Turbulent flow field prediction method based on deep fusion of multi-scale space-time convolution and physical constraint

Abstract

The invention discloses a turbulent flow field prediction method based on multi-scale space-time convolution and physical constraint deep fusion, and the method comprises the following steps: carrying out the fine processing and feature extraction of turbulent flow data: carrying out the space cutting and differential downsampling of an original turbulent flow data set, and forming a regular input data set on the premise of keeping a key flow structure; according to the multi-scale space-time convolution network architecture design, an encoder, a multi-scale pyramid feature extraction module, a space-time attention module and a decoder are included, and large, middle and small parallel convolution paths are adopted to capture vortex structures of different scales in a turbulent flow field. And in combination with Softmax normalization, contribution proportions of vortex structures with different scales are automatically adjusted, and the characterization capability of a complex turbulence structure is improved. Mathematical embedding of the law of conservation of physics: hard constraint and soft constraint are included, divergence constraint loss and boundary condition loss are introduced, it is ensured that the predicted flow field meets the law of conservation of mass and conservation of momentum, and a result violating the law of physics is avoided.

Description

Technical Field

[0001] This invention relates to the field of deep learning turbulent flow field prediction technology, and in particular to a turbulent flow field prediction method based on deep fusion of multi-scale spatiotemporal convolution and physical constraints. Background Technology

[0002] In the aerospace field, deep learning-based turbulence field prediction enables real-time, high-precision simulation of the flow field around an aircraft, predicting boundary layer separation and eddy evolution processes on wing surfaces, providing digital support for aerodynamic optimization design. In energy and power engineering, it can simulate complex turbulent structures within gas turbine blade channels, predict dynamic changes in the combustion chamber flow field, and help improve combustion efficiency. In meteorological and oceanographic applications, it can rapidly model the evolution of turbulent vortices in localized severe convective weather systems, improving the timeliness of extreme weather warnings. In industrial manufacturing, it can be used as a digital alternative for automotive wind tunnel testing, significantly reducing prototype testing costs.

[0003] Current turbulence field predictions primarily rely on traditional computational fluid dynamics methods and fundamental deep learning models. Direct numerical simulations in traditional methods require solving the complete Navier-Stokes equations, consuming millions of CPU hours per simulation at a 2048×512×1536 grid resolution. While large eddy simulations reduce computation by introducing sub-grid-scale models, they still need to address complex turbulent closure issues. Existing deep learning models, such as 3D convolutional neural networks, are limited by fixed receptive fields, making it difficult to simultaneously capture large-scale eddies and small-scale fluctuations. Hybrid models combining long short-term memory networks and convolutions suffer from gradient vanishing problems in long-term predictions, leading to error accumulation. Transformer-based architectures, due to the cubic relationship between the computational complexity of their self-attention mechanism and spatial resolution, face the challenge of excessive memory consumption when processing high-dimensional turbulence data.

