Non-steady flow field rapid prediction method based on cross-fidelity neural network

Abstract

The invention provides an unsteady flow field rapid prediction method based on a cross-fidelity neural network. The method belongs to the cross technical field of fluid mechanics (CFD) and deep learning. The method comprises the following steps: determining a fluid region needing to be simulated, performing grid division, and setting an initial fluid boundary condition; respectively executing low-fidelity CFD calculation and high-fidelity CFD calculation on the basis of the grid division and boundary conditions; dimensionality reduction and feature extraction are carried out on the flow field data by combining a convolutional neural network auto-encoder and a long short-term memory network; constructing a cross-fidelity neural network; performing error judgment on the prediction result, and checking whether the precision requirement is met or not; integrating the steps into a complete end-to-end flow field prediction framework; and outputting a high-fidelity flow field prediction result. The space and time features of the flow field can be efficiently extracted by combining the convolutional neural network auto-encoder and the long short-term memory network.

Description

Technical Field

[0001] The present invention proposes a fast prediction method for unsteady flow fields based on a cross-fidelity neural network, belonging to the cross technical field of fluid mechanics (CFD) and deep learning. Background Art

[0002] The numerical simulation of unsteady flow fields is a key technology for the design and performance analysis of rotating machinery. At present, two types of numerical simulation methods are mainly used in engineering practice: low-computation-cost methods based on RANS and high-fidelity simulation methods. However, due to the limitations of turbulence modeling, the RANS method is difficult to accurately capture complex unsteady flow characteristics, while the high-fidelity simulation method faces the challenge of huge computational resource consumption. Although the hybrid-fidelity method attempts to balance efficiency and accuracy, the model switching and grid limitations restrict its prediction reliability. Therefore, there is an urgent need for a new method to balance computational efficiency and prediction accuracy. Summary of the Invention

[0003] The present invention provides a fast prediction method for unsteady flow fields based on a cross-fidelity neural network to solve the problems mentioned in the above background art: A fast prediction method for unsteady flow fields based on a cross-fidelity neural network proposed by the present invention, the method comprising: S1. Determine the fluid region to be simulated, perform grid division, and set initial fluid boundary conditions; S2. Based on the above grid division and boundary conditions, perform low-fidelity and high-fidelity CFD calculations respectively; S3. Combine a convolutional neural network autoencoder and a long short-term memory network to perform dimensionality reduction and feature extraction on the flow field data; S4. Construct a cross-fidelity neural network; S5. Judge the error of the prediction result and check whether the accuracy requirement is met; S6. Integrate the above steps into a complete end-to-end flow field prediction framework; output a high-fidelity flow field prediction result.

[0004] Advantages of the present invention: By combining a convolutional neural network autoencoder and a long short-term memory network, it is possible to efficiently extract the spatial and temporal features of the flow field. When dealing with complex unsteady flow field data, a low-fidelity data is used to train the model, thereby improving the accuracy and speed of flow field prediction; using low-fidelity flow field data for training and combining high-fidelity flow field data for verification can improve the adaptability and accuracy of the model while ensuring computational efficiency. By extracting the multi-scale spatial features of low-fidelity data and performing dimensionality reduction processing on the latent vectors, it helps to effectively transfer knowledge between different fidelities and enhance the flow field prediction ability; by balancing different types of flow field data through data augmentation and undersampling techniques, the problem of data imbalance is effectively solved, thereby improving the generalization ability of the model and avoiding overfitting; by generating adversarial samples to evaluate the robustness of the CAE network, it ensures that the network can still maintain good prediction performance when facing noisy or uncertain data. This method helps to improve the stability and reliability of the network in practical applications; by visualizing, clustering, and performing regression analysis on the latent vector space, it is possible to identify the normal and abnormal states of the flow field and construct an anomaly detection model based on the distribution law of the latent vectors. This detection ability is of great significance for warning potential problems or abnormal states in the flow field, especially in industrial applications or weather forecasting; by the mapping relationship between the latent vector space and physical parameters, the physical laws of the flow field can be verified. This not only provides higher interpretability for flow field prediction but also provides a more detailed analysis tool for the study of fluid mechanics. Description of the Drawings

[0005] Figure 1 It is a neural network module diagram for cross-fidelity transfer learning of the present invention; Figure 2 It is a convolutional autoencoder-long short-term memory network module diagram of the present invention; Figure 3 It is a flowchart of the method of the present invention. Detailed Embodiments

[0006] The following describes the preferred embodiments of the present invention with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are only for the purpose of illustrating and explaining the present invention and are not intended to limit the present invention.

[0007] An embodiment of the present invention, as Figure 3 shown, a method for fast prediction of unsteady flow field based on cross-fidelity neural network, the method includes: S1. Determine the fluid region to be simulated, perform mesh division, and set the initial fluid boundary conditions; S2. Based on the above mesh division and boundary conditions, perform low-fidelity and high-fidelity CFD calculations respectively, and store the calculation results; S3. Combine a convolutional neural network autoencoder and a long short-term memory network to reduce the dimension and extract features of the flow field data; S4. Construct a cross-fidelity neural network; use the low-fidelity simulation results and preprocessing parameters as inputs, map them to the high-fidelity latent vectors through the cross-fidelity neural network; and use the decoder to reconstruct the latent vectors into a high-precision flow field; S5. Judge the error of the prediction result to check whether the accuracy requirement is met; if not, increase the sample points, return to S2 to perform CFD calculation and neural network training again until the prediction result meets the requirements; S6. Integrate the above steps into a complete end-to-end flow field prediction framework; finally output the high-fidelity flow field prediction result.

[0008] The working principle of the above technical solution is as follows: First, generate two grids with different densities for the target fluid region (such as the internal flow passage of an aero-engine compressor), including a low-fidelity grid (coarse grid) and a high-fidelity grid (fine grid). The low-fidelity grid is used to quickly obtain the basic features of the flow field, while the high-fidelity grid is used to capture the fine flow structures; based on the above grids and preset boundary conditions (such as flow velocity, pressure, temperature, etc.), perform low-fidelity and high-fidelity CFD calculations respectively. The low-fidelity calculation provides an approximate solution of the flow field, while the high-fidelity calculation provides accurate flow field information. The calculation results are stored for subsequent processing; use a convolutional neural network autoencoder (CAE) and a long short-term memory network (LSTM) to reduce the dimension and extract features of the flow field data; the CAE is used to extract the spatial multi-scale features of the flow field and capture the spatial distribution characteristics of the flow field; the LSTM is used to capture the time evolution law of the flow field and process the temporal characteristics of the flow field; through the CAE and LSTM, convert the original high-dimensional flow field data into low-dimensional latent vectors for subsequent processing by the neural network; construct a cross-fidelity neural network (TF-TLNN), which is used to establish the mapping relationship between the low-fidelity and high-fidelity flow fields; Figure 1 is the framework of the cross-fidelity transfer learning neural network module (TF-TLNN module).

[0009] Suppose 、 are the CFD preprocessing settings based on the coarse and fine grids respectively, corresponding to parameters such as geometry, computational boundary conditions, and turbulence models (usually 、 are the same), while and are the output features of the low-fidelity network and the high-fidelity network respectively. The cross-fidelity information is passed through This mapping connection, namely is jointly determined by and .

[0010] To make the mapping include both linear and non-linear relationships simultaneously, is decomposed into a linear part and a non-linear part , that is can be expressed as:

[0011] The cross-fidelity neural network architecture consists of three fully connected layer (FCL) neural networks. Among them, is used to establish the mapping between the low-fidelity data input features and the output features . , respectively establish the mappings , mentioned above. Therefore, the loss function:

[0012] In the formula, is the mean square error. By minimizing the loss function, the three neural networks are trained.

[0013] It should be noted that if the unsteady three-dimensional flow field is directly used to represent and , the corresponding dimensions are huge, which is not conducive to the efficiency and accuracy of neural network training. For this reason, it is proposed to combine the powerful ability of the convolutional autoencoder (CAE) to compress images and the long short-term memory network (LSTM), as Figure 2 shown, to retain the ability of time information and reduce the dimension of the flow field data. By combining CAE and LSTM, the convolutional autoencoder-long short-term memory network module as shown in Figure 2 is obtained.

