Fluid mechanics equation solving method based on physical information neural network

Abstract

The invention discloses a fluid mechanics equation solving method based on a physical information neural network, and relates to the technical field of fluid mechanics. The problems that in the prior art, a large amount of training data is needed, physical information is not embedded, prediction does not conform to physical laws, generalization is difficult, and sample generation consumes resources are solved. The fluid mechanics equation is solved through the physical information neural network, physical consistency and prediction precision of model training are ensured, mathematical descriptions of fluid motion and heat transmission are determined, accurate input is provided for the neural network, definition of a loss function is combined with a basic physical law of fluid mechanics, and the prediction precision is improved. The reliability of model output is guaranteed, the training and optimization process effectively guides the learning of the neural network and improves the solving efficiency, the numerical verification and prediction step combines the prediction capability of high-precision numerical simulation and the neural network, the solving precision is guaranteed, the prediction efficiency in an unsampled area is improved, and the prediction efficiency of the neural network is improved. And an efficient and accurate tool is provided for fluid mechanics research.

Description

Technical Field

[0001] The present invention relates to the technical field of fluid mechanics, and in particular to a method for solving fluid mechanics equations based on a physical information neural network. Background Art

[0002] The governing equations of fluid mechanics are an important tool for describing the laws of fluid motion. However, these equations are often nonlinear and difficult to solve directly, especially in complex geometric shapes and turbulent scenarios. The patent application with publication number: CN114841045A discloses a method and device for solving fluid mechanics based on deep learning, the method comprising: obtaining known quantities of the fluid mechanics problem to be solved, and dephysicalizing the known quantities to obtain model input quantities; inputting the model input quantities into a pre-trained general deep learning model to obtain output quantities; the general deep learning model is trained by dephysicalized training samples corresponding to the fluid mechanics problem to be solved, the dephysicalized training samples include dephysicalized input quantities and output quantities corresponding to the input quantities, the output quantities are calculated by inputting the input quantities into a preset computational fluid dynamics algorithm, and the input quantities are randomly sampled in a preset limited space; the output quantities are physicalized to obtain the solution results. The embodiments of the present invention can be quickly applied to solving large programs, reducing the learning, transplantation and optimization costs caused by the replacement of new algorithms, and improving the parallel efficiency based on GPUs.

[0003] However, although the above patents have improved efficiency to a certain extent, they still have the following problems:

[0004] 1. Existing technologies rely on large-scale training data generation, and the learning process does not directly embed physical information, which may cause model predictions to not conform to the basic laws of fluid mechanics, especially in boundary areas with insufficient data and high-dimensional nonlinear problems;

[0005] 2. Since the input-output relationship of the deep learning model depends on the distribution of preset data, the prediction accuracy of the model drops significantly for complex flow scenarios or geometric shape changes beyond the training range, making it difficult to generalize to new problems;

[0006] 3. A large number of samples need to be generated as training data through existing computational fluid dynamics algorithms. Although these data can be used for model training, the generation process is time-consuming and labor-intensive. Especially when dealing with complex scenes such as turbulence, the high resolution requirements of training samples significantly increase the computational overhead. Summary of the invention

[0007] The purpose of the present invention is to provide a method for solving fluid mechanics equations based on physical information neural networks. By combining high-precision numerical methods and neural network models based on physical constraints, it is possible to obtain high-resolution numerical solutions to flow and heat transfer problems, and to use the flexibility of physical information neural networks to perform efficient predictions in unsampled areas, thereby providing a powerful tool for the study of complex flows and heat transfer to solve the problems raised in the above-mentioned background technology.

