A Smart Storm Surge Forecasting Method Integrating Causal Structure and Graph Neural Networks
By combining the UNet-LSTM-DGCN model with graph structure learning, the causal relationships in storm surge forecasting are dynamically captured, solving the problems of high computational resource requirements and uncertainty in forecast results in existing methods, and realizing efficient and interpretable storm surge forecasting.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- OCEAN UNIV OF CHINA
- Filing Date
- 2026-04-15
- Publication Date
- 2026-06-30
AI Technical Summary
Existing storm surge forecasting methods are computationally intensive and time-consuming, making it difficult to meet the high-frequency and rapid update requirements under emergency response. Furthermore, deep learning models lack causal structure modeling, resulting in high uncertainty and poor interpretability of forecast results. Static graph structures cannot adapt to changes in typhoon paths, affecting forecast accuracy and timeliness.
A combined UNet-LSTM-DGCN model is used for storm surge forecasting. By fusing multi-source data and preprocessing data, and combining graph structure learning and graph convolutional neural networks, the causal relationships between stations are dynamically captured, achieving efficient forecasting of storm surge levels. The model's decision-making basis is revealed through visualization of the graph structure.
It improves the computational efficiency and accuracy of storm surge forecasting, enhances the reliability and interpretability of forecast results, adapts to dynamic changes under different typhoon paths, and solves the problems of high computational resource requirements of traditional methods and the "black box" problem of deep learning models.
Smart Images
Figure CN122022207B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the fields of artificial intelligence and marine storm surge forecasting technology, specifically to an intelligent storm surge forecasting method that integrates causal structure and graph neural network. Background Technology
[0002] Traditional storm surge forecasting relies heavily on complex numerical models that use numerical calculations to reconstruct the coupled dynamic processes of the ocean and atmosphere. These models need to comprehensively consider multiple physical factors such as seawater dynamic characteristics, complex coastlines and seabed topography, typhoon wind fields, and pressure fields, and characterize the interactions between different temporal and spatial scales. This not only involves a large amount of computation and is time-consuming, but also makes the forecast results somewhat complex and uncertain.
[0003] From the perspective of technological development, storm surge forecasting methods have mainly undergone two generations of evolution: the first generation is numerical forecasting methods based on physical equations, with representative models including MIKE, ADCIRC, and FVCOM; the second generation is intelligent forecasting methods based on deep learning.
[0004] Graph Neural Networks (GNNs) are of great significance for causal inference and interpretability analysis. GNNs can effectively represent and learn complex graph structure data, and are suitable for modeling the relationships between variables, thus providing a good framework for causal inference. Through the graph structure, it is possible to clearly identify which nodes or edges in the graph structure contribute the most to the prediction results, thereby providing interpretable feature importance and helping to understand the decision basis of the model.
[0005] In summary, the existing technology has the following drawbacks:
[0006] 1. Numerical weather prediction models, such as MIKE, ADCIRC, and FVCOM, rely on the finite difference or finite element method to discretize and solve shallow water equations, requiring the construction of high-precision computational grids. The preparation period for grid generation can last for weeks to months. At the computational level, each forecast by the numerical model requires a complete solution to the equations, and a single high-resolution simulation can take several hours to tens of hours, which is difficult to meet the high-frequency and rapid forecasting requirements under emergency response. When ensemble forecasts are needed to quantify uncertainty, the computational resource requirements increase exponentially, further limiting their application capabilities in scenarios with high timeliness requirements.
[0007] Existing deep learning methods such as convolutional neural networks, long short-term memory neural networks, and ConvLSTM have fundamental structural defects. First, these models are essentially purely data-driven methods rather than understanding the causal relationships between variables. Intelligent models generally lack explicit causal structure modeling modules, which makes them prone to learning false associations rather than real physical causal chains when faced with extreme typhoon events with different distributions than the training data. When the storm surge propagation path changes dynamically due to different typhoon paths, the model cannot adaptively adjust, which directly manifests as underestimation of peak water level forecasts and significant time lag between forecast and measured sequences, severely restricting the forecast robustness of the model in extreme disaster scenarios.
