Airfoil flow field prediction method based on multi-task learning

Abstract

The invention provides an airfoil flow field prediction method based on multi-task learning, and the method comprises the steps: firstly building an airfoil flow field prediction model based on multi-task learning, which comprises an encoder, a backbone network and a multi-head decoder; then training the established model by using an airfoil flow field data set and adopting an optimization strategy based on multi-task learning; and finally, performing geometric parameterization and grid generation processing on an airfoil which actually needs flow field prediction to obtain standardized airfoil flow field data, and inputting the airfoil flow field data into the trained airfoil flow field prediction model for prediction to obtain full flow field physical quantity distribution and lift-drag coefficient information. According to the method, a multi-task loss optimization strategy is used in the prediction model training process, so that the problem of conflict between airfoil profile surface loss and volume loss optimization can be effectively solved, and then the construction of an airfoil profile proxy model and the accurate prediction of flow field information and aerodynamic parameters are realized.

Description

Technical Field

[0001] The present invention relates to the fields of fluid mechanics and deep learning, and specifically to an airfoil flow field prediction method based on multi-task learning. Background Art

[0002] After decades of development, the discipline of fluid mechanics has formed a research method system integrating theoretical analysis, experimental research, and numerical simulation. The collaborative innovation of these three aspects has significantly promoted the development of aircraft aerodynamic design technology. In aerodynamic design practice, although experimental methods (such as wind tunnel experiments and flight tests) can provide high-confidence data, they have the inherent limitations of long test cycles and high economic costs. Although theoretical fluid mechanics can support preliminary design by obtaining analytical solutions through the establishment of simplified mathematical models, its overly simplified physical assumptions often lead to significant deviations between the predicted results and the actual complex flows. In this context, Computational Fluid Dynamics (CFD), with its visualization capabilities for the spatio-temporal evolution characteristics of multiple physical quantities in the flow field, engineering applicability for rapid iteration of design parameters, and numerical simulation advantages under extreme working conditions, has become a key enabling technology for modern aerodynamic design, demonstrating significant value in reducing R & D costs, improving safety margins, and expanding the design space. However, the CFD method still faces the bottleneck constraint of huge computational resource requirements in the refined simulation of real working conditions.

[0003] This limitation is particularly prominent in the aerodynamic optimization design of airfoils. The airfoil design is essentially a multi-objective topology optimization problem of maximizing lift-drag characteristics and minimizing cruise drag. Traditional optimization paradigms rely on high-precision CFD numerical simulations for design iteration. Although high-quality design solutions can be obtained, the high-performance computing resources required for a single iteration severely restrict the global exploration efficiency of the design space. To break through this limitation, constructing an efficient surrogate model has become a key research direction. Traditional reduced-order modeling methods (such as Proper Orthogonal Decomposition - POD, Dynamic Mode Decomposition - DMD, etc.) are limited by the assumption of a fixed geometric configuration and have the defect of reduced modeling accuracy in the scenario of geometric parameter changes.

[0004] The CFD surrogate model based on deep learning shows breakthrough advantages: its deep neural network architecture has strong representation capabilities for complex non-linear fluid-structure coupling relationships, the data-driven modeling paradigm supports the efficient processing of large-scale flow field datasets, and the self-feature extraction mechanism can adaptively capture the key physical features of the flow field. The fully trained model can achieve end-to-end rapid prediction of geometric parameter - flow field characteristics and has the capabilities of multi-fidelity data fusion and geometric topology adaptation.

[0005] However, there are still significant deficiencies in the current research on airfoil flow field surrogate models: First, the mainstream models are constructed based on Cartesian grids or body-fitted structured grids, which have discretization differences from the unstructured grids used in the finite volume method in engineering practice; Second, the model evaluation focuses on traditional machine learning metrics (such as mean square error), lacking performance verification for aerodynamic design goals (such as lift-to-drag ratio optimization); Third, the data partitioning strategy does not strictly follow the distribution law of the airfoil parameter space, and the test set often contains minor perturbations of the geometric configurations in the training set, resulting in distorted evaluation of the model's extrapolation ability.

