An intelligent selection method of iteration strategy and preconditioner for CFD sparse linear system based on structure-aware graph embedding

Abstract

The application discloses an intelligent selection method of CFD sparse linear system iteration strategy and preconditioner based on structure-aware graph embedding, and relates to the technical field of computers, comprising: in the process of executing a target simulation task based on a CFD simulation software, collecting data by using a residual-driven sampling mechanism to obtain a physically consistent data set, performing graph modeling based on the physically consistent data set, and determining a graph embedding vector by using a graph modeling result and a structure-aware graph embedding model; determining a combination selection result of the CFD sparse linear system iteration strategy and the preconditioner based on the graph embedding vector and a decoupled integrated decision recommendation system; and completing a CFD numerical simulation operation corresponding to the target simulation task based on the combination selection result and the CFD simulation software. The application effectively solves the problems in the prior art, thereby improving the efficiency of CFD numerical simulation and reducing the collapse risk in large-scale simulation.

Description

Technical Field

[0001] This invention relates to the field of computer technology, and in particular to an intelligent selection method for iterative strategies and preconditioners in CFD sparse linear systems based on structure-aware graph embedding. Background Technology

[0002] In CFD (Computational Fluid Dynamics) numerical simulations, sparse linear equation sets The solution time typically accounts for a high proportion of the entire numerical simulation task, reaching over 80%, and its solution efficiency directly determines the simulation performance and practicality of CFD simulation software.

[0003] To avoid the problems caused by the traditional approach of relying on expert manual experience or heuristic judgment criteria for solving equations, current related solutions often use a data-driven approach to automatically select solvers for CFD sparse linear systems. However, these existing related solutions still face serious challenges in deploying in real CFD simulation scenarios: (1) lack of physical consistency: because real matrices are usually synthesized with randomly generated vectors, the model suffers from severe generalization degradation on real physical trajectories; (2) decision failure under long-tailed distribution: in real CFD numerical simulations, ill-conditioned equations (which require robust sparse linear equation solvers) account for only a small minority, exhibiting a clear long-tailed distribution. Existing end-to-end deep learning models are easily dominated by the majority of simple samples during training, resulting in extremely low prediction accuracy on key, difficult samples that determine the success or failure of the simulation.

[0004] Therefore, how to construct an automatic solver selection method that is physically consistent, computationally efficient, and highly robust to long-tailed samples is a problem that needs to be solved by those skilled in the art. Summary of the Invention

[0005] In view of this, the purpose of this invention is to provide an intelligent selection method for iterative strategies and preconditioners in CFD sparse linear systems based on structure-aware graph embedding. This method effectively solves the problems existing in related schemes, thereby improving the efficiency of CFD numerical simulation and significantly reducing the risk of crashes during large-scale simulations. The specific scheme is as follows:

[0006] Firstly, this application provides an intelligent selection method for iterative strategies and preconditioners in CFD sparse linear systems based on structure-aware graph embedding, including:

[0007] During the execution of the target simulation task based on CFD simulation software, a residual-driven sampling mechanism is used to collect data in order to determine the physically consistent dataset; wherein, the target simulation task is a numerical simulation task of aerospace vehicle or fluid machinery in a target flow field environment;

[0008] Graph modeling is performed based on the physical consistency dataset, and graph embedding vectors are determined using the corresponding graph modeling results and a structure-aware graph embedding model. The structure-aware graph embedding model is a model built based on a global pooling layer and a training-free graph isomorphic network operator.

[0009] Based on the graph embedding vector and the decoupled ensemble decision recommendation system, intelligent selection of the combination of iterative strategies and preconditioners for CFD sparse linear systems is performed to determine the combination selection result; the sparse linear system is a sparse linear equation system, and the decoupled ensemble decision recommendation system includes a machine learning classifier and an automated hyperparameter optimization component;

[0010] Based on the combined selection results and the CFD simulation software, the CFD numerical simulation operation corresponding to the target simulation task is completed.

[0011] Optionally, during the execution of the target simulation task based on CFD simulation software, data acquisition is performed using a residual-driven sampling mechanism to determine the physically consistent dataset, including:

[0012] During the execution of the target simulation task based on CFD simulation software, data is collected using the online monitoring component in the CFD simulation software and the residual-driven sampling mechanism to determine the physical consistency dataset; wherein, the online monitoring component is the monitoring component corresponding to the sparse linear system solver.

[0013] Optionally, the method of using the online monitoring component in the CFD simulation software and employing a residual-driven sampling mechanism to collect data to determine the physical consistency dataset includes:

[0014] Based on the input / output extension interface of the CFD simulation software, a sparse matrix and an initial residual vector in a preset matrix storage format are obtained; wherein, the input / output extension interface is an input / output interface already integrated into the underlying simulation architecture of the CFD simulation software; the preset matrix storage format includes a block compressed sparse row format and a compressed sparse row format;

[0015] Based on the online monitoring component in the CFD simulation software, the instantaneous residual in the nonlinear iteration process is monitored to determine the instantaneous residual monitoring result;

[0016] Based on the online monitoring component, the instantaneous residual monitoring results, and multiple uniformly distributed logarithmic decline thresholds, numerical snapshots at each sampling point during the simulation process corresponding to the target simulation task are captured to determine the numerical sampling results; the logarithmic decline threshold is a logarithmic instantaneous residual decline threshold.

[0017] Based on the numerical sampling results, the initial sparse linear equations corresponding to the target simulation task, and the local correction equations at each sampling point, a physical consistency dataset is constructed.

[0018] Optionally, the step of capturing numerical snapshots at each sampling point during the simulation process corresponding to the target simulation task, based on the online monitoring component, the instantaneous residual monitoring results, and multiple uniformly distributed logarithmic descent thresholds, includes:

[0019] Based on the first-step triggering strategy and the online monitoring component, in the first step of the instantaneous residual monitoring process, a numerical snapshot capture command is automatically triggered to determine the first capture result;

[0020] In the instantaneous residual monitoring process, when the instantaneous residual monitoring result indicates that the current instantaneous residual is less than any of the logarithmic decrease thresholds for the first time, the numerical snapshot capture instruction is triggered based on the online monitoring component to determine the second capture result;

[0021] Based on the tail-step triggering strategy and the online monitoring component, the numerical snapshot capture command is automatically triggered at the tail step of the instantaneous residual monitoring process to determine the third capture result;

[0022] Based on the first capture result, several second capture results, and the third capture result, a numerical sampling result is determined.

