Low-order precision structured grid steady-state flow field correction method based on data driving

Abstract

The invention relates to a low-order precision structured grid steady-state flow field correction method based on data driving. The method comprises the steps that firstly, a flow field data set is acquired and preprocessed; then, a flow field correction model is constructed based on the convolutional neural network, and the model comprises a condition parameter expansion layer, a multistage convolutional coding layer, a residual feature fusion layer, a random inactivation regularization layer and a flow field residual projection layer; then, setting a model training target, and training the flow field correction model by adopting the preprocessed flow field data set based on the model training target; and finally, inputting to-be-corrected flow field data into the trained flow field correction model to obtain a target high-precision flow field. That is to say, numerical errors introduced by low-order discretization are directly quantized and compensated through a data driving method. The error of low-precision flow field calculation can be remarkably reduced while the low-order format calculation efficiency is kept, and the feasibility of a data driving method in format precision correction is verified.

Description

Technical Field

[0001] The present application relates to the technical field of low-order precision flow field correction, and in particular to a data-driven low-order precision structured grid steady-state flow field correction method. Background Art

[0002] Computational Fluid Dynamics (CFD) is a core tool for modern industrial design. Its high-fidelity simulation capabilities are crucial for accurately predicting complex flow fields such as turbulence in aircraft engine combustion chambers and transonic shock waves in aircraft. They can significantly reduce the cost of physical experiments and shorten the design cycle. The demand for high-fidelity simulation is reflected in two aspects: first, the numerical format must capture multi-scale physical phenomena such as shock waves and boundary layer transitions; second, the mesh in key areas (such as near-wall areas and shock surfaces) must maintain sufficient spatial resolution. Although data-driven methods have provided new insights for CFD, current high-fidelity simulations still face significant computational cost bottlenecks, especially in multi-scale, multi-physics field coupling scenarios.

[0003] Existing methods mainly attempt to make breakthroughs through three types of paths. 1. High-precision format optimization of traditional CFD formats: High-order formats (such as the WENO (Weighted Essentially Non-Oscillatory) series) improve accuracy by improving stability and multi-scale adaptability, but have problems such as complex implementation, high computational overhead, and mesh sensitivity, which limit engineering applications. 2. Reduced-Order Modeling (ROM): ROM methods based on projection or deep learning can compress computational costs, but they are prone to instability in scenarios with strong nonlinearity or drastic parameter changes, and lack physical constraints, making them difficult to apply to high reliability requirements. 3. Super-resolution reconstruction of flow fields: Using deep learning models such as CNN to reconstruct high-fidelity flow fields from coarse grids can improve spatial resolution, but it cannot effectively correct format errors such as numerical dissipation and dispersion. Non-physical phenomena may still exist under high-density grids.

[0004] Traditional CFD methods face a dilemma between efficiency and accuracy: high-order formats consume a significant amount of computational time, while low-order formats rely on empirical a posteriori corrections, making them difficult to meet engineering requirements. Existing technologies have yet to achieve an effective balance between high-fidelity simulation and computational efficiency.

[0005] Therefore, in related technologies, there is an urgent need for a new method that takes into account both high-precision prediction and low resource consumption to break through the application bottleneck in complex engineering scenarios. Summary of the Invention

[0006] Based on this, it is necessary to provide a data-driven low-order precision structured grid steady-state flow field correction method that can balance high-precision prediction and low resource consumption to address the above technical problems.

[0007] In a first aspect, the present application provides a data-driven low-order precision structured grid steady-state flow field correction method. The method comprises:

[0008] Obtain flow field dataset and perform preprocessing;

[0009] A flow field correction model is constructed based on a convolutional neural network, wherein the model includes a conditional parameter expansion layer, a multi-level convolutional coding layer, a residual feature fusion layer, a random inactivation regularization layer, and a flow field residual projection layer;

[0010] Setting a model training target, and based on the model training target, using the preprocessed flow field data set to train the flow field correction model;

[0011] The flow field data to be corrected is input into the trained flow field correction model to obtain the target high-precision flow field.

