Low-altitude wind field prediction method and system based on space-time diagram convolutional network

Abstract

The invention discloses a low-altitude wind field prediction method and system based on a space-time diagram convolutional network, and relates to the technical field of weather forecast and wind energy utilization, and the method comprises the steps: collecting wind field observation data and physical field data of all nodes of a target region, a dynamic space-time diagram is constructed based on a flow function-vorticity theory through a dynamic diagram construction module; extracting spatial information through a graph attention network to obtain a spatial feature tensor; the spatial feature tensor and the physical field data are processed by a PhysFusion-TransTCN encoder to obtain the deep spatial and temporal features of the wind field; performing hierarchical feature aggregation on the wind field deep spatial-temporal features through an output module to obtain a wind field prediction result of the target area; a wind field physical mechanism is deeply fused, multi-scale spatial-temporal feature fusion is realized, and prediction result precision and physical rationality are ensured.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of meteorological forecasting and wind energy utilization, in particular to a low-altitude wind field prediction method and system based on a spatio-temporal graph convolution network. BACKGROUND

[0002] Wind field prediction is of great significance to wind farm power prediction, aviation safety guarantee, weather warning and urban environmental governance. However, the atmospheric wind field is a complex system influenced by many factors, with strong nonlinearity and significant spatio-temporal correlation, especially in the near-surface layer and atmospheric boundary layer, where turbulent motion makes accurate prediction of the wind field extremely difficult.

[0003] Traditional wind field prediction methods mainly rely on numerical weather prediction (NWP) models. NWP models are based on physical equations, but they consume a huge amount of computing resources and are difficult to effectively assimilate high-frequency and high-density observation data, resulting in limited prediction accuracy for local areas and short-term changes in wind field. In recent years, with the development of deep learning technology, models such as convolutional neural networks (CNN) and long short-term memory networks (LSTM) have been applied to wind field prediction. However, existing deep learning models have obvious defects: CNNs have difficulty effectively handling the spatial relationships caused by the irregular topology of wind field measurement points, while LSTM and other models have problems with gradient vanishing or explosion when capturing long sequence temporal dependencies, and are difficult to explicitly model spatial information. Simple spatio-temporal separation modeling methods cannot fully capture the inherent physical mechanisms of "time-space" coupling in wind field evolution. In recent years, the spatio-temporal graph convolution network (ST-GCN) has provided a new paradigm for processing non-Euclidean spatio-temporal data, effectively modeling spatial relationships through graph convolution, but it still has limitations in capturing complex wind field temporal dependencies. The temporal convolution network (TCN) and its gated variant (GTU) provide an effective means of parallelizing long-term temporal dependencies. In particular, existing graph construction techniques based on dynamic time warping (DTW) and other statistical methods perform well in traffic prediction, but cannot effectively capture the physical correlation characteristics of wind fields. Wind field evolution is strictly constrained by physical laws such as the Navier-Stokes equation, and purely data-driven methods cannot guarantee the physical reasonableness of the prediction results.

[0004] In view of this, it is necessary to provide a new wind field prediction method that can deeply integrate physical mechanisms, implement multi-scale spatio-temporal feature fusion, and ensure the physical reasonableness of the prediction results. SUMMARY

[0005] To overcome the defects in the prior art described above, the present application provides a low-altitude wind field prediction method and system based on a spatio-temporal graph convolution network.

[0006] To achieve the above-mentioned purpose, the present application adopts the following technical solutions, comprising: The application discloses a low-altitude wind field prediction method based on a space-time graph convolution network, which is realized by adopting a low-altitude wind field prediction model, wherein the model comprises a dynamic graph construction module, a graph attention network, a PhysFusion-TransTCN encoder and an output module which are sequentially connected; the PhysFusion-TransTCN encoder is composed of multiple layers of stacking, and each layer comprises an attention preprocessing module, a multi-head attention module and a feedforward network module which are sequentially connected. The method comprises: S1: collecting wind field observation data and physical field data of all nodes in a target region, and constructing a dynamic space-time graph based on a flow function-vorticity theory through a dynamic graph construction module; the wind field observation data are three-dimensional wind speed vectors, and the three-dimensional wind speed vector of each node comprises a horizontal x-axis direction wind speed component, a horizontal y-axis direction wind speed component and a vertical z-axis direction wind speed component; the physical field data comprises temperature, air pressure and humidity; the node is an observation point in the target region; S2: extracting spatial information based on the dynamic space-time graph through the graph attention network to obtain a spatial feature tensor; S3: obtaining wind field deep space-time features through the PhysFusion-TransTCN encoder by taking the spatial feature tensor and the physical field data as input; S4: performing hierarchical feature aggregation on the wind field deep space-time features through the output module to obtain wind field prediction results of all nodes in the target region.

[0007] Preferably, in the step S1, the dynamic space-time graph is constructed based on the flow function-vorticity theory through the dynamic graph construction module, and the method comprises the following steps: S11: calculating a three-dimensional vorticity vector of each node based on wind field observation data of each node, and the calculation formula is as follows: ; Wherein, i is the node number; is the three-dimensional vorticity vector at the node i; , and are the horizontal x-axis direction wind speed component, the horizontal y-axis direction wind speed component and the vertical z-axis direction wind speed component of the i th node respectively; , , , , and respectively represent the wind speed change rate of the corresponding direction wind speed component in the corresponding direction at the node i; S12: constructing a wind field physical similarity matrix between nodes based on the three-dimensional vorticity vector of each node , and the calculation formula is as follows: ; where t is the time step number; j is another arbitrary node distinguished from node i; is the wind field physical similarity between node i and node j at time step t; and are the three-dimensional wind speed vectors of node i and node j at time step t, respectively, ; and are the three-dimensional vorticity vectors of node i and node j at time step t, respectively; is the scale parameter of vorticity similarity; is the scale parameter of velocity similarity; is the displacement vector from node i to node j; is the distance decay function between node i and node j; is the square of the Euclidean norm of the vector; is the learnable weight coefficient; S13: Based on the wind field observation data of each node, the node connection weight between nodes is constructed , the calculation formula is: ; where, is the node connection weight between node i and node j at time step t; (.) is the sigmoid function; is the learnable parameter; and are the node features of node i and node j, respectively, ; is the wind speed vector of node i; and are learnable parameters; is the concatenation operation; is the sine position encoding, i.e., the time step encoding of the target area; is the time series correlation between node i and node j, the time series correlation is used to measure the similarity of the sequence change pattern of the historical wind speed of node i and node j within the last time steps from to t; are the historical wind speed sequences of node i and node j in the time interval , t] respectively; (.) is the correlation calculation function; is the distance decay coefficient; is the spatial distance between node i and node i; S14: Based on the wind field physical similarity matrix at each time step and node connection weights constructing a dynamic spatiotemporal graph in the following way: ; wherein, is the spatiotemporal graph at time step t; is an adaptive weight function; is the velocity vector field formed by the wind speed of all nodes of the wind field; k is a scaling factor; is a velocity threshold value; is the gradient of the velocity vector field at time step t; is the physical similarity matrix of the wind field at time step t; is the node connection matrix at time step t; is a terrain constraint function; is the Frobenius norm.

[0008] Preferably, step S2 comprises: S21: calculating an attention coefficient based on the wind field observation data and the neighbor relationship defined by the dynamic spatiotemporal graph, the calculation formula being: ; wherein, p is any one node; node q is any one of the neighbor nodes of node p; is a set of neighbor nodes, including the node p itself; is the attention coefficient between node p and node q; (.) is a nonlinear activation function; is a learnable attention weight vector; is a trainable weight matrix; and are the node feature representations of node p and node q respectively, ; is the wind speed vector of node p; and are learnable parameters; denotes a concatenation operation; is the physical association strength between node p and node q; S22: normalizing the attention coefficients of node p and all neighbor nodes to obtain the attention weights between node p and all neighbor nodes; S23: based on the attention weights between each node and all neighbor nodes, aggregating the projection features between each node and the corresponding all neighbor nodes to obtain the spatial feature tensor of the node.