[0004] In handling boundary conditions, traditional deep learning methods cannot strictly guarantee no-slip boundary conditions, resulting in velocity prediction errors as high as 12%-15% in the near-wall region. Insufficient multi-scale feature extraction capabilities make it difficult for the model to simultaneously resolve large eddy structures at a grid scale of 50 times and small eddy motions at a grid scale of 2 times. Lack of physical consistency manifests as prediction results violating the law of mass conservation, with the divergence value of the velocity field deviating from zero beyond the allowable range. Regarding computational efficiency, traditional CFD methods take several hours to compute per time step, failing to meet the real-time requirements of engineering projects. Poor long-term prediction stability is reflected in the exponential growth of errors after more than 10 time steps, severely limiting its practical application value. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of existing technologies by providing a turbulent field prediction method based on deep fusion of multi-scale spatiotemporal convolution and physical constraints.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution: A turbulent field prediction method based on deep fusion of multi-scale spatiotemporal convolution and physical constraints, characterized by the following steps: Refined processing and feature extraction of turbulence data: Spatial cropping and feature preservation are performed on the original turbulence dataset, and differential downsampling optimization is performed to form an input dataset of 256×512×128; Multi-scale spatiotemporal convolutional network architecture design: including encoder, multi-scale pyramid feature extraction module, spatiotemporal attention module, and decoder; the input dataset first passes through the encoder to extract shallow features F0 of the turbulent field, and then the shallow features F0 of the turbulent field pass through three parallel convolutional paths of the multi-scale pyramid feature extraction module to extract deep features F1 respectively. L F1 M F1 S The F1 L F1 M F1 S These are large-scale path features, medium-scale path features, and small-scale path features, respectively, and F1... L F1 M F1 S Weighted fusion is performed to obtain the fused deep feature F1. F1 is then input into the spatiotemporal attention module to obtain the spatiotemporal attention feature F2. In the decoder, F2 is upsampled three times to obtain the feature F3. (3) ; The mathematical embedding of physical conservation laws includes hard and soft constraints. The hard constraints include boundary condition loss constraints, whereby the boundary velocity is explicitly forced to zero through a mask matrix, ensuring that the no-slip condition is strictly met. Where v represents the velocity vector, y max The maximum grid index is in the y-direction; the soft constraint includes a divergence constraint, which is that for an incompressible fluid, the velocity field divergence is zero and mass conservation is satisfied. Regarding the feature F3 (3) The output U of the flow field is obtained after 3D convolution and hard constraints. t+Δt : Where M represents the boundary mask matrix, M i,0,k =M i,Y-1,k =0, the rest are 1, Tanh() represents the Tanh activation function, Conv3D 1×1×1 () represents a three-dimensional convolution with a 1×1×1 kernel.

[0007] Furthermore, the spatial clipping and feature preservation includes employing a center-symmetric clipping strategy on the original turbulence data, truncating the center 1024 points from the original 2048 grid points in the x-axis direction, truncating the center 256 points from the original 1536 grid points in the z-axis direction, and retaining the original 512 grid points in the y-axis direction to ensure the integrity of the boundary layer.

[0008] Furthermore, the differential downsampling includes sampling one point every four grid points in the x-axis direction, sampling one point every two grid points in the z-axis direction, and keeping the original sampling unchanged in the y-axis direction, ultimately forming an input dataset of 256×512×128.

[0009] Furthermore, the shallow features U t Given the flow field at time t, for U t Apply hard constraints, that is, apply hard constraints to U. t Boundary condition encoding forces the boundary velocity to be 0, where Conv3D 3×3×3 () denotes a 3D convolution with a 3×3×3 kernel, used to extract local features, and M represents the boundary mask matrix, where M i,0,k =M i,Y-1,k =0, the rest are 1, forcing the wall velocity to 0. RELU() represents the RELU activation function, which is used to alleviate the gradient vanishing problem during training and enable the network to learn complex patterns.

[0010] Furthermore, the large-scale path features are extracted using a 7×3×5 dilated convolution kernel with a dilation rate of 2 to expand the receptive field, and are further enhanced by batch normalization and the LeakyReLU activation function to extract large eddy structure features. Where DilatedConv() represents dilated convolution, using a 7×3×5 dilated convolution kernel, d represents the dilation parameter of dilated convolution set to 2, BN() represents the batch normalization layer, and LeakyRELU() represents the LeakyReLU activation function.

[0011] Furthermore, the mesoscale path features employ a grouped convolution design, dividing the 64 channels into 8 groups, with each group undergoing an independent 5×3×3 convolution operation. Channel shuffling promotes information exchange between groups. In this context, GroupConv() represents grouped convolution, g=8 means 8 groups of convolution, each group uses a 5×3×3 convolution kernel, and shuffle() represents channel shuffling operation, which is used to enhance information exchange between groups.