[0012] Optionally, in one embodiment of the present application, the preprocessing includes:

[0013] The pressure values ​​of low-order flow field data are averaged.

[0014] Optionally, in one embodiment of the present application, the preprocessing further includes:

[0015] The flow field data set is normalized to eliminate magnitude differences.

[0016] Optionally, in one embodiment of the present application, the conditional parameter expansion layer broadcasts the conditional parameters as spatially distributed conditional tensors, the residual feature fusion layer alleviates gradient vanishing through identity mapping, and the flow field residual projection layer achieves high-order calibration of low-order solutions through vector correction.

[0017] Optionally, in one embodiment of the present application, the model training objective is to determine the minimum L2 norm between the target high-precision flow field and the flow field correction model output.

[0018] Optionally, in one embodiment of the present application, the training of the flow field correction model using the preprocessed flow field dataset based on the model training objective includes:

[0019] The mean square error is used as the loss function, and the back propagation method is used to train the flow field correction model.

[0020] Optionally, in one embodiment of the present application, the method further includes:

[0021] The coefficient of determination was used to evaluate the prediction performance of the flow field correction model.

[0022] In a second aspect, the present application also provides a data-driven low-order precision structured grid steady-state flow field correction device. The device comprises:

[0023] Data collection and preprocessing module, used to obtain flow field data sets and perform preprocessing;

[0024] A flow field correction model construction module is used to construct a flow field correction model based on a convolutional neural network. The model includes a conditional parameter expansion layer, a multi-level convolutional coding layer, a residual feature fusion layer, a random inactivation regularization layer, and a flow field residual projection layer.

[0025] A flow field correction model training module is used to set a model training target and, based on the model training target, train the flow field correction model using the preprocessed flow field data set;

[0026] The flow field correction module is used to input the flow field data to be corrected into the trained flow field correction model to obtain the target high-precision flow field.

[0027] In a third aspect, the present application further provides a computer device comprising a memory and a processor, wherein the memory stores a computer program and the processor executes the steps of the method described in each of the above embodiments.

[0028] In a fourth aspect, the present application further provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in each of the above embodiments.

[0029] The above-mentioned data-driven, low-order precision structured grid steady-state flow field correction method first obtains and preprocesses a flow field dataset. Next, a flow field correction model is constructed based on a convolutional neural network. The model includes a conditional parameter expansion layer, a multi-level convolutional coding layer, a residual feature fusion layer, a random dropout regularization layer, and a flow field residual projection layer. Next, a model training target is set, and based on this target, the flow field correction model is trained using the preprocessed flow field dataset. Finally, the flow field data to be corrected is input into the trained flow field correction model to obtain the target high-precision flow field. In other words, the original variables (velocity, pressure, and density) output by the low-order format are used as input, and the residual field between them and the high-order reference solution is predicted through supervised learning, thereby achieving point-by-point correction of the flow field accuracy. This data-driven approach directly quantifies and compensates for the numerical errors introduced by the low-order discretization. While maintaining the computational efficiency of the low-order format, it significantly reduces the errors in the low-precision flow field calculation, validating the feasibility of the data-driven approach for format accuracy correction. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1FIG1 is an application environment diagram of a data-driven low-order precision structured grid steady-state flow field correction method in one embodiment;

[0031] Figure 2 1 is a flow chart of a method for correcting a steady-state flow field based on a data-driven low-order precision structured grid in one embodiment;

[0032] Figure 3 A schematic diagram of parameters for flow field data processing in one embodiment;

[0033] Figure 4 A schematic structural diagram of a flow field correction model in one embodiment;

[0034] Figure 5 A schematic diagram of a grid showing a square cavity case in an embodiment;

[0035] Figure 6 A schematic diagram showing a comparison of comprehensive fitting degrees of a square cavity case in an embodiment;