[0009] Preferably, step S3 comprises: S31: In each layer of the PhysFusion-TransTCN encoder, the spatial input features and the physical field data are input into the attention preprocessing module for temporal feature enhancement and physical information fusion to obtain spliced features; wherein the spatial input features are the spatial feature tensor in the first layer of the PhysFusion-TransTCN encoder, and the output of the PhysFusion-TransTCN encoder in the previous layer is used as the input of the PhysFusion-TransTCN encoder in the remaining layers; S32: Based on the spliced features, the multi-head attention is obtained through the multi-head attention module; S33: The PhysFusion-TransTCN encoder performs residual connection and layer normalization on the multi-head attention to obtain comprehensive attention; S34: Based on the comprehensive attention, the feedforward features are obtained through the feedforward network module; S35: The PhysFusion-TransTCN encoder performs residual connection and layer normalization on the comprehensive attention and the feedforward features to obtain the output of each layer of the PhysFusion-TransTCN encoder, i.e., the comprehensive feedforward features; at the same time, the comprehensive feedforward features output by the last layer of the PhysFusion-TransTCN encoder are marked as the wind field deep spatiotemporal features.

[0010] Preferably, step S4 comprises: S41: Multi-scale feature aggregation is performed on the wind field deep spatiotemporal features to obtain aggregated features ; the calculation is represented as: ; ; ; ; wherein, is the global attention pooling; is the local graph reading; is the physical feature projection; L is the total number of layers of the PhysFusion-TransTCN encoder; is the wind field deep spatiotemporal feature; is the spatiotemporal graph at time step t; P is the physical field data; is the layer normalization operation; S42: Based on the aggregated features , the wind field prediction results of all nodes in the target region are obtained , the calculation is represented as: ; wherein, TemporalInterpolate(.) is a time interpolation function based on physical constraints; and are the learnable weights and bias of the output module, respectively.

[0011] Preferably, in step S31, the calculation formula of the spliced feature is: ; ; ; wherein, is the spliced feature of the i-th layer; k is the expansion convolution branch number; K is the total number of parallel expansion convolution branches; l is the physical perception gating signal of the k-th expansion convolution branch; denotes element-wise multiplication; is the k-th expansion convolution branch; is the spatial input feature of the i-th layer, which is equal to the output of the PhysFusion-TransTCN encoder in the previous layer when is equal to 1, l i.e., the spatial feature tensor; || represents the feature splicing operation; P is the physical field data; l is the Sigmoid activation function; and are the learnable gating parameters of the k-th expansion convolution branch; is the physical feature vector obtained by performing spatio-temporal pooling operation on the physical field data; and are the maximum pooling and average pooling along the time dimension, respectively; and represent the maximum pooling and average pooling along the spatial node dimension, respectively; Step S32 comprises: S321: based on the spliced feature, each attention head head in the multi-head attention module is calculated, represented as: ; ; ; wherein, softmax(.) is a normalization operation; are all learnable parameter matrices; is the attention score; is the feature dimension of the query vector and the key vector ; is a scaling factor; is the physical association strength between node i and node j; and ​is the flow function vector potential gradient of nodes i, j, respectively; and is the three-dimensional vorticity vector of node i and node j, respectively; denotes the square of the Euclidean norm; and is a learnable scale parameter; and is a learnable weight coefficient; is a lower triangular time sequence mask matrix; S322: splicing and linear transformation are performed on all attention heads to obtain the output of the multi-head attention module, i.e., the multi-head attention .

[0012] Preferably, in step S33, the calculation of the comprehensive attention is represented as: ; wherein, is the comprehensive attention of the PhysFusion-TransTCN encoder; l layer; (.) is a layer normalization operation; is the spatial input feature of the layer; l is the multi-head attention of the layer; In step S34, the calculation of the feedforward feature is represented as: l ; ; wherein, is the feedforward feature of the PhysFusion-TransTCN encoder; l layer; GELU(.) is a Gaussian error linear unit activation function; and is a learnable weight matrix; is a bias term; is physical field data; || represents a splicing operation in the feature dimension; is a physical-guided time sequence convolution operation.

[0013] Preferably, the loss function adopted by the PhysFusion-TransTCN encoder of the low-altitude wind field prediction model in the training process is a total physical residual loss , and the calculation formula is: ; ; ; ;​ wherein, is the index of the current layer; L is the total number of layers of the PhysFusion-TransTCN encoder; is the physical residual loss of the e-th layer of the PhysFusion-TransTCN encoder; l is the physical residual loss of the e-th layer of the PhysFusion-TransTCN encoder; is the adaptive weight assigned to the physical residual loss of the e-th layer of the PhysFusion-TransTCN encoder at the e-th training cycle; l is the adaptive weight assigned to the physical residual loss of the e-th layer of the PhysFusion-TransTCN encoder at the e-th training cycle; is the square of the L2 norm; is the vector differential operator; is the divergence operation of the velocity field; is the mass conservation constraint; is the momentum conservation constraint; is the local acceleration term; is the advection term; is the pressure gradient term; is the viscous diffusion term; is the predicted pressure field; is the air density; is the kinematic viscosity coefficient; is the scaling factor; is the physical residual loss calculated by the e-th layer at the e-th training cycle; is the main prediction task loss at the e-th training cycle; is the main prediction task loss at the e-th training cycle; is the length of the prediction sequence; is the three-dimensional wind field observation data at time step t; is the model-predicted three-dimensional wind field at time step t, (.) is the Huber loss function; e is the current training cycle number; is the anti-division-by-zero parameter; is the main prediction task loss; is the physical residual loss of the k-th layer at the e-th training cycle.

[0014] Preferably, the total loss function adopted by the low-altitude wind field prediction model in the training process is a multi-objective composite loss , and the calculation formula is: ; ; ; ; wherein, is the total physical residual loss; is the vortex topology conservation loss term; a spatiotemporal spectrum energy balance loss term; a heuristic dynamics regularization term; , , are weight coefficients of the respective loss terms, respectively; a main task prediction loss; a vorticity field or Q-criterion field calculated based on the wind speed field; a persistence map of a scalar field; a Wasserstein distance between two persistence maps; (.) is a spatiotemporal Fourier transform; is a three-dimensional wave number vector; is an angular frequency; is a target energy spectrum function; a spatiotemporal coherence loss term; a weight coefficient of the spatiotemporal coherence loss term; a weight coefficient of the dynamic smoothing loss term; a dynamic smoothing loss term.

[0015] A low-altitude wind field prediction system based on a spatiotemporal graph convolution network, to implement a low-altitude wind field prediction method based on a spatiotemporal graph convolution network, comprising a dynamic graph construction module, a graph attention network, an attention preprocessing module, a multi-head attention module, a feedforward network module, and an output module; the dynamic graph construction module is used to process wind field observation data to obtain a dynamic spatiotemporal graph; the graph attention network is used to extract a spatial feature tensor based on the wind field observation data and the dynamic spatiotemporal graph; the attention preprocessing module is used to perform time series feature enhancement and physical information fusion to obtain spliced features; the multi-head attention module is used to perform multi-head attention extraction based on the spliced features, and finally obtain comprehensive attention; the feedforward network module is used to finally obtain wind field deep spatiotemporal features based on the comprehensive attention; and the output module is used to obtain a wind field prediction result based on the wind field deep spatiotemporal features.

[0016] The present application has the following advantages: (1) The present application collects wind field observation data and physical field data of all nodes in a target region, constructs a dynamic spatiotemporal graph based on a dynamic graph construction module, extracts spatial information through a graph attention network to obtain a spatial feature tensor, obtains wind field deep spatiotemporal features through a PhysFusion-TransTCN encoder from the spatial input features and the physical field data, and obtains a wind field prediction result of the target region through hierarchical feature aggregation of the wind field deep spatiotemporal features by an output module. The wind field physical mechanism is deeply fused, multi-scale spatiotemporal feature fusion is achieved, and the prediction result accuracy and physical rationality are guaranteed.

[0017] (2) The present application constructs a complete GAT-PhysTransTCN low-altitude wind field prediction model, extracts spatial features through a graph attention network (GAT), and then realizes deep fusion of space-time features through a physical fusion PhysFusion-TransTCN encoder to form an end-to-end physically guided wind field prediction framework, which significantly improves the prediction accuracy and system practicability while ensuring physical consistency.