[0006] The AirfRANS two-dimensional airfoil dataset proposed by the Bonnet team has made important progress in unstructured grid RANS simulations. It adopts a split training strategy, constructs training-test sets by constructing independent airfoil families, and effectively verifies the model's generalization ability. It innovatively proposes a surface-volume dual-path loss function architecture, breaking through the limitations of traditional global unified loss functions, and providing a new paradigm for accurately capturing the dynamic characteristics of the near-wall boundary layer and the evolution law of the external flow field. Summary of the Invention

[0007] Technical problems to be solved:

[0008] In the process of further research, the applicant found that the prior art has at least the following technical problems:

[0009] There are significant physical mechanism differences between the surface region of the wall boundary layer and the mainstream volume region in CFD numerical simulations: the flow in the near-wall surface region is dominated by viscosity and needs to satisfy the no-slip boundary condition, while the mainstream volume region is controlled by the Navier-Stokes equation dominated by inertia, and the flow control laws of the two are completely different. When using a deep learning model to jointly optimize the surface pressure distribution and volume flow field characteristics, the traditional loss function architecture is prone to cause the gradient competition effect of multi-objective optimization, resulting in a convergence conflict in the parameter update direction between surface accuracy and volume field fidelity, and ultimately leading to deterioration of the prediction accuracy. This essential contradiction reveals the theoretical defect of the existing data-driven models in the integration of fluid-structure coupling mechanisms.

[0010] In view of the above technical problems, the present invention proposes an airfoil flow field prediction method based on multi-task learning, which treats airfoil surface and volume predictions as interrelated but different tasks, and effectively alleviates the conflict between airfoil surface and volume predictions by adopting a multi-head neural network architecture and a multi-task loss optimization strategy, realizing the construction of an airfoil surrogate model and the accurate prediction of flow field information and aerodynamic parameters.

[0011] The technical solution of the present invention is as follows:

[0012] An airfoil flow field prediction method based on multi-task learning, comprising the following steps:

[0013] Step 1: Establish an airfoil flow field prediction model based on multi-task learning;

[0014] The prediction model includes an encoder, a backbone network, and a multi-head decoder;

[0015] The encoder extracts node feature vectors from the input airfoil flow field data as the input of the prediction model; the airfoil flow field data is data reflecting the geometric features and flow conditions of the airfoil flow field;

[0016] The backbone network includes a shared feature extraction layer that performs deep feature extraction on the input node feature vectors according to the parameter sharing mechanism to obtain a multi-dimensional feature vector with unified representation;

[0017] The multi-head decoder performs parallel decoding processing on the multi-dimensional feature vector input from the backbone network according to the task division strategy to obtain airfoil surface pressure distribution, volume domain velocity field, volume domain pressure field, and turbulent viscosity field data, and further calculates aerodynamic data;

[0018] The task division strategy is to divide according to the surface area and volume area: the multi-head decoder architecture is divided into two different decoder branches: a surface decoder and a volume decoder; the surface decoder processes boundary-related parameters; the volume decoder processes internal flow characteristic parameters;

[0019] Step 2: Use the airfoil flow field dataset to train the model established in Step 1 using an optimization strategy based on multi-task learning, including the following steps:

[0020] Step 2.1: Preprocess the airfoil flow field dataset;

[0021] Step 2.2: Initialize the weights and biases of the airfoil flow field prediction model, and the input data performs forward propagation through each layer of the airfoil flow field prediction model. Each layer performs weighted summation, bias addition, and activation function processing on the input data to obtain the prediction result of the output layer;

[0022] Step 2.3: Calculate the MSE losses of the surface area and volume area respectively according to the multi-task learning optimization strategy adopted;

[0023] Step 2.4: On the basis of the multi-task learning optimization strategy, balance the gradient conflict between surface pressure prediction and volume flow field prediction by dynamically adjusting the weights of the surface area and volume area;

[0024] Step 2.5: Update the weights and biases of the model according to the gradient after weight adjustment until the total loss of the model reaches the minimum and the training ends;

[0025] Step 3: Parametrize the airfoil that actually needs to be predicted for the flow field and generate a mesh to obtain standardized airfoil flow field data. Input the airfoil flow field data into the trained airfoil flow field prediction model for prediction to obtain the distribution of physical quantities in the entire flow field and the information on lift and drag coefficients.