[0023] Optionally, the graph modeling based on the physically consistent dataset includes:

[0024] Node features and edge features are extracted from the sparse matrix in the physical consistency dataset to determine the feature extraction results;

[0025] Directed graph modeling is performed based on the feature extraction results to determine the graph modeling result.

[0026] Optionally, the step of extracting node features and edge features from the sparse matrix in the physically consistent dataset to determine the feature extraction results includes:

[0027] For the first sparse matrix in the physical consistency dataset that belongs to the block compressed sparse row format, node features of the first preset feature type are extracted to determine the first node feature set; the first preset feature type includes diagonal block Frobenius norm, block asymmetry, block condition number, block minimum real part eigenvalue, and block residual norm.

[0028] For the first sparse matrix, edge features of a second preset feature type are extracted to determine the first edge feature set; the second preset feature type includes off-diagonal block Frobenius norm, normalized coupling strength, and convection dominance index;

[0029] For the second sparse matrix in the physical consistency dataset that belongs to the compressed sparse row format, node features of a third preset feature type are extracted to determine the second node feature set; the third preset feature type includes the absolute value of the diagonal elements and the scalar value of the right-hand item.

[0030] For the second sparse matrix, edge features of a fourth preset feature type are extracted to determine the second edge feature set; the fourth preset feature type includes the absolute value of off-diagonal elements and normalized coupling strength.

[0031] Data standardization processing is performed on the first node feature set, the first edge feature set, the second node feature set, and the second edge feature set to determine the standardization processing result;

[0032] Based on the standardized processing results and the preset logarithmic scaling strategy, the feature extraction results are determined.

[0033] Optionally, determining the graph embedding vector using the corresponding graph modeling results and the structure-aware graph embedding model includes:

[0034] Input the graph modeling results into the structure-aware graph embedding model;

[0035] Based on the structure-aware graph embedding model, its parameters are orthogonally initialized, and node features and edge features are mapped to a high-dimensional space of the same dimension based on these parameters to determine the mapping result.

[0036] Based on the structure-aware graph embedding model and the mapping results, structure-aware feature encoding is performed to determine the graph embedding vector.

[0037] Optionally, the step of performing structure-aware feature encoding based on the structure-aware graph embedding model and the mapping result to determine the graph embedding vector includes:

[0038] Based on the training-free graph isomorphic network operator in the structure-aware graph embedding model, the mapping result is aggregated with information from neighboring nodes to determine the information aggregation result.

[0039] Based on the multilayer perceptron in the structure-aware graph embedding model, the information aggregation result is subjected to high-dimensional feature mapping to determine the high-dimensional mapping result.

[0040] Based on the global pooling layer in the structure-aware graph embedding model, and using the JL lemma and the high-dimensional mapping results, the graph embedding vector is determined.

[0041] Optionally, the intelligent selection of the combination of iterative strategies and preconditioners for CFD sparse linear systems based on the graph embedding vector and the decoupled ensemble decision recommendation system includes:

[0042] The graph is embedded into a vector input decoupled integrated decision recommendation system;

[0043] Based on the machine learning classifier in the decoupled integrated decision recommendation system, the graph embedding vector is processed to determine the vector processing result;

[0044] Based on the machine learning classifier and the corresponding automated hyperparameter optimization component, and using the vector processing results, intelligent selection is performed on the combination of iterative strategies and preconditioners for CFD sparse linear systems to determine the combination selection result.

[0045] Optionally, the step of performing the CFD numerical simulation operation corresponding to the target simulation task based on the combined selection result and the CFD simulation software includes:

[0046] Based on the combined selection results, the sparse linear equations corresponding to the target simulation task are solved to determine the target solution result;

[0047] Based on the solution results of the objective and the CFD simulation software, the CFD numerical simulation operation corresponding to the objective simulation task is completed.

[0048] Secondly, this application provides an intelligent selection device for iterative strategies and preconditioners of CFD sparse linear systems based on structure-aware graph embedding, comprising:

[0049] The data acquisition module is used to acquire data using a residual-driven sampling mechanism during the execution of a target simulation task based on CFD simulation software, in order to determine a physically consistent dataset; wherein, the target simulation task is a numerical simulation task of aerospace vehicle or fluid machinery in a target flow field environment;

[0050] The structure-aware graph embedding module is used to perform graph modeling based on the physical consistency dataset, and to determine the graph embedding vector using the corresponding graph modeling results and the structure-aware graph embedding model; the structure-aware graph embedding model is a model built based on a global pooling layer and a training-free graph isomorphic network operator.

[0051] The selection result determination module is used to intelligently select the combination of iterative strategies and preconditioners for the CFD sparse linear system based on the graph embedding vector and the decoupled integrated decision recommendation system, so as to determine the combination selection result; the sparse linear system is a sparse linear equation system, and the decoupled integrated decision recommendation system includes a machine learning classifier and an automated hyperparameter optimization component;

[0052] The numerical simulation completion module is used to complete the CFD numerical simulation operation corresponding to the target simulation task based on the combined selection result and the CFD simulation software.

[0053] Thirdly, this application provides an electronic device, comprising:

[0054] Memory, used to store computer programs;

[0055] A processor is configured to execute the computer program to implement the steps of the aforementioned intelligent selection method for iterative strategies and preconditioners in CFD sparse linear systems based on structure-aware graph embedding.

[0056] Fourthly, this application provides a computer-readable storage medium for storing a computer program, which, when executed by a processor, implements the steps of the aforementioned intelligent selection method for iterative strategies and preconditioners of CFD sparse linear systems based on structure-aware graph embedding.