[0012] Furthermore, the small-scale path features are captured using depthwise separable convolution, with a 3×3×1 convolution kernel specifically designed to capture subtle flow features near the wall. , where DSConv() represents depthwise separable convolution, which uses a 3×3×1 convolution kernel to focus on capturing subtle flow features near the wall.

[0013] Furthermore, F1 L F1 M F1 S The specific steps for obtaining the fused deep feature F1 by weight fusion are as follows: Let the unnormalized weights that can be learned during network training be: Obtained by softmax normalization : Fusion Output: Where W represents the learnable weight matrix, which can update parameters and adaptively adjust the contribution of each scale during network training. Softmax() is a mathematical function that maps any real vector to the interval [0,1], and the sum of all components is 1.

[0014] Furthermore, the spatiotemporal attention feature F2 is expressed as: The Q, K, and V matrices are generated by convolving F1 with a 1×1×1 convolution kernel, and D represents the wall distance weight matrix, which is 1 / (1+|yy wall |)

[0015] Furthermore, the divergence constraint, by being incorporated into the loss function, gradually constrains the network to convergence and conform to mass conservation during network training. The divergence loss is expressed as follows: Divergence loss affects the output velocity field v of the neural network. pred The divergence is calculated using a finite difference divergence operator. Where u, v, and w represent the velocity components along the x, y, and z axes, respectively; Δx represents the spacing between adjacent grid points in the x-direction of the computational domain; Δy represents the spacing between adjacent grid points in the y-direction of the computational domain; and Δz represents the spacing between adjacent grid points in the z-direction of the computational domain. These values ​​are determined by the physical length of the computational domain and the number of discrete grids in each direction. Where L x L y L z N represents the physical dimensions of the computational domain in three directions.x N y N z These represent the number of grid divisions in the corresponding direction.

[0016] Compared with the prior art, the beneficial effects of the present invention are: 1. Strictly satisfy physical boundary conditions: The boundary velocity is explicitly forced to zero by the mask matrix, ensuring that the no-slip condition is strictly met, thus avoiding the boundary non-convergence problem caused by numerical errors in traditional methods.

[0017] 2. Adaptive Multi-Scale Feature Fusion: Employing three parallel convolutional paths (large, medium, and small) to capture vortex structures at different scales in turbulent fields. Combined with learnable weights (Softmax normalization), the contribution ratio of vortex structures at different scales is automatically adjusted, enhancing the ability to represent complex turbulent structures.

[0018] 3. Significantly improved computational efficiency: Compared with traditional CFD methods (such as DNS / LES), this method uses end-to-end prediction through neural networks to achieve real-time or near real-time computation while ensuring accuracy, making it suitable for rapid simulation in engineering scenarios.

[0019] 4. Physical consistency guarantee: Divergence loss and boundary condition loss are introduced to ensure that the predicted flow field satisfies the laws of mass conservation and momentum conservation, and to avoid the generation of non-physical interpretations.

[0020] 5. Flexible adaptation to different scenarios: The network structure can be extended to problems such as non-uniform meshes and complex geometric boundaries, and is suitable for turbulence simulation needs in multiple fields such as aerospace, weather forecasting, and energy. Attached Figure Description

[0021] Figure 1 This is a flowchart of the turbulent flow field prediction method of the present invention; Figure 2 The following is a graph showing the variation of the loss function value with the number of training rounds in the comparative ablation experiment of the example. Figure 3 This is a schematic diagram comparing the experimental results of the examples and the comparative examples. Detailed Implementation

[0022] To enhance understanding of the present invention, we will now describe it in further detail with reference to the accompanying drawings. These embodiments are for illustrative purposes only and do not constitute a limitation on the scope of protection of the present invention.