[0026] Furthermore, the airfoil flow field data includes the positions of grid nodes, the velocity components at the flow field inlet, the distance from each grid node to the airfoil surface, and the normal vector of the airfoil surface.

[0027] Furthermore, the encoder encodes based on the airfoil flow field data according to the multi-layer perceptron or PointNet architecture to obtain node feature vectors.

[0028] Furthermore, the shared feature extraction layer also adopts the multi-layer perceptron or PointNet architecture.

[0029] Furthermore, the task partitioning strategy is adjusted as follows: Partitioning by physical parameters: After the multi-dimensional feature vector that obtains a unified representation according to the parameter sharing mechanism in the backbone network, the multi-dimensional feature vector is routed to five different decoders in the multi-head decoder, and each decoder is responsible for predicting different physical parameters.

[0030] Furthermore, in step 2.3, the multi-task learning optimization strategy adopts the fair gradient balancing strategy, the fast adaptive multi-task optimization strategy, or the smooth Chebyshev scalarization strategy.

[0031] Advantageous Effects

[0032] The airfoil flow field prediction method based on multi-task learning proposed by the present invention uses a multi-task loss optimization strategy during the training process of the prediction model, so it can effectively solve the problem of conflicts in the optimization of airfoil surface loss and volume loss, and further realizes the construction of the airfoil surrogate model and the accurate prediction of flow field information and aerodynamic parameters.

[0033] The additional aspects and advantages of the present invention will be partially given in the following description, partially will become obvious from the following description, or will be understood through the practice of the present invention. Description of the Drawings

[0034] The above and / or additional aspects and advantages of the present invention will become obvious and easy to understand from the description of the embodiments in conjunction with the following drawings, wherein:

[0035] Figure 1 is the logic block diagram of the airfoil flow field prediction method based on multi-task learning of the present invention;

[0036] Figure 2 is the network architecture diagram;

[0037] Figure 3 AndFigure 4 It is a detailed schematic diagram in the network architecture diagram;

[0038] Figure 5 It is a schematic diagram of a multi - head decoder with different decoding methods. Specific implementation manner

[0039] The embodiments of the present invention will be described in detail below. The embodiments are exemplary and are intended to explain the present invention, and should not be construed as a limitation to the present invention.

[0040] The airfoil flow field prediction method based on multi - task learning proposed in this embodiment solves the problem of conflict between the optimization of airfoil surface loss and volume loss in the prior art, and realizes the construction of an airfoil surrogate model and the accurate prediction of flow field information and aerodynamic parameters. It specifically includes the following steps:

[0041] Step 1: Establish an airfoil flow field prediction model based on multi - task learning; this model is general and applicable to different airfoil flow fields. Each airfoil flow field is represented by a corresponding grid X i denoted, and the grid X i is composed of a surface grid S i and a volume grid V i to facilitate a comprehensive description of the airfoil and its surrounding fluid domain.

[0042] The prediction model includes an encoder, a backbone network, and a multi - head decoder;

[0043] The encoder extracts node feature vectors from the input airfoil flow field data as the input of the prediction model;

[0044] The airfoil flow field data is data reflecting the geometric features and flow conditions of the airfoil flow field, specifically including grid node positions, flow field inlet velocity components, the distance from each grid node to the airfoil surface, and the airfoil surface normal vector.

[0045] The above - mentioned airfoil flow field data covers the basic geometric features and flow features required for accurate simulation. Among them, the inlet velocity component characterizes the oncoming flow conditions, the distance from each grid node to the airfoil surface is calculated by the signed distance function and characterizes the accurate geometric information relative to the airfoil surface, and the airfoil surface normal vector facilitates the accurate calculation of boundary conditions.

[0046] Based on the airfoil flow field data, encoding is performed according to the multi - layer perceptron (MLP) or PointNet architecture to obtain node feature vectors.