[0057] As can be seen, in this application, during the execution of the target simulation task based on CFD simulation software, a residual-driven sampling mechanism is used for data acquisition to determine a physically consistent dataset. The target simulation task is a numerical simulation task of the aerodynamic characteristics of aerospace vehicles or fluid machinery in a target flow field environment. Graph modeling is performed based on the physically consistent dataset, and graph embedding vectors are determined using the corresponding graph modeling results and a structure-aware graph embedding model. The structure-aware graph embedding model is a model constructed based on a global pooling layer and a training-free graph isomorphic network operator. Based on the graph embedding vectors and a decoupled ensemble decision recommendation system, intelligent selection is performed on the combination of iterative strategies and preconditioners for the CFD sparse linear system to determine the combination selection result. The sparse linear system is a sparse linear equation system, and the decoupled ensemble decision recommendation system includes a machine learning classifier and an automated hyperparameter optimization component. Based on the combination selection result and the CFD simulation software, the CFD numerical simulation operation corresponding to the target simulation task is completed. In other words, this application first constructs a physically consistent dataset using a residual-driven sampling mechanism during the execution of the target simulation task. Then, graph modeling is performed based on the physically consistent dataset, and a structure-aware graph embedding model is used to determine the graph embedding vectors. Next, a decoupled ensemble decision recommendation system processes the graph embedding vectors to intelligently select the appropriate combination of iterative strategies and preconditioners for the CFD sparse linear system. Finally, based on the corresponding combination selection results, the CFD numerical simulation operation corresponding to the target simulation task is completed. This effectively solves the problems existing in related schemes, thereby improving the efficiency of CFD numerical simulation and significantly reducing the risk of crashes during large-scale simulations. Attached Figure Description

[0058] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0059] Figure 1 A flowchart of an intelligent selection method for iterative strategies and preconditioners for CFD sparse linear systems based on structure-aware graph embedding provided in this application;

[0060] Figure 2 A schematic diagram of a data acquisition process provided for this application;

[0061] Figure 3 A schematic diagram of node features in the Frobenius norm dimension of a diagonal block provided in this application;

[0062] Figure 4 A schematic diagram of node features in a block asymmetry dimension provided in this application;

[0063] Figure 5 A schematic diagram of node features in the block condition number dimension provided in this application;

[0064] Figure 6 A schematic diagram of a node feature with a minimum real eigenvalue dimension provided in this application;

[0065] Figure 7 A schematic diagram of node features in the block residual norm dimension provided in this application;

[0066] Figure 8 A schematic diagram of the edge features of a non-diagonal block in the Frobenius norm dimension provided in this application;

[0067] Figure 9 A schematic diagram of edge features in the normalized coupling strength dimension provided in this application;

[0068] Figure 10 A schematic diagram of edge features in the convection dominance index dimension provided in this application;

[0069] Figure 11 A schematic diagram of a structure-aware graph embedding process provided in this application;

[0070] Figure 12 A flowchart illustrating a decoupled decision recommendation method provided in this application;

[0071] Figure 13 A comparative diagram illustrating the accuracy of each label on a constructed physically consistent dataset, provided for the purposes of this application;

[0072] Figure 14 A schematic diagram of the structure of an intelligent selection device for iterative strategies and preconditioners of a CFD sparse linear system based on structure-aware graph embedding provided in this application.

[0073] Figure 15 This application provides a structural diagram of an electronic device. Detailed Implementation

[0074] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0075] To avoid the problems caused by the traditional approach of relying on expert manual experience or heuristic judgment criteria for solving equations, current related solutions often use a data-driven approach to automatically select solvers for CFD sparse linear systems. However, these existing related solutions still face serious challenges in deploying in real CFD simulation scenarios: (1) lack of physical consistency: because real matrices are usually synthesized with randomly generated vectors, the model suffers from severe generalization degradation on real physical trajectories; (2) decision failure under long-tailed distribution: in real CFD numerical simulations, ill-conditioned equations (which require robust sparse linear equation solvers) account for only a small minority, exhibiting a clear long-tailed distribution. Existing end-to-end deep learning models are easily dominated by the majority of simple samples during training, resulting in extremely low prediction accuracy on key, difficult samples that determine the success or failure of the simulation.

[0076] To address this, this application provides an intelligent selection scheme for iterative strategies and preconditioners in CFD sparse linear systems based on structure-aware graph embedding. This scheme effectively solves the problems existing in related schemes, thereby improving the efficiency of CFD numerical simulation and significantly reducing the risk of crashes during large-scale simulations.

[0077] See Figure 1 As shown, this invention discloses an intelligent selection method for iterative strategies and preconditioners in CFD sparse linear systems based on structure-aware graph embedding, including:

[0078] Step S11: During the execution of the target simulation task based on CFD simulation software, data is collected using a residual-driven sampling mechanism to determine the physical consistency dataset; wherein, the target simulation task is a numerical simulation task of aerodynamic characteristics of aerospace vehicles or fluid machinery in a target flow field environment.

[0079] Specifically, in this embodiment, the CFD simulation software is used as a data extraction platform. Data is collected in real-time and accurately through the online monitoring component and residual-driven sampling mechanism within the software. That is, during the execution of the target simulation task based on the CFD simulation software, data is collected using the online monitoring component and the residual-driven sampling mechanism to determine the physically consistent dataset. The online monitoring component is the monitoring component corresponding to the sparse linear system solver. It can be understood that, combined with... Figure 2 As shown, the CFD simulation software can be the open-source simulation software SU2, or other open-source simulation software or custom simulation software can be selected according to actual needs.

[0080] Furthermore, based on the adoption of online monitoring components and residual-driven sampling mechanisms, and considering the lack of a direct output interface for linear systems in the software's native solver, this embodiment also integrates the HDF5 high-performance standard (Hierarchical Data Format Version 5) into the underlying software architecture to adaptively support Block Compressed Sparse Row (BSR) and Compressed Sparse Row (CSR). Two matrix storage formats (Row) are used to achieve lossless persistent data storage. Specifically: based on the input / output extension interface of the CFD simulation software, a sparse matrix and an initial residual vector in a preset matrix storage format are obtained; wherein, the input / output extension interface is an input / output interface already integrated into the underlying simulation architecture of the CFD simulation software; the preset matrix storage format includes a block compressed sparse row format and a compressed sparse row format; based on the online monitoring component in the CFD simulation software, the instantaneous residuals in the nonlinear iteration process are monitored to determine the instantaneous residual monitoring results; based on the online monitoring component, the instantaneous residual monitoring results, and multiple uniformly distributed logarithmic descent thresholds, numerical snapshots at each sampling point in the simulation process corresponding to the target simulation task are captured to determine the numerical sampling results; the logarithmic descent threshold is a logarithmic instantaneous residual descent threshold; based on the numerical sampling results, the initial sparse linear equation system corresponding to the target simulation task, and the local correction equations at each sampling point, a physically consistent dataset is constructed.