[0008] To achieve the above object, the present invention provides the following technical solutions:

[0009] The method for solving fluid mechanics equations based on physical information neural network includes the following steps:

[0010] Step 1: Problem modeling: Establish the governing equations describing fluid motion and heat transfer based on the problem area, and determine the required boundary conditions and initial conditions;

[0011] Step 2: Network construction: construct a physical information neural network model, input spatial coordinates and time as input samples into the physical information neural network model, and predict the velocity, pressure and temperature distribution data in the flow field;

[0012] Step 3: Define the loss function: The residual of the control equation, the deviation of the boundary conditions and the error of the initial conditions are taken as components of the loss function;

[0013] Step 4: Training and optimization: Initialize the physical information neural network model and start training. Adjust the parameters of the physical information neural network model based on minimizing the loss function until the loss function converges to obtain the trained physical information neural network model.

[0014] Step 5: Numerical verification and prediction: Perform direct numerical simulation based on the high-precision finite difference method and compare it with the prediction results of the physical information neural network model. Based on the comparison results, the qualified physical information neural network model will be verified to predict the fluid properties and output the final fluid property prediction results.

[0015] Furthermore, the control equations include momentum equations, mass conservation equations and energy conservation equations that describe fluid motion.

[0016] Furthermore, the control equation in step 1 also includes:

[0017] Preprocess the research problem, determine the geometry of the research area, define the physical properties of the boundary based on the geometry of the research area, and select the complex flow and heat transfer scenarios to be studied;

[0018] Construct corresponding momentum equations, mass conservation equations, and energy conservation equations to describe fluid motion and heat transfer based on complex flow and heat transfer scenarios;

[0019] Among them, the momentum equation is used to express the change of the fluid motion state, the mass conservation equation is used to express the incompressibility of the fluid, and the energy conservation equation is used to describe the law of temperature distribution changing with time and space.

[0020] Furthermore, the step 1: problem modeling also includes discretizing the control equations, and the specific process is as follows:

[0021] Spatial discretization: High-order discretization methods are used for fluid motion and heat transfer terms in the control equations to process spatial flow parameters with high resolution. High-order numerical methods are used for convection terms to reduce numerical dissipation and capture detailed structures and local changes in the flow field. High-precision differential methods are used to discretize Diouffusion terms.

[0022] Time discretization: Select the time marching method to discretize the time-varying process into a series of finite time steps to ensure computational stability in complex flow scenarios and implement an adaptive time step strategy for the nonlinear characteristics of fluid motion and heat transfer;

[0023] Mesh refinement strategy: Design a mesh refinement strategy based on the characteristics of complex flow areas. Use dense meshes in high-gradient areas where velocity or temperature changes significantly to accurately capture flow and heat transfer phenomena and improve calculation accuracy in high-gradient areas. Use sparse meshes in areas where flow is relatively smooth and optimize mesh distribution in boundary condition areas.

[0024] Furthermore, the governing equations describing fluid motion and heat transfer are established, including:

[0025] The preprocessed fluid mechanics data is stored, and before storage, the storage resources are identified to determine the empty blocks and a number of non-empty blocks in the storage structure;

[0026] Obtain and compare the verification information of each non-empty block with the preset verification information, mark the inconsistent blocks as abnormal blocks, and perform a cleanup operation on the abnormal blocks to obtain available storage blocks, and use the available storage blocks for subsequent data storage;

[0027] Setting a number of storage nodes according to the processed available storage blocks, and allocating corresponding fluid mechanics characteristic data to each storage node;

[0028] A key storage node is selected, and a connection relationship between the key storage node and other storage nodes is determined based on a communication topology algorithm to form a distributed communication tree.

[0029] Furthermore, the step three: loss function definition, specifically includes:

[0030] Equation residual loss, which is used to ensure that the prediction results of the neural network satisfy the fluid dynamics equations, including the residual loss of the momentum equation, the mass conservation equation, and the energy conservation equation;

[0031] Boundary condition loss, used to ensure that the prediction results meet the boundary constraints, including the difference between the fluid velocity, pressure and temperature at the boundary and the actual boundary value;

[0032] Initial condition loss, which is used to limit the physical field distribution at the predicted initial moment to be consistent with the actual initial conditions;

[0033] Dynamic weight adjustment: According to the different convergence speeds of the equation residual, boundary conditions and initial conditions, the weights of the equation residual loss, boundary condition loss and initial condition loss in the overall loss function are dynamically adjusted, and the equation residual loss, boundary condition loss and initial condition loss are weightedly combined to form a complete physical constraint loss function.