[0023] like Figure 1As shown, a specific embodiment of a turbulent field prediction method based on deep fusion of multi-scale spatiotemporal convolution and physical constraints is presented. The core of this method lies in constructing a multi-scale spatiotemporal convolution architecture that fuses physical constraints, specifically including the following steps: I. Refined Processing and Feature Extraction of High-Resolution Turbulent Data The JHTDB Channel dataset was used as the high-resolution raw turbulence dataset. The dataset size is x=2048, y=512, z=1536, the time step is 4000, and the dataset size is about 64Tb.

[0024] The original turbulence dataset employs a centrosymmetric cropping strategy to perform spatial cropping and feature preservation. In the x-axis direction, the center 1024 points are cropped from the original 2048 grid points, and in the z-axis direction, the center 256 points are cropped from the original 1536 grid points. In the y-axis direction, the complete original 512 grid points are retained to ensure the integrity of the boundary layer. The time step is 4000, and the dataset size is approximately 8Tb.

[0025] Subsequently, differential downsampling was performed, using interpolation to sample one point every four grid points in the x-axis direction, one point every two grid points in the z-axis direction, and keeping the original sampling unchanged in the y-axis direction. This resulted in an input flow field dataset of 256×512×128, with a time step of 4000 and a dataset size of approximately 128Gb.

[0026] II. Multi-scale Spatiotemporal Convolutional Network Architecture Design It includes modules such as an encoder, a multi-scale pyramid feature extraction module, a spatiotemporal attention module, and a decoder. During the feature propagation process in the neural network, let the input flow field at time t be U. t ∈R X×Y×Z×3 , that is U t A velocity field v containing three orthogonal directions t The target is the flow field U at time t+Δt. t+Δt .

[0027] (1) Encoder: For the input flow field U t First, the shallow features F0 of the turbulent field are extracted using an encoder. Simultaneously, U... t Apply hard constraints, that is, apply hard constraints to U. t Boundary condition encoding, forcing the boundary velocity to be 0: Among them, Conv3D 3×3×3 () denotes a 3D convolution with a 3×3×3 kernel, used to extract local features, where M represents the boundary mask matrix. i,0,k =M i,Y-1,k=0, the rest are 1, forcing the wall velocity to be 0. RELU() represents the ReLU activation function, which is used to alleviate the gradient vanishing problem during training, enabling the network to learn complex patterns.

[0028] (2) Multi-scale pyramid feature extraction module: To better extract turbulent features at different scales, a multi-scale feature pyramid is constructed using three parallel convolutional paths. The large-scale path uses a 7×3×5 dilated convolution kernel with a dilation rate of 2 to expand the receptive field, combined with batch normalization and the LeakyReLU activation function to extract large eddy structure features. The medium-scale path employs a grouped convolution design, dividing the 64 channels into 8 groups, each performing a 5×3×3 convolution operation independently, and promoting information exchange between groups through channel shuffling. The small-scale path uses depthwise separable convolution technology, employing a 3×3×1 convolution kernel to focus on capturing subtle flow features near the wall. After obtaining the shallow turbulent field feature F0, the deep feature F1 in F0 is extracted using the multi-scale pyramid feature extraction module. L F1 M F1 S .

[0029] Specifically, in large-scale paths (dilated convolution), the F1 score of large-scale path features... L Represented as: Where DilatedConv() represents dilated convolution, using a 7×3×5 dilated convolution kernel, d represents the dilation parameter of dilated convolution set to 2, BN() represents the batch normalization layer, and LeakyRELU() represents the LeakyReLU activation function.

[0030] In the mesoscale path (grouped convolution + channel shuffling), the F1 score of the mesoscale path features. M Represented as: GroupConv() represents grouped convolution, g=8 means 8 groups of convolution, each group uses a 5×3×3 convolution kernel, and shuffle() represents channel shuffling operation, which aims to enhance information exchange between groups.

[0031] In small-scale paths (depth-separable convolution), the F1 score of small-scale path features... S Represented as: DSConv() represents depthwise separable convolution, which uses a 3×3×1 convolution kernel to focus on capturing subtle flow features near the wall.