[0081] Understandably, regarding the construction of a physically consistent data acquisition pipeline, the first step is to extend the I / O (Input / Output) interface: integrate the HDF5 high-performance standard into the underlying simulation architecture to achieve processing of BSR format sparse matrices. and initial residual Real-time lossless persistent storage. Then, a logarithmic uniform sampling mechanism is executed: in the nonlinear iterative loop, a logarithmic uniform sampling mechanism and an online monitoring component are used to monitor the evolution of the numerical state to track the instantaneous residual R. When the instantaneous residual R meets a preset logarithmic decrease threshold (based on the residual decrease amount), the system will perform a logarithmic uniform sampling. When eight uniformly distributed thresholds are set, the online monitoring module triggers a data capture command. To avoid data redundancy, a "first-pass trigger" strategy is implemented to ensure that each threshold is sampled only once, with the first and last steps captured by default, thus capturing representative numerical snapshots throughout the simulation's entire lifecycle. Finally, numerical equivalence construction and label generation are performed: a 'snapshot-test-recovery' mechanism is used to construct local correction equations at each sampling point. Based on the principle of numerical equivalence, we prove the equivalence between solving the original system and solving the zero initial solution of the modified equation in the Krylov subspace, and perform online benchmark tests to obtain the optimal combination labels, ensuring that the spectral features of all samples originate from the real physical evolution trajectory.

[0082] Regarding the logarithmic uniform sampling mechanism, in this embodiment: based on the first-step triggering strategy and the online monitoring component, in the first step of the instantaneous residual monitoring process, a numerical snapshot capture command is automatically triggered to determine a first capture result; in the instantaneous residual monitoring process, when the instantaneous residual monitoring result indicates that the current instantaneous residual is less than any of the logarithmic decrease thresholds for the first time, the numerical snapshot capture command is triggered based on the online monitoring component to determine a second capture result; based on the last-step triggering strategy and the online monitoring component, in the last step of the instantaneous residual monitoring process, the numerical snapshot capture command is automatically triggered to determine a third capture result; based on the first capture result, several second capture results, and the third capture result, a numerical sampling result is determined.

[0083] It is important to understand that, regarding the numerical equivalent construction of samples, to ensure the physical consistency of the samples, this embodiment constructs local correction equations at the sampling points. The proof of its numerical equivalence is as follows: Let the original sparse linear system be... ,in, It is a sparse matrix. This is the right-hand side term. The initial solution is... The corresponding initial residual is Case I: From the initial solution Begin solving the original sparse linear system of equations, with the initial residuals being... Case II: Solving for the right-hand side is... And the initial solution is Corrected equation Its initial residual is Since both cases share the same initial residual vector. For any Krylov subspace method, the approximate solution at step k lies in the same Krylov subspace. The search is performed within the context. In case I, the iterative solution is updated to... Its residual is In case II, the iterative solution is generated directly. Its residual is Since the deterministic Krylov solver uniquely determines the update vector using the same optimization criterion within the same subspace, it is necessary that... This proves that in all iteration steps In this study, Case I and Case II exhibit identical convergence trajectories and residual evolution trajectories. This proof ensures that the modified equation samples constructed in this embodiment accurately reflect the physical evolution laws, thereby guaranteeing the physical consistency of the optimal combination of labels.

[0084] Furthermore, regarding the physically consistent dataset, the equations used to construct the dataset cover compressible Reynolds-averaged Navier-Stokes (RANS), Navier-Stokes, and Euler equations; thermochemical nonequilibrium Navier-Stokes and Euler equations; and incompressible Reynolds-averaged Navier-Stokes, Navier-Stokes, and Euler equations. During the machine learning classifier training phase, the examples used in the dataset include typical engineering shapes such as the ONERA M6 wing, NACA0012 airfoil, RAE2822 supercritical airfoil, S809 airfoil, DSMA661 model, LS89 turbine blade, flat plate, and cylinder; the operating conditions cover a variety of complex physical flow regimes from low speed, transonic to hypersonic, with Mach numbers ranging from 0 to 22.5.

[0085] Step S12: Perform graph modeling based on the physical consistency dataset, and determine the graph embedding vector using the corresponding graph modeling results and the structure-aware graph embedding model; the structure-aware graph embedding model is a model built based on a global pooling layer and a training-free graph isomorphic network operator.

[0086] In this embodiment, after obtaining the physically consistent dataset, graph modeling will be performed using the physically consistent dataset. That is, node features and edge features will be extracted from the sparse matrix in the physically consistent dataset to determine the feature extraction results; directed graph modeling will be performed based on the feature extraction results to determine the graph modeling results.

[0087] Regarding feature extraction, in this embodiment, corresponding methods are used to extract edge features and node features for different matrix formats. Specifically: for the first sparse matrix in the physically consistent dataset that belongs to the block-compressed sparse row format, node features of a first preset feature type are extracted to determine the first node feature set; the first preset feature type includes diagonal block Frobenius norm (i.e., diagonal block F norm), block asymmetry, block condition number, block minimum real part eigenvalue, and block residual norm; for the first sparse matrix, edge features of a second preset feature type are extracted to determine the first edge feature set; the second preset feature type includes off-diagonal block Frobenius norm (off-diagonal F norm), normalized coupling strength, and... The convection dominance index is used. For the second sparse matrix in the physically consistent dataset, which belongs to the compressed sparse row format, node features of a third preset feature type are extracted to determine the second node feature set. The third preset feature type includes the absolute values ​​of diagonal elements and the scalar values ​​of right-hand items. For the second sparse matrix, edge features of a fourth preset feature type are extracted to determine the second edge feature set. The fourth preset feature type includes the absolute values ​​of off-diagonal elements and the normalized coupling strength. Data standardization is performed on the first node feature set, the first edge feature set, the second node feature set, and the second edge feature set to determine the standardization result. Based on the standardization result and a preset logarithmic scaling strategy, the feature extraction result is determined. By performing Z-score standardization on the extracted feature space and combining it with a logarithmic scaling strategy, differences between different physical quantities can be eliminated.