[0014] For the unsteady CFD flow field snapshot , first, each snapshot is mapped to a low-dimensional space through the encoder . On this basis, LSTM is used to capture time information, and after further dimensionality reduction, a low-dimensional latent vector is obtained. This latent vector can be used as the Figure 1 in the TF-TLNN module in and 。Latent vector Through the LSTM and the decoder a reconstructed flow field is obtained 。The network architecture includes three fully connected layers (FCLs): The first layer: used to establish the mapping from low-fidelity input features to output features; The second layer: used for linear partial mapping; The third layer: used for non-linear partial mapping; Taking the low-fidelity simulation results and preprocessing parameters as inputs, they are mapped to high-fidelity latent vectors through a cross-fidelity neural network. Then, the decoder is used to reconstruct the latent vectors into a high-precision flow field; the error of the prediction result is judged to check whether the accuracy requirement is met; if the prediction result does not meet the accuracy requirement, sample points are added and the process returns to step S2 to perform CFD calculation and neural network training again until the prediction result meets the requirement; the above steps are integrated into a complete end-to-end flow field prediction framework. This framework starts from the input of CFD preprocessing parameters and goes through the following steps: low-fidelity simulation - data dimensionality reduction and feature extraction - fidelity mapping and flow field reconstruction; finally, a high-fidelity flow field prediction result is output.

[0015] The effects of the above technical solutions are as follows: Through preliminary rapid calculation using low-fidelity grids and combined with fine calculation using high-fidelity grids, the time cost of CFD calculation is effectively reduced, especially when dealing with complex flow fields. The rapid calculation of low-fidelity helps to pre-capture the basic characteristics of the flow field and provides preliminary guidance for subsequent high-fidelity calculations; using CAE (Convolutional Autoencoder) to extract the spatial multi-scale features of the flow field, while LSTM (Long Short-Term Memory Network) can capture the temporal evolution law of the flow field. This combined feature extraction method can effectively reduce the complexity of neural network training and improve the generalization ability of the model; by establishing the mapping relationship between low-fidelity and high-fidelity flow fields through TF-TLNN, the low-fidelity flow field data can be accurately converted into high-fidelity flow field data. This method can quickly generate high-precision flow field prediction results, reducing repeated calculations and a large number of expensive CFD simulations; based on the error judgment of the flow field prediction results, by increasing sample points and adjusting model training, the accuracy of flow field prediction can be continuously optimized to ensure that the final output result meets the actual engineering requirements; the constructed complete end-to-end prediction framework, from the input of CFD preprocessing parameters to the reconstruction of the flow field and the output of the prediction result, covers the entire process of flow field simulation and prediction, providing an automated, efficient and scalable prediction method, greatly reducing manual intervention and complex engineering calculations; this method is not only applicable to complex flow systems such as aero-engine compressors, but also can be extended to other fields, such as complex flow simulations in automotive engines, wind turbines, aircraft, etc., and has strong engineering application value.

[0016] In one embodiment of the present invention, S1 includes: S11. Determine the exact fluid region to be simulated according to engineering requirements; S12. Analyze the characteristics of the fluid region and perform mesh generation based on the analysis results; the mesh includes low-fidelity meshes and high-fidelity meshes; S13. Set the flow velocity boundary conditions according to the characteristics of the fluid region; ensure the accuracy and reliability of the simulation according to the boundary conditions; S14. Select a suitable turbulence model according to the flow characteristics and computing resources.

[0017] The working principle of the above technical solution is as follows: According to the specific engineering requirements of an aero-engine compressor, first determine the fluid regions to be simulated. These regions include the compressor inlet, rotor blades, stator blade regions, and the complex gaps between them. This step provides the necessary region definition for subsequent simulations; the fluid regions are analyzed in detail, involving physical quantities such as flow velocity, pressure gradient, and temperature distribution. Based on the analysis results, mesh generation is performed to ensure accurate simulation of fluid flow. Mesh generation is divided into low-fidelity meshes and high-fidelity meshes: Low-fidelity meshes: Use a relatively coarse mesh size, which can quickly calculate the overall characteristics of the flow field and is suitable for preliminary analysis and rough judgment of flow trends.

[0018] Mesh optimization: Increase the density and distribution of the mesh in key regions (such as blade edges and gap regions) to ensure sufficient detail resolution in these regions, thereby ensuring the accuracy of the simulation results.

[0019] High-fidelity meshes: Use an extremely fine mesh size to capture the fine structures of the fluid, such as vortices and boundary layers, which helps to accurately analyze complex flow phenomena.

[0020] Mesh quality inspection: Check the quality indicators of the mesh, such as orthogonality and continuity, to ensure that mesh generation does not introduce unnecessary computational errors; Set appropriate flow velocity boundary conditions according to the characteristics of the fluid region to ensure that the flow characteristics can truly reflect the actual working conditions. At the same time, set boundary conditions such as pressure and temperature according to engineering requirements to ensure that the physical conditions during the simulation are consistent with the actual working conditions, thereby ensuring the accuracy and reliability of the simulation results. Select a suitable turbulence model according to the flow characteristics and available computing resources. For common engineering applications, common turbulence models include: k-ε model: Suitable for most industrial flows and can better balance computational accuracy and computing resource requirements.

[0021] SA model: It is suitable for accurate simulation of rotating flow and complex flow, especially for complex geometries such as aircraft engines.

[0022] LES (Large Eddy Simulation) / DNS (Direct Numerical Simulation): This more advanced turbulence model can simulate the turbulent structure in detail, but requires stronger computing resources and is suitable for occasions with extremely high flow accuracy requirements.

[0023] The effects of the above technical solutions are as follows: by accurately determining the fluid area and analyzing it in detail, the coverage of key areas (such as blade edges, air inlets and gaps, etc.) during the simulation process is increased, the loss of accuracy is reduced, and thus the accuracy of the flow characteristics simulation is significantly improved; the calculation process is optimized by the reasonable use of a combination of low-fidelity grids and high-fidelity grids. Low-fidelity grids can quickly derive the basic characteristics of the flow field, while high-fidelity grids ensure the fine capture of key areas, reduce unnecessary calculation burdens, and thus improve the overall calculation efficiency; by reasonably setting boundary conditions such as flow velocity, pressure, and temperature, the adaptability of the simulation is increased, and the fluid behavior can be accurately reflected under different working conditions. This provides a more flexible option for engineering design and meets the changing engineering needs; through meticulous grid optimization and grid quality inspection, the errors caused by improper grid division are reduced, especially in complex flow areas (such as blade gaps, edges, etc.), effectively avoiding error propagation and ensuring the reliability and accuracy of the calculation results.

[0024] In one embodiment of the present invention, the S12 includes: Determine the complex fluid-solid coupling interface between the compressor rotor blades and the airflow, and between the stator blades and the airflow, and record the coupling relationship between the blade vibration frequency and the airflow pulsation frequency under different working conditions; Analyze the influence of temperature distribution inside the compressor on fluid viscosity, density and other thermophysical properties, and identify areas with large temperature gradients as key areas for high-precision meshing; The empirical formula and numerical simulation method are combined to estimate the turbulence intensity, turbulence scale and other parameters at different locations inside the compressor. According to the overall size and flow characteristics of the fluid region, an adaptive mesh generation algorithm is used to generate a coarse mesh covering the entire computational domain; In the edge area of the compressor rotor blades and stator blades, local encryption technology is used to increase the number of grids and improve the ability to capture the flow characteristics of the blade surface; During the calculation process, according to the changes in the flow field, the adaptive grid refinement technology is used to perform real-time grid encryption in areas with drastic flow changes; the grid is regularly smoothed to eliminate grid distortion and overlap; when the grid quality does not meet the requirements, the grid is reconstructed; For the key flow regions inside the compressor, a local grid refinement strategy is adopted to generate extremely fine grids to capture fine flow structures; between the coarse grids and the fine grids, a multi-scale grid fusion technology is used to achieve a smooth transition of the grids.

[0025] The working principle of the above technical solution is as follows: By determining the complex fluid-structure interaction interfaces between the compressor rotor blades and the airflow, and between the stator blades and the airflow, the coupling relationship between the blade vibration frequency and the airflow pulsation frequency is recorded. Analyze the influence of the internal temperature distribution of the compressor on the thermophysical properties of the fluid such as viscosity and density, especially in regions with large temperature gradients (such as the transition section between the combustor outlet and the compressor inlet). In these regions, the changes in the airflow and temperature field are relatively drastic, so key attention needs to be paid during grid division to ensure the accuracy of the calculation results; Combine empirical formulas with numerical simulations to estimate parameters such as the turbulence intensity and turbulence scale at different positions inside the compressor. These parameters provide data support for selecting an appropriate turbulence model and determining the grid size to ensure that the calculation can truly reflect the turbulence phenomenon; Based on streamline tracing and vorticity analysis techniques, predict the positions where flow separation and reattachment may occur on the compressor blade surface; Use an adaptive grid generation algorithm to dynamically adjust the grid density according to the characteristics of the flow. Larger grid sizes are used in regions with gentle flow changes, and smaller grid sizes are used in regions with drastic flow changes. This adaptive strategy helps to optimize the calculation efficiency and improve the accuracy; Local refinement techniques are adopted in the edge regions of the rotor and stator blades to increase the number of grids, thereby improving the ability to capture the flow characteristics on the blade surface. At the same time, in complex blade gap regions, special grid filling algorithms are used to generate grids that fit the gap shape to ensure that the flow in these regions can be accurately simulated; During the calculation process, the grids are encrypted in real time according to the changes in the flow field, especially in regions with drastic flow changes. The grids are smoothed regularly to eliminate grid distortion and overlap phenomena and ensure that the grid quality meets the calculation requirements. When the grid quality does not meet the standards, grid reconstruction is carried out to ensure the stability and accuracy of the simulation results; For key flow regions (such as blade wake regions, shock wave regions, etc.), a local grid refinement strategy is adopted to generate extremely fine grids to capture the details of the flow. Between the coarse grids and the fine grids, a multi-scale grid fusion technology is used to ensure a smooth grid transition and avoid calculation errors caused by sudden changes in grid size.

