Flow velocity prediction method, system, device and medium based on node optimization graph operator

Abstract

The present application relates to the field of fluid velocity prediction, and discloses a velocity prediction method, system, device and medium based on a node optimization graph operator. The method comprises: step S1, selecting different radii for each spatial point in the input velocity field through a multi-scale graph construction module to construct a neighborhood graph to complete the multi-scale graph construction; step S2, after constructing the multi-scale graph, obtaining multiple graph inputs of different scales, performing multi-layer solutions on each graph input through a node optimization graph operator, performing optimization extraction on each graph input using a node feature optimization network, performing graph message passing operations on the optimized graph input and outputting it; step S3, accumulating and averaging the outputs of each scale through a multi-scale information fusion module to fuse the information of the multi-scale graph, and obtaining the velocity prediction result of the final velocity field. The present application realizes the solution to the multi-scale nature of the fluid physical field; and realizes the deep optimization of graph node features through a node feature optimization network, and realizes the mining of deep features.

Description

Technical Field

[0001] The present application relates to the field of fluid velocity prediction, and specifically to a velocity prediction method, system, device and medium based on a node optimization graph operator. Background Art

[0002] Before data-driven machine learning made great progress, many fields of physics and engineering used physical model-driven methods for research and development. After years of development, these fields have accumulated a large number of physical models that are characterized or described in the form of partial differential equations, such as Darcy's law that describes fluid flow in porous media, which is widely used in oil and gas exploration, geothermal development, soil infiltration, biofiltration and other fields. Traditional numerical methods for solving partial differential equations include finite element methods, finite difference methods, spectral methods, etc., but these methods usually require discretization of the space domain and time domain in advance, requiring a lot of computing resources and time, and there are certain difficulties and limitations when dealing with complex geometric regions and high-dimensional space solutions.

[0003] At present, fluid velocity prediction is an important application of partial differential equation solution. The prediction of fluid velocity using neural operator-based methods has achieved remarkable results. However, there are still several problems: First, fluid physics usually exhibits different physical states at different observation scales and observation areas, that is, the fluid physics itself has multi-scale properties. For multi-scale problems, most operator learning schemes essentially capture the smooth part of the solution space, such as Fourier neural operators filtering out high-frequency information in the frequency domain; in addition, most existing deep learning multi-scale techniques (such as downsampling and upsampling) will cause information loss in the physical space, so how to solve the inherent multi-scale characteristics of fluid physics is still a major challenge. Second, graph-based methods have better interpretability when solving fluid physics than other neural operator methods. However, like other data-driven deep learning methods, the performance of such methods is affected by data quality, that is, the different construction methods of point features and edge features will have a direct impact on performance. Currently, most of the mainstream fluid physics field data sets are obtained by numerical solvers, from which the point features and edge features of the graph can be constructed. However, this method does not mine the deep-level graph node features, which leads to insufficient adjacent node information during the graph information aggregation process. Summary of the invention

[0004] The technical problem to be solved by the present application is to overcome the deficiencies of the prior art and provide a flow velocity prediction method, system, device and medium based on a node optimization graph operator, which can solve the multi-scale nature of the fluid physical field and mine deep-level graph node features.

[0005] To achieve the above object, the first aspect of the present application provides a flow velocity prediction method based on a node optimization graph operator, comprising the following steps:

[0006] Step S1, selecting different radii for each spatial point in the input velocity field to construct a neighborhood graph through a multi-scale graph construction module, so as to complete the multi-scale graph construction;

[0007] Step S2, after constructing the multi-scale graph, a plurality of graph inputs of different scales are obtained, and a node optimization graph operator is used to perform multi-layer solution on each graph input, wherein the node optimization graph operator uses a node feature optimization network to perform optimization extraction on each graph input, and performs a graph message passing operation on the optimized graph input and outputs it;

[0008] The node feature optimization network performs optimization extraction including:

[0009] The frequency domain information extraction module is used to extract frequency domain information through fast Fourier transform and inverse Fourier transform, and the spatial domain multi-scale information is extracted through the spatial domain information extraction module. The spatial domain multi-scale information and frequency domain information are fused through cross attention. The information compensation module is used to extract key information through the channel-space hybrid attention mechanism.