[0088] In other words, for the Block Compressed Sparse Row (BSR) format, the 5-dimensional node features of the matrix are extracted, including the diagonal block Frobenius norm (e.g., ...). Figure 3 As shown), block asymmetry (such as...) Figure 4 As shown), the number of block conditions (such as...) Figure 5 As shown), the smallest real eigenvalue (such as...) Figure 6 As shown), block residual norm (such as Figure 7 As shown); extract 3D edge features, including off-diagonal block Frobenius norm (e.g. Figure 8 As shown), normalized coupling strength (e.g.) Figure 9 As shown), the convection dominance index (such as...) Figure 10 As shown in the figure. For Compressed Sparse Row Format (CSR), 2D node features of the matrix are extracted, including the absolute values ​​of diagonal elements and the scalar values ​​of right-hand items; 2D edge features are extracted, including the absolute values ​​of off-diagonal elements and the normalized coupling strength. Specifically, the feature definition tables for different matrix storage formats are shown in Table 1 below, where, It is a numerical stability constant.

[0089] Table 1 Feature definition table under different matrix storage formats

[0090] ;

[0091] In addition, it should be pointed out that, regarding Figures 3 to 10 The value on the right side of the table represents... Figure 2 The example matrix displays the calculated numerical values ​​(dimensionless) of its node and edge features, with color intensity indicating the magnitude of the values. Figure 2 The matrix shown is a small-scale example matrix generated by the program, not a real CFD simulation matrix, but it has a similar block structure for display purposes.

[0092] for Figures 3 to 10 These eight graphs describe features in the same order as the BSR section in Table 1. The first five graphs use the color of the nodes to represent the numerical distribution of node features, while the last three graphs use the color of the edges to represent the numerical distribution of edge features.

[0093] Combination Figure 11 As shown, after feature extraction is completed, an algebraic attribute graph is constructed based on the obtained feature extraction results, and training-free random orthogonal projection and structure-aware feature encoding are performed to obtain the graph embedding vector. That is, the graph modeling result is input into the structure-aware graph embedding model; based on the structure-aware graph embedding model, its parameters are orthogonally initialized, and node features and edge features are mapped to a high-dimensional space of the same dimension based on these parameters to determine the mapping result; based on the structure-aware graph embedding model and the mapping result, structure-aware feature encoding is performed to determine the graph embedding vector.

[0094] It's important to understand that regarding the training-free random orthogonal projection, in this embodiment, the features extracted in the aforementioned steps are combined with the corresponding node indices and batch vectors, and input into the node linear encoder and edge linear encoder for feature encoding. Then, through a random projector, a randomly generated orthogonal projection matrix is ​​used to map the initial node and edge features to a unified hidden space. Orthogonal initialization ensures the isometry of the mapping, thereby maintaining residual strength information without introducing additional noise. Specifically, a randomly generated orthogonal projection matrix can be used... and The extracted initial features are projected into a unified hidden space, and orthogonal initialization is used to ensure isometry in order to avoid introducing random scaling noise.

[0095] After completing the training-free random orthogonal projection, structure-aware feature encoding is performed. In this embodiment, neighborhood information aggregation is performed based on the Graph Isomorphism Network with Edges (GINE) operator, nonlinear signal transformation is performed through the internal Multilayer Perceptron (MLP), and finally, a graph embedding vector representing global numerical characteristics is generated using global pooling. That is: based on the training-free graph isomorphism network operator in the structure-aware graph embedding model, the information aggregation of neighborhood nodes is performed on the mapping result to determine the information aggregation result; based on the MLP in the structure-aware graph embedding model, the feature high-dimensional mapping of the information aggregation result is performed to determine the high-dimensional mapping result; based on the global pooling layer in the structure-aware graph embedding model, and using the JL lemma and the high-dimensional mapping result, the graph embedding vector is determined. Among them, the internal multilayer perceptron, i.e. Figure 2 The built-in multilayer perceptron includes a linear layer and two corrected linear units. After processing the aggregation result, the internal multilayer perceptron passes it through a corrected linear unit before summing it with the residual path identification information.

[0096] Regarding the process of generating graph embedding vectors through structure-aware feature encoding, firstly, neighborhood information aggregation is performed. A summation aggregation method is used to summarize the algebraic features of neighboring nodes to reflect the cumulative stiffness of the operators, achieving structure-aware aggregation and preventing the dilution of key numerical signals in sparse structures. Next, high-dimensional feature mapping is performed. An internal multilayer perceptron is used to project the signal into a high-dimensional hidden space. Based on Cover's theorem, the linear separability probability of different numerical patterns in the feature space is increased to achieve feature decoupling and nonlinear transformation. Then, residual maintenance and global numerical pooling are performed. Residual connections are applied to ensure that local numerical identifiers are preserved in deep transformations. Non-normalized summation pooling is used to generate the final graph embedding vector. The Johnson-Lindenstrauss lemma is used to ensure topological stability within the projection space. That is, by generating the final embedding vector through non-normalized global summation pooling, the model naturally focuses on the numerical bottleneck nodes that cause convergence lag.

[0097] Step S13: Based on the graph embedding vector and the decoupled integrated decision recommendation system, perform intelligent selection of the combination of iterative strategy and preconditioner for the CFD sparse linear system to determine the combination selection result; the sparse linear system is a sparse linear equation system, and the decoupled integrated decision recommendation system includes a machine learning classifier and an automated hyperparameter optimization component.