[0018] (3) The present application introduces a physically guided dynamic graph construction method (formulas 1-4), overcomes the limitations of traditional static graph construction, and realizes a truly space-time adaptive physical graph structure.

[0019] (4) The present application proposes an innovative PhysFusion-TransTCN encoder architecture, realizes deep coupling of physical mechanisms and deep learning models through physical TCN attention preprocessing and physical enhancement multi-head attention mechanism (formulas 9-11), designs a physical TCN feedforward network (formula 14) that introduces multi-scale time convolution and physical process gating into the standard feedforward network to further enhance the model's ability to model complex physical processes, constructs a hierarchical physical consistency supervision mechanism (formula 17) that applies physical constraints at each layer of the encoder to ensure the overall physical reasonableness from low-level features to high-level representations, and innovatively introduces a physical violation degree-aware adaptive weight distribution strategy (formula 18) that dynamically adjusts the supervision strength of each layer through a weight factor The factor considers the physical constraint violation degree of each layer, the network level depth, and the training process to realize intelligent supervision that focuses on supervising severely violating layers, strengthens basic laws in shallow layers, and gradually tightens constraint strength, ensuring the overall physical reasonableness from low-level features to high-level representations.

[0020] (5) The present application creatively proposes a compound loss function based on vortex topological conservation and space-time spectral divergence balance (formula 21). This loss function goes beyond the traditional "data fitting + physical residual" simple paradigm, introduces a vortex topological conservation loss term to ensure the reasonableness of the key physical structure of the wind field at the topological invariance level, a space-time spectral energy balance loss term to force the model to follow the turbulent energy spectrum law in the frequency domain, and an innovative heuristic dynamic regularization term to guide the wind field dynamics to approach an efficient and robust natural mode. This all-around and deep-level physical constraint from geometric topology, frequency energy to heuristic dynamics forms a multi-dimensional supervision system, significantly improving the model's generalization ability and the physical credibility of the prediction results. BRIEF DESCRIPTION OF DRAWINGS

[0021] Figure 1 is a low-altitude wind field prediction model architecture of the present application. Figure 2 This is a diagram of the feedforward network module structure; Figure 3 Diagram of the hierarchical physical supervision architecture for the PhysFusion-TransTCN encoder; Figure 4 A comparison chart showing the convergence curve of the training loss and the prediction performance on the test set; Figure 5 This is a flowchart of the prediction method of the present invention. Detailed Implementation

[0022] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0023] Example 1 like Figures 1-5 As shown, this invention proposes a low-altitude wind field prediction method based on a spatiotemporal graph convolutional network. The method employs a low-altitude wind field prediction model, which includes a physically guided dynamic graph construction module (hereinafter referred to as the dynamic graph construction module), a GAT-PhysTransTCN network, and an output module, all connected sequentially. The GAT-PhysTransTCN network comprises a graph attention network (GAT) and a PhysFusion-TransTCN encoder. The PhysFusion-TransTCN encoder is composed of multiple stacked layers, with the output of the previous layer serving as the input of the next. Each layer includes a physically TCN attention preprocessing module (hereinafter referred to as the attention preprocessing module), a physically enhanced multi-head attention module (hereinafter referred to as the multi-head attention module), and a physically TCN feedforward network module (hereinafter referred to as the feedforward network module), all connected sequentially. The method includes: S1: Collect wind field observation data and physical field data of all nodes in the target area, and construct a physically guided dynamic spatiotemporal graph structure (referred to as dynamic spatiotemporal graph) based on the stream function-vorticity theory through the dynamic graph construction module. Historical wind field observation data over a period of one year was collected from 1000 observation points within the target area using wind profiler lidar. The data frequency is 6 minutes. A spatial coordinate system is constructed. The wind field observation data includes the three-dimensional wind speed vectors of all nodes, and the three-dimensional wind speed vector of each node... It includes the wind speed component U along the horizontal x-axis, the wind speed component V along the horizontal y-axis, and the wind speed component W along the vertical z-axis; it also collects physical field data. Physical field data including temperature, air pressure and humidity. Each observation point is regarded as a node in the graph structure, totaling 1000 nodes. is the total number of nodes; T is all time steps, and B is the batch size, is all dimensions.

[0024] The dynamic graph construction module constructs a physically guided dynamic spatiotemporal graph (referred to as dynamic spatiotemporal graph) based on the flow function-vorticity theory, including: S11: Calculate the three-dimensional vorticity vector based on wind field observation data The calculation formula is: ; where i is the node number; is the three-dimensional vorticity vector at node i; refers to the gradient operator, i.e., the vector differential operator; represents the curl operator, which is used to calculate the rotation degree of the vector field; is the wind speed component in the horizontal x-axis direction of the i th node; is the wind speed component in the horizontal y-axis direction of the i th node; is the wind speed component in the vertical z-axis direction of the i th node; represents the rate of change of the wind speed component in the horizontal x-axis direction at node i in the horizontal y-axis direction; represents the rate of change of the wind speed component in the horizontal x-axis direction at node i in the vertical z-axis direction; represents the rate of change of the wind speed component V in the horizontal y-axis direction at node i in the horizontal x-axis direction; represents the rate of change of the wind speed component V in the horizontal y-axis direction at node i in the vertical z-axis direction; represents the rate of change of the wind speed component W in the vertical z-axis direction at node i in the horizontal x-axis direction; represents the rate of change of the wind speed component W in the vertical z-axis direction at node i in the horizontal y-axis direction; are respectively the components of the three-dimensional vorticity vector at node i in the x, y, and z directions.

[0025] S12: Based on the three-dimensional vorticity vector of the wind field at each node, construct the wind field physical similarity matrix between nodes The calculation formula is: ; where t is the time step number; j is another arbitrary node distinguished from node i; is the wind field physical similarity matrix between node i and node j at time step t; and is the three-dimensional wind speed vector at node i and node j at time step t, respectively; ; and is the three-dimensional vorticity vector at node i and node j at time step t, respectively; is the scale parameter of vorticity similarity, controlling the sensitivity of the prediction model to the difference in vorticity; is the scale parameter of velocity similarity, controlling the sensitivity of the prediction model to the difference in velocity; is the displacement vector from node i to node j, calculated based on the three-dimensional spatial coordinates of the nodes; is the distance decay function between node i and node j; is the square of the Euclidean norm of the vector, measuring the difference in vorticity vector between the two nodes at time step t; is the learnable weight coefficient, used to balance the contribution of velocity similarity in the calculation of physical similarity.

[0026] Physical similarity matrix Through the three terms in formula (2), the similarity between nodes in the velocity field and the three-dimensional vorticity field is measured respectively, and the spatial proximity constraint is applied to capture the spatio-temporal correlation characteristics in the wind field based on physical laws. The velocity field reflects the overall flow pattern of the wind field; the vorticity field characterizes the local rotation characteristics; the distance decay function ensures the spatial proximity constraint, and the three together build a graph structure consistent with the principles of fluid mechanics.

[0027] S13: Based on the wind field observation data of each node, construct the node connection weight between nodes , the calculation formula is: ; where, is the node connection weight between node i and node j at time step t; (.) is the sigmoid function; is a learnable parameter; and are the node feature representations of node i and node j, respectively; ; is the wind speed vector of node i; and are learnable parameters; is the concatenation operation; is the sine position encoding, i.e., the time step encoding of the target region; is the temporal correlation between node i and node j, temporal correlation is used to measure the temporal correlation between node i and node j in the last time steps (from The similarity of the sequence variation pattern of the historical wind speed in t) captures the dynamic evolution pattern between nodes, enhancing the adaptability to non-stationary wind field changes; respectively, the historical wind speed sequence of node i and node j in the time interval[ ,t]; (.) is a correlation calculation function, and a Pearson correlation coefficient is used to measure the linear correlation degree of two sequences; is the distance attenuation coefficient; is the spatial distance between node i and node i; The dynamic graph construction module fuses node features , time encoding , the time sequence correlation between node i and node j and the spatial distance between node i and node i , through the learnable parameters to realize data-driven adjacency relationship discovery, and the finally calculated scalar is the dynamic connection weight between node i and node j learned by data-driven at time step t.