[0036] Figure 7 A schematic diagram showing the comparison of flow field results for a square cavity case in an embodiment;

[0037] Figure 8 A schematic diagram of a grid for a NACA0012 case in one embodiment;

[0038] Figure 9 Schematic diagram of comprehensive fit comparison of NACA0012 case in one embodiment;

[0039] Figure 10 A schematic diagram of physical quantity difference of a NACA0012 case in one embodiment;

[0040] Figure 11 A schematic diagram showing the flow field comparison results of a NACA0012 case in one embodiment;

[0041] Figure 12 A schematic diagram showing a comparison of pressure coefficients for a NACA0012 case in one embodiment;

[0042] Figure 13 1 is a structural block diagram of a data-driven low-order precision structured grid steady-state flow field correction device in one embodiment;

[0043] Figure 14 FIG. 1 is a diagram showing the internal structure of a computer device in one embodiment. DETAILED DESCRIPTION

[0044] In order to make the purpose, technical solutions and advantages of this application more clear, the following further describes this application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0045] The data-driven low-order precision structured grid steady-state flow field correction method provided in the embodiment of the present application can be applied to Figure 1 In the application environment shown, the terminal communicates with the server through the network. The data storage system can store data that the server needs to process. The data storage system can be integrated on the server or placed on the cloud or other network servers. The terminal can be, but is not limited to, various personal computers, laptops, smartphones, tablets, IoT devices, and portable wearable devices. IoT devices can be smart speakers, smart TVs, smart air conditioners, smart car devices, etc. Portable wearable devices can be smart watches, smart bracelets, head-mounted devices, etc. The server can be implemented as a standalone server or a server cluster consisting of multiple servers.

[0046] In one embodiment, Figure 2 As shown in the figure, a data-driven low-order precision structured grid steady-state flow field correction method is provided. Figure 1 The following steps are used as an example to illustrate the server in the example:

[0047] S201: Obtain a flow field dataset and perform preprocessing.

[0048] In the embodiment of the present application, first, a diversified data set is obtained, and based on the Navier-Stokes equations and turbulence model, high- and low-order format paired flow field data are generated at different Reynolds numbers, Mach numbers, and angles of attack. Among them, the low-precision flow field data set is S L ∈R H×W×d , where H is the computational domain height, W is the computational domain width, and d is the physical quantity dimension (density ρ, velocity u, v, pressure p); the high-precision flow field dataset is S H ∈R H×W×d . And preprocess the flow field data set to ensure numerical stability. Figure 3 The figure shows the parameters for flow field data processing.

[0049] Specifically, in one embodiment of the present application, the preprocessing includes:

[0050] The pressure values ​​of low-order flow field data are averaged.

[0051] In one embodiment of the present application, the pressure value parameters of the low-order flow field data are averaged to eliminate the gradient dominance problem caused by the difference in the variation range of the parameter pressure value p and other parameters during the neural network training process. Specifically, the average value of the pressure value p corresponding to each condition parameter (such as different Mach numbers) in the training set is first calculated, and the missing conditions are supplemented by linear interpolation to obtain the complete pressure data distribution p. filled , and then calculate the global arithmetic mean of the distribution And based on this, construct the averaging factor p′, that is:

[0052]

[0053] The final expression for completing the parameter averaging preprocessing operation is:

[0054]

[0055] After averaging, The nonlinear attenuation characteristics of are transformed into an approximately linear distribution, which matches the magnitude of the p, u, and v parameters.

[0056] In this embodiment, by averaging the pressure values ​​of low-order flow field data, the amplitude variation of the pressure variable under different working conditions is effectively reduced, and its participation in the training process is improved, thereby enhancing the model's adaptability to multiple physical conditions.

[0057] In one embodiment of the present application, the preprocessing further includes:

[0058] The flow field data set is normalized to eliminate magnitude differences.