[0034] Furthermore, the convergence criterion for the convergence of the loss function in step 4 includes: setting a threshold of the loss function or a maximum value of the training cycle, and terminating the training when one of the following conditions is met: the loss function value is less than a preset threshold, the validation set loss no longer decreases significantly, or the maximum number of training cycles is reached.

[0035] Furthermore, the output of the final fluid property prediction result in step 5 specifically includes:

[0036] Determination of prediction scenarios: Determine the spatial scope, time scope and initial conditions of the prediction scenarios according to actual research needs, determine the control parameters and input them into the physical information neural network model;

[0037] Flow field and temperature field prediction: Based on the physical information neural network model, the flow field evolution is gradually predicted within a given time range, and the velocity field, pressure field and temperature field distribution data for the entire time period are generated. Based on the nonlinear fitting capability, the fluid dynamic characteristics prediction data for complex flow scenarios are generated.

[0038] Extract key fluid characteristic parameters based on neural network prediction results, including turbulence energy spectrum: analyzing the energy distribution of turbulent field; boundary layer thickness: evaluating the interaction characteristics between fluid and wall; heat flux density: calculating the local or global heat flux distribution in the heat transfer area; vortex field distribution: capturing vortex structure and its evolution process;

[0039] Based on the extraction results of key fluid characteristic parameters, the completeness and accuracy of the neural network prediction results are evaluated, the possible deviation range is quantified, and based on the evaluation results, the qualified prediction results are used as the final flow field prediction results.

[0040] Furthermore, the completeness and accuracy of the neural network prediction results are evaluated, including:

[0041] Data transmission verification and anomaly detection: Build a data transmission control block to record the path, time step, and integrity verification information of the fluid mechanics data from the storage to the computing node during the training process, perform real-time verification of the transmission data content based on key storage nodes, and generate a verification information list;

[0042] Model prediction verification: When using the trained physical information neural network model to efficiently predict the fluid properties of unsampled areas, the integrity of the prediction input data is determined based on the verification information list, and the output results of the physical information neural network model are compared with the verification data. If the comparison deviation exceeds the preset threshold, the model input parameters are adjusted.

[0043] Furthermore, after numerical verification and prediction, it also includes: visualizing and analyzing the final flow field prediction results, and extracting the flow pattern, turbulence structure and heat transfer characteristics of the predicted scenario.

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] The fluid mechanics equations are solved through physical information neural networks, ensuring the physical consistency and prediction accuracy of model training. The mathematical description of fluid motion and heat transfer is established in the problem modeling stage, providing accurate input for the neural network. The definition of the loss function combines the basic physical laws of fluid mechanics to ensure the reliability of the model output. The training and optimization process effectively guides the learning of the neural network and improves the solution efficiency. The numerical verification and prediction steps combine high-precision numerical simulation with the predictive ability of neural networks, which not only ensures the accuracy of the solution, but also improves the efficiency of prediction in unsampled areas. It provides an efficient and accurate tool for fluid mechanics research and greatly promotes the efficient analysis and prediction of complex flow and heat transfer problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 This is a flow chart of the method for solving fluid mechanics equations based on physical information neural network of the present invention. DETAILED DESCRIPTION

[0047] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0048] In order to solve the technical problems of existing technologies that require a large amount of training data, do not embed physical information, do not conform to physical laws, are difficult to generalize, and consume resources for sample generation, please refer to Figure 1, this embodiment provides the following technical solutions:

[0049] The method for solving fluid mechanics equations based on physical information neural network includes the following steps:

[0050] Step 1: Problem modeling: Establish the control equations describing fluid motion and heat transfer based on the research problem area, and determine the required boundary conditions and initial conditions, such as the velocity and temperature distribution of the fluid and the heat flux conditions on the boundary. The control equations include the momentum equation, mass conservation equation, and energy conservation equation that describe fluid motion.

