A method and system for deducing fluid velocity and pressure fields based on fusion network

Abstract

The present invention belongs to the technical field of fluid velocity and pressure field deduction, and discloses a fluid velocity and pressure field deduction method and system based on a fusion network. The method uses a computational fluid dynamics method to obtain a flow field information data set required for training; constructs a KAN network; constructs a fusion network based on KAN and PINN; uses the constructed training set for the constructed training based on the KAN and PINN fusion network, and uses a verification set for verification, and finally obtains a flow field deduction result. The present invention establishes a neural network data set, constructs a KAN type neural network structure, and uses fluid-related physical equations to constrain the neural network, thereby predicting the values ​​of velocity and pressure in the flow field in real time, so that the surrounding flow field conditions can be predicted in real time during the ship's travel, and the velocity and pressure field can be deduced for a specific fluid domain.

Description

Technical Field

[0001] The present invention belongs to the technical field of fluid velocity pressure field deduction, and in particular relates to a fluid velocity pressure field deduction method and system based on a fusion network. Background Art

[0002] In traditional methods, if you want to know the flow field information, you need to conduct actual ship measurements, and the flow field information changes with time, making it very difficult to control the real-time information of the entire fluid domain. The fluid intelligent prediction method combined with neural networks can solve this problem, but the previous network model has the disadvantages of slow calculation and low accuracy. A new type of network model is urgently needed to make the calculation of flow field information fast and achieve almost error-free results.

[0003] Through the above analysis, the problems and defects of the existing technology are as follows: the existing technology cannot accurately and real-time predict the surrounding flow field conditions during the navigation of the ship, and the data processing effect of the velocity pressure field deduction for a specific fluid domain is poor. Summary of the invention

[0004] In order to overcome the problems existing in the related art, the disclosed embodiment of the present invention provides a fluid velocity and pressure field deduction method and system based on a fusion network.

[0005] The technical solution is as follows: A fluid velocity pressure field deduction method based on a fusion network includes:

[0006] S1. Using computational fluid dynamics methods to obtain the flow field information data set required for training;

[0007] S2, constructing a KAN network based on the obtained flow field information data set;

[0008] S3, using the fluid physics control equation to constrain the KAN network and construct a fusion network based on KAN and PINN;

[0009] S4. Use the constructed KAN and PINN fusion network to train the data set and use the validation set for verification to obtain the flow field deduction results.

[0010] In step S1, a computational fluid dynamics method is used to obtain a flow field information data set required for training, including:

[0011] S101, constructing a two-dimensional cylinder flow fluid domain based on computational fluid dynamics method and setting boundary conditions;

[0012] S102, computational fluid dynamics simulation and data set construction.

[0013] In step S101, a two-dimensional cylindrical flow fluid domain is constructed based on a computational fluid dynamics method and boundary conditions are set, including:

[0014] Select a rectangular basin with a length 15 times the diameter of the cylinder, a width 7 times the diameter of the cylinder, and a height 1.5 times the height of the cylinder;

[0015] The boundary conditions include velocity inlet, pressure outlet, symmetry plane, overlapping grids, mass flow inlet, stagnation inlet, outlet and wall; the area covered by the water flow below is set as the fluid domain, the water flow inlet is set as the velocity inlet, the surface on which the water flows out is set as the pressure outlet, and the length direction surface of the rectangular fluid domain is set as the wall.

[0016] In step S102, computational fluid dynamics simulation and data set construction include: in the water part, a plane is taken along the direction perpendicular to the axis of the cylinder, and the plane is a two-dimensional flow field around the cylinder; the flow field information data set required for training includes: time , the coordinates of the observation point , the observation point Speed ​​of direction , Speed ​​of direction , and the pressure at the observation point The flow field information data set is divided into 70% of the data as a training set and 30% of the data as a validation set.

[0017] In step S2, a KAN network is constructed, including:

[0018] The input fluid control point coordinates and time The data is mapped to a high-dimensional space, and the input is gradually mapped to the output through a multi-layer combination of nonlinear activation functions and linear mappings. The network approximates any continuous function through depth and breadth. The last layer performs a linear transformation on the implicit state to obtain the predicted values ​​of the velocity field and pressure field, completing the construction of the KAN network.