[0032] After extracting deep features F1 L F1M F1 S Next, weight fusion is needed to obtain the fused deep feature F1. Let the unnormalized weights that can be learned during network training be: Obtained by softmax normalization : Fusion Output: Here, W represents the learnable weight matrix, which can update parameters and adaptively adjust the contribution at each scale during network training. Softmax() is a commonly used mathematical function that maps any real vector to the interval [0,1], with the sum of all components being 1, making it very suitable for representing probabilities.

[0033] Multi-scale path output F1 L F1 M F1 S Obtained through Softmax To ensure that the weights are non-negative and sum to 1, this can be interpreted as "the contribution ratio of features at different scales".

[0034] (3) Spatiotemporal attention module: The spatiotemporal attention feature F2 is represented as The Q, K, and V matrices are generated by convolving the F1 algorithm with a 1×1×1 kernel, rather than using a fully connected layer. This saves computation. D represents the wall distance weight matrix, which is calculated by 1 / (1+|yy) wall |) This makes the spatial attention weights inversely proportional to the wall distance, thus strengthening the boundary layer modeling.

[0035] (4) Decoder module: F2 is deconvolved and upsampled to obtain F3. (3) : Among them, DeConv3D 4×4×4 () indicates a deconvolution with a 4×4×4 kernel, which, after three levels of upsampling, yields feature F3. (3) .

[0036] Finally, regarding F3 (3) After 3D convolution and hard constraints, the network output U is obtained. t+Δt Where M represents the boundary mask matrix, M i,0,k =M i,Y-1,k =0, the rest are 1, Tanh() represents the Tanh activation function.

[0037] III. Mathematical Embedding of Physical Conservation Laws (1) Hard constraints The physical constraints are rigorously enforced through mathematical means. For no-slip boundary conditions, an explicit zero-velocity constraint is applied at the output layer, i.e., a hard constraint. Where v represents the velocity vector, y max This is the maximum grid index in the y-direction.

[0038] The specific implementation process is as follows: the boundary mask matrix M in the encoder and decoder, where M... i,0,k =M i,Y-1,k =0, all others are 1, forcing the wall velocity to be 0, and performing element-wise multiplication with the original feature to enforce the hard constraint that the wall velocity is 0. (2) Soft constraints Mass conservation constraints are implemented through a divergence penalty term. For incompressible fluids, the law of mass conservation requires zero divergence in the velocity field. This is implemented as a soft constraint during network training, i.e., by adding the soft constraint to the loss function, gradually constraining the network to converge and conform to mass conservation during training. The divergence loss is expressed as: Divergence loss affects the output velocity field v of the neural network. pred The divergence is calculated using the finite difference divergence operator.

[0039] Where u, v, and w represent the velocity components along the x, y, and z axes, respectively. To ensure the completeness of the formula, the symbols Δx, Δy, and Δz are defined as follows: Δx represents the spacing between adjacent grid points in the x-direction of the computational domain; Δy represents the spacing between adjacent grid points in the y-direction (perpendicular to the wall); and Δz represents the spacing between adjacent grid points in the z-direction of the computational domain. These are determined by the physical length of the computational domain and the number of discrete grids in each direction, i.e.: Where L x L y L z N represents the physical dimensions of the computational domain in three directions.x N y N z These represent the number of grid divisions in the corresponding direction.

[0040] In addition, the data matching term loss is designed using the mean squared error (MSE) loss, i.e.: Among them, v true The labels are real. The joint loss is expressed as: Where α and β are hyperparameters.

[0041] A comparative ablation experiment was conducted on the above embodiment: This embodiment is based on a constructed multi-scale spatiotemporal convolutional network (Full Model with all modules, FULL). The multi-scale pyramid feature extraction module (Without Pyramid Convolution, w / o-PC), the spatiotemporal attention module (Without Attention Module, w / o-ATT), and the physical constraints (Without Physical Constraints, w / o-PHYS) were removed respectively as a comparative ablation experiment, while the other settings remained unchanged.