[0047] The backbone network includes a shared feature extraction layer that performs deep feature extraction on the input node feature vectors according to the parameter sharing mechanism to obtain a multi-dimensional feature vector with unified representation. The shared feature extraction layer also adopts a multi-layer perceptron (MLP) or PointNet architecture.

[0048] The multi-head decoder performs parallel decoding processing on the multi-dimensional feature vector input from the backbone network according to the task division strategy to obtain data on the airfoil surface pressure distribution, volume domain velocity field, volume domain pressure field, and turbulent viscosity field. These output quantities provide important bases for studying fluid behavior and its interaction with the airfoil geometry and can be used to calculate aerodynamic data such as drag coefficient and lift coefficient.

[0049] Since completely different methods are used for the surface region and volume region calculations in CFD, this embodiment realizes separation in the model architecture design. Through different decoder branches, it focuses on their respective corresponding flow characteristics.

[0050] The task division strategy is divided into two types:

[0051] The first is to divide according to the surface region and volume region: the multi-head decoder architecture is divided into two different decoder branches: the surface decoder and the volume decoder. The surface decoder focuses on processing boundary-related parameters, including the velocity components, pressure distribution, and kinematic turbulent viscosity on the airfoil surface, while the volume decoder processes internal flow characteristics, including the velocity components, pressure distribution, and kinematic turbulent viscosity in the flow region. This separation enables each decoder branch to be specialized, thereby enhancing prediction accuracy and reducing potential interference between tasks.

[0052] The second is to divide according to physical parameters: after the multi-dimensional feature vector with unified representation is obtained in the backbone network according to the parameter sharing mechanism, the multi-dimensional feature vector is routed to five different decoders in the multi-head decoder. Each decoder is responsible for predicting different physical parameters, thereby reducing unnecessary calculations and ensuring consistent and accurate predictions between different parameters by using the shared representation.

[0053] Step 2: Use the airfoil flow field dataset to train the model established in Step 1 by adopting an optimization strategy based on multi-task learning, including the following steps:

[0054] Step 2.1: Preprocess the airfoil flow field dataset: normalize the airfoil dataset, adopt the Z-score normalization method, crop the computational domain to the specified range, and randomly subsample 32,000 nodes twice per epoch.

[0055] In this embodiment, the AirfRANS dataset is used as the training data, which is used to evaluate the effectiveness of deep learning models in solving two-dimensional incompressible steady Reynolds-averaged Navier-Stokes (RANS) equations using unstructured grids. It includes different airfoil shapes from the 4-digit and 5-digit series of NASA and various turbulent condition characteristics, characterized by the Reynolds number Re ∈ [2×10 6 , 6×10 6 and the angle of attack AoA ∈ [-2.5°, 15°].

[0056] The grid of each sample in the dataset contains approximately 150,000 grid nodes with detailed flow characteristics. Since the computational requirement of processing 150,000 grid nodes for each sample is very high, in this embodiment, the Z-score normalization method is adopted, the computational domain is cropped to the specified range, and 32,000 nodes are randomly subsampled twice per epoch to effectively manage the computational load. A total of 1,000 samples are used, among which 720 samples are used for training, 80 for validation, and 200 for testing. Each sample has a unique airfoil shape, ensuring that the airfoils present in the test set are completely absent from the training set.

[0057] Step 2.2: Initialize the weights and biases of the airfoil flow field prediction model. The input data propagates forward through each layer of the airfoil flow field prediction model. Each layer processes the input data by summing the weights, adding the bias, and applying an activation function to obtain the prediction result of the output layer.