[0028] S14: Based on the wind field physical similarity matrix and the node connection weight at each time step, a dynamic space-time graph is constructed, and the construction method is: ; wherein, is the space-time graph at time step t; is an adaptive weight function balancing physical priori and data-driven, which dynamically adjusts the contribution proportion of physical priori and data-driven according to the wind field gradient; is the velocity vector field formed by the wind speed of all nodes of the wind field; k is a scaling factor, that is, a hyperparameter, which is set to 1.0 in this embodiment; is the velocity threshold, that is, a reference value, in this embodiment, it is set to 1.5 times of the average wind speed of the target area; is the gradient of the velocity vector field at time step t; is the wind field physical similarity matrix at time step t; is the node connection matrix at time step t; is a terrain constraint function, which fuses terrain factors such as elevation and surface roughness; is the Frobenius norm, which acts on the velocity gradient tensor v(t) to calculate its size.

[0029] A dynamic graph construction module is designed to dynamically adjust the connection weight between nodes (dynamic adjacency weight matrix). Meanwhile, the dynamic spatio-temporal graph adopts a ternary fusion architecture to realize the synergistic effect of physical law, data-driven and terrain constraint. When the wind field changes dramatically (larger), the guidance role of physical prior is enhanced; when the wind field is relatively stable, the dynamic learning of data-driven is focused; the terrain constraint ensures that the graph structure conforms to the actual geographical environment, forming a truly spatio-temporal adaptive physical graph construction method.

[0030] S2: Extract spatial information based on the spatio-temporal graph through the graph attention network to obtain the spatial feature tensor ; including: S21: Based on the neighbor relationship defined by the dynamic spatio-temporal graph, the attention coefficient with physical bias is calculated based on the wind field observation data, and the calculation formula is: ; Where p is any node; node q is any one of the neighbor nodes of node p; the neighbor node , is the set of neighbor nodes (including itself p); is the attention coefficient between node p and node q; (.) is a nonlinear activation function (negative slope is 0.2); is a learnable attention weight vector; used to map the high-dimensional vector after splicing to a scalar attention coefficient; is a trainable weight matrix, used for shared feature transformation (linear projection) of all nodes; and are the node feature representations of nodes p and q respectively; and are learnable parameters; is the wind speed vector of node p; represents the splicing operation; is the physical relationship bias function between node p and node q, which calculates the physical correlation strength based on the similarity between the stream function vector potential field gradient and the vorticity vector between node p and node q; For each node p, its neighbor node set N p is determined by the dynamic spatio-temporal graph A(t), which usually contains all nodes connected with node p in the dynamic spatio-temporal graph A (t) with non-zero connection weight.

[0031] Based on the three-dimensional vorticity vector, the stream function vector potential field is obtained by solving the vector Poisson equation: ; ​Equation (6) describes a global physical constraint relationship, which is used to solve the entire wind field vector potential distribution from the entire wind field vorticity distribution. The stream function vector potential at the pth node is the entire stream function vector potential field is the discrete value at node p, which is obtained by globally solving the equation .

[0032] S22: Normalize the attention coefficients of node p and all neighbor nodes to obtain the attention weight between node p and all neighbor nodes q , the calculation formula is: ; wherein, is the attention weight between node p and neighbor node q; k is the neighbor node index of node p, and the set is traversed. denotes the set of p and the neighbor nodes of p. is the attention coefficient between node p and neighbor node k.

[0033] This normalization operation ensures that the sum of the attention weights of all neighbor nodes of node p is 1.

[0034] S23: Based on the attention weight between each node and all neighbor nodes, aggregate the projection features between each node and the corresponding all neighbor nodes to obtain the spatial feature tensor of each node. The calculation formula is: ; wherein, ; is a trainable weight matrix. is the projection feature of node q after linear transformation; ELU(.) is an exponential linear unit activation function.

[0035] The above operation dynamically captures spatial dependency relationships using a graph attention network and injects physical bias information.

[0036] S3: Obtain the deep spatiotemporal features of the wind field by encoding the spatial feature tensor and the physical field data P through the PhysFusion-TransTCN encoder. The PhysFusion-TransTCN encoder is composed of multiple layers of stacking, each of which includes a physical TCN attention preprocessing module (referred to as an attention preprocessing module), a physically enhanced multi-head attention module (referred to as a multi-head attention module), and a physical TCN feedforward network (referred to as a feedforward network) connected in turn. Step S3 includes: ​S31: The spatial input features and the physical field data are input into the attention preprocessing module for time sequence feature enhancement and physical information fusion to obtain spliced features , and the calculation formula is: ; wherein, is the spliced feature of the kth layer; k is the expansion convolution branch number; K is the total number of parallel expansion convolution branches, which is set to 4 in this embodiment; l is the physical perception gating signal of the kth expansion convolution branch; represents element-wise multiplication (Hadamard product); is the kth expansion convolution branch, and the expansion factor is , in this embodiment, the expansion factor is set to increase exponentially: , that is, 1, 2, 4, 8; is the spatial input feature of the kth layer, which is equal to the output of the PhysFusion-TransTCN encoder in the previous layer, when is equal to 1, l = spatial feature tensor l ; || represents the feature splicing operation; P is the physical field data, including temperature, air pressure and humidity; The calculation of the physical perception gating signal of the kth expansion convolution branch is as follows: ; ; wherein, is a Sigmoid activation function; and are learnable gating parameters of the kth expansion convolution branch; is a physical feature vector obtained by performing spatio-temporal pooling operation on the physical field data P, and the calculation is:

[0037] wherein, and are maximum pooling and average pooling along the time dimension, respectively; and represent maximum pooling and average pooling along the spatial (node) dimension, respectively.

[0038] For example, the expansion convolution with an expansion factor of , the expansion factor increases exponentially, , that is, 1, 2, 4, 8. Each expansion convolution branch adopts causal convolution to ensure the causal relationship of time sequence, and the convolution kernel size​ Each branch in the multi-scale feature fusion process independently processes features of different time scales: Branch 1 ( ): captures local temporal patterns (minute scale), Branch 2 ( 2): captures short-term temporal patterns (10-minute scale), Branch 3 ( 4): captures medium-term temporal patterns (hour scale), Branch 4 ( 8): captures long-term temporal patterns (hours scale); adaptive multi-scale fusion is achieved through gated weighted summation to obtain the first l layer of spliced features :

[0039] wherein, .

[0040] Physical process adaptive mechanism: gating signal According to the spatio-temporal statistical characteristics of physical field features (extracted through ), the weight contribution of each branch is dynamically adjusted: when the temperature gradient is large, the weight of the branch related to wave propagation is enhanced; when the pressure distribution is uniform, the weight of the branch related to translational diffusion is enhanced; when the humidity changes dramatically, the contribution of the branch related to convection is adjusted.

[0041] The attention preprocessing module adopts a four-branch parallel structure, corresponding to different time scales. Each branch contains dilated convolution and physical perception gating, with dilation factors of 1, 2, 4, and 8, respectively, and receptive fields of 3, 7, 15, and 31 time steps. The physical perception gating dynamically adjusts the weight proportion of each branch in feature fusion by analyzing the spatial distribution and temporal variation of temperature and pressure fields, enabling the model to adopt the optimal multi-scale feature extraction strategy for different meteorological conditions.

[0042] S32: Based on the spliced features obtained through the multi-head attention module, the multi-head attention is obtained, including: S321: Based on the spliced features, each attention head head in the multi-head attention module is calculated, represented as: (11) ; wherein, softmax(.) is a normalization operation; and are all learnable parameter matrices; the attention score is calculated; is the feature dimension of the query vector and the key vector (i.e., the length of the Q / K vector in each attention head); is the scaling factor for scaling the attention score, controlling the variance to be constant as 1 and independent of the input dimension; is the physical relation bias function, which is based on the similarity of the flow function vector potential gradient and the vorticity vector between node i and node j, to enhance the attention weight between the physical relation tight node pairs, where, and are the flow function vector potential gradient of node i, j, and are the three-dimensional vorticity vector of node i, j, denotes the square of the Euclidean norm; and are learnable scale parameters, respectively controlling the sensitivity of the flow function gradient similarity and the vorticity similarity, and are learnable weight coefficients for balancing the contributions of the two terms; is the lower triangular time mask matrix, which ensures the temporal causal relationship, prevents future information leakage, and maintains the time physical law of wind field evolution; then the scaled attention score is normalized using softmax to obtain the attention weight matrix (each row sum is 1), and finally the attention weight matrix is multiplied by to obtain the attention head head.