[0051] Step 2: Network construction: construct a physical information neural network model, input spatial coordinates and time as input samples into the physical information neural network model, and predict the velocity, pressure and temperature distribution data in the flow field;

[0052] Step 3: Define the loss function: The residual of the control equation, the deviation of the boundary conditions and the error of the initial conditions are taken as components of the loss function;

[0053] Step 4: Training and optimization: Initialize the physical information neural network model and start training. Adjust the parameters of the physical information neural network model based on minimizing the loss function until the loss function converges to obtain the trained physical information neural network model.

[0054] In this embodiment, the convergence criteria of the loss function convergence include: setting a threshold of the loss function or a maximum value of the training cycle, and terminating the training when one of the following conditions is met: the loss function value is less than the preset threshold, the validation set loss no longer decreases significantly, or the maximum number of training cycles is reached.

[0055] Step 5: Numerical verification and prediction: Direct numerical simulation is performed based on the high-precision finite difference method to generate high-resolution flow field and temperature field data, which are compared with the prediction results of the physical information neural network model. Based on the comparison results, the qualified physical information neural network model is used to predict the fluid properties and the final fluid property prediction results are output.

[0056] In this embodiment, through problem modeling, the control equations and corresponding physical conditions are established, the physical characteristics and initial state of the study area are clarified, and accurate input data is provided for the subsequent numerical solution based on physical information neural network. The definition of the loss function covers the core physical constraints of the fluid mechanics problem, provides a strict guarantee for the physical consistency of the neural network prediction results, and improves the training efficiency and accuracy. Training and optimization can more effectively guide the training process of the physical information neural network model, while ensuring the accuracy and efficiency of solving fluid mechanics problems. By combining high-precision numerical methods and neural network models based on physical constraints, high-resolution numerical solutions to flow and heat transfer problems can be obtained, and the flexibility of physical information neural networks can be used to make efficient predictions in unsampled areas, providing a powerful tool for the study of complex flows and heat transfer.

[0057] In this embodiment, the control equation in step 1 also includes:

[0058] Preprocess the research problem and determine the geometric shape of the research area, such as a two-dimensional rectangle or a three-dimensional cuboid. Based on the geometric shape of the research area, define the physical properties of the boundary, such as surface material and thermal conductivity. Select the complex flow and heat transfer scenarios to be studied, such as Rayleigh-Bénard convection, which is a phenomenon of natural convection between two horizontal plates with a temperature difference, and is often used to study turbulence and heat transfer laws.

[0059] Construct corresponding momentum equations, mass conservation equations, and energy conservation equations to describe fluid motion and heat transfer based on complex flow and heat transfer scenarios;

[0060] Among them, the momentum equation is used to express the changes in the fluid motion state, ensuring that the fluid can reflect the correct velocity distribution under the action of force; the mass conservation equation is used to express the incompressibility of the fluid, ensuring that the total amount of fluid in the study area remains unchanged; the energy conservation equation is used to describe the law of temperature distribution changing with time and space, reflecting the diffusion and convection process of heat in the fluid.

[0061] In this embodiment, the step 1: problem modeling also includes discretizing the control equation. The specific process is as follows:

[0062] Spatial discretization: High-order discretization methods are used for fluid motion and heat transfer terms in the control equations to process spatial flow parameters with high resolution, ensuring high accuracy when solving convection and diffusion terms. High-order numerical methods are used for convection terms to reduce numerical dissipation and capture detailed structures and local changes in the flow field. High-precision differential methods are used to discretize Dio diffusion terms to ensure high accuracy in spatial calculations of physical processes such as heat transfer.