[0008] 2. Existing deep learning models generally suffer from the "black box" problem. Their internal computation process involves multiple layers of nonlinear transformations. Features gradually lose their physical meaning as they are passed layer by layer. The decision boundary is difficult for humans to understand, which makes it impossible for forecasters to know which sites, times, and physical factors the model is based on to arrive at the final forecast conclusion, resulting in interpretability problems.
[0009] 3. Although graph neural network methods have begun to attempt to model spatial dependencies between sites, most existing methods are based on static graph structures. These methods usually predefine an adjacency matrix based on the geographical distance between sites and assume that the relationship remains constant under different typhoon events and different time steps. However, the physical propagation process of storm surge has obvious dynamic characteristics. When a typhoon makes landfall from different directions, the propagation path of the storm surge, the order of affected sites, and the strength of the causal relationship between sites will all change significantly. The static graph structure is essentially a rigid constraint and cannot dynamically adjust the information transmission relationship between sites according to the real-time typhoon. Summary of the Invention
[0010] This invention provides an intelligent storm surge forecasting method that integrates causal structures and graph neural networks. The aim is to construct an intelligent method combining dynamic graph neural networks for storm surge forecasting, capturing the dynamic causal relationships in water level changes at multiple stations under typhoon influence. While improving forecast accuracy, it reveals the decision-making basis within the model through a visualized graph structure, effectively alleviating the "black box" problem of intelligent models and enhancing the reliability and credibility of forecast results. This model not only focuses on the temporal evolution patterns of multiple stations but also emphasizes incorporating the physical propagation mechanism of storm surges, identifying and modeling potential causal relationships between stations. Compared to traditional numerical forecasting models, this invention has higher computational efficiency and stronger operational timeliness. Compared to existing intelligent forecasting models, this invention fully considers the spatiotemporal causal relationships between stations, effectively alleviating the time lag problem in forecast results and significantly improving the forecast accuracy of extreme storm surge water levels.
[0011] To achieve the above objectives, the technical solution of the present invention is as follows:
[0012] A smart storm surge forecasting method integrating causal structures and graph neural networks includes the following steps:
[0013] Step 1. Multi-source data fusion: Collect water level data from multiple hydrological stations, meteorological stations, and authoritative global weather forecasting systems. The station water level data includes historical and real-time water level changes; the meteorological station and weather forecasting system data includes wind speed, wind direction, and air pressure.
[0014] Step 2. Data preprocessing and standardization;
[0015] Step 3. Use UNet-LSTM to achieve the fusion modeling of storm surge meteorological spatiotemporal features and water level temporal features; use the UNet-LSTM combined model to complete the preliminary water level prediction, extract the spatial features of the meteorological field through UNet, model the water level temporal dependence through LSTM, and deeply fuse the two types of features to output the preliminary forecast results;
[0016] Step 4. Causal structure inference and graph structure learning;
[0017] Step 5. Use a graph convolutional neural network to obtain a combined UNet-LSTM-DGCN model for the final storm surge water level forecast;
[0018] Step 6. Training and validation of the UNet-LSTM-DGCN combined model;
[0019] Step 7. Visualize the prediction results;
[0020] Step 8. Interpretability analysis.
[0021] Preferably, step 2 includes the following specific steps:
[0022] (a) Outlier Detection and Removal: Anomalies were identified and cleaned in the time-series data of water level, wind speed, and air pressure. Outlier detection was performed using a method based on the time-series rate of change and local neighborhood consistency test. Let the water level time series be... The corresponding time is Define the rate of change of water level between adjacent time points:
[0023] ;
[0024] Based on the statistical analysis of historical storm surge events in the studied sea area, a reasonable threshold range for water level change rate was determined:
[0025] [ , For moments when the rate of change exceeds this interval, the average rate of change within its local neighborhood is further calculated. If the rate of change at a point deviates significantly from the overall trend of the neighborhood and is not supported by physical continuous evolution, it is determined to be an outlier caused by equipment failure or transmission error, and is removed and marked as missing.