[0059] In one embodiment of the present application, a normalization operation is performed on the flow field data set to eliminate the magnitude differences between different physical quantities. Specifically, by performing a linear transformation on each physical quantity and mapping it to a unified standard range [0,1], the magnitude differences between different physical quantities are eliminated and the model convergence is accelerated, that is:

[0060]

[0061] Where x represents the original physical quantity, x min Represents the global minimum value of the physical quantity (pre-calculated), x max Indicates the global maximum value (pre-calculated) of the physical quantity, x norm It is the normalized value, ranging from [0,1].

[0062] In this embodiment, the normalized data distribution is closer to the standard normal distribution, which helps stabilize the gradient optimization algorithm. Normalization also eliminates scale differences between different physical quantities, preventing certain features from dominating the loss function calculation due to excessively large values.

[0063] S203: Constructing a flow field correction model based on a convolutional neural network, wherein the model includes a conditional parameter expansion layer, a multi-level convolutional coding layer, a residual feature fusion layer, a random inactivation regularization layer, and a flow field residual projection layer.

[0064] In the embodiment of the present application, a flow field correction model is constructed according to a machine learning method, and the machine learning method is a convolutional neural network CNN. The CNN model adopts an encoder-decoder architecture and realizes flow field correction through conditional parameter fusion and residual learning. Figure 4 As shown in the figure, the network layer of the model is decomposed into a conditional parameter expansion layer, a multi-level convolutional coding layer, a residual feature fusion layer, a random inactivation regularization layer, and a flow field residual projection layer.

[0065] Specifically, in one embodiment of the present application, the conditional parameter expansion layer broadcasts the conditional parameters as spatially distributed conditional tensors, the residual feature fusion layer alleviates gradient vanishing through identity mapping, and the flow field residual projection layer achieves high-order calibration of low-order solutions through vector correction.

[0066] In one embodiment of the present application, the conditional parameter expansion layer broadcasts the conditional parameter α (Reynolds number, Mach number) as a spatially distributed conditional tensor, achieving modal mixing of flow field characteristics and operating parameters, which can enhance the model's sensitivity to changes in conditional parameters. The conditional parameter distribution and vector concatenation are represented as follows:

[0067]

[0068] Among them, α represents the conditional parameters (such as Reynolds number Re, Mach number Ma), which characterizes the flow conditions. 1×H×W A tensor of all ones, whose shape matches the spatial dimensions of the flow grid (height H, width W), used to expand scalar conditional parameters into spatial distributions. represents a broadcast multiplication, which evenly distributes the value of α to all spatial locations in the flow field, forming a conditional tensor aligned with the flow field characteristics. X represents the input flow field feature map, which contains the spatial distribution of flow physical quantities (such as velocity, pressure, and density). After the mixed features are expressed, the position value of each newly added channel is α, which enables the model to perceive both the local flow field characteristics and the global working conditions.

[0069] The multi-level convolutional coding layer is designed with a convolution kernel size parameter of 3, and zero padding is used to keep the spatial resolution consistent. The channel expansion rate C (l) / C(l-1)=2 (except the first layer), so that the hierarchical characteristics correspond to the multi-scale structure of the flow field (boundary layer velocity gradient → shock wave pressure jump).

[0070] Residual feature fusion alleviates gradient vanishing through identity mapping and can focus on learning high-frequency components of flow field errors (such as shock wave oscillations). The specific expression is as follows:

[0071] F (k) =F (k-1) +G(F (k-1) )

[0072] Among them, F (k) represents the output feature map of the kth layer, and G represents the residual function.

[0073] The random dropout regularization layer randomly blocks 50% of neurons through Bernoulli sampling, forcing the network to build a robust feature representation. This can suppress overfitting to the specific grid distribution of the training set and improve the generalization ability across working conditions. The specific description is as follows:

[0074] F (L-1) =Dropout(F (L-1) ,p=0.5)

[0075] Among them, F (L-1) The output feature map of the L-1 layer contains hidden feature representations of flow field physical quantities (such as velocity and pressure). Dropout represents a random deactivation function that randomly masks the neurons in the input feature map with probability p = 0.5.