[0026] The effects of the above technical solution are as follows: through meticulous grid division and adaptive grid refinement technology, the complex flow characteristics inside the compressor, such as turbulence, flow separation and reattachment, can be captured to ensure the consistency of the simulation results with the actual flow state and avoid errors caused by coarse grids; traditional technologies often use fixed grids and cannot dynamically adjust the grid density according to changes in the flow field, making it impossible to refine the grid in areas where the flow changes drastically (such as blade wake areas, shock wave areas, etc.), resulting in inconsistency between the calculation results and the actual flow state, which is prone to errors; by recording the coupling of blade vibration and airflow pulsation under different operating conditions, data support can be provided for vibration control and performance optimization of the compressor. Understanding this coupling relationship helps reduce the impact of adverse vibrations on the compressor structure and improve overall operational stability. Under different operating conditions, by analyzing the changes in the temperature gradient inside the compressor and the thermophysical properties of the fluid, such as viscosity and density, a more accurate prediction of the thermodynamic behavior of the airflow can be made, thereby optimizing the thermal management design. By combining empirical formulas with numerical simulations, the turbulence intensity and turbulence scale inside the compressor can be estimated more accurately, helping to select a more suitable turbulence model and providing reliable basic data for flow simulation. In traditional methods, parameters such as turbulence intensity and turbulence scale often rely on simplified empirical formulas, lacking a detailed estimate based on the actual flow field conditions, which may lead to deviations in the selection of turbulence models and the determination of grids, affecting the accuracy of flow simulation. In complex areas between compressor blades and airflow, such as the edge area between the rotor and the stator, the blade wake area, etc., local grid encryption technology is used to accurately capture the flow details in these areas and avoid the calculation results being affected by neglected details. Adaptive grid generation and optimization technology is used to perform real-time grid encryption according to changes in the flow field to ensure that a high grid resolution is maintained in areas with drastic flow changes. This helps to improve computing efficiency and accuracy, and ensure the comprehensiveness and accuracy of flow field analysis; a smooth transition is achieved between coarse grids and fine grids through multi-scale grid fusion technology, which effectively avoids sudden changes in grid size, reduces computational errors, and ensures a smooth transition of flow field changes during the simulation process; combined with streamline tracing and vortex analysis technology, flow separation and reattachment are predicted, ensuring that the grids in key areas are detailed enough to provide support for capturing flow details, especially in complex blade gap flows and shock wave areas.

[0027] In one embodiment of the present invention, the S2 includes: S21, select a CFD solver, set the calculation parameters of the solver according to the grid division and boundary conditions, and output the basic characteristics of the flow field; S22. Perform high-precision CFD calculations on fine grids to capture fine flow structures; use parallel computing to optimize the use of computing resources and store high-precision flow field information in a database.

[0028] The working principle of the above technical solution is as follows: Select a suitable CFD solver according to specific engineering requirements and problem types. For example, Fluent is commonly used for fluid dynamics and heat transfer simulations, while CFX usually performs better in rotating machinery and complex flow simulations; Before conducting a CFD simulation, it is first necessary to mesh the computational domain. The quality of the mesh has a direct impact on the accuracy of the calculation results. Unstructured meshes or structured meshes are usually adopted, depending on the specific problem. Boundary conditions include inlet flow velocity, outlet pressure, wall slip conditions, etc., which need to be reasonably set according to physical problems; Set appropriate calculation parameters according to the characteristics of the problem, such as the number of iterations, convergence criteria, etc. The number of iterations determines the computational effort during the solution process, while the convergence criterion is used to judge whether the calculation has reached the predetermined accuracy standard; Through the solution process, the CFD solver generates relevant data of the flow field, including velocity distribution, pressure distribution, turbulence characteristics, etc. These output data are the basis for subsequent analysis and design optimization; Conduct high-precision CFD calculations on a fine mesh to capture the fine structures in the flow. By using a higher mesh resolution, complex flow phenomena such as turbulence, flow separation, and reattachment can be better captured, resulting in more accurate flow field prediction results; Since CFD calculations usually require a large amount of computing resources, parallel computing technology can significantly accelerate the calculation process. By distributing the computational tasks to multiple processing units, the calculation time can be effectively shortened and the computational efficiency can be improved. Parallel computing helps to maintain a high computational efficiency when dealing with large-scale meshes and reduce the overall computational cost; After the calculation is completed, store the high-precision data of the flow field in the database for subsequent further analysis and optimization. The flow field data includes key information such as velocity field, pressure field, and turbulence intensity. These data can provide important bases for subsequent design modifications, performance evaluations, and system optimizations.

[0029] The effects of the above technical solutions are as follows: By selecting an appropriate CFD solver and fine grid division, the detailed structures in the flow are accurately captured, significantly increasing the accuracy of the flow field calculation. This enables a more accurate description of key features such as velocity distribution and pressure distribution, enhancing the accuracy in the design process; Through parallel computing technology, the use of computing resources is optimized, significantly reducing the calculation time required. Especially when conducting large-scale and high-precision flow field simulations, the computing efficiency is greatly improved, providing effective support for rapid decision-making and design optimization; Parallel computing is used to optimize the allocation of computing resources, improving the utilization rate of computing resources and ensuring the completion of large-scale computing tasks in a shorter time. This optimization not only enhances the computing efficiency but also avoids resource waste and reduces the computing cost; The high-precision flow field data is stored in the database, enhancing the data management and access capabilities. This systematic data management method makes subsequent analysis and design optimization more efficient, enabling better comparison of multiple solutions and rapid adjustment; Through precise flow analysis, more options for optimization solutions are provided to designers, reducing the trial-and-error cost and time in the design process. Potential problems can be identified more quickly and effectively adjusted at an early stage, thus enhancing the flexibility and response speed of the design process; High-precision flow field analysis helps optimize the system design, improving the performance and stability of the final product. For example, in designs related to aerodynamics and thermodynamics, it can effectively reduce energy consumption, improve the overall efficiency of the system, and ensure that the product performs more stably and reliably in actual applications.

[0030] In one embodiment of the present invention, S22 includes: According to the topological structure of the fine grid and the distribution of computing resources, formulate a domain decomposition strategy; divide the computational domain into multiple subdomains, and each subdomain is assigned to one or more computing nodes for parallel computing; and optimize the communication mechanism between subdomains; During the calculation process, monitor the performance indicators of the computing platform in real time, and adjust the allocation of computing resources according to the monitoring results; based on the calculation progress tracking mechanism, record the calculation time and remaining calculation time of each time step; According to the numerical stability situation during the calculation process, adopt an adaptive time step adjustment strategy; when the calculation becomes unstable, automatically reduce the time step; when the calculation is stable, appropriately increase the time step; Based on the error detection and handling mechanism, monitor the possible errors in the calculation process in real time; if an error is detected, take corresponding handling measures in a timely manner; Conduct multi-scale flow feature analysis on the fine grid calculation results; and adopt post-processing technology to deeply explore the detailed information of the flow structure; Compare the fine-grid calculation results with the experimental data to verify and evaluate the accuracy and reliability of the calculation results; analyze the differences between the calculation results and the experimental data, and make corresponding adjustments and improvements to the calculation model and parameters; Conduct grid independence verification by calculating with fine grids of different densities and comparing the differences in the calculation results; Dynamically adjust the allocation of computing resources according to the actual requirements during the calculation process; Store and manage the flow field data obtained from the fine-grid calculation through a high-precision flow field information database.