[0026] (b) Missing value interpolation: For a one-dimensional water level time series, linear time series interpolation is used to fill in missing points; let time be... water level Missing, with the valid observations before and after being respectively , The corresponding time is , The interpolation formula is:
[0027] ;
[0028] For two-dimensional meteorological gridded field data of wind speed and air pressure, bilinear interpolation is used to complete spatial missing data, maintaining the rationality of the spatial distribution of the meteorological field while ensuring the spatiotemporal continuity and integrity of multi-source data; let the coordinates of the points to be interpolated be... The values of its four surrounding known grid points are respectively First Directional interpolation, and then in The final value is obtained by directional interpolation, using the following formula:
[0029] ;
[0030] ;
[0031] ;
[0032] (c) Data Standardization: The Z-score standardization method is used to normalize the preprocessed data, mapping it to a standard normal distribution with a mean of 0 and a standard deviation of 1; let a certain feature sequence be... Its mean and standard deviation The calculation is as follows:
[0033] ;
[0034] ;
[0035] ;
[0036] in, These are the standardized feature values.
[0037] Preferably, step 3 includes the following specific steps:
[0038] (a) For meteorological gridded field data such as wind speed and air pressure, the UNet network is used to capture their spatial distribution and evolution patterns; let the input meteorological gridded field be... ,in, Divided into the height and width of the region matrix, For meteorological features, spatial features are extracted using a UNet encoder-decoder structure. In the encoding stage, multi-scale spatial features are extracted through convolutional layer downsampling; in the decoding stage, the spatial dimension is restored through upsampling and skip connections, ultimately outputting meteorological spatial features. ,in, For feature dimensions;
[0039] (b) Use The convolution kernel will capture the spatial characteristics of meteorology. Mapped to each station, the data is concatenated with the time-series water level data of each station along the feature dimension to form a multi-feature matrix of stations that integrates meteorological spatiotemporal information. ,in, For the number of sites, For time step, For feature dimensions;
[0040] (c) An LSTM network is used to model the long- and short-term time-series dependencies of the multi-feature matrices of the stations, and the final output is a preliminary forecast of the storm surge level of the stations. The specific formula is as follows:
[0041] ;
[0042] ;
[0043] ;
[0044] ;
[0045] ;
[0046] ;
[0047] Among them, the Gate of Oblivion This determines which information will be removed from long-term memory; This represents the Sigmoid activation function; It is the weight matrix related to the forget gate; It is the output of the previous time step; It is the input value at the current time step; It is the bias term of the forget gate; input gate Determines the current input The degree of impact on the memory of the updated unit; It is the weight matrix of the input gate. and It is a bias term; It is the weight matrix of the candidate unit states; memory unit Used to store long-term dependencies in data; This represents the multi-feature matrix of a site.
[0048] Preferably, step 4 includes the following specific steps:
[0049] (a) Temporal matrix concatenation: The water levels at previous times of multiple stations are concatenated with the preliminary forecast results of UNet-LSTM in the time dimension to form a continuous water level change matrix. ;
[0050] (b) Static global structure learning: through two learnable node embedding layers , This maps the stable statistical characteristics of the site to a high-order feature space, while introducing hyperparameters. Control activation function To control the saturation level and avoid excessive saturation of eigenvalues, the formula is expressed as:
[0051] ;
[0052] ;
[0053] in, , This represents the output dimension of the embedding layer, used to encode the core attribute associations of the site.