[0076] The residual projection layer of the flow field constructs the residual field of density ρ, velocity u,v, and pressure p, and realizes the high-order calibration of the low-order solution through the W vector correction:

[0077]

[0078] in, Represents the corrected high-order flow field residual prediction value, W (L) Represents the learnable projection matrix of the Lth layer, * represents the linear transformation operation, and the low-order features are projected into high-order residual fields through matrix multiplication to complete the residual modeling from feature space to physical quantities.

[0079] The local receptive field mechanism of CNN can accurately capture the characteristics of flow field parameters showing drastic gradient changes and exponential decay in locations such as shock waves and separation zones. In addition, the CFD structured grid is essentially a regular topological tensor, which perfectly matches the raster data processing characteristics of CNN.

[0080] S205: Setting a model training target, and based on the model training target, using the preprocessed flow field data set to train the flow field correction model.

[0081] In an embodiment of the present application, a training target of the model is set, and based on the training target, a flow field correction model is constructed by training the preprocessed flow field dataset, wherein the low-precision flow field dataset is used as input data and the high-precision flow field dataset is used as supervised output data. Through training, the flow field correction model can correct the input low-precision flow field dataset to a high-precision flow field dataset that is almost close to or the same as the supervised output data.

[0082] In one embodiment of the present application, the model training goal is to determine the minimum L2 norm between the target high-precision flow field and the flow field correction model output.

[0083] In one embodiment of the present application, the model training goal is to train the model to predict the residual field F(S L ;ω), that is, to find the minimum L2 norm between the target high-precision flow field and the output of the flow field correction model, so that the low-order solution can approach the high-order solution after superimposing the residual, that is:

[0084]

[0085] Among them, S L is a low-precision flow field dataset, S H is a high-precision flow field dataset. When the model parameter ω is optimized, it can be Realize flow field reconstruction.

[0086] In one embodiment of the present application, training the flow field correction model using the preprocessed flow field dataset based on the model training objective includes:

[0087] The mean square error is used as the loss function, and the back propagation method is used to train the flow field correction model.

[0088] In one embodiment of the present application, the mean square error (MSE) is used as the loss function, and the back propagation method is performed in the model training. The initial learning rate uses a low learning rate to ensure fine correction. When the change in the loss function is less than a preset threshold, it indicates that the loss function has converged and the model training is completed. The loss function calculation formula is as follows:

[0089]

[0090] in, As the standard high-precision flow field data for supervision, is the high-precision flow field data for model correction, B is the batch size, that is, the number of flow field samples input for a single training, b is the batch index, indicating the position of the current sample in the batch, H is the computational domain height, h is the height index, W is the computational domain width, w is the width index, d is the physical quantity dimension, and c is the physical quantity index.

[0091] In one embodiment of the present application, the method further includes:

[0092] The coefficient of determination was used to evaluate the prediction performance of the flow field correction model.

[0093] In one embodiment of the present application, the coefficient of determination (R 2 ) is used as the core indicator to evaluate the prediction performance of the flow field correction model. 2 It can intuitively reflect the correlation between the predicted value and the true value. The calculation method is as follows: For each physical quantity (density ρ, velocity component u, v, pressure p), the channel level R is calculated independently. 2 :

[0094]

[0095] Global R 2 Through each channel R 2 The arithmetic mean of :

[0096]

[0097] The final model predicts performance through the global coefficient of determination It is measured by approaching the theoretical optimal value 1.

[0098] S207: Input the flow field data to be corrected into the trained flow field correction model to obtain the target high-precision flow field.

[0099] In the embodiment of the present application, the flow field data to be corrected is input into the trained flow field correction model, and the corrected target high-precision flow field is output.