[0010] The fused spatial domain multi-scale information, frequency domain information and key information are fused and added through a nonlinear activation function;

[0011] Step S3, the output of each scale is accumulated and averaged through the multi-scale information fusion module to fuse the information of the multi-scale graph to obtain the flow velocity prediction result of the final flow velocity field.

[0012] Furthermore, in step S1, constructing a multi-scale graph through the multi-scale graph construction module includes selecting K discrete spatial points in the velocity field space domain D as nodes of the multi-scale graph G, drawing circles with each node as the center and r as the radius, and the points included in the circle drawn by each node are regarded as having an edge with the central node, and constructing neighborhood graphs of different scales by selecting different radii in the physical space, and combining neighborhood graphs of different scales in a hierarchical manner to realize multi-scale graph construction.

[0013] Furthermore, in step S2, the iterative formula of the node optimization graph operator is expressed as:

[0014] ;

[0015] in, is the number of different scales, k is an integer, , Optimize the network for node characteristics, represents the edge features of x and y at scale k, Represents a node optimization graph operator at scale k.

[0016] Furthermore, in step S2, the node feature optimization network performs optimization extraction on each graph input, which is expressed as:

[0017] ;

[0018] in, Optimize the network for node characteristics, represents the frequency domain information extraction module, is the spatial domain information extraction module, It is the information compensation module. Indicates cross attention, is a nonlinear activation function, x is a point in the velocity field space domain D, is the input flow rate.

[0019] Furthermore, in step S2, the frequency domain information extraction module performs an operation using a convolution operator defined in Fourier space, which is expressed as follows:

[0020] ;

[0021] in, represents the Fourier transform of the input flow rate, is a linear transformation, is the inverse Fourier transform; the spatial domain information extraction module uses the Unet architecture to extract spatial domain multi-scale information, and fuses the extracted frequency domain information with the spatial domain multi-scale information through cross attention, which is expressed as:

[0022] ;

[0023] in, , , , , , is a learnable matrix, is the scaling factor, Indicates cross attention, for function, express The transpose of , T represents the matrix transpose operation.

[0024] Furthermore, in step S2, the information compensation module performs key information compensation and extracts key information using a channel-space hybrid attention mechanism, which is expressed as:

[0025] ;

[0026] ;

[0027] in, is the channel attention module, is the spatial attention module, is a multi-layer perceptron, is average pooling, is the maximum pooling, is convolution, is a non-linear activation function.

[0028] To achieve the above-mentioned purpose, the second aspect of the present application provides a flow velocity prediction system based on a node optimization graph operator, the system comprising:

[0029] A multi-scale graph construction module, wherein the multi-scale graph construction module selects different radii for each spatial point in the input velocity field to construct a neighborhood graph to complete the multi-scale graph construction;

[0030] A node optimization graph operator, wherein the node optimization graph operator includes a node feature optimization network, the multi-scale graph construction module outputs a plurality of graph inputs of different scales, and each graph input is subjected to multi-layer solution by the node optimization graph operator. The node optimization graph operator uses the node feature optimization network to perform optimization extraction on each graph input, and performs a graph message passing operation on the optimized graph input and outputs the result;

[0031] The node feature optimization network performs optimization extraction including:

[0032] The frequency domain information extraction module is used to extract frequency domain information through fast Fourier transform and inverse Fourier transform, and the spatial domain multi-scale information is extracted through the spatial domain information extraction module. The spatial domain multi-scale information and frequency domain information are fused through cross attention. The information compensation module is used to extract key information through the channel-space hybrid attention mechanism.

[0033] The fused spatial domain multi-scale information, frequency domain information and key information are fused and added through a nonlinear activation function;

[0034] A multi-scale information fusion module accumulates and averages the output of each scale to fuse the information of the multi-scale graph to obtain the flow velocity prediction result of the final flow velocity field.

[0035] To achieve the above-mentioned purpose, the third aspect of the present application provides a flow rate prediction device based on a node optimization graph operator, including a processor and a memory, wherein a computer program is stored in the memory, and when the computer program is executed by the processor, the flow rate prediction method based on the node optimization graph operator as described above is implemented.