[0063] Time discretization: Select the time marching method to discretize the time-varying process into a series of finite time steps to ensure computational stability in complex flow scenarios, implement an adaptive time step strategy for the nonlinear characteristics of fluid motion and heat transfer, use a smaller time step in areas where the flow changes rapidly to ensure accuracy, and use a larger time step in stable areas to improve efficiency;

[0064] Mesh refinement strategy: Design a mesh refinement strategy based on the characteristics of complex flow areas. Use dense meshes in high-gradient areas where velocity or temperature changes significantly to accurately capture flow and heat transfer phenomena and improve calculation accuracy in high-gradient areas. Use sparse meshes in areas where flow is relatively stable to reduce computing resource consumption and improve overall computing efficiency. Optimize mesh distribution in boundary condition areas to ensure that the flow and heat transfer processes near the boundaries are accurately simulated.

[0065] In this embodiment, the control equations describing fluid motion and heat transfer are established, and also include:

[0066] The pre-processed fluid mechanics data (such as velocity field, pressure field, temperature field) is stored, and the storage resources are identified before storage to determine the empty blocks and several non-empty blocks in the storage structure;

[0067] Obtain and compare the verification information of each non-empty block with the preset verification information (such as data hash value or content summary), mark the inconsistent blocks as abnormal blocks, and perform cleaning operations on the abnormal blocks to obtain available storage blocks, and use the available storage blocks for subsequent data storage;

[0068] A number of storage nodes are set according to the processed available storage blocks, and corresponding fluid mechanics characteristic data (such as specific flow field or area data) are allocated to each storage node;

[0069] Select key storage nodes, determine the connection relationship between the key storage nodes and other storage nodes based on the communication topology algorithm, form a distributed communication tree, build an efficient path for data storage and reading, and provide an efficient data management mechanism for subsequent neural network model training.

[0070] In this embodiment, through efficient data storage and management mechanisms, the accuracy and availability of fluid mechanics characteristic data are ensured, providing reliable data support for neural network model training; storage resource identification and cleanup operations ensure the security of data storage, and distributed communication tree construction optimizes data access efficiency, significantly improving the speed and accuracy of model training.

[0071] In this embodiment, the step three: loss function definition, specifically includes:

[0072] Equation residual loss is used to ensure that the prediction results of the neural network satisfy the fluid mechanics equations, including the residual loss of the momentum equation, mass conservation equation, and energy conservation equation:

[0073] Momentum equation residual: calculates the momentum error generated by the predicted velocity field in the governing equations, including deviations in convection terms, diffusion terms, and pressure gradients, used to verify whether the fluid motion state is consistent with the force balance, complex flow behavior in highly turbulent areas or unsteady flow fields;

[0074] Residual of the mass conservation equation: For incompressible fluids, calculate whether the divergence of the flow field in the neural network prediction result is zero to ensure that the fluid mass conservation is satisfied; for compressible fluids, add constraints on the relationship between the density change rate and mass conservation;

[0075] Energy conservation equation residual: Constrain the temperature field and heat conduction and convection terms predicted by the neural network to ensure the conservation of energy in spatial transfer and time evolution; minimize the energy residual of complex flow and heat transfer scenarios (such as turbulent heat transfer and temperature difference driven convection);

[0076] Boundary condition loss is used to ensure that the prediction results meet the boundary constraints, including the difference between the fluid velocity, pressure and temperature at the boundary and the actual boundary value, which is added to the loss function in the form of a penalty function:

[0077] Velocity boundary conditions: For wall boundaries, a no-slip condition is imposed to make the fluid velocity zero at the wall; for inlet boundaries, the fluid velocity distribution is ensured to be consistent with the specified inlet velocity field; at the outlet boundary, the normal velocity component is constrained to be consistent with the fluid mass conservation to ensure the natural extension of the flow field;