[0100] In one embodiment of the present application, a precision correction experiment was conducted on a two-dimensional top cover driven square cavity flow. An autoencoder was used for simulation, and a vertex-centered scheme was adopted. The grid was a 20x20 structured grid with data accuracy of 3rd order and 5th order, respectively. The top cover driven square cavity flow used a 20x20 two-dimensional structured grid, such as Figure 5 As shown; Finally, the numerical simulation is carried out with the Reynolds number between 100 and 3000 as the conditional parameter. The comprehensive fit comparison obtained by the test set is as follows: Figure 6 As shown in Figure 2, it can be seen that the fitting degree has been significantly improved after training, and the low-order accuracy has reached a level comparable to the high-order accuracy. The pressure, density, and velocity flow field comparisons at the same Reynolds number under different accuracies are obtained (3rd order accuracy o3 / after training / 5th order accuracy o5). Figure 7 As shown in the figure, the effect of precision correction can be intuitively seen through the cloud map, which has good correction capabilities.

[0101] In one embodiment of the present application, the NACA0012 airfoil is used as the research object, and the accuracy correction experiment is carried out based on the HOSTA program. The specific configuration is as follows: Grid system: A structured grid is generated using a three-dimensional to two-dimensional conversion scheme (such as Figure 8 ), mesh refinement was implemented along the normal direction of the object surface, ultimately obtaining a 98×98 grid-centric grid. The numerical method was based on the finite volume method (FVM) to construct a discrete format. Finally, numerical simulations were performed using Mach numbers between 0.3 and 0.85 as conditional parameters. The R2 comprehensive fit comparison chart with Mach number as the conditional parameter was obtained through evaluation on the test set. Figure 9 As shown in the figure; the difference diagram of physical quantities under different accuracies and Mach numbers (the difference between low precision and the flow field after training and high precision) is compared as shown in the figure. Figure 10 As shown, it can be clearly seen that the improvement effect after training; the pressure, density, and velocity flow fields at the same Mach number under different accuracies (respectively 2nd order accuracy o2 / after training / 3rd order accuracy o3) are as follows Figure 11 As shown in the figure; the pressure coefficient comparison of the same Mach number under different accuracies is as follows: Figure 12 As shown, it can be seen that the pressure coefficient curve after training correction obviously fits the high-order accuracy level.

[0102] In the above-mentioned data-driven, low-order precision structured grid steady-state flow field correction method, a flow field dataset is first acquired and preprocessed. Next, a flow field correction model is constructed based on a convolutional neural network. The model includes a conditional parameter expansion layer, a multi-level convolutional coding layer, a residual feature fusion layer, a random dropout regularization layer, and a flow field residual projection layer. A model training target is then set, and based on this target, the flow field correction model is trained using the preprocessed flow field dataset. Finally, the flow field data to be corrected is input into the trained flow field correction model to obtain the target high-precision flow field. In other words, the original variables (velocity, pressure, and density) output by the low-order format are used as input, and the residual field between them and the high-order reference solution is predicted through supervised learning, thereby achieving point-by-point correction of the flow field accuracy. This data-driven approach directly quantifies and compensates for the numerical errors introduced by the low-order discretization. This method significantly reduces the errors in low-precision flow field calculations while maintaining the computational efficiency of the low-order format, validating the feasibility of the data-driven approach for format accuracy correction.

[0103] It should be understood that, although the various steps in the flowcharts involved in the various embodiments described above are displayed in sequence according to the instructions of the arrows, these steps are not necessarily executed in sequence in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order restriction on the execution of these steps, and these steps can be executed in other orders. Moreover, at least a portion of the steps in the flowcharts involved in the various embodiments described above can include multiple steps or multiple stages, and these steps or stages are not necessarily executed and completed at the same time, but can be executed at different times, and the execution order of these steps or stages is not necessarily to be carried out in sequence, but can be executed in turn or alternately with other steps or at least a portion of steps or stages in other steps.