[0058] Step 2.3: Multi-task loss calculation: During the training process, it is necessary to use the loss function to calculate the difference between the prediction result and the true value, and at the same time combine the loss function to update the entire network parameters for training. In this embodiment, the MSE losses of the surface region (about 1,500 nodes) and the volume region (about 30,500 nodes) are calculated respectively according to the multi-task learning (MTL) optimization strategy adopted; the multi-task learning optimization strategy includes the Fair Gradient Balance strategy (FairGrad), whose core idea is to ensure that all tasks benefit evenly during training by dynamically adjusting the gradient contributions of each task and avoid a single task dominating the optimization direction; the Fast Adaptive Multi-task Optimization strategy (Fast Adaptive Multi-task Optimization, FAMO), whose core idea is to automatically adjust the loss weights by implicitly modeling the correlations between tasks to maximize the efficiency of multi-task joint learning; the Smooth Tchebycheff scalarization strategy (Smooth Tchebycheff, STCH), whose core idea is to transform multi-objective optimization into a smooth min-max problem to approximate the Pareto optimal solution set.

[0059] Step 2.4: Gradient coordination optimization: During the training process, based on the multi-task learning (MTL) optimization strategy, further balance the gradient conflict between surface pressure prediction (which directly affects the aerodynamic coefficient) and volume flow field prediction (which dominates the accuracy of the computational domain) by dynamically adjusting the weights of the surface area and volume area.

[0060] Step 2.5: Update the weights and biases of the model according to the gradients after weight adjustment until the total loss of the model reaches the minimum, and the training ends.

[0061] After that, use the validation samples and test samples to confirm the effectiveness of the trained airfoil flow field prediction model.

[0062] Step 3: Parametrize the geometry and generate grids for the airfoil that actually needs flow field prediction to obtain standardized airfoil flow field data, including grid node position coordinates, flow field inlet velocity components, the distance from each grid node to the airfoil surface, and the airfoil surface normal vector; input the airfoil flow field data into the trained airfoil flow field prediction model for prediction to obtain the distribution of physical quantities in the entire flow field and the lift and drag coefficient information.

[0063] Comparison and verification:

[0064] Experiments were carried out under two different configurations: a baseline configuration without the multi-task learning (MTL) loss optimization strategy and an optimized configuration with the multi-task learning loss optimization strategy. In the baseline configuration, a single decoder is used to calculate the total loss and individual losses. In the optimized configuration, three different MTL loss optimization strategies are adopted, including Fair Gradient Balance (FairGrad), whose core idea is to ensure that all tasks benefit evenly during training by dynamically adjusting the gradient contributions of each task and avoid a single task dominating the optimization direction; Fast Adaptive Multi-task Optimization (FAMO), whose core idea is to automatically adjust the loss weights by implicitly modeling the correlations between tasks to maximize the efficiency of multi-task joint learning; Smooth Tchebycheff (STCH), whose core idea is to transform multi-objective optimization into a smooth min-max problem to approximate the Pareto optimal solution set. And in the optimized configuration, both the encoder and the multi-head decoder are defined as multi-layer perceptrons with ReLU activation functions and no batch normalization is performed. The encoder structure consists of neurons configured as 7→64→64→8, which is the same for all methods. The two branches of the multi-head decoder, Decoder I and Decoder II, where the neurons of Decoder I are configured as 8→64→64→4 and the neurons of Decoder II are configured as 8→64→64→1. All encoders and decoders are co-trained with the selected backbone network.

[0065] The backbone network uses an MLP with a ReLU activation function, and batch normalization is applied before each activation. Its structure consists of neuron layers, and the arrangement order of neurons is 8→64→64→64→8. In all experiments, the learning rate, the number of epochs, and the optimizer settings are kept consistent. The learning rate is configured using a one-cycle cosine schedule with a maximum value of 0.001. The training process is set with a fixed number of 800 epochs. All experiments use the Adam optimizer. In addition, all data is normalized using z-score.

[0066] The encoder extracts node feature vectors from the input dataset. Then it is processed by the shared backbone network to obtain a multi-dimensional feature vector with unified representation. The multi-head decoder classifies and trains according to the surface and volume or through separate physical parameters. During the model training process, the MTL loss optimization strategy is adopted to balance the conflict between fluid surface and volume predictions, so as to output the predicted flow field information and aerodynamic coefficients.

[0067] The comparison and verification results are shown in Tables 1 and 2.