[0078] Pressure boundary conditions: control the pressure boundary of the flow field to ensure that the pressure value at the opening or specified area conforms to the actual distribution; add pressure gradient constraints to key areas in the fluid (such as the turbulent core area) to reflect the laws of physical field changes;

[0079] Temperature boundary conditions: ensure that the temperature distribution meets the boundary conditions (such as constant temperature wall, adiabatic boundary or natural convection heat flux) to reflect the physical laws of heat transfer; add constraints on the consistency of temperature gradients in complex heat transfer areas (such as porous media and hot and cold interfaces);

[0080] Initial condition loss is used to limit the predicted physical field distribution at the initial moment to be consistent with the actual initial conditions:

[0081] Initial velocity distribution: Calculate the deviation between the predicted value of fluid velocity at the initial moment and the actual initial velocity field; for non-steady-state problems, ensure that the initial velocity field conforms to the actual fluid state;

[0082] Initial pressure distribution: impose constraints on the initial pressure distribution of the fluid so that the pressure gradient matches the initial velocity field; in complex flow problems (such as vortex generation or turbulent initial conditions), add constraints on the initial pressure change;

[0083] Initial temperature distribution: constrain the initial distribution of the temperature field to ensure that the predicted value of the thermal field at the initial moment is consistent with the physical conditions; temperature difference driving problems (such as natural convection) to ensure the accuracy of the initial temperature gradient;

[0084] Dynamic weight adjustment: According to the different convergence speeds of the equation residual, boundary conditions and initial conditions, the weights of the equation residual loss, boundary condition loss and initial condition loss in the overall loss function are dynamically adjusted, and the equation residual loss, boundary condition loss and initial condition loss are weightedly combined to form a complete physical constraint loss function.

[0085] In this embodiment, by defining a comprehensive loss function, the physical consistency of the neural network prediction is ensured, and the prediction accuracy of the model for complex fluid mechanics problems is improved; the dynamic weight adjustment mechanism optimizes the training process, enhances the model's adaptability to boundary and initial conditions, and significantly improves the solution efficiency and the reliability of the prediction results.

[0086] In this embodiment, the output of the final fluid property prediction result in step 5 specifically includes:

[0087] Determination of prediction scenarios: Determine the spatial scope, time scope and initial conditions of the prediction scenarios according to actual research needs, determine the control parameters and input them into the physical information neural network model;

[0088] Flow field and temperature field prediction: Based on the physical information neural network model, the flow field evolution is gradually predicted for a given time range, and the velocity field, pressure field and temperature field distribution data for the entire time period are generated. Based on the nonlinear fitting ability, the fluid dynamic characteristics prediction data for complex flow scenarios such as turbulent fields, natural convection or porous media are generated.

[0089] Extract key fluid characteristic parameters based on neural network prediction results, including turbulence energy spectrum: analyzing the energy distribution of turbulent field; boundary layer thickness: evaluating the interaction characteristics between fluid and wall; heat flux density: calculating the local or global heat flux distribution in the heat transfer area; vortex field distribution: capturing vortex structure and its evolution process;

[0090] Based on the extraction results of key fluid characteristic parameters, the integrity and accuracy of the neural network prediction results are evaluated, the possible deviation range is quantified, and based on the evaluation results, the qualified prediction results are used as the final flow field prediction results;

[0091] The final flow field prediction results are visualized and analyzed to extract the flow pattern (including separation zone, reattachment zone and flow transition phenomenon), turbulent structure and heat transfer characteristics of the predicted scenario.

[0092] In this embodiment, the completeness and accuracy of the neural network prediction results are evaluated, specifically including:

[0093] Data transmission verification and anomaly detection: Build a data transmission control block to record the path, time step, and integrity verification information of the fluid mechanics data from the storage to the computing node during the training process. Perform real-time verification of the content of the transmitted data based on key storage nodes and generate a verification information list to detect anomalies in the data transmission process, such as data loss or inconsistency. If an anomaly is found, an alarm is immediately triggered and storage resources are reallocated or data is repaired. If no anomaly is found, the data integrity is confirmed and the training or prediction process continues.