[0031] The working principle of the above technical solution is as follows: According to the topological structure of the fine grid and the distribution of computing resources, a reasonable domain decomposition strategy is formulated to divide the computational domain into multiple subdomains. Each subdomain is assigned to one or more computing nodes for parallel computing, thereby improving the computing efficiency and performance; optimizing the communication mechanism between subdomains to ensure efficient and smooth data exchange between subdomains during the computing process, avoiding resource waste or delays; real-time monitoring of the performance metrics of the computing platform (such as CPU utilization rate, memory occupancy rate, disk I / O throughput, etc.) to analyze the usage of computing resources; based on the monitoring results, perform dynamic resource adjustment to ensure the optimal utilization of the resources of the computing platform. For example, when the resource utilization rate is too high or the computing progress lags behind, the system will adjust the allocation of computing resources to ensure that the computing tasks are completed on time; through a computing progress tracking mechanism, record the computing time and remaining computing time for each time step. And display the computing progress to the user through a visualization interface, enabling the user to understand the computing status and progress in real time; provide an operable interface that allows the user to flexibly adjust the computing parameters and optimize the computing process; during the computing process, dynamically adjust the time step according to numerical stability. If the computing becomes unstable (such as numerical oscillation or divergence), the system will automatically reduce the time step; conversely, when the computing is stable, the system will appropriately increase the time step to improve the computing efficiency; introduce a real-time error detection and handling mechanism to monitor possible errors such as numerical overflow and grid distortion. Once an error is detected, the system will take corresponding measures, such as re-initializing the computing, adjusting the computing parameters, etc., to ensure the correctness and reliability of the computing results; analyze the macroscopic and microscopic flow characteristics of the fine grid computing results, including identifying macroscopic structures such as vortices and shock waves and microscopic structures such as turbulent pulsations and boundary layer flows; use post-processing techniques, such as vortex identification algorithms and turbulent statistical analysis methods, to further explore the detailed information of the flow structure and help better understand the flow field characteristics; compare the computing results with experimental data to evaluate the accuracy and reliability of the computing results. Analyze the differences between the computing results and experimental data, find out the reasons for the differences, and optimize and adjust the computing model and parameters; conduct grid independence verification to ensure that the computing results are not affected by the grid density. By performing fine grid computing with different densities and comparing the results, find the optimal grid density at which the computing results tend to be stable to ensure the accuracy and stability of the computing; according to the actual requirements during the computing process, dynamically adjust the allocation of computing resources. For example, when the flow field changes greatly in the initial stage of computing, more computing resources are required, while when the flow field tends to be stable in the later stage of computing, the resource requirements decrease, thereby effectively improving the computing efficiency and resource utilization rate; store the flow field data obtained from the fine grid computing in a high-precision flow field information database for convenient subsequent data analysis, backtracking, and optimization, providing data support for further research.

[0032] The effects of the above technical solution are as follows: Through a reasonable domain decomposition strategy, the computing tasks are reasonably allocated to multiple computing nodes, and parallel computing is used to improve the computing efficiency. Moreover, the communication mechanism between subdomains is optimized to avoid computing bottleneck problems and ensure the high efficiency of computing. Traditional fluid computing often uses a fixed resource allocation method and cannot monitor and adjust resource allocation in real time during the computing process. This static resource allocation method may lead to overuse or underuse of resources during the computing process. Especially when the computing progress is uneven, some computing nodes may be idle while other nodes may be overloaded, resulting in performance bottlenecks or computing delays. At the same time, based on the error detection and handling mechanism, possible numerical problems are monitored in real time to reduce errors in computing and improve the computing accuracy. During the computing process, the allocation of computing resources is dynamically adjusted, which not only ensures the efficiency under high resource requirements at the initial stage of computing but also avoids unnecessary resource waste in the later stage of computing, thus improving the utilization rate of computing resources. At the same time, adjusting the resource allocation based on the performance monitoring results can ensure that the platform is always in the best operating state during the computing process. Through the computing progress tracking mechanism, the computing time and remaining computing time of each time step are recorded, and the computing progress can be monitored in real time. Combined with the visualization interface, users can timely understand the computing status, optimize the user experience, and improve the controllability of the computing process. Through the adaptive time step adjustment strategy, the system can automatically adjust the time step according to the numerical stability of the computing to avoid the occurrence of unstable phenomena, thereby improving the computing stability and accuracy. Traditional technologies usually adopt a fixed time step during the computing process and are difficult to adjust adaptively. In complex flow simulations, a fixed time step may lead to numerical instability, resulting in oscillation or divergence phenomena, especially when dealing with complex flows such as turbulence and shock waves. In this case, it is difficult to ensure the computing stability and the computing accuracy is reduced. By using multi-scale flow feature analysis, the detailed information of the flow can be deeply explored, especially in the identification of flow phenomena such as turbulence, shock waves, and vortices, providing accurate flow characteristics. This multi-dimensional analysis method is of great significance for understanding complex flow phenomena. Through grid independence verification, it is ensured that the computing results do not depend on the grid density, enhancing the reliability and generality of the computing results. This process helps to ensure the consistency and stability of the computing results under different grid partitions. By comparing and verifying with experimental data, the accuracy of the computing results can be ensured, deviations in the model can be found and corrected, and it is ensured that the computing model is consistent with the physical experiment, thereby improving the credibility of the computing results. By managing the flow field data of fine grid computing through a high-precision flow field information database, it is convenient for subsequent analysis, reproduction, and long-term archiving, and at the same time, the organization and usability of the data are strengthened.

[0033] In one embodiment of the present invention, S3 includes: S31. Preprocess the data; and design the network structure of CAE, including a convolutional layer, a pooling layer, and a fully connected layer; S32. Train the CAE using low-fidelity flow field data, optimize the network parameters, use the trained CAE to extract the spatial multi-scale features of the flow field, and compress them into low-dimensional latent vectors; S33. Arrange the flow field data in time series as the input of the LSTM; train the LSTM network to learn the time evolution law of the flow field; S34. Use the trained LSTM to extract the time features of the flow field.

[0034] The working principle of the above technical solution is as follows: Preprocess the original flow field data, including operations such as denoising, normalization, and scale conversion, to ensure that the data has good quality and consistency during the training process; Design the structure of a convolutional neural network autoencoder (CAE), which includes multiple convolutional layers, pooling layers, and fully connected layers. The convolutional layer is used to extract local features in the data, the pooling layer is used to reduce the dimension of the data and extract key features, and the fully connected layer is used for the final mapping of the data and the generation of latent vectors; Input the low-fidelity flow field data into the designed CAE network for training. During the training process, the network will learn how to extract spatial features in the data through convolutional operations and optimize the network parameters through the reconstruction error of the autoencoder; After training, the CAE network can effectively extract the spatial multi-scale features from the flow field data. By mapping the data to a low-dimensional latent space, the network compresses the flow field data, thus obtaining a simplified, low-dimensional latent vector; Arrange the flow field data in chronological order. The flow field data at each moment corresponds to a specific state, which is regarded as time series data and input into the LSTM network; LSTM (Long Short-Term Memory network) is a recursive neural network (RNN) that can capture long-term dependencies. In this stage, the LSTM network is used to learn the time evolution law of the flow field data. During the training process, the LSTM will gradually update its internal state according to the input time series data, thus modeling the time-varying characteristics of the flow field; Through the trained LSTM network, the model can extract the features of the flow field data changing over time. These time features can help us understand the change trend of the flow field at different time points and how it affects the future state.

[0035] The effects of the above technical solutions are as follows: By designing a CAE network, multi-scale spatial features can be extracted from low-fidelity flow field data. The combination of convolutional layers and pooling layers can effectively capture local features in the flow field data, and the dimensionality of the data is compressed through the structure of the autoencoder, enabling the model to significantly reduce computational and storage requirements while maintaining important spatial information; Using the trained CAE model to generate low-dimensional latent vectors can transform high-dimensional flow field data into a more concise representation. The low-dimensional latent vectors not only reduce the complexity of subsequent calculations but also effectively retain the key information of the flow field, facilitating further analysis and prediction; By performing time series modeling on the flow field data through an LSTM network, long-term dependencies in the flow field data over time can be effectively captured, such as CFD results at different times. The memory ability of the LSTM enables the model to accurately predict the evolution trend of the flow field at future times. Especially in the dynamic characteristics and temporal variations of the flow field, the LSTM can provide a more accurate understanding. By combining CAE and LSTM, spatial and temporal features of the flow field data can be extracted simultaneously. In the analysis process of the flow field data, the comprehensive consideration of spatial and temporal features can provide a more comprehensive understanding of the evolution law of the flow field, providing a more accurate basis for subsequent prediction, optimization, and control; Through the low-dimensional latent vector representation of CAE and the temporal modeling of LSTM, the overall solution can effectively reduce the dimensionality of the data and improve computational efficiency. When dealing with high-dimensional flow field data, the model can not only retain key information but also save resources in terms of computation and improve processing speed; Through the comprehensive learning of spatial and temporal features of the flow field data, the solution can effectively improve the accuracy of flow field prediction. The model can perform efficient predictions at different time steps. Especially in complex flow field change scenarios, it can provide more stable and accurate prediction results.