[0098] In this embodiment, after determining the graph embedding vector, the graph embedding vector can be input into a decoupled ensemble decision recommendation system for intelligent selection. Specifically: the graph embedding vector is input into the decoupled ensemble decision recommendation system; based on the machine learning classifier in the decoupled ensemble decision recommendation system, the graph embedding vector is processed to determine the vector processing result; based on the machine learning classifier and its corresponding automated hyperparameter optimization component, and using the vector processing result, an intelligent selection is performed on the combination of iterative strategies and preconditioners for the CFD sparse linear system to determine the combined selection result. Combined with... Figure 12 As shown, the machine learning classifier includes, but is not limited to, a random forest classifier. It is understandable that during the training phase of the machine learning classifier, the input to the decoupled ensemble decision recommendation system includes not only the graph embedding vector but also the corresponding labels.

[0099] It is important to understand that, in combination Figure 12 As shown, the construction process of the decoupled ensemble decision recommendation system involves several steps. First, the graph embedding module is used as a static feature encoder, with its output directly serving as the input to the backend classifier. This separation of feature extraction and classification logic avoids the gradient update overhead of the end-to-end model on the high-dimensional matrix. Next, ensemble learning classification is performed. A random forest classifier is used as the decision core, leveraging its parallel voting mechanism and random subspace sampling characteristics to effectively alleviate the sample imbalance problem caused by the long-tail distribution. Finally, adaptive parameter tuning is performed. An integrated automatic hyperparameter optimization module uses a search strategy based on the Tree-structured Parzen Estimator algorithm to determine the optimal model configuration, ensuring the adaptability of the decision logic under different physical conditions.

[0100] Step S14: Based on the combined selection result and the CFD simulation software, complete the CFD numerical simulation operation corresponding to the target simulation task.

[0101] In this embodiment, after determining the optimal combination of solver and preconditioner, this combination will be used to solve the sparse linear equation system. To improve simulation efficiency, the following steps are taken: based on the combined selection results, the sparse linear equation system corresponding to the target simulation task is solved to determine the target solution result; based on the target solution result and the CFD simulation software, the CFD numerical simulation operation corresponding to the target simulation task is completed.

[0102] In summary, the beneficial effects of the proposed solution in this embodiment include: (1) Solving the problem of physical consistency generalization. By constructing a large-scale real physical consistency dataset and introducing residual-driven sampling, the machine learning classifier can perceive the real physical convergence evolution law, completely eliminating the risk of model failure caused by synthetic data. (2) Significantly improving decision robustness under long-tail distribution. By adopting a structure-aware embedding and decoupling architecture, the recognition accuracy on the key minority class samples that determine the success or failure of the simulation is greatly improved, significantly reducing the risk of collapse in large-scale simulations.

[0103] Therefore, in this embodiment of the application, during the execution of the target simulation task based on CFD simulation software, a residual-driven sampling mechanism is used to collect data to determine a physically consistent dataset. The target simulation task is a numerical simulation task of the aerodynamic characteristics of aerospace vehicles or fluid machinery in a target flow field environment. Graph modeling is performed based on the physically consistent dataset, and graph embedding vectors are determined using the corresponding graph modeling results and a structure-aware graph embedding model. The structure-aware graph embedding model is a model constructed based on a global pooling layer and a training-free graph isomorphic network operator. Based on the graph embedding vectors and a decoupled ensemble decision recommendation system, intelligent selection is performed on the combination of iterative strategies and preconditioners for the CFD sparse linear system to determine the combination selection result. The sparse linear system is a sparse linear equation system, and the decoupled ensemble decision recommendation system includes a machine learning classifier and an automated hyperparameter optimization component. Based on the combination selection result and the CFD simulation software, the CFD numerical simulation operation corresponding to the target simulation task is completed. In other words, this application first constructs a physically consistent dataset using a residual-driven sampling mechanism during the execution of the target simulation task. Then, graph modeling is performed based on the physically consistent dataset, and a structure-aware graph embedding model is used to determine the graph embedding vectors. Next, a decoupled ensemble decision recommendation system processes the graph embedding vectors to intelligently select the appropriate combination of iterative strategies and preconditioners for the CFD sparse linear system. Finally, based on the corresponding combination selection results, the CFD numerical simulation operation corresponding to the target simulation task is completed. This effectively solves the problems existing in related schemes, thereby improving the efficiency of CFD numerical simulation and significantly reducing the risk of crashes during large-scale simulations.

[0104] The following is combined Figure 13 The schematic diagram disclosed herein provides a detailed description of the technical solutions of the embodiments of this application.

[0105] In this embodiment, validation was performed on a high-performance server, and the test dataset contained 25,303 independent physically consistent samples. The validation results show that the SAGE (Structure-Aware Graph Embedding) framework for intelligent selection proposed in this embodiment significantly outperforms the state-of-the-art method MM-AutoSolver (an adaptive selection model based on a multimodal deep learning framework) in multiple metrics. Specific comparisons are shown in Table 2 below:

[0106] Table 2 Performance Comparison Table

[0107] ;

[0108] In Table 2, F1 (i.e., F1 score) is a composite metric, which is the harmonic mean of precision and recall. F2 is a variant of F1 score, the core feature of which is that recall is given a higher weight than precision. G-Mean Recall combines the concepts of G-Mean (geometric mean) and Recall (recall rate), and is designed to measure the geometric mean of recall across all categories.

[0109] At the micro level, such as Figure 13 The diagram illustrates the prediction accuracy of this embodiment for each specific label on the physically consistent dataset. Even with extreme long-tail distributions, the proposed scheme still demonstrates robust decision-making capabilities. For combinations with extremely low sample percentages, such as fgmres+ilu (only 0.59%) and... +jacobi (accounting for only 0.15%), the proposed solutions in this embodiment maintained a high prediction accuracy of 80.00%. In contrast, MM-AutoSolver's accuracy on these two labels was only 6.67% and 20%, respectively. This fully demonstrates the extremely high reliability of this invention in handling ill-conditioned systems, which are scarce but crucial in scientific computing.