[0043] Each attention head independently calculates the physically enhanced attention to capture the correlation patterns in different physical dimensions.

[0044] S322: Concatenate and linearly transform all attention heads to obtain the output of the multi-head attention module, i.e., the multi-head attention, which is calculated as: ; where, is the multi-head attention in the l layer of the encoder; h is the number of attention heads in each layer, and each attention head has an independent weight matrix that will independently project the input QKV, independently calculate the attention score and weight; is the first attention head; is the hth attention head; Concat is the concatenation operation, which preserves the independent information of each attention head, and the concatenated matrix is multiplied by the output weight matrix to restore its dimension; The attention mechanism enables the model to focus on the most critical time points in the historical sequence for predicting future time points. The attention mechanism calculates the QK similarity on the basis of the standard multi-head attention, injects physical bias based on the gradient of the flow function and the vorticity field , enabling the model to identify node pairs with strong physical correlations. Temporal masks are used simultaneously to maintain causality and ensure that predictions only rely on historical information. The multi-head design allows the model to focus on spatial correlation patterns at different physical scales in parallel.

[0045] The multi-head attention module adopts a physically enhanced multi-head attention mechanism to inject physical bias on the basis of the standard multi-head attention, enhancing the model's ability to model the physical correlations of wind fields.

[0046] S33: The PhysFusion-TransTCN encoder performs residual connection and layer normalization on the multi-head attention to obtain the integrated attention, which is calculated as follows: ; wherein, is the integrated attention of the PhysFusion-TransTCN encoder at the l layer; (.) is the layer normalization operation; is the spatial input feature at the l layer, which is the output of the encoder in the previous layer, when l is 1, is the output of the graph attention network, which is the spatial feature tensor .

[0047] S34: The feedforward feature is obtained based on the integrated attention through the feedforward network module, which is calculated as follows: ; wherein, is the feedforward feature of the PhysFusion-TransTCN encoder at the l layer; GELU(.) is the Gaussian Error Linear Unit activation function; and are learnable weight matrices; is the bias term; is the physical field data, including temperature, air pressure, and humidity; || represents the concatenation operation in the feature dimension; is the physically guided temporal convolution operation, which is specifically defined as The PhysTCN operation contains K=4 parallel branches with dilation factors of 1, 2, 4, and 8, respectively, corresponding to feature extraction at different time scales; the physical process gating mechanism ; The physical perception gate signal is the k-th dilated convolution branch; PhysPool(P) performs pooling operations on the physical field data to extract physical features; The sigmoid activation function outputs gate weights in the range [0,1]. The expansion factor is The dilated convolution, the dilation factor grows exponentially ( ); The contribution weights of each branch are dynamically adjusted based on the spatial distribution of the physical field data, enabling the model to adaptively integrate the influence of different physical processes.

[0048] The feedforward network module introduces multi-scale temporal convolution and physical process gating on the basis of the standard feedforward network.

[0049] S35: The PhysFusion-TransTCN encoder performs residual connections and layer normalization on the integrated attention and feedforward features to obtain the integrated feedforward features. This is to preserve information from previous layers and enhance the stability of feature representations.

[0050] ; in, (.) represents the layer normalization operation.

[0051] Integrated feedforward features This represents the output of each layer in the PhysFusion-TransTCN encoder; simultaneously, between adjacent layers, the output of the previous layer serves as one of the inputs to the attention preprocessing module in the next layer of the PhysFusion-TransTCN encoder, i.e., spatial input features. Secondly, the output of the last layer of the PhysFusion-TransTCN encoder is combined with the feedforward features of the Lth layer. As a deep spatiotemporal characteristic of wind fields.

[0052] Physical consistency supervision: Physical consistency supervision applies Navier-Stokes equation constraints to each layer of the encoder to ensure that the network learns feature representations that conform to the laws of fluid dynamics. First, a lightweight linear projection head is used to project the encoder's... l Layer output - Synthetic feedforward features Mapped to a three-dimensional wind speed vector : (16); in, Indicates the first l The predicted wind field output by the layer (containing three velocity components: U, V, and W).

[0053] Then the residual of Navier-Stokes equation is calculated to get the physical residual loss (physical consistency loss) , which is calculated as follows: (17); where, is the square of L2 norm; is the Nabla operator (vector differential operator); is the divergence operation, representing the "source-sink" strength of the velocity field; is the mass conservation constraint, forcing the predicted wind field to satisfy the continuity equation of incompressible fluid , ensuring that the predicted wind field maintains the characteristics of incompressible fluid; is the momentum conservation constraint, forcing the predicted wind field to satisfy the Navier-Stokes equation; is the local acceleration term; is the convection term; is the pressure gradient term; is the viscous diffusion term; is the predicted pressure field; is the air density; is the kinematic viscosity coefficient.

[0054] The hierarchical supervision mechanism calculates the physical consistency loss at each layer of the encoder ( l = 1, 2,..., L), then the shallow layers focus on local physical laws, and the deep layers focus on global physical consistency, and finally the adaptive weight balances the contribution of each layer.

[0055] where, the adaptive weight format is as follows: (18); where, exp(.) is the exponential function with base natural number e; is the adaptive weight assigned to the layer physical loss at the e-th training cycle (epoch); is the scaling factor (hyperparameter), controlling the sharpness of the weight distribution; is the physical residual loss calculated by the layer at the e-th training cycle (i.e., the value of formula 17); is the main prediction task loss at the e-th training cycle; is the index of the current layer ( ); L is the total number of network layers; e is the current training cycle number; is the anti-division-by-zero parameter, a very small number (set to ), prevent division by zero; Physical residual loss of the k-th layer in the e-th training cycle.

[0056] The adaptive weight The design contains multiple mechanisms working together: Physical violation awareness: The control weight is positively correlated with the physical residual loss of the layer itself. If the output of a layer seriously violates the physical law (i.e. is large), it will receive a stronger supervision signal (larger ) in the next round of training, implementing a dynamic feedback mechanism of "where the error is more, where the focus is more supervision". The ratio to the main prediction task loss makes it a dimensionless relative measure; Hierarchical depth attenuation: is a factor that decreases with increasing layer depth. It embodies the priori knowledge of "local learning for shallow layers and global learning for deep layers". For shallow layers ( l small), the factor is large, encouraging the model to lay a solid physical foundation at the bottom; for deep layers ( l large), the factor is small, allowing the deep network to learn complex spatiotemporal correlations more flexibly under the premise of meeting basic physical constraints; Training process awareness: is a factor that slowly grows with the training cycle e. In the early stages of training, all are gently amplified, allowing the model to smoothly accept physical constraints. As training progresses, the factor gradually increases, gradually tightening the "valve" of physical constraints, guiding the model to pursue higher physical consistency in the late convergence period, which avoids the training difficulty that may be caused by early strong constraints; Softmax normalization: normalizes all layer weights through the Softmax function. This ensures that the total strength of physical supervision is stable and controllable throughout the training process, while achieving dynamic and competitive resource allocation among layers.

[0057] After each encoder output, the Navier-Stokes equation residual is calculated, containing both mass conservation and momentum conservation constraints. The mass conservation term ensures that the predicted wind field satisfies the incompressibility condition , and the momentum conservation term enforces the complete NS equation. Through hierarchical supervision, the shallow network focuses on local physical law consistency, and the deep network ensures global physical constraints, significantly improving the physical credibility of the prediction results.

[0058] The physical consistency loss of each layer of the encoder is weighted and summed through the adaptive weight to obtain the total physical residual loss L is the total number of layers of the encoder, is the adaptive weight of the e th layer in the l th training cycle, is the physical residual loss of the l th layer.