[0042] The final experimental results are shown in Table 1. Observing the changes in the prediction results of each model, it can be found that removing the multi-scale pyramid module leads to a significant increase in prediction error; omitting physical constraints causes the flow field divergence to deviate from zero, resulting in an increase in divergence error. In addition, removing the attention module reduces the prediction MSE error by approximately 40% (see data in the table).

[0043] Table 1 Ablation test results

[0044] In the four sets of comparative ablation experiments, the loss function decreased during the experimental training process as follows: Figure 2 As shown, a lower loss function value indicates better model convergence. Figure 2 It can be seen that all four sets of experiments show that the loss function gradually decreases and tends to converge with the increase of the number of iterations, indicating that the network structure has a certain learning ability and stability under different settings. In addition, the FULL model maintains the lowest loss value throughout the entire training process, and its convergence speed is significantly faster than the other three comparative ablation experiments. This shows that multi-scale convolution, spatiotemporal attention, and physical constraints have a synergistic gain effect, which can significantly improve the network's learning and fitting ability.

[0045] A comparison of the FULL and w / o-PC experiments reveals that removing the multi-scale pyramid convolution slows down the model's convergence speed, resulting in a slightly higher final loss value compared to FULL. This indicates that multi-scale convolution plays a crucial role in capturing vortex structures at different scales in turbulent fields, and the absence of this module leads to insufficient representation of multi-scale features in the model.

[0046] A comparison of the FULL and w / o-ATT experiments reveals that removing the attention module consistently results in a higher loss value in the mid-to-late stages compared to FULL, with a slower convergence slope. This indicates that spatiotemporal attention effectively enhances the network's focus on key regions and time steps, and its absence makes it difficult for the model to fully utilize input features.

[0047] A comparison of the FULL and w / o-PHYS experiments reveals that the model lacking physical constraints performs the worst, with slow convergence and the highest final loss. This demonstrates that physical constraints (hard constraints and divergence penalty soft constraints) are crucial for ensuring the physical consistency of predictions. Missing constraints not only increase the loss but may also cause predictions to deviate from no-slip boundaries and mass conservation conditions.

[0048] Experimental results fully demonstrate the importance and synergistic effect of each module in the method of this invention, especially the key role of physical constraints in maintaining the physical consistency of prediction results, which makes the full model significantly better than other ablation models in terms of loss reduction speed and final accuracy.

[0049] Comparative example: Under the same experimental settings, common deep networks were selected as comparative examples, including UNet, Transformer (self-attention architecture), and ConvLSTM. The deep networks used in this invention were compared to these comparative examples, with typical network architectures selected for comparison.

[0050] Comparative experimental results as follows Figure 3As shown, for ease of observation, the three-dimensional turbulent field was downsampled to obtain a 64×64×64 turbulent field. Furthermore, the three-dimensional turbulent field was sliced ​​into two dimensions. It can be seen from the figure that the U-Net, Transformer, and ConvLSTM methods, due to the lack of physical constraints, predict results that do not conform to the no-slip boundary conditions (velocities are not zero on the planes y=0 and y=Max), thus failing to meet real physical conditions. Additionally, their turbulence prediction performance is clearly inferior to the method of this invention. Table 2 shows the test evaluation metrics for each neural network in the comparative examples, listing the mean square error (MSE), velocity field divergence error, velocity error, and computation time comparisons for each method. It can be seen that the method of this invention outperforms the other comparative examples in both MSE and physical consistency (divergence error). Especially compared to traditional networks without physical constraints, the velocity field predicted by this method satisfies the no-slip boundary conditions and the divergence is close to zero, ensuring mass conservation.

[0051] Table 2. Comparative experimental test results of the examples and comparative examples.