[0068] Table 1. Comparison of Mean Squared Error (MSE) of Different Optimization Schemes

[0069]

[0070] Table 2. Comparison of Lift / Drag Coefficient and Spearman Correlation Coefficient of Different Optimization Schemes

[0071]

[0072] It can be seen that compared with the traditional overall loss and composite loss, this scheme uses a multi-head decoder combined with a multi-task learning loss balance strategy, which can effectively alleviate the conflict between fluid surface and volume predictions, so as to output flow field information and aerodynamic coefficient prediction results with higher accuracy.

[0073] Although the embodiments of the present invention have been shown and described above, it can be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those of ordinary skill in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention without departing from the principles and purposes of the present invention.

Claims

1. A method for airfoil flow field prediction based on multi-task learning, characterized by: The following steps are involved: Step 1: Establish an airfoil flow field prediction model based on multi-task learning; The prediction model includes an encoder, a backbone network, and a multi-head decoder; The encoder extracts node feature vectors from the input airfoil flow field data as input of the prediction model; the airfoil flow field data is data reflecting the geometric characteristics and flow conditions of the airfoil flow field; The backbone network includes a shared feature extraction layer, which performs deep feature extraction on the input node feature vector according to the parameter sharing mechanism to obtain a multi-dimensional feature vector with unified representation; The multi-head decoder performs parallel decoding processing on the multi-dimensional feature vector input from the backbone network according to the task division strategy to obtain the airfoil surface pressure distribution, volume domain velocity field, volume domain pressure field, turbulent viscosity field data, and further calculates the aerodynamic data; The task division strategy is to divide according to the surface area and the volume area: the multi-head decoder architecture is divided into two different decoder branches: the surface decoder and the volume decoder; The surface decoder processes boundary-related parameters; The volume decoder processes the internal flow characteristic parameters; Step 2: Using the airfoil flow field dataset, the model established in step 1 is trained using an optimization strategy based on multi-task learning, including the following steps: Step 2.1: Preprocess the airfoil flow field data set; Step 2.2: Initialize the weights and biases of the airfoil flow field prediction model. The input data is forward propagated through each layer of the airfoil flow field prediction model. Each layer performs weight summation, bias addition and activation function processing on the input data to obtain the prediction result of the output layer. Step 2.3: Calculate the MSE loss of the surface area and volume area respectively according to the adopted multi-task learning optimization strategy; Step 2.4: Based on the multi-task learning optimization strategy, the gradient conflict between the surface pressure prediction and the volume flow field prediction is balanced by dynamically adjusting the weights of the surface area and the volume area; Step 2.5: Update the model weights and biases according to the weight-adjusted gradients until the total loss of the model is minimized and the training ends. Step 3: Perform geometric parameterization and mesh generation on the airfoil that actually needs flow field prediction to obtain standardized airfoil flow field data. Input the airfoil flow field data into the trained airfoil flow field prediction model for prediction to obtain the distribution of physical quantities in the entire flow field and lift and drag coefficient information.

2. The airfoil flow field prediction method based on multi-task learning according to claim 1, characterized in that: The airfoil flow field data includes grid node positions, flow field inlet velocity components, distances from each grid node to the airfoil surface, and airfoil surface normal vectors.

3. The airfoil flow field prediction method based on multi-task learning according to claim 1, characterized in that: The encoder is based on the airfoil flow field data and encodes according to a multi-layer perceptron or PointNet architecture to obtain a node feature vector.

4. The airfoil flow field prediction method based on multi-task learning according to claim 3 is characterized by: The shared feature extraction layer also adopts a multi-layer perceptron or PointNet architecture.

5. The airfoil flow field prediction method based on multi-task learning according to claim 1, characterized in that: The task division strategy is adjusted to: division by physical parameters: after the backbone network obtains a multi-dimensional feature vector with unified representation according to the parameter sharing mechanism, the multi-dimensional feature vector is routed to five different decoders in the multi-head decoder, and each decoder is responsible for predicting different physical parameters.

6. According to claim 1, a method for predicting airfoil flow field based on multi-task learning is characterized in that: In step 2.3, the multi-task learning optimization strategy adopts a fair gradient balancing strategy, a fast adaptive multi-task optimization strategy, or a smooth Chebyshev scalarization strategy.

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