[0036] To achieve the above-mentioned purpose, the fourth aspect of the present application provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the flow rate prediction method based on the node optimization graph operator as described above.

[0037] After adopting the above technical solution, the present application has the following beneficial effects compared with the prior art:

[0038] In the present application, multi-scale feature extraction based on graph structure is realized by constructing a multi-scale graph, which is conducive to the graph operator to make full use of the information of different physical states of fluid physical fields at different scales, and avoid the information loss caused by other multi-scale technologies based on spatial domain. It can better capture the different physical characteristics of fluid physical fields at different scales, and realize the solution of the multi-scale nature of fluid physical fields; the present application realizes deep optimization of graph node features through a node feature optimization network, and then solves the optimized graph nodes, enriches the adjacent node information in the process of graph information aggregation, enhances the solution ability of graph operators, and realizes the mining of deep-level features, which is superior to other non-graph methods that directly solve in physical space and other graph-based methods that directly solve graph structures constructed using physical space.

[0039] The specific implementation methods of the present application are further described in detail below in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] The accompanying drawings are part of this application and are used to provide a further understanding of this application. The illustrative embodiments of this application and their descriptions are used to explain this application, but do not constitute an improper limitation on this application. Obviously, the drawings described below are only some embodiments. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0041] In the drawings of the specification:

[0042] Figure 1 is a logical schematic diagram of flow velocity prediction based on the node optimization graph operator in this specific implementation mode;

[0043] Figure 2 is a logical schematic diagram of a node feature optimization network in this specific implementation mode;

[0044] Figure 3 This is a diagram of the prediction results of the Darcy equation at a resolution of 31×31 in this specific implementation mode;

[0045] Figure 4 This is a diagram of the prediction results of the Darcy equation at a resolution of 61×61 in this specific implementation mode;

[0046] Figure 5This is a prediction result diagram of the Navier-Stokes equation at a resolution of 32×32 in this specific implementation mode;

[0047] Figure 6 This is a diagram of the prediction results of the Navier-Stokes equation at a resolution of 64×64 in this specific implementation manner. DETAILED DESCRIPTION

[0048] In order to make the purpose, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. The following embodiments are used to illustrate the present application but are not used to limit the scope of the present application.

[0049] The related technologies mentioned in the background technology are explained as follows:

[0050] Graph neural networks are different from traditional convolutional neural networks and recurrent neural networks. With their unique graph data structure modeling capabilities, graph neural networks can process graph structured data of arbitrary shapes and can handle non-Euclidean data well. Compared with purely data-driven methods, graph neural networks can better capture the relationship between nodes in dealing with fluid flow rate prediction problems, can explicitly handle the physical constraints between discrete data points, and have shown significant advantages in modeling complex relationships and interpretability. One of the paradigms of graph neural networks is to aggregate the features of each node with the features of its surrounding nodes through message passing to form a new node representation. The standard message passing graph neural network formula using cumulative aggregation is as follows, denoted as Formula 1:

[0051] ;

[0052] in, represents the characteristics of node i, t is the number of message passing layers, represents the set of neighbor nodes of node i, represents the edge feature between node i and node j. MP is the message passing function, which calculates the message passed by node j to node i based on the features of the node and the edge. U is the update function of the tth layer, which updates the hidden state of node i based on its own features and the messages from neighboring nodes.

[0053] The fluid velocity prediction method based on neural operators learns the mapping relationship from the input space to the solution space in the physical space data to predict the fluid velocity. The neural operator aims to learn the mapping from the function defined in the domain (usually Euclidean space). The goal is to learn a mapping ,in, , are two function spaces defined in the spatial domain D. Under the guidance of the Green function method, the iterative architecture of the neural operator can be designed as follows, expressed as formula 2:

[0054] ;

[0055] Among them, t is the number of layers to be solved, x and y are points on the spatial domain D, is the t-th solution for the flow velocity at the spatial point x, represents the velocity at the spatial point y solved for the tth time, It is a nonlinear activation function. Since the Green function method is based on the superposition principle, and the superposition principle only holds true in linear differential equations, a nonlinear activation function is needed to solve nonlinear equations. is a neural network; the parameters φ and the neural network Learn from data; is the Borel measure, and under the Lebesgue measure we have , then formula 2 can be written as:

[0056] ;

[0057] Will Denoted as the kernel integral operator, it is:

[0058] ;

[0059] In this formal language, different solutions for different neural operators are how to handle the kernel integral operator.