[0052] As shown in the table, our proposed method significantly outperforms traditional network structures in terms of MSE, velocity error, and divergence error. Introducing multi-scale pyramid convolution and attention modules reduces MSE by (0.035→0.019) and (0.027→0.019), respectively. Without physical constraints, the divergence error surges (1.24E-4→8.47E-4), validating the importance of hard boundary constraints and divergence loss. Compared with other networks, our method maintains lower computational cost while preserving small-scale vortex details. In summary, the analysis of various metrics demonstrates that our proposed method effectively captures complex turbulent structures through adaptive multi-scale feature fusion and spatiotemporal attention, while simultaneously enforcing physical conservation laws, resulting in more accurate and stable turbulence field predictions, superior to existing network models.

[0053] The above specific embodiments are only for illustrating the technical concept and structural features of the present invention, and are intended to enable those skilled in the art to implement them. However, the above content does not limit the scope of protection of the present invention. Any equivalent changes or modifications made in accordance with the spirit and essence of the present invention should fall within the scope of protection of the present invention.

Claims

1. A turbulent field prediction method based on deep fusion of multi-scale spatiotemporal convolution and physical constraints, characterized in that, Includes the following steps: Refined processing and feature extraction of turbulence data: Spatial cropping and feature preservation are performed on the original turbulence dataset, and differential downsampling optimization is performed to form an input dataset of 256×512×128; Multi-scale spatiotemporal convolutional network architecture design: including encoder, multi-scale pyramid feature extraction module, spatiotemporal attention module, and decoder; the input dataset first passes through the encoder to extract shallow features F0 of the turbulent field, and then the shallow features F0 of the turbulent field pass through three parallel convolutional paths of the multi-scale pyramid feature extraction module to extract deep features F1 respectively. L F1 M F1 S The F1 L F1 M F1 S These are large-scale path features, medium-scale path features, and small-scale path features, respectively, and F1... L F1 M F1 S Weighted fusion is performed to obtain the fused deep feature F1. F1 is then input into the spatiotemporal attention module to obtain the spatiotemporal attention feature F2. In the decoder, F2 is upsampled three times to obtain the feature F3. (3) ; The mathematical embedding of physical conservation laws includes hard and soft constraints. The hard constraints include boundary condition loss constraints, whereby the boundary velocity is explicitly forced to zero through a mask matrix, ensuring that the no-slip condition is strictly met. Where v represents the velocity vector, y max The maximum grid index is in the y-direction; the soft constraint includes a divergence constraint, which is that for an incompressible fluid, the velocity field divergence is zero and mass conservation is satisfied. Regarding the feature F3 (3) The output U of the flow field is obtained after 3D convolution and hard constraints. t+Δt : Where M represents the boundary mask matrix, M i,0,k =M i,Y-1,k =0, the rest are 1, Tanh() represents the Tanh activation function, Conv3D 1×1×1 () represents a three-dimensional convolution with a 1×1×1 kernel.

2. The turbulent field prediction method based on deep fusion of multi-scale spatiotemporal convolution and physical constraints as described in claim 1, characterized in that: The spatial clipping and feature preservation include a centrosymmetric clipping strategy on the original turbulence data, which truncates the center 1024 points from the original 2048 grid points in the x-axis direction, the center 256 points from the original 1536 grid points in the z-axis direction, and retains the original 512 grid points in the y-axis direction to ensure the integrity of the boundary layer.

3. The turbulent field prediction method based on deep fusion of multi-scale spatiotemporal convolution and physical constraints as described in claim 2, characterized in that: The differential downsampling includes sampling one point every four grid points in the x-axis direction, sampling one point every two grid points in the z-axis direction, and keeping the original sampling unchanged in the y-axis direction, ultimately forming an input dataset of 256×512×128.