[0036] In one embodiment of the present invention, the S32 includes: S321. Divide the preprocessed and enhanced low-fidelity flow field data into a training set, a validation set, and a test set; S322. Balance the quantities of different types of flow field data through undersampling; Update the parameters of the CAE network based on the stochastic gradient descent method; S323. Adjust the learning rate and batch size of the optimization algorithm; During the training process, regularly calculate the evaluation metrics on the validation set to monitor the training effect of the network; S324. Apply the trained CAE network to the low-fidelity flow field data, extract the spatial multi-scale features of the flow field, and compress them into low-dimensional latent vectors; Analyze the distribution law of different flow field states in the latent vector space; S325. If the dimension of the latent vector is still relatively high, a dimensionality reduction algorithm is used to further reduce the dimension of the latent vector; meanwhile, clustering analysis is performed on the dimension-reduced latent vector to cluster similar flow field states together. S326. Generate adversarial samples for the CAE network, that is, add tiny perturbations to the original flow field data to make the network make incorrect judgments on the reconstructed flow field data; evaluate the robustness of the network by generating adversarial samples.

[0037] The working principle of the above technical solution is as follows: The preprocessed and enhanced low-fidelity flow field data is divided into a training set, a validation set, and a test set. The training set is used to train the CAE network so that it can learn spatial features from the flow field data; the validation set is used to monitor the performance of the network during training to prevent overfitting; the test set is used to finally evaluate the performance of the network to ensure its generalization ability for new data; to ensure that the network can effectively learn different categories of flow field data, the data categories are balanced through undersampling technology to avoid the situation where the number of data in a certain category is too large, causing the model to be biased towards a certain category. Then, the parameters of the CAE network are updated by the Stochastic Gradient Descent (SGD) method to optimize the learning effect of the network. The SGD optimization algorithm adjusts the network weights step by step by minimizing the loss function to achieve the optimal training result. The learning rate and batch size of the optimization algorithm are adjusted. The size of the learning rate has an important impact on the parameter update rate during training, and too large or too small a learning rate may lead to unsatisfactory training effects. The batch size determines the number of input data for each training, affecting the stability and computational efficiency of the training process. Through techniques such as grid search or random search, the optimal learning rate and batch size are automatically found, thereby improving the efficiency and accuracy of model training. At the same time, evaluation metrics on the validation set are calculated regularly during training to monitor the training effect to prevent overfitting or underfitting. The trained CAE network is applied to the low-fidelity flow field data, and the spatial multi-scale features of the flow field data are extracted through the encoder part of the network, and then compressed into low-dimensional latent vectors through the decoder part. These latent vectors are condensed representations of the spatial features of the flow field data, which can effectively reduce the data dimension while retaining important feature information. The analysis of the latent vectors helps to understand the distribution characteristics of the flow field state in the high-dimensional space, providing a basis for subsequent analysis and prediction. If the dimension of the latent vectors is still high, further dimensionality reduction may be required. Commonly used dimensionality reduction methods include Principal Component Analysis (PCA) and t-Distributed Stochastic Neighbor Embedding (t-SNE). These algorithms can effectively reduce the dimension of the latent vectors, simplify the data structure, and retain the key information of the data as much as possible. Through the dimensionality-reduced latent vectors, cluster analysis can be performed on the flow field state, clustering similar flow field states together, thereby further exploring the internal laws and characteristics of the flow field. The robustness of the CAE network is evaluated by generating adversarial samples. Adversarial samples are deliberately generated by adding small perturbations (usually generated through gradient information) to the original flow field data to disrupt the network's reconstruction judgment. By testing the performance of the network on these adversarial samples, the stability and robustness of the network in the face of uncertain and noisy data can be understood. This step helps to improve the robustness of the network so that it can better handle complex and noisy data in practical applications.

[0038] The effects of the above technical solution are as follows: By dividing the low-fidelity flow field data into a training set, a validation set, and a test set, and using the undersampling technique to balance the data, the negative impact of data imbalance on model training can be effectively avoided, and the training effect can be improved. At the same time, based on the parameter update method of Stochastic Gradient Descent (SGD), the training process of the CAE network can be optimized, enabling the model to better learn the characteristics of the flow field data on the training set; when adjusting the learning rate and batch size of the optimization algorithm, by using the grid search or random search method, the most suitable hyperparameter configuration can be accurately selected. This not only helps to improve the stability of network training but also accelerates the convergence process, avoiding overtraining or under-training, thereby improving the performance of the final model. Using the CAE network to extract the spatial multi-scale features of the flow field data and compress them into low-dimensional latent vectors effectively reduces the dimension of the data, enabling the model to retain the key information of the flow field data under a lower computational complexity. This process helps to further reveal the internal laws of the flow field state in the high-dimensional space and promotes the depth and accuracy of flow field analysis. By reducing the dimension of the latent vector (such as Principal Component Analysis PCA, t-SNE, etc.), the data structure can be further simplified, making it more efficient for visualization and analysis. At the same time, clustering analysis aggregates similar flow field states together, helping to discover potential patterns and laws in the flow field data, thus providing support for subsequent prediction and decision-making; in the prior art, for high-dimensional flow field data, dimensionality reduction techniques such as Principal Component Analysis (PCA) are usually relied on, but these methods do not fully consider the non-linear relationships in the data; and traditional clustering analysis methods, such as K-means, often rely on distance metrics and are easily affected by noise and the curse of dimensionality in the high-dimensional space, resulting in unsatisfactory clustering effects. By generating adversarial samples and evaluating the robustness of the CAE network, the stability of the network in the face of uncertain and noisy data can be effectively tested. This helps to enhance the adaptability of the model in practical applications, enabling it to maintain a high prediction accuracy and stability under complex and changing flow field conditions. This technical solution can not only improve the ability to process and analyze flow field data but also be applied to engineering problems in different fields, such as airflow simulation, aerodynamic analysis, hydraulic simulation, etc. This method can improve the analysis and prediction ability of flow field data and promote the technological progress and development of related fields.

[0039] In one embodiment of the present invention, the S324 includes: S3241. Select a part of the low-fidelity flow field data, analyze the known spatial features, extract features through the CAE network, and compare with the analysis results to verify the effectiveness of the network in extracting features; S3242. Extract features from the convolutional layer, pooling layer, and fully connected layer of the CAE network respectively; analyze the influence of the energy dissipation rate during the feature extraction process at different levels; S3243. Use the feature fusion method to fuse the features extracted at different levels; adjust the weights according to the importance of the features at different levels and the distribution of the energy dissipation rate to obtain comprehensive spatial multi-scale features. S3244. Analyze the correlation between the extracted features; find out the feature combinations with high correlation by calculating the correlation coefficient matrix between the features; when analyzing the feature correlation, combine the distribution of the energy dissipation rate to explore the association between the feature correlation and the energy dissipation rate. S3245. Input the extracted spatial multi-scale features of the flow field into the encoder part of the CAE network, and map the high-dimensional features to a low-dimensional latent vector space through a series of convolution, pooling, and fully connected operations. S3246. Calculate the gradient of the mapping function through the backpropagation algorithm to analyze the contribution degree of different features to the latent vector; use the optimization algorithm to optimize the latent vector during the generation of the latent vector.

[0040] The working principle of the above technical solution is as follows: Select low-fidelity flow field data, automatically extract the spatial features (such as vortices, boundary layers, etc.) in the flow field through the CAE network, and compare them with the results of manual analysis to verify the accuracy of the features extracted by the network; further observe the potential association between the energy dissipation rate and the features extracted by the CAE, and explore whether in the regions with a high energy dissipation rate, the features extracted by the network show a specific pattern to help reveal the relationship between the energy dissipation and the spatial structure of the flow field; extract features at different levels from different levels (convolutional layer, pooling layer, and fully connected layer) of the CAE.

[0041] Convolutional layer: Extract the local spatial features of the flow field, such as the shape and direction of vortices. Pooling layer: Extract the larger-scale spatial features of the flow field, such as the flow trend. Fully connected layer: Synthesize and abstract the features from the previous layers to form a high-level feature representation.