[0094] Model prediction verification: When using the trained physical information neural network model to efficiently predict the fluid properties of unsampled areas, the integrity of the prediction input data is determined based on the verification information list, and the output results of the physical information neural network model are compared with the verification data. If the comparison deviation exceeds the preset threshold, the model input parameters are adjusted.

[0095] In this embodiment, the high accuracy and reliability of the neural network model in fluid mechanics problems are ensured through accurate fluid property prediction and strict data verification. The data transmission verification and anomaly detection mechanism ensure data integrity and avoid potential errors in the training process. The model prediction verification further verifies the accuracy of the prediction results. Through real-time monitoring and adjustment, the integrity and credibility of the prediction are significantly improved, which improves the practicality and engineering application value of fluid property prediction, and provides a powerful support tool for fluid mechanics research and industrial design.

[0096] 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 technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A method for solving fluid mechanics equations based on physical information neural network, characterized in that: The following steps are involved: Step 1: Problem modeling: Establish the governing equations describing fluid motion and heat transfer based on the problem area, and determine the required boundary conditions and initial conditions; Step 2: Network construction: construct a physical information neural network model, input spatial coordinates and time as input samples into the physical information neural network model, and predict the velocity, pressure and temperature distribution data in the flow field; Step 3: Define the loss function: The residual of the control equation, the deviation of the boundary conditions and the error of the initial conditions are taken as components of the loss function; Step 4: Training and optimization: Initialize the physical information neural network model and start training. Adjust the parameters of the physical information neural network model based on minimizing the loss function until the loss function converges to obtain the trained physical information neural network model. Step 5: Numerical verification and prediction: Perform direct numerical simulation based on the high-precision finite difference method and compare it with the prediction results of the physical information neural network model. Based on the comparison results, the qualified physical information neural network model will be verified to predict the fluid properties and output the final fluid property prediction results.

2. The method for solving fluid mechanics equations based on physical information neural network according to claim 1, characterized in that: The control equations include momentum equations, mass conservation equations and energy conservation equations that describe fluid motion.

3. The method for solving fluid mechanics equations based on physical information neural network according to claim 2, characterized in that: The control equation of step 1 also includes: Preprocess the research problem, determine the geometry of the research area, define the physical properties of the boundary based on the geometry of the research area, and select the complex flow and heat transfer scenarios to be studied; Construct corresponding momentum equations, mass conservation equations, and energy conservation equations to describe fluid motion and heat transfer based on complex flow and heat transfer scenarios; Among them, the momentum equation is used to express the change of the fluid motion state, the mass conservation equation is used to express the incompressibility of the fluid, and the energy conservation equation is used to describe the law of temperature distribution changing with time and space.

4. The method for solving fluid mechanics equations based on physical information neural network according to claim 3, characterized in that: The step 1: problem modeling also includes discretizing the control equations. The specific process is as follows: Spatial discretization: High-order discretization methods are used for fluid motion and heat transfer terms in the control equations to process spatial flow parameters with high resolution. High-order numerical methods are used for convection terms to reduce numerical dissipation and capture detailed structures and local changes in the flow field. High-precision differential methods are used to discretize Diouffusion terms. Time discretization: Select the time marching method to discretize the time-varying process into a series of finite time steps, and implement an adaptive time step strategy for the nonlinear characteristics of fluid motion and heat transfer; Mesh refinement strategy: Design a mesh refinement strategy based on the characteristics of complex flow areas. Use dense meshes in high gradient areas where velocity or temperature changes significantly, use sparse meshes in areas where flow is relatively stable, and optimize mesh distribution in boundary condition areas.