[0110] Understandable Figure 13 bcgstab in fgmres and bcgstab belong to different iterative strategies, i.e., solvers, for sparse linear systems. Among them, bcgstab, biconjugate gradient stabilized method, is an iterative solver; fgmres, flexible generalized minimal residual, is a flexible generalized minimal residual method, an iterative algorithm for solving large sparse linear equation systems. The flexible generalized minimum residual method, representing restart, is an improved version of fgmres and is mainly used for efficiently solving large sparse linear equation systems. (ilu, ...) Jacobi and linelet are different preconditioners. Among them, ilu is Incomplete LU Decomposition; Jacobi preconditioner is also called diagonal preconditioner. The lower-upper symmetric gauss-seidel is an iterative method commonly used in computational fluid dynamics to solve discretized control equations. The linelet is a preconditioner designed to address the convergence difficulties caused by anisotropic meshes. The 'line' refers to the core operation object of the algorithm. In unstructured meshes, lines are artificially constructed by connecting strongly coupled elements. The 'let' means 'tiny' or 'component', implying that this preconditioner is not globally implicit, but rather decomposes the global problem into countless local one-dimensional implicit problems.

[0111] See Figure 14 As shown in the embodiments, this application also discloses a smart selection device for iterative strategies and preconditioners of CFD sparse linear systems based on structure-aware graph embedding, including:

[0112] Data acquisition module 11 is used to acquire data using a residual-driven sampling mechanism during the execution of a target simulation task based on CFD simulation software, so as to determine a physically consistent dataset; wherein, the target simulation task is a numerical simulation task of aerodynamic characteristics of aerospace vehicles or fluid machinery in a target flow field environment;

[0113] The structure-aware graph embedding module 12 is used to perform graph modeling based on the physical consistency dataset, and to determine the graph embedding vector using the corresponding graph modeling results and the structure-aware graph embedding model; the structure-aware graph embedding model is a model built based on a global pooling layer and a training-free graph isomorphic network operator.

[0114] The selection result determination module 13 is used to intelligently select the combination of iterative strategy and preconditioner of CFD sparse linear system based on the graph embedding vector and the decoupled integrated decision recommendation system, so as to determine the combination selection result; the sparse linear system is a sparse linear equation system, and the decoupled integrated decision recommendation system includes a machine learning classifier and an automated hyperparameter optimization component;

[0115] The numerical simulation completion module 14 is used to complete the CFD numerical simulation operation corresponding to the target simulation task based on the combined selection result and the CFD simulation software.

[0116] Furthermore, embodiments of this application also disclose an electronic device, Figure 15This is a structural diagram of an electronic device 20 according to an exemplary embodiment. The content of the diagram should not be construed as limiting the scope of this application.

[0117] Figure 15 This is a schematic diagram of the structure of an electronic device 20 provided in an embodiment of this application. Specifically, the electronic device 20 may include: at least one processor 21, at least one memory 22, a power supply 23, a communication interface 24, an input / output interface 25, and a communication bus 26. The memory 22 stores a computer program, which is loaded and executed by the processor 21 to implement the relevant steps in the intelligent selection method for iterative strategies and preconditioners of CFD sparse linear systems based on structure-aware graph embedding disclosed in any of the foregoing embodiments. Alternatively, the electronic device 20 in this embodiment may specifically be an electronic computer.

[0118] In this embodiment, the power supply 23 is used to provide operating voltage for each hardware device on the electronic device 20; the communication interface 24 can create a data transmission channel between the electronic device 20 and external devices, and the communication protocol it follows can be any communication protocol applicable to the technical solution of this application, and is not specifically limited here; the input / output interface 25 is used to acquire external input data or output data to the outside world, and its specific interface type can be selected according to specific application needs, and is not specifically limited here.

[0119] In addition, the memory 22, as a carrier for resource storage, can be a read-only memory, random access memory, disk or optical disk, etc. The resources stored thereon can include operating system 221, computer program 222, etc., and the storage method can be temporary storage or permanent storage.

[0120] The operating system 221 is used to manage and control the various hardware devices on the electronic device 20 and the computer program 222, which may be Windows Server, Netware, Unix, Linux, etc. In addition to including a computer program capable of performing the intelligent selection method for iterative strategies and preconditioners of CFD sparse linear systems based on structure-aware graph embedding disclosed in any of the foregoing embodiments, the computer program 222 may further include computer programs capable of performing other specific tasks.

[0121] Furthermore, this application also discloses a computer-readable storage medium for storing a computer program; wherein, when the computer program is executed by a processor, it implements the aforementioned disclosed intelligent selection method for iterative strategies and preconditioners of CFD sparse linear systems based on structure-aware graph embedding. Specific steps of this method can be found in the corresponding content disclosed in the foregoing embodiments, and will not be repeated here.

[0122] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to in the method section.

[0123] Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0124] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein can be implemented directly by hardware, a software module executed by a processor, or a combination of both. The software module can be located in random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium known in the art.

[0125] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0126] The technical solutions provided in this application have been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for intelligent selection of iterative strategies and preconditioners for CFD sparse linear systems based on structure-aware graph embedding, characterized in that, include: During the execution of the target simulation task based on CFD simulation software, a residual-driven sampling mechanism is used to collect data in order to determine the physically consistent dataset; wherein, the target simulation task is a numerical simulation task of aerospace vehicle or fluid machinery in a target flow field environment; Graph modeling is performed based on the physical consistency dataset, and graph embedding vectors are determined using the corresponding graph modeling results and a structure-aware graph embedding model. The structure-aware graph embedding model is a model built based on a global pooling layer and a training-free graph isomorphic network operator. Based on the graph embedding vector and the decoupled ensemble decision recommendation system, intelligent selection of the combination of iterative strategies and preconditioners for CFD sparse linear systems is performed to determine the combination selection result; the sparse linear system is a sparse linear equation system, and the decoupled ensemble decision recommendation system includes a machine learning classifier and an automated hyperparameter optimization component; Based on the combined selection results and the CFD simulation software, complete the CFD numerical simulation operation corresponding to the target simulation task. The step of determining the graph embedding vector using the corresponding graph modeling results and the structure-aware graph embedding model includes: Input the graph modeling results into the structure-aware graph embedding model; Based on the structure-aware graph embedding model, its parameters are orthogonally initialized, and node features and edge features are mapped to a high-dimensional space of the same dimension based on these parameters to determine the mapping result. Based on the structure-aware graph embedding model and the mapping result, structure-aware feature encoding is performed to determine the graph embedding vector; The step of performing structure-aware feature encoding based on the structure-aware graph embedding model and the mapping result to determine the graph embedding vector includes: Based on the training-free graph isomorphic network operator in the structure-aware graph embedding model, the mapping result is aggregated with information from neighboring nodes to determine the information aggregation result. Based on the multilayer perceptron in the structure-aware graph embedding model, the information aggregation result is subjected to high-dimensional feature mapping to determine the high-dimensional mapping result. Based on the global pooling layer in the structure-aware graph embedding model, and using the JL lemma and the high-dimensional mapping results, the graph embedding vector is determined; The intelligent selection of combinations of iterative strategies and preconditioners for CFD sparse linear systems based on the graph embedding vector and decoupled ensemble decision recommendation system includes: The graph is embedded into a vector input decoupled integrated decision recommendation system; Based on the machine learning classifier in the decoupled integrated decision recommendation system, the graph embedding vector is processed to determine the vector processing result; Based on the machine learning classifier and the corresponding automated hyperparameter optimization component, and using the vector processing results, intelligent selection is performed on the combination of iterative strategies and preconditioners for CFD sparse linear systems to determine the combination selection result.