[0019] Furthermore, the KAN network is divided into three layers. The first layer is the input layer, and the input parameters are the coordinates of the fluid control points. and the current time , and is represented to high dimensions using spline functions; the second hidden layer is reduced to low dimensions using spline function fitting; the third layer is the output layer, and the output is the velocity and pressure field of the fluid, that is, Speed ​​of direction and pressure .

[0020] Furthermore, the last layer performs a linear transformation on the hidden state to obtain the predicted values ​​of the velocity field and pressure field, including:

[0021] Define the input as ,in and are the coordinates of the fluid control point, is time; the input layer has 2 nodes, accepting and , the three nodes in the hidden layer are used to predict , through the nonlinear activation function of the hidden layer, the input data is mapped to a high-dimensional space, and then the operation of the hidden layer is output to the output layer through a linear transformation;

[0022] The inherent mean square error loss of the constructed KAN network is expressed as:

[0023] ;

[0024] In the formula, is the actual value, is the predicted value, is the total number of fluid control points calculated, is the counting symbol, for Actual value of direction speed, for Direction speed prediction value, for Actual value of direction speed, for Direction speed prediction value, is the actual value of pressure, is the predicted value of pressure.

[0025] In step S3, a fusion network based on KAN and PINN is constructed, including:

[0026] The physical loss equations of fluid velocity and pressure field prediction, including mass conservation, momentum conservation, and NS equations, are added to the mean square error loss function of the KAN network to construct a fusion network based on KAN and PINN.

[0027] The mass conservation equation is:

[0028] ;

[0029] In the formula, is the control volume boundary, is the fluid density, is the fluid velocity vector, The control volume boundary The unit external normal vector on , is the volume, For time, is the infinitesimal area on the boundary, is the volume element;

[0030] The momentum conservation equation is:

[0031] ;

[0032] In the formula, is the sum of the external forces acting on the control body;

[0033] The NS equation is:

[0034] ;

[0035] In the formula, is the fluid velocity vector The material derivative of is the volume force acting on the fluid, is the gradient of the pressure field, is the kinematic viscosity coefficient of the fluid, is the Laplace operator of the fluid velocity field, is the gradient of the fluid velocity field divergence;

[0036] The above is the physical loss equation, plus the mean square error loss inherent in the KAN network calculation, which together constitute the network's loss function, calculated as:

[0037] ;

[0038] In the formula, is the mean square error between the neural network and the true value, is the number of samples in the training set, For in time and location The function value at .

[0039] Another object of the present invention is to provide a fluid velocity pressure field deduction system based on a fusion network, the system implements the fluid velocity pressure field deduction method based on the fusion network, and the system comprises:

[0040] The flow field information data set acquisition module is used to obtain the flow field information data set required for training using computational fluid dynamics methods

[0041] KAN network construction module, constructs the KAN network based on the obtained flow field information data set;

[0042] Based on the KAN and PINN fusion network construction module, it is used to constrain the KAN network by using the fluid physics control equation to build a KAN and PINN fusion network;

[0043] The flow field deduction result acquisition module uses the constructed KAN and PINN fusion network to train the data set and uses the verification set for verification to obtain the flow field deduction results.

[0044] Furthermore, the system is mounted on a computer device, which includes: at least one processor, a memory, and a computer program stored in the memory and executable on the at least one processor, and when the processor executes the computer program, the functions of the fluid velocity and pressure field deduction system based on the KAN and PINN fusion network are realized.

[0045] Combining all the above-mentioned technical solutions, the beneficial effects possessed by the present invention are as follows: the present invention realizes the intelligent deduction of velocity and pressure of the flow field. First, the computational fluid dynamics method is used to calculate the velocity field and pressure field data set of the fluid domain, which is used as the training and verification data of the network. Then, a KAN network structure is established, and the input is determined as the coordinates and time of the fluid domain control point, and the output is determined as the velocity and pressure. Then, the mass conservation equation, momentum conservation equation, and NS equation of the fluid are added to the loss function of the network as physical constraints, so that its output results meet the actual physical laws. The present invention establishes a neural network data set, constructs a KAN-type neural network structure, and uses fluid-related physical equations to constrain the neural network, thereby predicting the values ​​of velocity and pressure in the flow field in real time, so that the surrounding flow field conditions can be predicted in real time during the ship's navigation, and the velocity and pressure field can be deduced for a specific fluid domain.