[0042] Analyze the influence of the change in the energy dissipation rate on feature extraction during the feature extraction process of each layer. For example, observe whether regions with a higher energy dissipation rate lead to a stronger response of the convolutional kernel, thereby affecting feature extraction; use feature fusion techniques to fuse features from layers such as convolutional layers, pooling layers, and fully connected layers; adjust the weights of features in each layer according to the importance of different-level features and the distribution of the energy dissipation rate to obtain comprehensive multi-scale spatial features and improve the accuracy and expressiveness of feature representation; calculate the correlation between different features and analyze which feature combinations have a higher correlation through the correlation coefficient matrix; combine the distribution of the energy dissipation rate with feature correlation to explore the potential association between features and the energy dissipation rate. For example, certain feature combinations with a higher correlation may appear more frequently in regions with a higher energy dissipation rate, revealing the close relationship between these features and the energy dissipation process; input the extracted multi-scale spatial features into the encoder part of the CAE, and after a series of convolutional, pooling, and fully connected operations, generate a low-dimensional latent vector; this latent vector can effectively represent the core features of the flow field, facilitating subsequent analysis and modeling; calculate the gradient of the latent vector space through the backpropagation algorithm to analyze the contribution of different features to the latent vector; use an optimization algorithm (such as the gradient descent method or the Adam optimization algorithm) to optimize the latent vector and further improve the quality of the latent vector and the accuracy of feature representation.

[0043] The effects of the above technical solution are as follows: By performing multi-level and multi-scale feature extraction on the flow field data through the CAE network, it is possible to effectively extract and analyze the spatial features in the flow field (such as vortices, boundary layers, etc.), thereby improving the accuracy and efficiency of feature extraction; By extracting features at different levels (convolutional layer, pooling layer, and fully connected layer) of the CAE network and performing fusion processing on them, information at different levels can be integrated to obtain the global and local features of the flow field, making the features more representative and rich; By analyzing the relationship between the energy dissipation rate and the extracted features, the process of energy conversion and dissipation in the flow field can be better understood, further revealing the dynamic evolution law of the flow field. This analysis can help identify the potential association between the regions with high energy dissipation and specific features, providing a theoretical basis for optimizing flow field control and design; In the prior art, the role of the energy dissipation rate in feature extraction is not considered, and it often relies only on physical models or predefined rules, making it difficult to reveal the energy conversion and dissipation law in the flow field; By analyzing the correlation between different features, the variation law of different feature combinations in different flow field regions can be found, helping to deeply explore the complex physical phenomena in the flow field (such as vortex formation, turbulence, etc.), and then providing guidance for flow field simulation and control; By mapping the high-dimensional features to a low-dimensional latent vector space through the encoder, the key information of the flow field can be effectively compressed and expressed, providing a more concise and effective feature representation for subsequent flow field prediction, control, or analysis; Through backpropagation and optimization algorithms (such as gradient descent method, Adam optimization algorithm, etc.), the feature representation can be effectively optimized when generating the latent vector, improving the quality and robustness of the flow field feature representation, and helping to improve the performance of subsequent tasks (such as flow field prediction or control). Traditional feature extraction and latent vector generation methods mainly focus on spatial features and ignore the energy characteristics; By introducing the energy dissipation rate of the flow field, the energy characteristics of the flow field can be considered in each link of feature extraction, feature fusion, latent vector generation, and optimization, making the generated latent vector more comprehensively reflect the characteristics of the flow field, and helping to more accurately analyze the flow field state, perform flow field prediction and control, etc.

[0044] In one embodiment of the present invention, the S325 includes: Use a dimensionality reduction algorithm to reduce the dimensionality of the latent vector to two-dimensional or three-dimensional space and perform visualization; Through the visualization results, observe the distribution form of the latent vector space, calculate the distribution statistical features of the latent vector space, analyze the differences in the distribution statistical features of the latent vectors corresponding to different flow field states, and obtain the distribution law of the latent vector space; Perform clustering analysis on the latent vectors to cluster the latent vectors corresponding to similar flow field states together; Establish a regression model between the flow field state parameters and the latent vectors; Through regression analysis, obtain the quantitative relationship between the latent vectors and the flow field state parameters; Distinguish the normal flow field and the abnormal flow field according to the distribution characteristics of the latent vector space; Analyze the evolution law of different flow field states in the latent vector space; map the latent vector space to the physical parameters of the flow field; analyze the distribution changes of the latent vector space under different physical parameters; Based on the correlation between the latent vector space and physical parameters, verify the physical laws of the flow field; construct a statistics-based anomaly detection model according to the distribution statistical characteristics of the latent vector space; Use machine learning algorithms to construct an anomaly detection model; train the model with the latent vectors corresponding to the normal flow field, and detect new latent vectors to determine whether they are abnormal; Analyze the detected abnormal latent vectors and identify their corresponding abnormal types.

[0045] The working principle of the above technical solution is as follows: First, use a dimensionality reduction algorithm to map the high-dimensional latent vectors to a two-dimensional or three-dimensional space for visualization. Through these visualization results, the structure in the latent vector space can be observed, such as clustering and manifold structures, etc. This provides an intuitive basis for subsequent analysis; conduct statistical feature analysis on the latent vector space, and calculate the mean, variance, covariance, etc. of the latent vectors. This helps to understand the distribution law of the latent vectors, thereby providing a basis for subsequent identification of the flow field state; establish a model for the relationship between the physical parameters (such as velocity, pressure, etc.) of the flow field state and the latent vectors through regression analysis, and then obtain the quantitative relationship between the flow field state parameters and the latent vectors; according to the distribution characteristics of the latent vector space, analyze the differences between the normal flow field and the abnormal flow field. For example, the normal flow field may correspond to the latent vectors concentrated in a certain area, while the abnormal flow field may appear in other areas. Combine statistical methods (such as the 3σ principle) and machine learning algorithms (such as support vector machines, isolation forests, etc.) to establish an anomaly detection model to detect whether there are abnormalities in the latent vectors and classify them; further analyze the evolution law of the latent vectors in the time dimension. For example, the flow field state may move along a certain trajectory in the latent vector space over time. By analyzing the trajectory, the evolution trend of the flow field state can be understood. In addition, by mapping the latent vector space to the physical parameters of the flow field (such as Reynolds number, Mach number, etc.), it can be analyzed how these physical parameters affect the distribution of the latent vector space; for the detected abnormal latent vectors, identify their abnormal types (such as vortex anomalies, boundary layer separation, etc.), and based on these anomaly detection results, give early warnings and take appropriate treatment measures, such as adjusting boundary conditions, changing flow parameters, etc., to eliminate the anomalies and restore the normal flow field.

[0046] The effects of the above technical solution are as follows: By reducing the high-dimensional latent vectors to two-dimensional or three-dimensional space, the distribution of the flow field state can be visually observed, and characteristics such as clustering structures and manifold structures can be identified, helping to deeply understand the internal laws of the flow field; By calculating statistical features such as the mean, variance, and covariance of the latent vector space, the variation law of the flow field state can be quantitatively described, and then the differences between different flow field states can be helped to be judged; A regression model between the latent vector and the flow field state parameters (such as velocity, pressure, etc.) is established to provide a quantitative basis for flow field state prediction and control, and help to optimize the flow field in practical applications; Through the distribution characteristics of the latent vector space, the normal flow field and the abnormal flow field can be effectively distinguished. Using statistical and machine learning algorithms to construct an anomaly detection model can timely detect the abnormal state in the flow field and give an early warning; Analyzing the evolution of the latent vectors of different flow field states can predict the change trend of the flow field state. Especially in a dynamic flow field, the law of flow field evolution can be identified, helping to formulate more accurate control strategies; Through the distribution analysis of the latent vector space, it is verified whether the physical laws (such as conservation laws, similarity principles, etc.) are followed in the flow field, improving the understanding of the physical characteristics of the flow field; Through the detected abnormal latent vectors, different abnormal types in the flow field can be identified, such as vortex anomalies, boundary layer separation anomalies, etc., providing targeted solutions for the optimization and adjustment of the flow field.

[0047] In one embodiment of the present invention, the S4 includes: S41. Design three fully connected layers, which are respectively used to establish the mapping from low-fidelity input features to output features, the linear part mapping, and the nonlinear part mapping; and select activation functions; S42. Integrate the low-fidelity flow field data, preprocessing parameters, and the extracted spatial and temporal features into input data; perform standardization processing on the input data; S43. Define a loss function to measure the difference between the prediction result and the actual result; S44. Select an optimization algorithm to optimize the weight and bias parameters of the neural network; S45. Apply the trained cross-fidelity neural network to the new low-fidelity simulation results to obtain the corresponding high-fidelity latent vectors; S46. Based on the decoder network, reconstruct the high-fidelity latent vectors into a high-precision flow field; verify the reconstruction effect by comparing the reconstruction result with the actual high-fidelity flow field data.