[0104] Based on the same inventive concept, the embodiments of the present application also provide a data-driven low-order precision structured grid steady-state flow field correction device for implementing the above-mentioned data-driven low-order precision structured grid steady-state flow field correction method. The implementation solution provided by this device is similar to the implementation solution described in the above-mentioned method. Therefore, the specific limitations of one or more embodiments of the data-driven low-order precision structured grid steady-state flow field correction device provided below can be found in the above-mentioned limitations of the data-driven low-order precision structured grid steady-state flow field correction method, and will not be repeated here.

[0105] In one embodiment, Figure 13 As shown, a data-driven low-order precision structured grid steady-state flow field correction device 1300 is provided, comprising: a data collection and preprocessing module 1301, a flow field correction model construction module 1303, a flow field correction model training module 1305 and a flow field correction module 1307, wherein:

[0106] The data collection and preprocessing module 1301 is used to obtain flow field data sets and perform preprocessing.

[0107] The flow field correction model construction module 1303 is used to construct a flow field correction model based on a convolutional neural network. The model includes a conditional parameter expansion layer, a multi-level convolutional coding layer, a residual feature fusion layer, a random inactivation regularization layer, and a flow field residual projection layer.

[0108] The flow field correction model training module 1305 is used to set a model training target, and based on the model training target, train the flow field correction model using the preprocessed flow field data set.

[0109] The flow field correction module 1307 is used to input the flow field data to be corrected into the trained flow field correction model to obtain the target high-precision flow field.

[0110] In one embodiment of the present application, the data collection and preprocessing module is further configured to:

[0111] The pressure values ​​of low-order flow field data are averaged.

[0112] In one embodiment of the present application, the data collection and preprocessing module is further configured to:

[0113] The flow field data set is normalized to eliminate magnitude differences.

[0114] In one embodiment of the present application, the conditional parameter expansion layer broadcasts the conditional parameters as spatially distributed conditional tensors, the residual feature fusion layer alleviates gradient vanishing through identity mapping, and the flow field residual projection layer achieves high-order calibration of low-order solutions through vector correction.

[0115] In one embodiment of the present application, the model training goal is to determine the minimum L2 norm between the target high-precision flow field and the flow field correction model output.

[0116] In one embodiment of the present application, the flow field correction model training module is further used to:

[0117] The mean square error is used as the loss function, and the back propagation method is used to train the flow field correction model.

[0118] The data-driven low-order precision structured grid steady-state flow field correction device further includes a model evaluation module. In one embodiment of the present application, the model evaluation module is used to:

[0119] The coefficient of determination was used to evaluate the prediction performance of the flow field correction model.

[0120] Each module in the aforementioned data-driven low-order precision structured grid steady-state flow field correction device can be implemented in whole or in part through software, hardware, or a combination thereof. Each module can be embedded in or independent of a processor in a computer device in the form of hardware, or can be stored in a computer device memory in the form of software, so that the processor can call and execute the corresponding operations of each module.

[0121] In one embodiment, a computer device is provided. The computer device may be a terminal, and its internal structure diagram may be as follows: Figure 14As shown. The computer device includes a processor, a memory, a communication interface, a display screen and an input device connected via a system bus. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The communication interface of the computer device is used to communicate with an external terminal in a wired or wireless manner, and the wireless manner can be achieved through WIFI, a mobile cellular network, NFC (near field communication) or other technologies. When the computer program is executed by the processor, a data-driven low-order precision structured grid steady-state flow field correction method is implemented. The display screen of the computer device can be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer device can be a touch layer covering the display screen, or a button, trackball or touchpad provided on the computer device housing, or an external keyboard, touchpad or mouse.

[0122] Those skilled in the art will understand that Figure 14 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than shown in the figure, or combine certain components, or have a different component arrangement.