[0046] This invention fills the technical gaps in the domestic ship and ocean industries such as fluid information forecasting and ship resistance forecasting to a certain extent, solves the technical difficulties of real-time deduction of flow field pressure and velocity field, and can push the flow field forecast results to ship resistance forecasting, which is the first time in China. At the same time, the application of KAN network in the field of ship and ocean is the first time at home and abroad, and the fusion of KAN+PINN is also the first time in the industry at home and abroad. There is no such fusion network in the existing papers, patents and other achievements. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] The accompanying drawings herein are incorporated in and constitute a part of the specification, illustrate embodiments consistent with the present disclosure, and together with the description, serve to explain the principles of the present disclosure;

[0048] Figure 1 It is a flow chart of a fluid velocity and pressure field deduction method based on a KAN and PINN fusion network provided by an embodiment of the present invention;

[0049] Figure 2 It is a simulation diagram of the computational domain and boundary conditions when constructing the training and verification data sets of the present invention;

[0050] Figure 3 It is a schematic diagram of the present invention for collecting data points using computational fluid dynamics simulation results;

[0051] Figure 4It is a structural diagram of the KAN+PINN fusion network of the present invention;

[0052] Figure 5 It is a velocity field deduction result diagram of the flow velocity u in the x direction of the present invention, wherein the abscissa refers to the distance from the point on the x-axis to the center of the cylinder, and the ordinate refers to the distance from the point on the y-axis to the center of the cylinder;

[0053] Figure 6 It is a velocity field deduction result diagram of the flow velocity v in the y direction of the present invention, wherein the abscissa refers to the distance from the point on the x-axis to the center of the cylinder, and the ordinate refers to the distance from the point on the y-axis to the center of the cylinder;

[0054] Figure 7 It is a diagram of the pressure field deduction result of the present invention, wherein the horizontal axis refers to the distance from the point on the x-axis to the center of the cylinder, and the vertical axis refers to the distance from the point on the y-axis to the center of the cylinder. DETAILED DESCRIPTION

[0055] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific embodiments of the present invention are described in detail below in conjunction with the accompanying drawings. In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without violating the connotation of the present invention, so the present invention is not limited by the specific implementation disclosed below.

[0056] The innovation of the present invention is that: the present invention combines KAN and PINN for the first time at home and abroad, and the KAN network is more interpretable than other network structures by means of spline functions; the addition of PINN makes the output results conform to the real physical laws, and will not be limited by the initial conditions and boundary conditions of the flow field, and the fitting speed is faster than the single mean square error loss; the present invention constructs the flow field information data set and construction method required for training based on the computational fluid dynamics method; the present invention proposes a KAN+PINN fusion network, whose structure and model. The prediction accuracy is very high, the error does not exceed 2%, and the calculation speed is very high, which is about 15% faster than the fitting speed of network types such as the fully connected network.

[0057] Embodiment 1, as Figure 1 As shown, the fluid velocity pressure field deduction method based on the fusion network provided in the embodiment of the present invention includes:

[0058] S1. Using computational fluid dynamics methods to obtain the flow field information data set required for training;

[0059] S101, constructing a two-dimensional cylinder flow fluid domain based on computational fluid dynamics method and setting boundary conditions;

[0060] Select a rectangular basin with a length of 15 times the diameter of the cylinder, a width of 7 times the diameter of the cylinder, and a height of 1.5 times the height of the cylinder. Figure 2 As shown in the figure, the mesh model uses a prismatic mesh generator, applies a generalized cylinder and a surface reconstruction model. The purpose of surface reconstruction is to improve the quality of the existing model surface as a whole, especially to optimize the existing mesh model. Surface reconstruction is mainly based on the side length expansion of the model, and can also perform feature encryption based on curvature and surface proximity values, including local encryption at the connection between cylinder faces, etc. The biggest help of surface reconstruction for this model is that it can help the prismatic layer mesh generator run the mesh generation work of the sub-surface. The boundary conditions are divided into eight types, as follows: velocity inlet, pressure outlet, symmetry plane, overlapping grid, mass flow inlet, stagnation inlet, outlet and wall. Set the lower water flow coverage area as the fluid domain, the water flow inlet as the velocity inlet, the surface of the water outflow as the pressure outlet, and the length direction surface of the rectangular fluid domain as the wall.