[0048] The working principle of the above technical solution is as follows: Three fully connected layers are designed, which are respectively used to map low-fidelity input features to output features, the mapping of the linear part, and the mapping of the non-linear part. The fully connected layer processes the input data through a linear transformation and uses activation functions (such as ReLU, Sigmoid, etc.) to perform non-linear transformation on the data to enhance the expression ability of the network; the low-fidelity flow field data, pre-processing parameters (such as mesh division, boundary conditions), and spatio-temporal features are integrated into the input data of the network. To improve the stability and training effect of the data, the input data is normalized to have zero mean and unit variance, thereby accelerating the model convergence speed and improving the training effect; a loss function (such as mean square error MSE) is defined to measure the difference between the predicted output and the actual result. Mean square error is a commonly used loss function in regression problems and can effectively guide model optimization; an optimization algorithm (such as Adam, SGD, etc.) is selected to minimize the loss function. The Adam optimizer improves the optimization efficiency by adaptively adjusting the learning rate, while SGD (stochastic gradient descent) optimizes the weights and bias parameters of the network by continuously updating the parameters. During the training process, indicators such as the loss function value and accuracy are also monitored to ensure that the model converges gradually; the trained cross-fidelity neural network is applied to the new low-fidelity simulation results to obtain the corresponding high-fidelity latent vectors. In this process, the low-fidelity flow field data is mapped through the neural network to generate the corresponding high-fidelity latent vectors. These latent vectors contain sufficient detailed information and can be used for the reconstruction of high-precision flow fields; the high-fidelity latent vectors are reconstructed into high-precision flow fields through the decoder network. The role of the decoder is to reverse-transform the latent vectors into actual flow field data. By comparing with the actual high-fidelity flow field data, the accuracy and effectiveness of the reconstruction effect are verified. If the difference between the reconstructed flow field data and the actual data is small, it indicates that the cross-fidelity neural network can successfully predict the high-fidelity flow field from the low-fidelity flow field data.

[0049] The effects of the above technical solution are as follows: By designing a cross-fidelity neural network, high-fidelity flow fields can be predicted from low-fidelity flow field data. This method can significantly improve the accuracy of flow field simulation, thus meeting the actual engineering requirements, especially in application scenarios that require high-precision simulation (such as aerodynamic design, environmental simulation, etc.); Traditional high-fidelity flow field simulations often require a large amount of computing resources and time. This solution predicts by using low-fidelity flow field data, obtains a high-fidelity latent vector through neural network mapping, and then reconstructs the high-fidelity flow field through a decoder, avoiding the high computational burden of directly using high-fidelity simulations, thus significantly saving computing resources and time; Through the design of the cross-fidelity neural network, conversion can be carried out between flow field simulations at different fidelity levels. This method has strong generalization ability and can adapt to different flow field data and simulation environments, enhancing the applicability and scalability of the model; By defining the loss function (such as mean square error) and selecting the optimization algorithm (such as Adam, SGD), the training process can effectively reduce errors while improving the learning efficiency of the network. Monitoring indicators such as the loss function value and accuracy during the training process ensures the stability and accuracy of the model during training; This solution can integrate a variety of different input features (such as low-fidelity flow field data, preprocessing parameters, spatial and temporal features) into the neural network for training. This flexible input feature processing method enables the model to be applied in complex physical scenarios and adapt to different types of input data; Through the design of the decoder network, the high-fidelity latent vector can be accurately reconstructed into a high-precision flow field. The reconstructed flow field can be compared with the actual high-fidelity data to verify the effect of this method. This reconstruction technology can effectively improve the quality of flow field data, making the prediction results more in line with actual requirements.

[0050] In one embodiment of the present invention, step S5 includes: S51. Calculate the error between the prediction result and the actual result, and optimize the source and distribution of the error; S52. According to the error analysis result, increase the sample points in the key area; S53. Refine the grid in the area with a large error; S54. Adjust the architecture and parameters of the neural network.

[0051] The working principle of the above technical solution is as follows: By calculating the errors (such as mean squared error (MSE) and relative error, etc.) between the prediction results and the actual results of the calculation model, the performance of the model can be evaluated. The goal of error analysis is to identify the reasons why the model makes inaccurate predictions in certain regions or conditions. Usually, the distribution of errors will reflect the learning ability and adaptability of the model to different features, thus providing a direction for subsequent optimization; According to the results of error analysis, the model may have a large prediction deviation in certain key regions or special situations. Therefore, it is necessary to increase the sample points in these regions to expand the diversity and representativeness of the training data. By increasing the amount of training data, especially in regions with large errors, the neural network can better learn and adapt to the features of these specific regions; For regions with large errors, the prediction accuracy of the model can be improved by grid refinement in these regions. Grid refinement refers to increasing the calculation resolution in regions with large errors, that is, the way of refining data processing. This can enable the model to capture more fine-grained features in the local area, thereby reducing errors; The architecture and parameters of the neural network (such as the number of layers, the number of neurons in each layer, activation functions, learning rate, regularization, etc.) have an important impact on the learning ability and generalization ability of the model. By adjusting these parameters, the neural network can be helped to better capture the complex patterns in the data, thereby improving the prediction accuracy.

[0052] The effects of the above technical solution are as follows: By calculating the prediction errors and analyzing the sources of errors, the deficiencies of the model in specific regions or conditions can be identified, and targeted optimization can be carried out. This helps to gradually reduce the overall prediction error, especially in those regions with large errors, thereby improving the overall prediction accuracy of the model; By increasing the sample points in key regions, especially those with large errors, the adaptability of the model to different data distributions and complex scenarios can be enhanced. This can prevent the model from overfitting or underfitting, and improve its generalization ability on unknown data; Grid refinement helps to improve the prediction accuracy in local regions with large errors. By increasing the calculation accuracy in local regions, the model can better capture the features of these regions, thereby reducing the prediction errors in these regions and improving the local prediction effect; Adjusting the neural network architecture and parameters (such as the number of layers, the number of neurons, learning rate, etc.) can optimize the learning ability of the network, making it better fit complex input data. This adjustment can help the model learn and predict complex patterns more effectively, improving the performance of the overall model; Steps such as increasing the sample points in key regions, grid refinement, and adjusting the neural network architecture can enable the model to more accurately capture these features when processing data with different features, thereby improving the performance of the model in different datasets or application scenarios; Through the above optimization process, the model can self-adjust and improve at multiple levels, thereby enhancing the stability and reliability of the model, avoiding inaccurate predictions caused by certain data features, and improving the overall performance.

[0053] One embodiment of the present invention, S6 includes: S61. Integrate all the above steps into a complete end-to-end flow field prediction framework; optimize data processing processes, calculation processes, etc. within the framework to improve overall efficiency.

[0054] S62. Write an automated script to execute the full automation process from input to output; and monitor the running status of the automated process in real time to ensure the stability and reliability of the process.

[0055] The working principle of the above technical solution is as follows: Integrate all optimization steps (such as data preprocessing, model training, prediction error analysis, error source identification, grid refinement, neural network adjustment, etc.) to construct an end-to-end flow field prediction framework. This framework can perform full-process processing from input data (such as flow field data, boundary conditions, etc.) to output prediction results (such as flow field distribution, velocity field, pressure field, etc.); each link within the framework, such as data preprocessing, data cleaning, feature engineering, etc., will be optimized to reduce data bottlenecks and ensure the efficient flow of data. Specifically, data processing can be accelerated through parallel computing, batch processing, data compression, etc.; at the computing level, the model training, optimization, and inference processes can be accelerated. For example, adopt efficient optimization algorithms, use GPUs / TPUs for computing acceleration, and distributed computing and other technologies to improve the overall computing efficiency of the framework. By reasonably designing the computing process, redundant calculations are reduced to ensure the real-time and accuracy of the prediction task; write an automated script to automatically execute each step in the entire process, including data reading, model training, verification, prediction, result output, etc. Through the automated processing of the script, the errors and time delays caused by manual operations are eliminated, realizing the efficient and seamless operation of flow field prediction; to ensure the stability of the entire automated process, a real-time monitoring mechanism is set up. The monitoring script can check the execution status of each link in real time, including the usage of computing resources, the integrity of data processing, the training progress of the model, etc. Through logging, anomaly detection, and alarm systems, any problems in the process can be discovered and addressed in a timely manner to ensure the smooth progress of the prediction task; in the automated script, a fault detection and recovery mechanism can be added. In the event of an abnormal situation, the script can automatically pause and perform self-repair operations, or resume the normal state by restarting relevant processes. In this way, the entire automated process is not only efficient but also has high fault tolerance and robustness.