[0060] Based on this, this application proposes a flow velocity prediction method based on node optimization graph operator, comprising the following steps:

[0061] Step S1, selecting different radii for each spatial point in the input velocity field to construct a neighborhood graph through a multi-scale graph construction module, so as to complete the multi-scale graph construction;

[0062] Step S2, after constructing a multi-scale graph, a plurality of graph inputs of different scales are obtained, and a node optimization graph operator is used to perform multi-layer solution on each graph input. The node optimization graph operator uses a node feature optimization network to perform optimization extraction on each graph input, and performs a graph message passing operation on the optimized graph input and outputs it;

[0063] Node feature optimization network performs optimization extraction including:

[0064] The frequency domain information extraction module is used to extract frequency domain information through fast Fourier transform and inverse Fourier transform, and the spatial domain multi-scale information is extracted through the spatial domain information extraction module. The spatial domain multi-scale information and frequency domain information are fused through cross attention. The information compensation module is used to extract key information through the channel-space hybrid attention mechanism.

[0065] The fused spatial domain multi-scale information, frequency domain information and key information are fused and added through a nonlinear activation function;

[0066] Step S3, the output of each scale is accumulated and averaged through the multi-scale information fusion module to fuse the information of the multi-scale graph to obtain the flow velocity prediction result of the final flow velocity field.

[0067] It should be noted that the execution subject of the flow rate prediction method based on the node optimization graph operator in this embodiment is a flow rate prediction device based on the node optimization graph operator, which can be an electronic device, a component in an electronic device, an integrated circuit, or a chip. The electronic device can be a mobile electronic device or a non-mobile electronic device. Exemplarily, the mobile electronic device can be a mobile phone, a tablet computer, a laptop computer, a PDA, a vehicle-mounted electronic device, a wearable device, etc., and the non-mobile electronic device can be a server and a personal computer, etc., which are not specifically limited in this application. The following takes the execution subject as an example of a server to describe the flow rate prediction method based on the node optimization graph operator in this embodiment.

[0068] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of the embodiments of the present application, the meaning of "multiple" is two or more, unless otherwise clearly and specifically defined.

[0069] See also Figure 1 In one achievable implementation, in step S1, constructing a neighborhood graph through a multi-scale graph construction module includes first selecting K discrete spatial points in the velocity field space domain D as nodes of the multi-scale graph G, and these nodes of the multi-scale graph G represent specific positions of the velocity field. Then, circles are drawn with each node as the center and r as the radius, and the points included in the circle drawn by each node are considered to have an edge with the central node, that is, all points in the circle (including points on the boundary) are considered to have a direct neighborhood relationship with the central node, so as to define the neighborhood, and then by selecting different radii r in the physical space 1 , r 2 ,......r ωConstruct a neighborhood graph, where each radius defines a different neighborhood size, thus forming neighborhood graphs of different scales. These neighborhood graphs of different scales are combined in a hierarchical manner to achieve multi-scale graph construction.

[0070] For the first graph message passing process, each point Aggregated from the neighborhood information, and each subsequent iteration All points in its neighborhood Obtained from Neighborhood information, which obviously includes Information in the neighborhood, after M iterations In theory, approximately global information can be obtained.

[0071] It should be noted that in Figure 1 middle, For the i-th spatial point in the input velocity field A, a point feature is constructed for each point in the space , thus converting the spatial points into nodes of the graph, represents the point feature of node i, represents the point feature of node j, represents the edge feature between node i and node j, Indicates The radius selected under each scale, Represents quantities of different scales.

[0072] Based on the above characteristics, for neighborhood graphs constructed with different radii, approximate global information can be obtained after iteration. However, due to different radii and different neighborhood ranges, the information finally obtained is also different. When a smaller radius is used to construct a neighborhood graph, each point obtains features from a relatively smaller neighborhood. After completing the same iteration, each point obtains relatively weakened global information, but the key information obtained from the local neighborhood will not be weakened like the global information, that is, it has scale invariance similar to Gaussian scale space.

