mobile phone, etc.

[0185] The present invention also provides a computer program product, which, when executed on an electronic device, is suitable for executing a program that initializes the steps of a large-scale grid intelligent generation method based on operator learning.

[0186] The present invention is described with reference to flowcharts and / or block diagrams of methods, apparatuses, electronic devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable device to produce a machine, so that the instructions executed by the processor of the computer or other programmable device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0187] In a typical configuration, an electronic device includes one or more processors (CPUs), a memory, and a bus. The electronic device may also include an input / output interface, a network interface, and the like.

[0188] Memory may include non-permanent memory in a computer-readable medium, random access memory (RAM), and / or non-volatile memory, such as read-only memory (ROM) or flash RAM. Memory includes at least one memory chip. Memory is an example of a computer-readable medium.

[0189] Computer-readable media include permanent and non-permanent, removable and non-removable media that can be implemented by any method or technology to store information. The information can be computer-readable instructions, data structures, program modules or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassettes, magnetic disk storage or other magnetic storage devices or any other non-transmission media that can be used to store information that can be accessed by a computing device. As defined herein, computer-readable media does not include transitory media such as modulated data signals and carrier waves.

[0190] In the description of the present invention, it should be understood that if the terms "up", "down", "front", "back", "left" and "right" are used to indicate directions or positional relationships, they are based on the directions or positional relationships shown in the accompanying drawings. They are only used to facilitate the description of the present invention and simplify the description, and do not indicate or imply that the positions or elements referred to must have a specific direction, be constructed and operate in a specific direction. Therefore, they should not be understood as limitations of the present invention.

[0191] It should be noted that, in this document, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. It should also be noted that the terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, commodity, or device comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, commodity, or device. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of other identical elements in the process, method, commodity, or device comprising the element.

[0192] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROMs, optical storage, etc.) containing computer-usable program code.

[0193] The above are merely embodiments of the present invention and are not intended to limit the present invention. It will be apparent to those skilled in the art that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention are intended to be within the scope of the present invention.

Claims

1. A large-scale grid intelligent generation method based on operator learning, characterized by: Applied to a dual-branch shared backbone network architecture, the dual-branch shared backbone network architecture consists of a shared backbone network, a first branch network, and a second branch network, the method includes: Obtaining a computational domain coordinate set of a target geometric shape, wherein the computational domain coordinate set includes computational domain coordinates of grid points extracted from a square uniform grid mapped on the computational domain by the target geometric shape; Obtaining a first boundary function and a second boundary function of the target geometric shape, wherein the first boundary function is composed of abscissas of boundary points of the target geometric shape collected from a physical domain, and the second boundary function is composed of ordinates of the boundary points; Using the first branch network to perform feature extraction on the horizontal coordinate of each boundary point in the first boundary function to obtain a first boundary feature vector of the target geometric shape; Using the second branch network to perform feature extraction on the ordinate of each boundary point in the second boundary function to obtain a second boundary feature vector of the target geometric shape; Using the shared backbone network to perform feature extraction on the computational domain coordinates of each grid point in the computational domain coordinate set to obtain a high-dimensional shared feature vector of the target geometric shape; Based on an operator learning algorithm, the high-dimensional shared feature vector is respectively fused with the first boundary feature vector and the second boundary feature vector to obtain the physical domain coordinates of the grid points corresponding to the computational domain coordinates of the grid points in the physical domain; The physical domain coordinates of each of the grid points are used to generate a physical domain grid of the target geometric shape.

2. The method according to claim 1, characterized in that The obtaining of the first boundary function and the second boundary function of the target geometric shape comprises: Using a subsampling strategy, collecting position coordinates of a preset number of boundary points of the target geometric shape in the physical domain by fixing the sensor position; The position coordinates of each of the boundary points are converted into a first boundary function and a second boundary function represented by a finite-dimensional vector.

3. The method according to claim 1, characterized in that Also includes: Defining a joint loss function, wherein the joint loss function is equal to a weighted sum of an internal loss term and a boundary loss term; Based on the joint loss function, the network parameters of the dual-branch shared backbone network architecture are optimized to minimize the value of the joint loss function and realize nonlinear mapping from boundary conditions to grid nodes.

4. The method according to claim 1, wherein The step of using the first branch network to perform feature extraction on the horizontal coordinate of each boundary point in the first boundary function to obtain a first boundary feature vector of the target geometric shape includes: Inputting the first boundary function into the multi-layer fully connected network of the first branch network, performing dimensionality reduction on the horizontal coordinate of each boundary point in the first boundary function to extract features, and obtaining a first dimensionality reduction feature representation of the first boundary function; The first dimensionality reduction feature representation is input into the branch layer of the first branch network, and feature extraction is performed on the first dimensionality reduction feature representation to obtain a first boundary feature vector of the target geometric shape.