[0054] calculate The difference between the outer products of two embedding matrices forms an antisymmetric matrix. The calculation is expressed as:
[0055] ;
[0056] ;
[0057] The sign of the elements in the antisymmetric matrix directly reflects the direction of the edges between stations, while the magnitude of the values reflects the strength of the association. Finally, the values are compressed to the range [-1, 1] using the tanh function, and then the ReLU function is used to filter out invalid negative associations, retaining only positive propagation associations, resulting in a static global adjacency matrix. ;
[0058] (c) Local Dynamic Structure Learning: Through time-delay modeling, the focus is on learning the local correlations that dynamically change with the storm surge process. First, the site time series features are expanded. Conv2D is used to extract the global features of the site time series, and then linear mapping is used to increase the dimensionality to obtain the overall time series feature matrix F. Then, the number of hidden features after dimensionality increase is... Based on the time delay coefficient Decomposed into cause fragments Fruit fragments ; Characteristics representing the triggers of transmission The similarity matrix represents the propagation response characteristics, used to learn the response of early propagation triggers to later sites after dynamic time delays; it calculates the similarity between causal and effect segments using batch matrix multiplication to quantify the time-varying and time-delayed correlation strength between sites throughout the entire time period; the element values of the similarity matrix are dynamically adjusted as the storm surge develops to capture changes in the correlation strength between sites when the typhoon path shifts; the relationship between sites is learned using the similarity of two segments, resulting in a dynamic graph structure, the calculation formula of which is expressed as:
[0059] ;
[0060] ;
[0061] ;
[0062] in, This represents the learnable linear layer parameters. Represents a dynamic graph structure;
[0063] (d) Graph fusion and sparsification: The fusion formula is expressed as:
[0064] ;
[0065] Using a Top-k sparsity strategy, for For each row, retain the one with the strongest correlation. One value is set to 0, and the rest are set to 0; this process is implemented through a mask matrix, and finally the dynamic adjacency matrix At is obtained;
[0066] ;
[0067] ;
[0068] Where ⊙ represents the Hadamard product.
[0069] Preferably, step 5 includes the following specific steps:
[0070] First, to ensure that the unique characteristics of each site are not lost during propagation, an identity matrix is added to the adjacency matrix. Add the self-loop terms; then sum the rows to obtain the node degree vector, and finally construct the degree matrix. Then calculate the inverse square root of the degree matrix. Symmetric normalization is achieved through matrix multiplication; this process is expressed as:
[0071] ;
[0072] ;
[0073] ;
[0074] Considering the complexity of the spatiotemporal correlation of storm surges, a multi-layered stacked graph convolutional structure is adopted, with the number of graph convolutional layers set to n. , and These are represented by the preceding time length and the predicted time length, respectively, and the feature dimension sequence is as follows: Each layer represents the hidden layer dimension, and each layer shares the normalized dynamic adjacency matrix. , define the first The input features of the layer are The output features are The hierarchical iteration formula and the final output are expressed as follows:
[0075] ;
[0076] ;
[0077] in, For the first Learnable weights of linear layers For the final forecast results, .
[0078] Preferably, step 6 specifically includes:
[0079] The UNet-LSTM-DGCN combined model takes standardized storm surge water level time series data and meteorological gridded field data as input, and station water levels at corresponding times as supervision labels. It uses mean squared error (MSE) as the loss function to quantify the deviation between predicted and actual values. The calculation formula is as follows:
[0080] ;
[0081] in, The total number of samples, For the first Real-time measured storm surge level The predicted water level output by the model;
[0082] The UNet-LSTM-DGCN combined model training uses the Adam optimizer to update network parameters and minimizes the loss function through the backpropagation algorithm. At the same time, the dataset is divided into training and validation sets in a 7:3 ratio. The training set is used for parameter learning, and the validation set is used to monitor loss changes in real time. An early stopping strategy is used to suppress overfitting.