4. The turbulent field prediction method based on deep fusion of multi-scale spatiotemporal convolution and physical constraints as described in claim 1, characterized in that: The shallow features U t Given the flow field at time t, for U t Apply hard constraints, that is, apply hard constraints to U. t Boundary condition encoding forces the boundary velocity to be 0, where Conv3D 3×3×3 () denotes a 3D convolution with a 3×3×3 kernel, used to extract local features, and M represents the boundary mask matrix, where M i,0,k =M i,Y-1,k =0, the rest are 1, forcing the wall velocity to 0. RELU() represents the RELU activation function, which is used to alleviate the gradient vanishing problem during training and enable the network to learn complex patterns.

5. The turbulent field prediction method based on deep fusion of multi-scale spatiotemporal convolution and physical constraints as described in claim 1, characterized in that: The large-scale path features are extracted using a 7×3×5 dilated convolution kernel with a dilation rate of 2 to expand the receptive field, and are further enhanced by batch normalization and LeakyReLU activation function to extract large eddy structure features. Where DilatedConv() represents dilated convolution, using a 7×3×5 dilated convolution kernel, d represents the dilation parameter of dilated convolution set to 2, BN() represents the batch normalization layer, and LeakyRELU() represents the LeakyReLU activation function.

6. The turbulent field prediction method based on deep fusion of multi-scale spatiotemporal convolution and physical constraints as described in claim 1, characterized in that: The mesoscale path features employ a grouped convolution design, dividing the 64 channels into 8 groups. Each group undergoes an independent 5×3×3 convolution operation, and channel shuffling promotes information exchange between groups. In this context, GroupConv() represents grouped convolution, g=8 means 8 groups of convolution, each group uses a 5×3×3 convolution kernel, and shuffle() represents channel shuffling operation, which is used to enhance information exchange between groups.

7. The turbulent field prediction method based on deep fusion of multi-scale spatiotemporal convolution and physical constraints as described in claim 1, characterized in that: The small-scale path features are captured using depthwise separable convolution, with a 3×3×1 convolution kernel specifically designed to capture subtle flow features near the wall. , where DSConv() represents depthwise separable convolution, which uses a 3×3×1 convolution kernel to focus on capturing subtle flow features near the wall.

8. The turbulent field prediction method based on deep fusion of multi-scale spatiotemporal convolution and physical constraints as described in claim 1, characterized in that: F1 L F1 M F1 S The specific steps for obtaining the fused deep feature F1 by weight fusion are as follows: Let the unnormalized weights that can be learned during network training be: Obtained by softmax normalization : Fusion Output: Where W represents the learnable weight matrix, which can update parameters and adaptively adjust the contribution of each scale during network training. Softmax() is a mathematical function that maps any real vector to the interval [0,1], and the sum of all components is 1.

9. The turbulent field prediction method based on deep fusion of multi-scale spatiotemporal convolution and physical constraints as described in claim 1, characterized in that: The spatiotemporal attention feature F2 is represented as follows: The Q, K, and V matrices are generated by convolving F1 with a 1×1×1 convolution kernel, and D represents the wall distance weight matrix, which is 1 / (1+|yy wall |) 10. The turbulent field prediction method based on multi-scale spatiotemporal convolution and physical constraint deep fusion as described in claim 1, characterized in that: The divergence constraint, added to the loss function, gradually constrains the network to convergence and conform to mass conservation during network training. The divergence loss is expressed as: Divergence loss affects the output velocity field v of the neural network. pred The divergence is calculated using a finite difference divergence operator. Where u, v, and w represent the velocity components along the x, y, and z axes, respectively; Δx represents the spacing between adjacent grid points in the x-direction of the computational domain; Δy represents the spacing between adjacent grid points in the y-direction of the computational domain; and Δz represents the spacing between adjacent grid points in the z-direction of the computational domain. These values ​​are determined by the physical length of the computational domain and the number of discrete grids in each direction. Where L x L y L z N represents the physical dimensions of the computational domain in three directions. x N y N z These represent the number of grid divisions in the corresponding direction.

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