[0073] It is worth noting that this embodiment adopts a multi-scale graph construction module, which constructs a multi-scale graph by selecting different radius parameters in the physical space, solves the graphs of different scales by message passing through graph operators, and accumulates and averages the output of each scale to fuse the information of the multi-scale graph to obtain the final output, thereby realizing the solution to the multi-scale nature of the fluid physical field.

[0074] For details, see Figure 1 Step S1 constructs a multi-scale graph module for each spatial point in the input velocity field Select different radii to construct neighborhood graphs and output multi-scale graphs ,in Indicates that a multi-scale graph is constructed by selecting different radii; Step S2 inputs the graph obtained by the multi-scale graph construction module into the multi-scale graph , using M-layer nodes to optimize graph operators ... Perform iterative solution and add residual connections to each layer to obtain multi-scale graphs ... ,in Representation of multi-scale graphs The M-layer solution, Represents a set of multi-scale graph outputs obtained by solving the M-layer node optimization graph operator; graph operator exist Solved In the process, the node characteristics are used to optimize the network Perform feature optimization to obtain , using message passing MP to get , ,in represents the multi-scale graph output after solving the mth layer, express After The multi-scale graph output after layer solution, where NFON represents the node feature optimization network, represents the point feature of node i after solving the mth layer, represents the point feature of node j after solving the mth layer, represents the edge feature between node i and node j after the mth layer is solved, m represents the number of layers to be solved, , represents the point feature of node i after feature optimization, represents the point feature of node j after feature optimization; Step S3 uses a multi-scale information fusion module to Accumulate and average to fuse the information of multi-scale images. Represents the point feature of node i after solving the Mth layer, and obtains the final velocity field prediction result U, is the spatial point in the velocity field prediction result U, Represents a spatial point in the velocity field The flow rate prediction results.

[0075] Please continue to see Figure 1 In one achievable implementation, according to the architecture of the general graph operator described above, the formula of the node optimization graph operator is derived. The Borel metric can be regarded as a Lebesgue metric supported on a sphere with a radius of r, and the integration domain becomes the range of the sphere. , which is expressed as:

[0076] ;

[0077] Assuming that the distribution of spatial points y is uniform, the kernel integral operator can be approximated by summation. By using the property that the kernel integral on the spatial domain D is equivalent to the message passing aggregation of the graph G constructed on the spatial domain D, assuming that the message passing graph neural network adopts a standard architecture, given the node features , edge features And graph G, and using the average aggregation method, we can get:

[0078] ;

[0079] in, is a nonlinear activation function, x and y are spatial points in the velocity field space domain D, and t is the number of layers of the graph operator. is the input flow velocity at the spatial point x for the tth solution, Indicates that the flow rate will be input Through a simple neural network processing, it plays a role similar to residual connection, W is the weight matrix of the neural network, For bias. is the neighborhood of x determined according to graph G, | | represents the number of points in the neighborhood, Represents the edge features of graph G The neural network input, edge features , used to describe the properties of the edge between x and y, represents the features related to x, represents the features related to y, represents the velocity at the spatial point y solved for the tth time, Indicates The flow velocity at x for the solution iteration.

[0080] According to the above derivation process, the iterative formula of the node optimization graph operator using the node optimization network in step S2 in this embodiment can be expressed as:

[0081] ;

[0082] in, is the number of different scales, k is an integer, and each scale is traversed. , Optimize the network for node characteristics, represents the edge features of x and y at the corresponding scale k, Represents the node optimization graph operator at the corresponding scale k.

[0083] It should be noted that the node optimization graph operator of this embodiment adds a node feature optimization network compared to the general graph operator to perform feature optimization on the input point features and edge features.

[0084] After the multi-scale graph is constructed in step S1, multiple graph inputs of different scales are obtained, and each graph input is processed using a node feature optimization network.