2. The intelligent selection method for iterative strategies and preconditioners of CFD sparse linear systems based on structure-aware graph embedding as described in claim 1, characterized in that, During the execution of the target simulation task based on CFD simulation software, data acquisition is performed using a residual-driven sampling mechanism to determine the physically consistent dataset, including: During the execution of the target simulation task based on CFD simulation software, data is collected using the online monitoring component in the CFD simulation software and the residual-driven sampling mechanism to determine the physical consistency dataset; wherein, the online monitoring component is the monitoring component corresponding to the sparse linear system solver.

3. The intelligent selection method for iterative strategies and preconditioners of CFD sparse linear systems based on structure-aware graph embedding as described in claim 2, characterized in that, The online monitoring component in the CFD simulation software, and the data acquisition using a residual-driven sampling mechanism to determine the physical consistency dataset, includes: Based on the input / output extension interface of the CFD simulation software, a sparse matrix and an initial residual vector in a preset matrix storage format are obtained; wherein, the input / output extension interface is an input / output interface already integrated into the underlying simulation architecture of the CFD simulation software; the preset matrix storage format includes a block compressed sparse row format and a compressed sparse row format; Based on the online monitoring component in the CFD simulation software, the instantaneous residual in the nonlinear iteration process is monitored to determine the instantaneous residual monitoring result; Based on the online monitoring component, the instantaneous residual monitoring results, and multiple uniformly distributed logarithmic decline thresholds, numerical snapshots at each sampling point during the simulation process corresponding to the target simulation task are captured to determine the numerical sampling results; the logarithmic decline threshold is a logarithmic instantaneous residual decline threshold. Based on the numerical sampling results, the initial sparse linear equations corresponding to the target simulation task, and the local correction equations at each sampling point, a physical consistency dataset is constructed.

4. The intelligent selection method for iterative strategies and preconditioners of CFD sparse linear systems based on structure-aware graph embedding as described in claim 3, characterized in that, The method of capturing numerical snapshots at each sampling point during the simulation process corresponding to the target simulation task, based on the online monitoring component, the instantaneous residual monitoring results, and multiple uniformly distributed logarithmic descent thresholds, includes: Based on the first-step triggering strategy and the online monitoring component, in the first step of the instantaneous residual monitoring process, a numerical snapshot capture command is automatically triggered to determine the first capture result; In the instantaneous residual monitoring process, when the instantaneous residual monitoring result indicates that the current instantaneous residual is less than any of the logarithmic decrease thresholds for the first time, the numerical snapshot capture instruction is triggered based on the online monitoring component to determine the second capture result; Based on the tail-step triggering strategy and the online monitoring component, the numerical snapshot capture command is automatically triggered at the tail step of the instantaneous residual monitoring process to determine the third capture result; Based on the first capture result, several second capture results, and the third capture result, a numerical sampling result is determined.

5. The intelligent selection method for iterative strategies and preconditioners of CFD sparse linear systems based on structure-aware graph embedding according to claim 3, characterized in that, The graph modeling based on the physically consistent dataset includes: Node features and edge features are extracted from the sparse matrix in the physical consistency dataset to determine the feature extraction results; Directed graph modeling is performed based on the feature extraction results to determine the graph modeling result.

6. The intelligent selection method for iterative strategies and preconditioners of CFD sparse linear systems based on structure-aware graph embedding as described in claim 5, characterized in that, The step of extracting node features and edge features from the sparse matrix in the physically consistent dataset to determine the feature extraction results includes: For the first sparse matrix in the physical consistency dataset that belongs to the block compressed sparse row format, node features of the first preset feature type are extracted to determine the first node feature set; the first preset feature type includes diagonal block Frobenius norm, block asymmetry, block condition number, block minimum real part eigenvalue, and block residual norm. For the first sparse matrix, edge features of a second preset feature type are extracted to determine the first edge feature set; the second preset feature type includes off-diagonal block Frobenius norm, normalized coupling strength, and convection dominance index; For the second sparse matrix in the physical consistency dataset that belongs to the compressed sparse row format, node features of a third preset feature type are extracted to determine the second node feature set; the third preset feature type includes the absolute value of the diagonal elements and the scalar value of the right-hand item. For the second sparse matrix, edge features of a fourth preset feature type are extracted to determine the second edge feature set; the fourth preset feature type includes the absolute value of off-diagonal elements and normalized coupling strength. Data standardization processing is performed on the first node feature set, the first edge feature set, the second node feature set, and the second edge feature set to determine the standardization processing result; Based on the standardized processing results and the preset logarithmic scaling strategy, the feature extraction results are determined.

7. The intelligent selection method for iterative strategies and preconditioners of CFD sparse linear systems based on structure-aware graph embedding as described in claim 1, characterized in that, The step of performing CFD numerical simulation operations corresponding to the target simulation task based on the combined selection results and the CFD simulation software includes: Based on the combined selection results, the sparse linear equations corresponding to the target simulation task are solved to determine the target solution result; Based on the solution results of the objective and the CFD simulation software, the CFD numerical simulation operation corresponding to the objective simulation task is completed.

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