[0083] Preferably, step 7 specifically includes: drawing a comparison curve of the measured water level at a single station, the preliminary prediction sequence, and the final prediction sequence to present the fitting effect on the storm surge increase, decrease, and peak process; drawing a multi-station water level spatial heat map in combination with regional geographic information, and superimposing causal relationship edges between stations to intuitively show the spatial distribution and propagation path of water level; presenting the learned causal relationship matrix in the form of a network graph, with nodes representing stations and weighted directed edges representing the causal influence intensity between stations, clearly presenting the core causal link of storm surge water level propagation.
[0084] Preferably, step 8 specifically includes: quantifying the contribution of meteorological elements and historical water levels to the prediction results through feature importance indicators; quantifying the causal influence weights between different stations based on the causal edges output by the graph structure; identifying key driving stations and their dominant role in water level changes of surrounding stations; explaining the model decision basis from the perspective of physical mechanisms; and further locating the prediction bias caused by insufficient correlation capture by combining the prediction residuals and causal structure distribution, thus providing traceable and explainable scientific support for model optimization and business applications.
[0085] The intelligent storm surge forecasting method of the present invention, which integrates causal structure and graph neural network, has the following beneficial effects:
[0086] 1. Using intelligent models based on deep learning methods for multi-site storm surge forecasting does not require a large amount of computing resources, significantly shortens forecasting time, reduces hardware deployment costs, and can quickly output multi-site storm surge forecast results, adapting to real-time early warning needs;
[0087] 2. By adopting the UNet-LSTM fusion architecture, features are extracted from meteorological grid data such as wind field and pressure field and multi-station water level time series data respectively, realizing the deep fusion of meteorological spatial features and hydrological time series features, and efficiently simulating the nonlinear and complex dynamic changes of storm surge process;
[0088] 3. By introducing Graph Structure Learning (GSL) and Graph Convolutional Neural Network (GCN), the dynamic causal relationships between stations under different typhoon paths can be adaptively captured, solving the problems of time lag and short forecast timeliness of traditional methods. Based on the causal relationship matrix, the visualization and interpretability analysis of causal structure can be carried out, solving the "black box" problem of traditional deep learning models and enhancing the credibility and business application value of forecast results. Attached Figure Description
[0089] Figure 1 This is a schematic diagram of the implementation process of the present invention. Detailed Implementation
[0090] The following is a detailed description of the embodiments of the present invention in a step-by-step manner. The description takes the quality control process of environmental observation data from a discarded temperature, salinity, and depth instrument in a certain sea area in May 2024 as an example. The described embodiments are only some embodiments of the present invention, and not all embodiments.
[0091] In the initial embodiment, the present invention provides an intelligent storm surge forecasting method that integrates causal structures and graph neural networks, such as... Figure 1 As shown, it includes the following steps:
[0092] Step 1. Multi-source data fusion: Collect water level data from multiple hydrological stations, meteorological stations, and authoritative global weather forecasting systems. The station water level data includes historical and real-time water level changes to meet practical operational needs; the meteorological station and weather forecasting system data includes wind speed, wind direction, and air pressure to achieve synergistic complementarity between hydrological and meteorological information.
[0093] Step 2. Data preprocessing and standardization;
[0094] Step 3. Use UNet-LSTM to achieve the fusion modeling of storm surge meteorological spatiotemporal features and water level temporal features; use the UNet-LSTM combined model to complete the preliminary water level prediction. The core is to extract the spatial features of the meteorological field through UNet, model the water level temporal dependence through LSTM, and deeply fuse the two types of features to output the preliminary forecast results.
[0095] Step 4. Causal structure inference and graph structure learning;
[0096] Step 5. Use a graph convolutional neural network to obtain a combined UNet-LSTM-DGCN model for the final storm surge water level forecast;
[0097] Step 6. Training and validation of the UNet-LSTM-DGCN combined model;
[0098] Step 7. Visualize the prediction results;
[0099] Step 8. Interpretability analysis.