[0085] See also Figure 1 and Figure 2 In one achievable implementation, in step S2, the node feature optimization network performs optimization extraction on each graph input, which is expressed as:

[0086] ;

[0087] in, Optimize the network for node characteristics, represents the frequency domain information extraction module, is the spatial domain information extraction module, It is the information compensation module. Indicates cross attention, is a nonlinear activation function that optimizes the extracted result That is .

[0088] Specifically, It is a frequency domain information extraction module, which is implemented through fast Fourier transform and its inverse transform to extract frequency domain information; It is a spatial domain information extraction module, used to extract multi-scale information in the spatial domain; It is an information compensation module that extracts key information based on the attention mechanism; Cross attention is used to fuse spatial domain information and frequency domain information; is a nonlinear activation function. After the frequency domain information and multi-scale information are fused, Added with key information, multi-domain information fusion is finally performed to achieve optimized extraction of graph node information.

[0089] Please refer to Figure 2 ,In actual applications, in step S2, the frequency domain information extraction module uses the convolution operator defined in Fourier space to perform the operation, which is expressed as:

[0090] ;

[0091] in, represents the Fourier transform of the input flow rate, is a linear transformation, is the inverse Fourier transform;

[0092] Based on the multi-scale nature of fluid physical fields, the spatial domain information extraction module uses the Unet architecture to extract multi-scale information in the spatial domain, and fuses the extracted frequency domain information with the multi-scale information in the spatial domain through cross attention, which is expressed as:

[0093] ;

[0094] in, , , , , , is a learnable matrix, is the scaling factor, Indicates cross attention, for function, express The transpose of , T represents the matrix transpose operation.

[0095] Since the feature extraction in the frequency domain filters out high-frequency information, the Unet architecture causes loss of spatial information by downsampling through convolution during scale change. This embodiment compensates for key information through an information compensation module.

[0096] Please continue to see Figure 2 In this embodiment, in step S2, the information compensation module performs key information compensation and uses the channel space hybrid attention mechanism to extract key information, which is expressed as:

[0097] ;

[0098] ;

[0099] in, is the channel attention module, is the spatial attention module, is a multi-layer perceptron, is average pooling, is the maximum pooling, is convolution, is a non-linear activation function.

[0100] It is worth noting that this embodiment uses a node feature optimization network to convert the numerically solved spatial domain features into the frequency domain for frequency domain information extraction, and uses cross-attention to fuse the multi-scale information in the spatial domain with the frequency domain information. In addition, the attention mechanism is used to extract richer and more critical spatial domain features. By fusing the above multi-domain information, the optimized extraction of graph node information is achieved.

[0101] See also Figure 3 , Figure 4 , Figure 5 and Figure 6 , this application proves that the model of this application can effectively predict fluid flow rate through experiments on two fluid mechanics equations (Darcy equation and Navier-Stokes equation) data sets.

[0102] The Darcy equation describes the flow of fluid in porous media, such as water passing through sand. The two-dimensional Darcy equation in a unit space is as follows:

[0103] ;

[0104] in, is the nabla operator, is the diffusion coefficient, is the flow rate, represents external force; the velocity on the boundary of two-dimensional space Both are 0.

[0105] The Navier-Stokes equation data set used in the experiment of this application is a special form of the Navier-Stokes equation. The Navier-Stokes equation in this form simulates the incompressible viscous flow on the unit annulus. The formula is as follows:

[0106] ;

[0107] in, is the nabla operator, represents the velocity vector of the two-dimensional field, represents the vorticity, Indicates time, yes The initial vorticity at Indicates viscosity, is the Laplace operator, represents the time derivative of vorticity, Indicates external force.

[0108] The model of this application was tested with different training data amounts on the Darcy and Navier-Stokes equation data sets. The prediction accuracy is higher than that of several mature models currently used for flow velocity prediction, such as U-Net, GNO, FNO, NKN, U-FNO and LSM. The experimental results are shown in the following table:

[0109] ;

[0110] Among them, N represents the amount of training data, and the data in the table are mean square errors. The lower the value, the higher the prediction accuracy. It can be seen that the prediction error of the model of this application is lower than that of other models on the two data sets, which means that the flow velocity prediction accuracy of this application is higher than that of other models.