[0056] The effects of the above technical solutions are as follows: integrating all steps into a complete flow field prediction framework, optimizing the data processing and calculation processes, can significantly reduce the latency between various links and improve the operation efficiency of the entire system. By uniformly managing the data flow and calculation process, duplicate calculations and redundant operations are avoided, and a high degree of automation and parallelization of the process are achieved, thereby greatly enhancing the speed of flow field prediction; after writing the automation script, each link in the process (such as data reading, processing, model training, and prediction) can be automatically executed, eliminating the errors and latency brought by manual intervention. In addition, the automation script can also implement batch processing tasks to further improve the processing efficiency; after the data processing and calculation processes in the framework are optimized, not only the efficiency is improved, but also the prediction accuracy is enhanced. Through more efficient data processing and calculation, errors caused by improper data processing or calculation bottlenecks can be reduced, thus ensuring the accuracy of model prediction; the writing of the automation script eliminates the inconsistency of manual operations and ensures that the processes executed each time are strictly consistent. This consistency is particularly important in long-term prediction tasks and can ensure the reliability of the results; the real-time monitoring function in the automation process can track the system operation status in real time, discover and solve potential problems in a timely manner. By setting up an alarm mechanism, a rapid response can be made when an abnormality occurs to prevent the expansion of the problem and ensure the stable operation of the system; the fault detection and recovery mechanism in the automation script can automatically take measures to repair or restart the process when the system has problems, thereby improving the fault tolerance of the system and ensuring continuous and stable operation in a complex operating environment; the automation process eliminates the need for manual operations, enabling the flow field prediction to be fully automated, greatly saving human resources. Staff can focus more on system optimization and result analysis, rather than spending a lot of time on tedious links such as data processing and model training; the automation script supports batch task processing and can handle multiple prediction tasks simultaneously, further improving the work efficiency; through the automation script and integration framework, R & D personnel can quickly adjust the model, optimize the algorithm, update the data processing method, etc., without starting from scratch, and the effects after each adjustment can be quickly verified. This provides strong support for accelerating the experiment and R & D process and shortens the cycle from problem definition to solution verification; by optimizing the calculation process, the system can use computing resources more efficiently and reduce unnecessary resource waste. Utilizing hardware acceleration such as GPUs and TPUs, combined with distributed computing, can also improve the processing capacity, enabling large-scale computing tasks to be successfully completed.

[0057] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention is also intended to include these modifications and variations.

Claims

1. A fast prediction method for unsteady flow fields based on a cross-fidelity neural network, characterized in that, The method includes: S1. Determine the fluid region to be simulated, perform mesh generation, and set initial fluid boundary conditions; S2. Based on the above mesh generation and boundary conditions, perform low-fidelity and high-fidelity CFD calculations respectively; S3. Combine a convolutional neural network autoencoder and a long short-term memory network to reduce the dimension and extract features of the flow field data; S4. Construct a cross-fidelity neural network; S5. Judge the error of the prediction result and check whether the accuracy requirement is met; S6. Integrate the above steps into a complete end-to-end flow field prediction framework; output the high-fidelity flow field prediction result.

2. The fast prediction method of unsteady flow field based on cross-fidelity neural network according to claim 1, wherein The said S1 includes: S11. Determine the exact fluid region to be simulated; S12. Analyze the characteristics of the fluid region and perform mesh generation based on the analysis results; S13. Set the velocity boundary conditions according to the characteristics of the fluid region; S14. Select a turbulence model.

3. The rapid prediction method for unsteady flow fields based on a cross-fidelity neural network according to claim 1, wherein The said S2 includes: S21. Select a CFD solver, set the calculation parameters of the solver according to the mesh generation and boundary conditions, and output the basic characteristics of the flow field; S22. Perform high-precision CFD calculations on the fine mesh; optimize the use of computing resources with parallel computing.

4. The rapid prediction method of unsteady flow field based on cross-fidelity neural network according to claim 1, characterized in that The said S3 includes: S31. Preprocess the data; and design the network structure of the CAE; S32. Train the CAE using the low-fidelity flow field data, extract the spatial multi-scale features of the flow field using the trained CAE, and compress them into low-dimensional latent vectors; S33. Arrange the flow field data in time series as the input of the LSTM; train the LSTM network; S34. Extract the time features of the flow field using the trained LSTM.

5. The fast prediction method for unsteady flow fields based on a cross-fidelity neural network according to claim 4, wherein The said S32 includes: S321. Divide the preprocessed and enhanced low-fidelity flow field data into a training set, a validation set, and a test set; S322. Balance the quantity of different types of flow field data by undersampling; update the parameters of the CAE network based on the stochastic gradient descent method; S323. Adjust the learning rate and batch size of the optimization algorithm; during the training process, regularly calculate the evaluation metrics on the validation set to monitor the training effect of the network; S324. Apply the trained CAE network to the low-fidelity flow field data, extract the spatial multi-scale features of the flow field, and compress them into low-dimensional latent vectors; analyze the distribution law of different flow field states in the latent vector space; S325. If the dimension of the latent vector is still high, use a dimensionality reduction algorithm to further reduce the dimension of the latent vector; at the same time, perform clustering analysis on the reduced-dimensional latent vector to cluster similar flow field states together; S326. Generate adversarial samples for the CAE network; evaluate the robustness of the network by generating adversarial samples.

6. The rapid prediction method for unsteady flow fields based on a cross-fidelity neural network according to claim 5, characterized in that The said S324 includes: Select some low-fidelity flow field data, analyze the known spatial features, extract features through the CAE network, compare with the analysis results to verify the effectiveness of the network in extracting features; during the comparison process, judge the potential correlation between the energy dissipation rate and the analysis results and the features extracted by the CAE; Extract features from different layers respectively; and analyze the influence of the energy dissipation rate during the feature extraction process at different levels; Adopt a feature fusion method to fuse the features extracted from different levels; according to the importance of the features at different levels and the distribution of the energy dissipation rate, adjust the weights to obtain comprehensive spatial multi-scale features; Analyze the correlation between the extracted features; and by calculating the correlation coefficient matrix between the features, find out the feature combinations with higher correlation; combined with the distribution of the energy dissipation rate, explore the relationship between feature correlation and energy dissipation rate; Input the extracted spatial multi-scale features of the flow field into the encoder part of the CAE network, and map the high-dimensional features to the low-dimensional latent vector space; Calculate the gradient of the mapping function through the backpropagation algorithm, and analyze the contribution degree of different features to the latent vector.

7. The rapid prediction method for unsteady flow fields based on a cross-fidelity neural network according to claim 5, wherein The S325 includes: Adopt a dimensionality reduction algorithm to reduce the dimensionality of the latent vector to two or three dimensions and perform visualization; through the visualization results, observe the distribution pattern of the latent vector space, analyze the differences in the distribution statistical features of the latent vectors corresponding to different flow field states, and obtain the distribution law of the latent vector space; Perform clustering analysis on the latent vectors, and cluster the latent vectors corresponding to similar flow field states together; establish a regression model between the flow field state parameters and the latent vectors; Distinguish normal flow fields and abnormal flow fields according to the distribution characteristics of the latent vector space; Analyze the evolution law of different flow field states in the latent vector space; map the latent vector space to the physical parameters of the flow field; Based on the association between the latent vector space and the physical parameters, verify the physical laws of the flow field; according to the distribution statistical features of the latent vector space, construct a statistics-based anomaly detection model; Adopt a machine learning algorithm to construct an anomaly detection model; use the latent vectors corresponding to the normal flow field to train the model, and detect new latent vectors to determine whether they are abnormal; Analyze the detected abnormal latent vectors and identify their corresponding abnormal types.

8. The rapid prediction method of unsteady flow field based on cross-fidelity neural network according to claim 1, characterized in that The S4 includes: S41. Design three fully connected layers; S42. Integrate the low-fidelity flow field data, preprocessing parameters, and the extracted spatial and temporal features into input data; S43. Define a loss function; S44. Select an optimization algorithm; S45. Apply the trained cross-fidelity neural network to the new low-fidelity simulation results to obtain the corresponding high-fidelity latent vectors; S46. Reconstruct the high-fidelity latent vectors into high-precision flow fields.

9. The fast prediction method for unsteady flow fields based on a cross-fidelity neural network according to claim 1, characterized in that The S5 includes: S51. Calculate the error between the prediction result and the actual result; S52. According to the error analysis result, increase the sample points in the key area; S53. Refine the grid in the area with larger errors; S54. Adjust the architecture and parameters of the neural network.

10. The rapid prediction method for unsteady flow fields based on a cross-fidelity neural network according to claim 1, wherein The S6 includes: S61. Integrate all the above steps into a complete end-to-end flow field prediction framework; S62. Write an automated script to execute the full automation process from input to output; and monitor the running status of the automation process in real time.

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