[0061] S102, computational fluid dynamics simulation and data set construction;

[0062] In the water part, take a plane perpendicular to the axis of the cylinder, and the plane is the two-dimensional flow field around the cylinder. The flow field information data set required for training includes: time t, coordinates of the observation point (x, y), speed u in the x direction of the observation point, speed v in the y direction, and pressure p at the location of the observation point. See Table 1; the present invention constructs a large number of data points to ensure the training intensity of the KAN+PINN fusion network and improve the calculation speed and accuracy of the network. 70% of the data is used as a training set and 30% of the data is used as a verification set.

[0063] Table 1 Flow field information dataset required for training

[0064]

[0065] It can be understood that the present invention innovatively proposes the types and quantities of data sets to be constructed and the method of collecting data points, such as Figure 3 The principle of collecting data points using computational fluid dynamics simulation results;

[0066] S2, constructing a KAN network based on the obtained flow field information data set;

[0067] KAN is used to extract flow field features and capture nonlinear relationships. The input of the KAN network is defined as the fluid control point coordinates (x, y) and time t, and the output is the fluid velocity u, v and pressure p. The principle of building the network is to map the input data to a high-dimensional space, and gradually map the input to the output through a multi-layer combination of nonlinear activation functions and linear mappings. The network approximates any continuous function through depth and breadth, and the last layer performs a linear transformation on the implicit state to obtain the predicted values ​​of the velocity field and pressure field. The KAN network structure of this method is divided into three layers, and the detailed structure can be found in the appendix of the manual. Figure 4 shown.

[0068] Exemplary, non-linear activation function expression:

[0069] Sigmoid function: ;

[0070] Tanh function: ;

[0071] ReLU (Rectified Linear Unit) function: ;

[0072] ELU (Exponential Linear Unit) function: , >0; , , ;

[0073] Each network node is equipped with a random nonlinear function expression. There are 8 KAN network nodes in this network model, so the above function needs to be applied eight times randomly.

[0074] Linear mapping: In the KAN network, the linear mapping passes the input to the next layer through a linear transformation (such as weighted sum). It can be expressed as: ,in, For output, is the weight matrix, is the input vector, is the bias term.

[0075] In another exemplary embodiment, the network approximates any continuous function through depth and breadth, including: its depth refers to the number of layers and breadth refers to the number of nodes in each layer. The network has three layers. Increasing the number of layers can increase the nonlinear representation ability of the network, so that the network can capture more complex features. The three-layer network ensures strong representation ability without making the network overly complex. The first layer of the network has two nodes, the second layer has three nodes, and the third layer has three nodes, for a total of eight nodes. Increasing the number of nodes in each layer can also improve the approximation ability of the network, allowing the model to capture more information in each layer. The number of nodes ensures the approximation ability and prevents overfitting.

[0076] In another exemplary embodiment, the last layer performs a linear transformation on the implicit state to obtain the predicted values ​​of the velocity field and the pressure field, including:

[0077] Define the input as ,in and are the coordinates of the fluid control point, is time; the input layer has 2 nodes, accepting and , the three nodes in the hidden layer are used to predict , through the nonlinear activation function of the hidden layer, the input data is mapped to a high-dimensional space, and then the operation of the hidden layer is output to the output layer through a linear transformation;

[0078] The inherent mean square error loss of the constructed KAN network is expressed as:

[0079] ;

[0080] In the formula, is the actual value, is the predicted value, is the total number of fluid control points calculated, is the counting symbol, for Actual value of direction speed, for Direction speed prediction value, for Actual value of direction speed, for Direction speed prediction value, is the actual value of pressure, is the predicted value of pressure.

[0081] S3, using the fluid physics control equation to constrain the KAN network and construct a fusion network based on KAN and PINN;

[0082] like Figure 4 As shown, specifically including:

[0083] The physical equations involved in fluid velocity and pressure field prediction include mass conservation, momentum conservation, and NS equations. Therefore, the above equations are added to the mean square error loss function of the KAN network.