[0111] This application has conducted experiments on the Darcy equation at 31×31 resolution and 61×61 resolution and on the Navier-Stokes equation at 32×32 resolution and 64×64 resolution, and visualized the experimental results. Compared with the currently popular operator model FNO and an advanced operator model LSM, the model of this application has achieved good results in the experiments at two resolutions of the two equations. The visualization effect is shown in the figure below. Figures 3 to 6 shown.

[0112] Based on the same inventive concept, the present application also provides a flow velocity prediction system based on a node optimization graph operator, the system comprising:

[0113] A multi-scale graph construction module selects different radii for each spatial point in the input velocity field to construct a neighborhood graph to complete the multi-scale graph construction;

[0114] Node optimization graph operator, which includes a node feature optimization network. The multi-scale graph construction module outputs multiple graph inputs of different scales. The node optimization graph operator performs multi-layer solutions on each graph input. The node optimization graph operator uses the node feature optimization network to perform optimization extraction on each graph input, performs graph message passing operations on the optimized graph input and outputs it.

[0115] Node feature optimization network performs optimization extraction including:

[0116] The frequency domain information extraction module is used to extract frequency domain information through fast Fourier transform and inverse Fourier transform, and the spatial domain multi-scale information is extracted through the spatial domain information extraction module. The spatial domain multi-scale information and frequency domain information are fused through cross attention. The information compensation module is used to extract key information through the channel-space hybrid attention mechanism.

[0117] The fused spatial domain multi-scale information, frequency domain information and key information are fused and added through a nonlinear activation function;

[0118] Multi-scale information fusion module,The multi-scale fusion module accumulates and averages the output of each scale to fuse the information of the multi-scale graph and obtains the velocity prediction result of the final velocity field.

[0119] Based on the same inventive concept, the present application also provides a flow rate prediction device based on a node optimization graph operator, including a processor and a memory, wherein a computer program is stored in the memory. When the computer program is executed by the processor, the flow rate prediction method based on the node optimization graph operator as described above is implemented.

[0120] Based on the same inventive concept, the present application also provides a computer-readable storage medium storing a computer program, characterized in that when the computer program is executed by a processor, it implements the flow rate prediction method based on the node optimization graph operator as described above.

[0121] The program product of the present application for implementing the above method may adopt a portable compact disk read-only memory and include program code, and may be run on a terminal device, such as a personal computer. However, the program product of the present application is not limited thereto. In the present application, a readable storage medium may be any tangible medium containing or storing a program, which may be used by or in combination with an instruction execution system, device or device.

[0122] It should be noted that a computer-readable storage medium may include a data signal propagated in a baseband or as part of a carrier wave, which carries a readable program code. Such propagated data signals may take a variety of forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the above. The readable storage medium may also be any readable medium other than a readable storage medium, which may send, propagate, or transmit a program for use by or in conjunction with an instruction execution system, device, or device. The program code contained on the readable storage medium may be transmitted using any appropriate medium, including but not limited to wireless, wired, optical cable, RF, etc., or any suitable combination of the above.

[0123] The above are only preferred embodiments of the present application, and are not intended to limit the present application in any form. Although the present application has been disclosed as above with preferred embodiments, it is not intended to limit the present application. Any technician familiar with the present application can make some changes or modifications to equivalent embodiments of equivalent changes using the above-mentioned technical contents without departing from the scope of the technical solution of the present application. The implementation schemes in the above embodiments can also be further combined or replaced. However, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present application without departing from the content of the technical solution of the present application are still within the scope of the solution of the present application.

Claims

1. A flow velocity prediction method based on node optimization graph operators, characterized in that: The steps include: Step S1, selecting different radii for each spatial point in the input velocity field to construct a neighborhood graph through a multi-scale graph construction module, so as to complete the multi-scale graph construction; Step S2, after constructing the multi-scale graph, a plurality of graph inputs of different scales are obtained, and a node optimization graph operator is used to perform multi-layer solution on each graph input, wherein the node optimization graph operator uses a node feature optimization network to perform optimization extraction on each graph input, and performs a graph message passing operation on the optimized graph input and outputs it; The node feature optimization network performs optimization extraction including: The frequency domain information extraction module is used to extract frequency domain information through fast Fourier transform and inverse Fourier transform, and the spatial domain multi-scale information is extracted through the spatial domain information extraction module. The spatial domain multi-scale information and frequency domain information are fused through cross attention. The information compensation module is used to extract key information through the channel-space hybrid attention mechanism. The fused spatial domain multi-scale information, frequency domain information and key information are fused and added through a nonlinear activation function; Step S3, the output of each scale is accumulated and averaged through the multi-scale information fusion module to fuse the information of the multi-scale graph to obtain the flow velocity prediction result of the final flow velocity field.