[0059] S4: The wind field deep spatio-temporal features are aggregated by the output module to obtain the wind field prediction results of all nodes in the target area . Including: S41: Multi-scale feature aggregation is performed on the wind field deep spatio-temporal features to obtain aggregated features , which is calculated as: ; ; ; ; wherein, is global attention pooling, which captures the overall evolution trend and large-scale circulation features of the wind field through the attention mechanism; is local graph reading, which aggregates neighborhood information based on dynamic spatio-temporal graph to preserve fine local spatial correlation features; is physical feature projection, which embeds the physical field data P into the feature space through linear transformation and incorporates the inherent laws of meteorological elements; is a layer normalization operation.

[0060] S42: Based on the aggregated features, the physical-guided wind field prediction results of all nodes in the target area are obtained , which is calculated as: ; wherein, TemporalInterpolate(.) is a time interpolation function based on physical constraints, which ensures the smooth continuity of the prediction sequence in the time dimension through techniques such as cubic spline interpolation, meets the time physical laws of wind field evolution, and the interpolation process meets the time smoothness constraints of wind field evolution; and are the learnable weights and biases of the output module, respectively; C is the number of output variables (U, V, W wind speed components); ; S is the prediction step; N is the number of nodes; C is the number of output variables.

[0061] The output module adopts a multi-scale fusion mechanism, which can cooperatively capture large-scale global evolution trends and fine local spatial details. By introducing physical feature projection, the internal laws of meteorological elements such as temperature and pressure are embedded into the feature representation, thereby ensuring that the output results strictly follow the basic principles of atmospheric motion. The use of time interpolation technology further ensures smooth transition of the prediction sequence in the time dimension, effectively avoiding non-physical mutations. Each level of features realizes adaptive weight allocation through layer normalization operations, balancing the contribution of information at different scales. The overall design realizes efficient mapping from deep abstract features to physically reasonable predictions, maintaining high prediction accuracy while significantly enhancing the physical credibility and practical application value of the results.

[0062] The composite loss function containing the physical constraint loss is calculated to optimize the entire deep learning prediction model parameters. The loss function of the entire prediction model adopts a composite loss function based on the conservation of vortex topology and the balance of space-time spectral divergence, specifically the loss function is designed as a multi-objective composite structure, balancing prediction accuracy and physical consistency: Multi-objective composite loss The calculation method is: ; Wherein, , , are the weight coefficients of each loss term, used to balance the contribution of each loss in the total loss; is the main task prediction loss, which adopts Huber loss to balance the advantages of L1 / L2 loss, and has stronger robustness to outliers; is the length of the prediction sequence (i.e. the number of time steps S); is the true three-dimensional wind field observation data at time step t; is the model predicted three-dimensional wind field at time step t, (.) is the Huber loss function.

[0063] is the total physical residual loss, L is the total number of layers of the encoder, is the adaptive weight of the e th layer in the l th training cycle, is the physical residual loss of the l th layer.

[0064] Vortex topology conservation loss term This loss term aims to maintain the topological invariance of the key physical structure in the wind field, vortex. We achieve this by calculating the difference in persistent homology between the predicted wind field and the real wind field on the vortex field, ; the vorticity field or Q-criterion field based on the wind speed field calculation, for identifying vortex structures; the real 3D wind field observation data at time step t; the model-predicted 3D wind field at time step t; the persistence diagram of the scalar field, which describes the generation (“birth”) and disappearance (“death”) of vortex structures; the Wasserstein distance between two persistence diagrams, which is a robust method to measure the difference in topological structure. This loss term does not directly constrain the wind speed values, but forces the model-predicted wind field to have homotopically equivalent vortex structures with the real wind field, i.e., the generation, evolution, and extinction patterns of vortices are consistent in the topological sense. This can greatly improve the physical structure rationality of the predicted wind field.

[0065] spatiotemporal spectral energy balance loss term This loss term enforces the model to obey the energy spectrum law derived from turbulence theory in the Fourier frequency domain, ; (.) is the spatiotemporal Fourier transform, which transforms the wind field into the wave number-frequency domain ; is the 3D wave number vector, with the unit of rad / m, representing the spatial frequency, corresponding to the wavelength of the wind field in x, y, z directions; is the angular frequency, with the unit of rad / s, representing the temporal frequency, corresponding to the speed of the wind field changing over time; is the target energy spectrum function, which is defined based on physical prior knowledge, such as setting it to in the inertial subregion to comply with the Kolmogorov theory. This constraint ensures that the energy distribution of the predicted wind field at different spatial scales and temporal frequencies complies with the physical laws of turbulence.

[0066] heuristic dynamic regularization term This regularization term aims to improve the dynamic rationality and robustness of the predicted wind field in complex scenarios (such as over terrain, encountering wind shear), and its design inspiration comes from the observation of general laws of efficient and stable dynamic systems. It improves the generalization ability by encouraging the wind field evolution to have moderate spatiotemporal coordination, while avoiding non-physical disordered or overly rigid patterns, where, is the weight coefficient of the spatiotemporal coordination loss term ; is the weight coefficient of the dynamic smoothing loss term ; The spatiotemporal coordination loss is used to calculate the coordination degree of the wind speed change direction of different regions of the wind field, and it punishes non-physical extreme patterns that lead to complete disorder (chaos) or complete synchronization (loss of details) in space, and encourages the formation of a "structured chaos" state that is both coordinated and maintains local flexibility, which is closer to the real atmospheric turbulence; , Here, PearsonCorr calculates the Pearson correlation coefficient of the time derivative (acceleration) of the wind speed between different nodes; is a target coordination hyperparameter used to control the "order degree" of the system; The dynamic smoothing loss ensures that the wind field prediction has physically reasonable smoothness in time and space, avoiding non-physical abrupt changes, This term respectively constrains the jerk of the wind field in time and the Laplacian in space.

[0067] This paradigm goes beyond the traditional simple superposition mode of "data fitting + physical residual", and by introducing the topological invariance constraint of the vortex field and the spatiotemporal spectral energy balance constraint implemented in the Fourier frequency domain, it starts from the deeper physical conservation laws to guide the model to learn the essential laws of wind field evolution.

[0068] Embodiment 2 The present application proposes a low-altitude wind field prediction system based on a spatiotemporal graph convolution network, to realize a low-altitude wind field prediction method based on a spatiotemporal graph convolution network, which includes a dynamic graph construction module, a graph attention network, an attention preprocessing module, a multi-head attention module, a feedforward network module, and an output module. The dynamic graph construction module is used to process wind field observation data to obtain a dynamic spatiotemporal graph. The graph attention network is used to extract a spatial feature tensor based on the wind field observation data and the dynamic spatiotemporal graph. The attention preprocessing module is used for time series feature enhancement and physical information fusion to obtain splicing features. The multi-head attention module is used to extract multi-head attention based on the splicing features, and finally obtain comprehensive attention. The feedforward network module is used to finally obtain wind field deep spatiotemporal features based on the comprehensive attention. The output module is used to obtain wind field prediction results based on the wind field deep spatiotemporal features.

[0069] Embodiment 3 To verify the effectiveness of the model proposed in the present application, in this embodiment, all experiments are implemented based on the PyTorch deep learning framework, and are performed on a server equipped with an NVIDIA Tesla V100 32GB GPU. The key parameter settings for model training and testing are as follows: a) Data configuration: the ratio of training set, validation set and test set is 7:2:1; the input sequence length (T) is set to 12 (i.e. 1.2 hours of past data); the output prediction sequence length (S) is set to 6 (i.e. 0.6 hours of future wind field); the batch size (B) is set to 16.

[0070] b) Graph structure construction parameters: the scale parameter in the physical similarity matrix The balance factor is adaptively determined by the data standard deviation and is set to 0.5; the distance decay coefficient in the dynamic adjacency weight learning is set to 0.1; the parameters k and in the adaptive weight function are respectively set to 1.0 and 1.5 times of the average wind speed in the region.

[0071] c) GAT-PhysTransTCN network core parameters: the number of layers of the graph attention network GAT is set to 1, the number of heads is set to 4, the intermediate layer feature dimension is 128; the number of layers (L) of the PhysFusion-TransTCN encoder is set to 3; the number of parallel branches of the physical TCN attention preprocessing and the physical TCN feedforward network (K) is both 4, and the dilation factor sequence is [1, 2, 4, 8]; the number of heads of the physical enhanced multi-head attention is set to 8, the key-value dimension is 32; the internal dimension of the feedforward network is 512.