[0084] The mass conservation equation is:

[0085] ;

[0086] In the formula, is the control volume boundary, is the fluid density, is the fluid velocity vector, The control volume boundary The unit external normal vector on , is the volume, For time, is the infinitesimal area on the boundary, is the volume element;

[0087] The momentum conservation equation is:

[0088] ;

[0089] In the formula, is the sum of the external forces acting on the control body;

[0090] The NS equation is:

[0091] ;

[0092] In the formula, is the fluid velocity vector The material derivative of is the volume force acting on the fluid, is the gradient of the pressure field, is the kinematic viscosity coefficient of the fluid, is the Laplace operator of the fluid velocity field, is the gradient of the fluid velocity field divergence;

[0093] The above is the physical loss equation, plus the mean square error loss inherent in the KAN network calculation, which together constitute the network's loss function, calculated as:

[0094] ;

[0095] In the formula, is the mean square error between the neural network and the true value, is the number of samples in the training set, For in time and location The function value at .

[0096] It can be understood that the above formula is edited into the KAN network (neural network) loss function. The technical role is to make the neural network calculation results conform to the real physical theorems through physical equation constraints, reduce the number of iterations, and increase accuracy and calculation speed.

[0097] S4. Use the constructed KAN and PINN fusion network to train the data set and use the validation set for verification to obtain the flow field deduction results.

[0098] It can be concluded that the flow field deduction result based on the KAN and PINN fusion network of the present invention is very accurate, and the error with the actual value does not exceed 2%.

[0099] Embodiment 2, the embodiment of the present invention provides a fluid velocity pressure field deduction system based on a fusion network, comprising:

[0100] The flow field information data set acquisition module is used to obtain the flow field information data set required for training using computational fluid dynamics methods

[0101] KAN network construction module, constructs the KAN network based on the obtained flow field information data set;

[0102] Based on the KAN and PINN fusion network construction module, it is used to constrain the KAN network by using the fluid physics control equation to build a KAN and PINN fusion network;

[0103] The flow field deduction result acquisition module uses the constructed KAN and PINN fusion network to train the data set and uses the verification set for verification to obtain the flow field deduction results.

[0104] Figure 5-Figure 7 The following is a description of the simulation test: The present invention constructs a flow field model of a two-dimensional cylinder, and collects 30,100 data points according to the method of constructing a data set. Each data point contains point coordinates x, y, time t, flow velocity u, v in the x, y direction, and pressure p. 21,070 of these data points are used to train the neural network. The trained network inputs x, y coordinates to give the results of u, v, and p. The output results are compared with the remaining 9,030 data points, and the error is ≤2%, proving that the network design is successful.

[0105] The present invention can be applied in the fields of measuring the velocity pressure field of the fluid around the ship and then deriving the ship resistance, and predicting the blood pressure value through the network for medical purposes.

[0106] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with the technical field within the technical scope disclosed by the present invention and within the spirit and principles of the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for deriving fluid velocity and pressure fields based on a fusion network, characterized in that: The method includes: S1. Using computational fluid dynamics methods to obtain the flow field information data set required for training; S2, constructing a KAN network based on the obtained flow field information data set; S3, using the fluid physics control equation to constrain the KAN network and construct a fusion network based on KAN and PINN; S4, use the constructed KAN and PINN fusion network to train the data set, and use the validation set for verification to obtain the flow field deduction results; In step S3, a fusion network based on KAN and PINN is constructed, including: The physical loss equations of fluid velocity and pressure field prediction, including mass conservation, momentum conservation, and NS equations, are added to the mean square error loss function of the KAN network to construct a fusion network based on KAN and PINN. The mass conservation equation is: ； In the formula, is the control volume boundary, is the fluid density, is the fluid velocity vector, The control volume boundary The unit external normal vector on , is the volume, For time, is the infinitesimal area on the boundary, is the volume element; The momentum conservation equation is: ； In the formula, is the sum of the external forces acting on the control body; The NS equation is: ； In the formula, is the fluid velocity vector The material derivative of is the volume force acting on the fluid, is the gradient of the pressure field, is the kinematic viscosity coefficient of the fluid, is the Laplace operator of the fluid velocity field, is the gradient of the fluid velocity field divergence; The above is the physical loss equation, plus the mean square error loss inherent in the KAN network calculation, which together constitutes the network's loss function, calculated as ； In the formula, is the mean square error between the neural network and the true value, is the number of samples in the training set, For in time and location The function value at .