2. The method according to claim 1, characterized in that In step S1, constructing a multi-scale graph through the multi-scale graph construction module includes selecting K discrete spatial points in the velocity field space domain D as nodes of the multi-scale graph G, drawing circles with each node as the center and r as the radius, and the points included in the circle drawn by each node are regarded as having an edge with the central node. By selecting different radii in the physical space to construct neighborhood graphs of different scales, the neighborhood graphs of different scales are combined in a hierarchical manner to realize multi-scale graph construction.

3. The method according to claim 2, characterized in that In step S2, the iterative formula of the node optimization graph operator is expressed as: ； in, is the number of different scales, k is an integer, , Optimize the network for node characteristics, represents the edge features of x and y at scale k, Represents a node optimization graph operator at scale k.

4. The method according to claim 3, characterized in that In step S2, the node feature optimization network performs optimization extraction on each graph input, which is expressed as: ； in, Optimize the network for node characteristics, represents the frequency domain information extraction module, is the spatial domain information extraction module, It is the information compensation module. Indicates cross attention, is a non-linear activation function.

5. The method according to claim 4, characterized in that In step S2, the frequency domain information extraction module performs an operation using a convolution operator defined in Fourier space, which is expressed as follows: ； in, represents the Fourier transform of the input flow rate, is a linear transformation, is the inverse Fourier transform; the spatial domain information extraction module uses the Unet architecture to extract spatial domain multi-scale information, and fuses the extracted frequency domain information with the spatial domain multi-scale information through cross attention, which is expressed as: ； in, , , , , , is a learnable matrix, is the scaling factor, Indicates cross attention, for function, express The transpose of , T represents the matrix transpose operation.

6. The method according to claim 5, characterized in that In step S2, the information compensation module performs key information compensation and extracts key information using a channel-space hybrid attention mechanism, which is expressed as: ； ； in, is the channel attention module, is the spatial attention module, is a multi-layer perceptron, is average pooling, is the maximum pooling, is convolution, is a non-linear activation function.

7. The flow rate prediction system based on node optimization graph operator is characterized by: The system comprises: A multi-scale graph construction module, wherein the multi-scale graph construction module selects different radii for each spatial point in the input velocity field to construct a neighborhood graph to complete the multi-scale graph construction; A node optimization graph operator, wherein the node optimization graph operator includes a node feature optimization network, the multi-scale graph construction module outputs a plurality of graph inputs of different scales, and each graph input is subjected to multi-layer solution by the node optimization graph operator. The node optimization graph operator uses the node feature optimization network to perform optimization extraction on each graph input, and performs a graph message passing operation on the optimized graph input and outputs the result; The node feature optimization network performs optimization extraction including: The frequency domain information extraction module is used to extract frequency domain information through fast Fourier transform and inverse Fourier transform, and the spatial domain multi-scale information is extracted through the spatial domain information extraction module. The spatial domain multi-scale information and frequency domain information are fused through cross attention. The information compensation module is used to extract key information through the channel-space hybrid attention mechanism. The fused spatial domain multi-scale information, frequency domain information and key information are fused and added through a nonlinear activation function; A multi-scale information fusion module accumulates and averages the output of each scale to fuse the information of the multi-scale graph to obtain the flow velocity prediction result of the final flow velocity field.

8. A flow velocity prediction device based on a node optimization graph operator, characterized in that: It includes a processor and a memory, wherein a computer program is stored in the memory, and when the computer program is executed by the processor, the flow velocity prediction method based on the node optimization graph operator as described in any one of claims 1 to 6 is implemented.

9. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the flow velocity prediction method based on the node optimization graph operator as described in any one of claims 1 to 6 is implemented.

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