[0072] d) Training strategy and hyperparameters: the optimizer adopts AdamW, the initial learning rate is set to , and the cosine annealing scheduler is adopted; the number of training cycles (epoch) is 200; the weight coefficients in the compound loss function are determined by grid search, and finally set to: , , ; the adaptive weight hyperparameter of hierarchical physical supervision is set to 1.0.

[0073] The above parameters achieve the best performance on the wind farm data set described in the embodiment, and can be fine-tuned according to the specific data characteristics when applied to other scenarios.

[0074] To verify the effectiveness of the prediction model proposed in the application, the model (GAT-PhysTransTCN) proposed in the application is compared with the following baseline models on the wind farm data set described in the embodiment:​​​​​ Historical Persistence: Use the current time observation as the future prediction.

[0075] Long Short-Term Memory (LSTM): A classic recurrent neural network.

[0076] Temporal Convolutional Network (TCN): A modern sequential model based on dilated causal convolution.

[0077] Spatiotemporal Graph Convolutional Network (STGCN): A classic spatiotemporal graph convolutional model without integrated attention mechanism.

[0078] All deep learning models use the same training, validation, and test sets, and are adjusted to their best hyperparameters as much as possible. The evaluation metrics use root mean square error (RMSE) and mean absolute error (MAE), and the results are shown in Table 1.

[0079] Table 1: Comparison of prediction performance of different models on the test set ; As can be seen from Table 1, the GAT-PhysTransTCN model proposed in the present application is significantly better than all baseline models in terms of RMSE and MAE. This shows that through physical-guided dynamic graph construction and physically-enhanced spatiotemporal feature extraction, the present application can more accurately capture the complex spatiotemporal coupling evolution law in the wind field, thereby achieving more accurate multi-step prediction.

[0080] To further verify the effectiveness of the composite loss function proposed in the present application, we conducted a rigorous ablation experiment. The results show that when the vortex topological conservation term ( ) is removed, the key indicators of the model in the vortex identification task are significantly degraded: the vortex average duration error increases by 15.3% (p < 0.01, paired t-test), and the average Hausdorff distance of vortex center positioning increases by 22.1%. This proves that this loss term is crucial for maintaining the spatiotemporal continuity of the key physical structure of the wind field. When the spatiotemporal spectral energy balance term ( ) is removed, the fitting coefficient of determination (R²) of the predicted wind field energy spectrum with the Kolmogorov -5 / 3 law decreases from 0.94 to 0.81, indicating that the physical reasonableness of its energy spectrum distribution is significantly reduced.

[0081] When the heuristic dynamic regularization term ( ) is removed, the root mean square error (RMSE) of the model in the wind shear and other sudden scene prediction increases by an average of 8.7%, and the abnormal jitter frequency of the predicted sequence increases by nearly 3 times. The above results quantitatively demonstrate the necessity and synergistic effect of each term in the composite loss function.

[0082] Figure 4 The loss change curve of the algorithm in the training process of the application is shown. It can be seen that the training loss and the validation loss can be smoothly decreased and finally converged, proving the stability and effectiveness of the training process of the proposed GAT-PhysTransTCN model and verifying the rationality of the model architecture design.

[0083] Of course, the application is not limited to the details of the above exemplary embodiments, but also includes the same or similar structures that can be implemented in other specific forms without departing from the spirit or essential characteristics of the application. Therefore, the embodiments should be regarded as exemplary and non-limiting, and the scope of the application is defined by the appended claims rather than the above description, and therefore all changes falling within the meaning and scope of the equivalent elements of the claims are intended to be included in the application. Any reference signs in the claims should not be regarded as limiting the claims involved.

[0084] In addition, it should be understood that although the present specification is described in terms of embodiments, not every embodiment contains only one independent technical solution, and the description manner of the specification is only for the sake of clarity, and those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be properly combined to form other embodiments that those skilled in the art can understand.

[0085] The technologies, shapes, and structural parts not described in detail in the application are well-known technologies.

Claims

1. A method for predicting low-altitude wind fields based on spatiotemporal graph convolutional networks, characterized in that, The low-altitude wind field prediction model is adopted. The model includes a dynamic graph construction module, a graph attention network, a PhysFusion-TransTCN encoder, and an output module connected in sequence. The PhysFusion-TransTCN encoder is composed of multiple stacked layers, each of which includes an attention preprocessing module, a multi-head attention module, and a feedforward network module connected in sequence. The method includes: S1: Collect wind field observation data and physical field data from all nodes in the target area, and construct a dynamic spatiotemporal map based on the stream function-vorticity theory using the dynamic graph construction module; the wind field observation data is a three-dimensional wind speed vector, and the three-dimensional wind speed vector of each node includes wind speed components in the horizontal x-axis direction, the horizontal y-axis direction, and the vertical z-axis direction; the physical field data includes temperature, air pressure, and humidity; the nodes are the observation points in the target area; S2: Based on the dynamic spatiotemporal graph, spatial information is extracted through a graph attention network to obtain the spatial feature tensor; S3: Obtain deep spatiotemporal features of the wind field by using the PhysFusion-TransTCN encoder to obtain spatial feature tensors and physical field data; S4: The deep spatiotemporal features of the wind field are hierarchically aggregated through the output module to obtain the wind field prediction results for all nodes in the target area.

2. The low-altitude wind field prediction method based on spatiotemporal graph convolutional networks as described in claim 1, characterized in that, In step S1, the construction of a dynamic spatiotemporal graph based on the stream function-vorticity theory using the dynamic graph construction module includes: S11: Calculate the three-dimensional vorticity vector for each node based on the wind field observation data for each node. The calculation formula is as follows: Where i is the node number; Let i be the three-dimensional vorticity vector at node i; , and These are the wind speed components along the horizontal x-axis, the horizontal y-axis, and the vertical z-axis of the i-th node, respectively. , , , , and These represent the rate of change of the wind speed component in the corresponding direction at node i. S12: Construct a wind field physical similarity matrix between nodes based on the three-dimensional vorticity vector of each node. The calculation formula is: Where t is the time step number; j is another arbitrary node that is different from node i; The physical similarity of the wind field between node i and node j at time step t; and Let be the three-dimensional wind speed vectors of nodes i and j at time step t, respectively. ; and These are the three-dimensional vorticity vectors of nodes i and j at time step t, respectively. It is the scale parameter of vorticity similarity; It is a scale parameter for velocity similarity; It is the displacement vector from node i to node j; Let i be the distance decay function between node i and node j; Let be the square of the Euclidean norm of the vector; These are learnable weight coefficients; S13: Based on the wind field observation data of each node, construct the node connection weights between nodes. The calculation formula is: in, The node connection weights between node i and node j at time step t; (.) represents the sigmoid function; These are learnable parameters; and Let i and j be the node characteristics, respectively. ; Let i be the wind speed vector at node i; and These are learnable parameters; For splicing operations; This is sinusoidal position encoding, i.e., time step encoding of the target area; Let i represent the temporal correlation between node i and node j. Time-series correlation Used to measure the relationship between node i and node j. The closest to t Similarity of the sequence variation patterns of historical wind speed within a time step; For nodes i and j respectively, in the time interval [ Historical wind speed sequence of [t]; (.) is the correlation calculation function; This is the distance attenuation coefficient; Let be the spatial distance between node i and node i; S14: Wind field physical similarity matrix at each time step Node connection weight Construct a dynamic spatiotemporal graph, the construction method is as follows: in, The spacetime diagram at time step t; It is an adaptive weighting function; This represents the velocity vector field formed by the wind speeds at all nodes in the wind field; k is the scaling factor. The speed threshold; The gradient of the velocity vector field at time step t; Let be the wind field physical similarity matrix at time step t; This is the node connection matrix at time step t; For terrain constraint functions; It is the Frobenius norm.