2. The method for fluid velocity and pressure field deduction based on fusion network according to claim 1 is characterized in that: In step S1, a computational fluid dynamics method is used to obtain a flow field information data set required for training, including: S101, constructing a two-dimensional cylinder flow fluid domain based on computational fluid dynamics method and setting boundary conditions; S102, computational fluid dynamics simulation and data set construction.

3. The method for fluid velocity and pressure field deduction based on fusion network according to claim 2 is characterized in that: In step S101, a two-dimensional cylindrical flow fluid domain is constructed based on a computational fluid dynamics method and boundary conditions are set, including: Select a rectangular basin with a length 15 times the diameter of the cylinder, a width 7 times the diameter of the cylinder, and a height 1.5 times the height of the cylinder; The boundary conditions include velocity inlet, pressure outlet, symmetry plane, overlapping grids, mass flow inlet, stagnation inlet, outlet and wall; the area covered by the water flow below is set as the fluid domain, the water flow inlet is set as the velocity inlet, the surface on which the water flows out is set as the pressure outlet, and the length direction surface of the rectangular fluid domain is set as the wall.

4. The method for deriving fluid velocity and pressure fields based on a fusion network according to claim 2 is characterized in that: In step S102, computational fluid dynamics simulation and data set construction include: in the water part, a plane is taken along the direction perpendicular to the axis of the cylinder, and the plane is a two-dimensional flow field around the cylinder; the flow field information data set required for training includes: time , the coordinates of the observation point , the observation point Speed ​​of direction , Speed ​​of direction , and the pressure at the observation point The flow field information data set is divided into 70% of the data as a training set and 30% of the data as a validation set.

5. The method for deriving fluid velocity and pressure fields based on a fusion network according to claim 4 is characterized in that: In step S2, a KAN network is constructed, including: The input fluid control point coordinates and time The data is mapped to a high-dimensional space, and the input is gradually mapped to the output through a multi-layer combination of nonlinear activation functions and linear mappings. The network approximates any continuous function through depth and breadth. The last layer performs a linear transformation on the implicit state to obtain the predicted values ​​of the velocity field and pressure field, completing the construction of the KAN network.

6. The method for fluid velocity and pressure field deduction based on fusion network according to claim 5 is characterized in that: The KAN network is divided into three layers. The first layer is the input layer, and the input parameters are the coordinates of the fluid control points. and the current time , using spline function to represent it in high dimension; the second hidden layer uses spline function fitting to reduce it to low dimension; The third layer is the output layer, and the output is the velocity pressure field of the fluid, that is, Speed ​​of direction and pressure .

7. The method for fluid velocity and pressure field deduction based on fusion network according to claim 5 is characterized in that: The last layer performs a linear transformation on the hidden state to obtain the predicted values ​​of the velocity field and pressure field, including: Define the input as ,in and are the coordinates of the fluid control point, is time; the input layer has 2 nodes, accepting and , the three nodes in the hidden layer are used to predict , through the nonlinear activation function of the hidden layer, the input data is mapped to a high-dimensional space, and then the operation of the hidden layer is output to the output layer through a linear transformation; The inherent mean square error loss of the constructed KAN network is expressed as: ； In the formula, is the actual value, is the predicted value, is the total number of fluid control points calculated, is the counting symbol, for Actual value of direction speed, for Direction speed prediction value, for Actual value of direction speed, for Direction speed prediction value, is the actual value of pressure, is the predicted value of pressure.

8. A fluid velocity and pressure field deduction system based on a fusion network, characterized in that: The system implements the fluid velocity and pressure field deduction method based on the fusion network as described in any one of claims 1 to 7, and the system comprises: A flow field information data set acquisition module is used to obtain the flow field information data set required for training using a computational fluid dynamics method; KAN network construction module, constructs the KAN network based on the obtained flow field information data set; Based on the KAN and PINN fusion network construction module, it is used to constrain the KAN network by using the fluid physics control equation to build a KAN and PINN fusion network; The flow field deduction result acquisition module uses the constructed KAN and PINN fusion network to train the data set and uses the verification set for verification to obtain the flow field deduction results.

9. The fluid velocity and pressure field deduction system based on fusion network according to claim 8 is characterized in that: The system is mounted on a computer device, which includes: at least one processor, a memory, and a computer program stored in the memory and running on the at least one processor. When the processor executes the computer program, the functions of the fluid velocity and pressure field deduction system based on the KAN and PINN fusion network are realized.

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