5. The method for solving fluid mechanics equations based on physical information neural network according to claim 4, characterized in that: Establish the governing equations that describe fluid motion and heat transfer, including: The preprocessed fluid mechanics data is stored, and before storage, the storage resources are identified to determine the empty blocks and a number of non-empty blocks in the storage structure; Obtain and compare the verification information of each non-empty block with the preset verification information, mark the inconsistent blocks as abnormal blocks, and perform a cleanup operation on the abnormal blocks to obtain available storage blocks, and use the available storage blocks for subsequent data storage; Setting a number of storage nodes according to the processed available storage blocks, and allocating corresponding fluid mechanics characteristic data to each storage node; A key storage node is selected, and a connection relationship between the key storage node and other storage nodes is determined based on a communication topology algorithm to form a distributed communication tree.

6. The method for solving fluid mechanics equations based on physical information neural network according to claim 5, characterized in that: The step three: loss function definition, specifically includes: Equation residual loss, which is used to ensure that the prediction results of the neural network satisfy the fluid dynamics equations, including the residual loss of the momentum equation, the mass conservation equation, and the energy conservation equation; Boundary condition loss, used to ensure that the prediction results meet the boundary constraints, including the difference between the fluid velocity, pressure and temperature at the boundary and the actual boundary value; Initial condition loss, which is used to limit the physical field distribution at the predicted initial moment to be consistent with the actual initial conditions; Dynamic weight adjustment: According to the different convergence speeds of the equation residual, boundary conditions and initial conditions, the weights of the equation residual loss, boundary condition loss and initial condition loss in the overall loss function are dynamically adjusted, and the equation residual loss, boundary condition loss and initial condition loss are weightedly combined to form a complete physical constraint loss function.

7. The method for solving fluid mechanics equations based on physical information neural network according to claim 6, characterized in that: The convergence criterion for the convergence of the loss function in step 4 includes: setting a threshold of the loss function or a maximum value of the training cycle, and terminating the training when one of the following conditions is met: the loss function value is less than a preset threshold, the validation set loss no longer decreases significantly, or the maximum number of training cycles is reached.

8. The method for solving fluid mechanics equations based on physical information neural network according to claim 7, characterized in that: The final fluid property prediction result is output in step 5, which specifically includes: Determination of prediction scenarios: Determine the spatial scope, time scope and initial conditions of the prediction scenarios according to actual research needs, determine the control parameters and input them into the physical information neural network model; Flow field and temperature field prediction: Based on the physical information neural network model, the flow field evolution is gradually predicted within a given time range, and the velocity field, pressure field and temperature field distribution data for the entire time period are generated. Based on the nonlinear fitting capability, the fluid dynamic characteristics prediction data for complex flow scenarios are generated. Extract key fluid characteristic parameters based on neural network prediction results, including turbulent energy spectrum, boundary layer thickness, heat flux density and vorticity field distribution; Based on the extraction results of key fluid characteristic parameters, the completeness and accuracy of the neural network prediction results are evaluated, the possible deviation range is quantified, and based on the evaluation results, the qualified prediction results are used as the final flow field prediction results.

9. The method for solving fluid mechanics equations based on physical information neural network according to claim 8, characterized in that: Evaluate the completeness and accuracy of the neural network predictions, including: Data transmission verification and anomaly detection: Build a data transmission control block to record the path, time step, and integrity verification information of the fluid mechanics data from the storage to the computing node during the training process, perform real-time verification of the transmission data content based on key storage nodes, and generate a verification information list; Model prediction verification: When using the trained physical information neural network model to efficiently predict the fluid properties of unsampled areas, the integrity of the prediction input data is determined based on the verification information list, and the output results of the physical information neural network model are compared with the verification data. If the comparison deviation exceeds the preset threshold, the model input parameters are adjusted.

10. The method for solving fluid mechanics equations based on physical information neural network according to claim 9, characterized in that: After numerical verification and prediction, it also includes: visualizing and analyzing the final flow field prediction results, and extracting the flow pattern, turbulence structure and heat transfer characteristics of the predicted scenario.

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