3. The low-altitude wind field prediction method based on spatiotemporal graph convolutional networks as described in claim 1, characterized in that, Step S2 includes: S21: Based on wind field observation data and neighbor relationships defined through a dynamic spatiotemporal graph, calculate the attention coefficient using the following formula: Where p is any node; and q is any one of the neighboring nodes of node p. It is the set of neighboring nodes, including the node itself, p; Let be the attention coefficient between node p and node q; (.) is a non-linear activation function; It is a learnable attention weight vector; is a trainable weight matrix; These are the node feature representations of nodes p and q, respectively. ; Let be the wind speed vector of node p; and These are learnable parameters; Indicates a splicing operation; The strength of the physical association between node p and node q; S22: Normalize the attention coefficients between node p and all its neighboring nodes to obtain the attention weights between node p and all its neighboring nodes; S23: Based on the attention weights between each node and all its neighboring nodes, aggregate the projection features between each node and all its corresponding neighboring nodes to obtain the spatial feature tensor of the node.

4. The low-altitude wind field prediction method based on spatiotemporal graph convolutional networks as described in claim 1, characterized in that, Step S3 includes: S31: In each layer of the PhysFusion-TransTCN encoder, spatial input features and physical field data are enhanced with temporal features and fused with physical information through the attention preprocessing module to obtain spliced ​​features; among them, the spatial input features in the first layer of the PhysFusion-TransTCN encoder are spatial feature tensors, and the remaining layers are the outputs of the PhysFusion-TransTCN encoder in the previous layer. S32: Obtain multi-head attention based on splicing features using a multi-head attention module; S33: The PhysFusion-TransTCN encoder performs residual connections and layer normalization on the multi-head attention to obtain the comprehensive attention; S34: Based on integrated attention, feedforward features are obtained through a feedforward network module; S35: The PhysFusion-TransTCN encoder performs residual connections and layer normalization on the integrated attention and feedforward features to obtain the output of each layer of the PhysFusion-TransTCN encoder, i.e., the integrated feedforward features; at the same time, the integrated feedforward features output by the last layer of the PhysFusion-TransTCN encoder are marked as deep spatiotemporal features of the wind field.

5. The low-altitude wind field prediction method based on spatiotemporal graph convolutional networks as described in claim 1, characterized in that, Step S4 includes: S41: Perform multi-scale feature aggregation on the deep spatiotemporal features of the wind field to obtain aggregated features. The calculation is expressed as: in, For global attention pooling; Read out the partial image; For physical feature projection; L is the total number of layers in the PhysFusion-TransTCN encoder; This represents the deep spatiotemporal characteristics of the wind field; This is the spacetime diagram at time step t; P represents the physical field data. For layer normalization operation; S42: Based on aggregation features Obtain wind field prediction results for all nodes in the target area. The calculation is expressed as: Where TemporalInterpolate(.) is a time interpolation function based on physical constraints; and These are the learnable weights and biases of the output module, respectively.

6. The low-altitude wind field prediction method based on spatiotemporal graph convolutional networks as described in claim 4, characterized in that, In step S31, the formula for calculating the splicing features is: in, For the first l Layer splicing features; k is the dilated convolution branch number; K is the total number of parallel dilated convolution branches; For the physical perception gate signal of the k-th dilated convolution branch; This indicates element-wise multiplication; This is the k-th dilated convolution branch; For the first l The spatial input features of the layer are equal to the output of the PhysFusion-TransTCN encoder in the previous layer, when l When equal to 1, That is, the spatial feature tensor; || represents the feature concatenation operation; P is the physical field data; Use the Sigmoid activation function; and represents the learnable gating parameters for the k-th dilated convolutional branch; It is a physical feature vector obtained after performing a spatiotemporal pooling operation on the physical field data; and These represent max pooling and average pooling along the time dimension, respectively. and These represent max pooling and average pooling along the spatial node dimension, respectively; Step S32 includes: S321: Obtain each attention head in the multi-head attention module based on the concatenation features, and calculate its representation as follows: Here, softmax(.) is the normalization operation; All are learnable parameter matrices; Attention score; It is a query vector and key vector Feature dimensions; This is the scaling factor; The strength of the physical association between node i and node j; and Let be the potential gradients of the stream function vectors at nodes i and j, respectively; and These are the three-dimensional vorticity vectors of nodes i and j, respectively. Represents the square of the Euclidean norm; and These are learnable scale parameters; and These are learnable weight coefficients; This is the lower triangular timing mask matrix; S322: Concatenate all attention heads and perform a linear transformation to obtain the output of the multi-head attention module, i.e., multi-head attention. .

7. The low-altitude wind field prediction method based on spatiotemporal graph convolutional networks as described in claim 6, characterized in that, In step S33, the calculation of comprehensive attention is expressed as follows: in, For the PhysFusion-TransTCN encoder l Layer-wide attention; (.) represents the layer normalization operation; For the first l Spatial input features of the layer; For the first l Multi-head attention in layers; In step S34, the calculation of the feedforward feature is expressed as follows: in, For the PhysFusion-TransTCN encoder l Feedforward features of the layer; GELU(.) is the activation function of the Gaussian error linear unit; and The weight matrix is ​​a learnable matrix; For bias terms; For physical field data; || represents a concatenation operation along the feature dimension; This is a physical-guided temporal convolution operation.

8. The low-altitude wind field prediction method based on spatiotemporal graph convolutional networks as described in claim 1, characterized in that, The PhysFusion-TransTCN encoder of the low-altitude wind field prediction model uses the total physical residual loss as the loss function during training. The calculation formula is: in, L is the index of the current layer; L is the total number of layers in the PhysFusion-TransTCN encoder. For the PhysFusion-TransTCN encoder l Physical residual loss of the layer; To assign the e-th training epoch to the PhysFusion-TransTCN encoder l Adaptive weights for layer physical residual loss; The square of the L2 norm; It is a vector differential operator; For the divergence calculation of the velocity field; For the constraint of mass conservation; For the momentum conservation constraint; This is a local acceleration term; For convection terms; For pressure gradient terms; This is the viscous diffusion term; For the predicted pressure field; air density; The kinematic viscosity coefficient; This is the scaling factor; For the e-th training cycle, The physical residual loss calculated by the layer; The loss for the primary prediction task in the e-th training epoch; To predict the length of the sequence; Three-dimensional wind field observation data at time step t; To predict the three-dimensional wind field for a model at time step t, (.) represents the Huber loss function; e is the current training epoch number; To prevent division by zero; To predict the loss of the main task; Let be the physical residual loss of the k-th layer in the e-th training epoch.

9. The low-altitude wind field prediction method based on spatiotemporal graph convolutional networks as described in claim 8, characterized in that, The low-altitude wind field prediction model uses a multi-objective composite loss function during training. The calculation formula is: in, This represents the total physical residual loss. This is the topological conservation loss term for vortexes; This is the energy balance loss term in the spatiotemporal spectrum; For heuristic dynamic regularization terms; , , These are the weighting coefficients for each corresponding loss term; Predict losses for the primary task; This refers to the vorticity field or Q-criterion field calculated based on the wind speed field. A persistent graph of a scalar field; The Wasserstein distance between the two persistent graphs; (.) represents the spacetime Fourier transform; It is a three-dimensional wavenumber vector; Angular frequency; The target energy spectrum function; This is a loss term related to spatiotemporal coordination. The weighting coefficients for the spatiotemporal coordination loss term; These are the weighting coefficients for the dynamic smoothing loss term; This is the loss term for dynamic smoothing.

10. A low-altitude wind field prediction system based on spatiotemporal graph convolutional networks, characterized in that, To implement a low-altitude wind field prediction method based on a spatiotemporal graph convolutional network as described in any one of claims 1-9, the method comprises: a dynamic graph construction module, a graph attention network, an attention preprocessing module, a multi-head attention module, a feedforward network module, and an output module; the dynamic graph construction module is used to process wind field observation data to obtain a dynamic spatiotemporal graph; the graph attention network is used to extract spatial feature tensors based on wind field observation data and the dynamic spatiotemporal graph; the attention preprocessing module is used to perform temporal feature enhancement and physical information fusion to obtain spliced ​​features; the multi-head attention module is used to extract multi-head attention based on the spliced ​​features, and finally obtain comprehensive attention; the feedforward network module is used to finally obtain deep spatiotemporal features of the wind field based on the comprehensive attention; and the output module is used to obtain wind field prediction results based on the deep spatiotemporal features of the wind field.

Images