[0123] In one embodiment, a computer device is provided, including a memory and a processor. The memory stores a computer program, and the processor implements the steps in the above method embodiments when executing the computer program.

[0124] In one embodiment, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the steps in the above-mentioned method embodiments are implemented.

[0125] In one embodiment, a computer program product is provided, including a computer program, which implements the steps in the above method embodiments when executed by a processor.

[0126] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties.

[0127] Those skilled in the art will appreciate that all or part of the processes in the above-mentioned embodiment methods can be implemented by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, database or other media used in the embodiments provided in this application may include at least one of non-volatile and volatile memory. Non-volatile memory may include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory may include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM). The database involved in the various embodiments provided herein may include at least one of a relational database and a non-relational database. Non-relational databases may include, but are not limited to, distributed databases based on blockchains. The processor involved in the various embodiments provided herein may be, but are not limited to, a general-purpose processor, a central processing unit, a graphics processing unit, a digital signal processor, a programmable logic unit, a data processing logic unit based on quantum computing, and the like.

[0128] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0129] The above-described embodiments merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present application. It should be noted that a person of ordinary skill in the art may make various modifications and improvements without departing from the spirit of the present application, and these modifications and improvements fall within the scope of protection of the present application. Therefore, the scope of protection of the present application shall be determined by the appended claims.

Claims

1. A data-driven low-order precision structured grid steady-state flow field correction method, characterized in that: The method comprises: Obtain flow field dataset and perform preprocessing; A flow field correction model is constructed based on a convolutional neural network, wherein the model includes a conditional parameter expansion layer, a multi-level convolutional coding layer, a residual feature fusion layer, a random inactivation regularization layer, and a flow field residual projection layer; Setting a model training target, and based on the model training target, using the preprocessed flow field data set to train the flow field correction model; The flow field data to be corrected is input into the trained flow field correction model to obtain the target high-precision flow field.

2. The data-driven low-order precision structured grid steady-state flow field correction method according to claim 1 is characterized in that: The pretreatment includes: The pressure values ​​of low-order flow field data are averaged.

3. The data-driven low-order precision structured grid steady-state flow field correction method according to claim 1 is characterized in that: The pre-processing further comprises: The flow field data set is normalized to eliminate magnitude differences.

4. The data-driven low-order precision structured grid steady-state flow field correction method according to claim 1 is characterized in that: The conditional parameter expansion layer broadcasts the conditional parameters as spatially distributed conditional tensors, the residual feature fusion layer alleviates gradient vanishing through identity mapping, and the flow field residual projection layer achieves high-order calibration of low-order solutions through vector correction.

5. The data-driven low-order precision structured grid steady-state flow field correction method according to claim 1 is characterized in that: The model training goal is to determine the minimum L2 norm between the target high-precision flow field and the flow field correction model output.

6. The data-driven low-order precision structured grid steady-state flow field correction method according to claim 1 is characterized in that: The method of training the flow field correction model based on the model training objective and using the pre-processed flow field data set includes: The mean square error is used as the loss function, and the back propagation method is used to train the flow field correction model.

7. The data-driven low-order precision structured grid steady-state flow field correction method according to claim 1 is characterized in that: The method further comprises: The coefficient of determination was used to evaluate the prediction performance of the flow field correction model.

8. A data-driven low-order precision structured grid steady-state flow field correction device, characterized in that: The device comprises: Data collection and preprocessing module, used to obtain flow field data sets and perform preprocessing; A flow field correction model construction module is used to construct a flow field correction model based on a convolutional neural network. The model includes a conditional parameter expansion layer, a multi-level convolutional coding layer, a residual feature fusion layer, a random inactivation regularization layer, and a flow field residual projection layer. A flow field correction model training module is used to set a model training target and, based on the model training target, train the flow field correction model using the preprocessed flow field data set; The flow field correction module is used to input the flow field data to be corrected into the trained flow field correction model to obtain the target high-precision flow field.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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