5. The method according to claim 1, wherein The step of using the second branch network to perform feature extraction on the ordinate of each boundary point in the second boundary function to obtain a second boundary feature vector of the target geometric shape includes: Inputting the second boundary function into the multi-layer fully connected network of the second branch network, performing dimensionality reduction on the ordinate of each boundary point in the second boundary function to extract features, and obtaining a second dimensionality reduction feature representation of the second boundary function; The second dimensionality reduction feature representation is input into the branch layer of the second branch network, and feature extraction is performed on the second dimensionality reduction feature representation to obtain a second boundary feature vector of the target geometric shape.

6. The method according to claim 1, characterized in that The step of using the shared backbone network to perform feature extraction on the computational domain coordinates of each grid point in the computational domain coordinate set to obtain a high-dimensional shared feature vector of the target geometric shape includes: Inputting the computational domain coordinate set into the dimensionality-increasing layer of the shared backbone network, expanding the computational domain coordinates of each grid point in the computational domain coordinate set into a high-dimensional space, and obtaining a high-dimensional shared feature representation of the computational domain coordinate set; The high-dimensional feature representation is input into the backbone layer of the shared backbone network, and feature extraction is performed on the high-dimensional shared feature representation to obtain a high-dimensional shared feature vector of the target geometric shape.

7. The method according to claim 1, characterized in that The operator-based learning algorithm is used to perform feature fusion on the high-dimensional shared feature vector with the first boundary feature vector and the second boundary feature vector to obtain the physical domain coordinates of the grid points corresponding to the computational domain coordinates of the grid points in the physical domain, including: The high-dimensional shared feature vector, the first boundary feature vector, and the second boundary feature vector are input into the formula: Obtain the physical domain coordinates of the grid points corresponding to the computational domain coordinates of each grid point in the physical domain, wherein: Number The physical domain abscissa of the physical domain coordinate of the grid point; Number The physical domain ordinate of the physical domain coordinate of the grid point; is the operator corresponding to the first branch network; is the operator corresponding to the second branch network; is the first boundary function; is the second boundary function; For and number The computational domain abscissa corresponding to the physical domain abscissa of the physical domain coordinate of the grid point; For and number The computational domain ordinate corresponding to the physical domain ordinate of the physical domain coordinate of the grid point; is the first boundary eigenvector; is the second boundary eigenvector; is the high-dimensional shared feature vector; The first branch network output Weight coefficients; The second branch network output Weight coefficients; The first Features, used for linear combination with the weights of branch network output; is the bias term corresponding to the first branch network; is the bias term corresponding to the second branch network.

8. A large-scale grid intelligent generation device based on operator learning, characterized in that: The invention is applied to a dual-branch shared backbone network architecture, which is composed of a shared backbone network, a first branch network and a second branch network. The device includes: a computational domain coordinate set acquisition unit, a boundary function acquisition unit, a first boundary feature vector acquisition unit, a second boundary feature vector acquisition unit, a high-dimensional shared feature vector acquisition unit, a feature fusion unit and a grid generation unit. The calculation domain coordinate set obtaining unit is used to obtain a calculation domain coordinate set of a target geometric shape, wherein the calculation domain coordinate set includes calculation domain coordinates of grid points extracted from a square uniform grid mapped on the calculation domain by the target geometric shape; The boundary function obtaining unit is configured to obtain a first boundary function and a second boundary function of the target geometric shape, wherein the first boundary function is composed of abscissas of boundary points of the target geometric shape collected from a physical domain, and the second boundary function is composed of ordinates of the boundary points; The first boundary feature vector obtaining unit is configured to use the first branch network to perform feature extraction on the horizontal coordinate of each boundary point in the first boundary function to obtain a first boundary feature vector of the target geometric shape; The second boundary feature vector obtaining unit is configured to use the second branch network to perform feature extraction on the ordinate of each boundary point in the second boundary function to obtain a second boundary feature vector of the target geometric shape; The high-dimensional shared feature vector obtaining unit is configured to use the shared backbone network to perform feature extraction on the computational domain coordinates of each grid point in the computational domain coordinate set to obtain a high-dimensional shared feature vector of the target geometric shape; The feature fusion unit is configured to perform feature fusion on the high-dimensional shared feature vector with the first boundary feature vector and the second boundary feature vector based on an operator learning algorithm to obtain the physical domain coordinates of the grid points corresponding to the computational domain coordinates of the grid points in the physical domain; The grid generation unit is used to generate a physical domain grid of the target geometric shape using the physical domain coordinates of each grid point.

9. A computer-readable storage medium having a program stored thereon, characterized in that: When the program is executed by a processor, the large-scale grid intelligent generation method based on operator learning according to any one of claims 1 to 7 is implemented.

10. An electronic device, characterized in that: The electronic device includes at least one processor, and at least one memory and bus connected to the processor; wherein the processor and the memory communicate with each other through the bus; the processor is used to call program instructions in the memory to execute the large-scale grid intelligent generation method based on operator learning as described in any one of claims 1 to 7.

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