[0100] In a further embodiment, to eliminate the problems of dimensional differences, outlier interference, and uneven temporal and spatial distribution, it is necessary to systematically preprocess the hydrological time-series data and meteorological gridded data, and map the data to a unified numerical range through a standardization method to ensure stable convergence of the model training process. Step 2 includes the following specific steps:
[0101] (a) Outlier Detection and Removal: In multi-source hydrological and meteorological data, due to equipment malfunctions, transmission errors, and extreme weather changes, the original observation sequences often contain outliers that significantly deviate from normal variation patterns. To ensure the quality of subsequent modeling, it is necessary to first identify and clean the time-series data of water level, wind speed, and air pressure. This scheme uses a method based on the time-series rate of change and local neighborhood consistency test for outlier detection. Let the water level time series be... The corresponding time is Define the rate of change of water level between adjacent time points:
[0102] ;
[0103] Based on the statistical analysis of historical storm surge events in the studied sea area, a reasonable threshold range for water level change rate was determined:
[0104] [ , For moments when the rate of change exceeds this interval, the average rate of change within its local neighborhood is further calculated. If the rate of change at a point deviates significantly from the overall trend of the neighborhood and is not supported by physical continuous evolution, it is determined to be an outlier caused by equipment failure or transmission error, and is removed and marked as missing. This method can effectively retain the real and violent water level fluctuations that exist during storm surge and flood reduction, and only remove outlier data that obviously does not conform to the physical change law.
[0105] (b) Missing Value Interpolation: To ensure temporal continuity and spatial integrity, missing value interpolation is required for station water level and meteorological grid data. For one-dimensional water level time series, linear time series interpolation is used to fill in the missing points; let time... water level Missing, with the valid observations before and after being respectively , The corresponding time is , The interpolation formula is:
[0106] ;
[0107] For two-dimensional meteorological gridded field data of wind speed and air pressure, bilinear interpolation is used to complete spatial missing data. This maintains the rationality of the spatial distribution of the meteorological field while ensuring the spatiotemporal continuity and integrity of multi-source data, providing a regular input sequence for subsequent feature extraction and model training. Let the coordinates of the points to be interpolated be... The values of its four surrounding known grid points are respectively First Directional interpolation, and then in The final value is obtained by directional interpolation, using the following formula:
[0108] ;
[0109] ;
[0110] ;
[0111] (c) Data Standardization: To eliminate the differences in dimensions and scales between water level and meteorological elements, and to ensure the stability and convergence of model training, this scheme uses the Z-score standardization method to normalize the preprocessed data, mapping the data to a standard normal distribution with a mean of 0 and a standard deviation of 1. This preserves the distribution characteristics of the original data while avoiding the gradient vanishing or exploding problem, making it suitable for uniform scale processing of heterogeneous data such as station water level, wind speed, and air pressure; let a certain feature sequence be... Its mean and standard deviation The calculation is as follows:
[0112] ;
[0113] ;
[0114] ;
[0115] in, These are the standardized feature values.
[0116] In a further embodiment, step 3 includes the following specific steps:
[0117] (a) For meteorological gridded field data such as wind speed and air pressure, the UNet network is used to capture their spatial distribution and evolution patterns; let the input meteorological gridded field be... ,in, Divided into the height and width of the region matrix, For meteorological features, spatial features are extracted using a UNet encoder-decoder structure. In the encoding stage, multi-scale spatial features are extracted through convolutional layer downsampling; in the decoding stage, the spatial dimension is restored through upsampling and skip connections, ultimately outputting meteorological spatial features. ,in, For feature dimensions;
[0118] (b) Use The convolution kernel will capture the spatial characteristics of meteorology. Mapped to each station, the data is concatenated with the time-series water level data of each station along the feature dimension to form a multi-feature matrix of stations that integrates meteorological spatiotemporal information. ,in, For the number of sites, For time step, For feature dimensions;
[0119] (c) An LSTM network is used to model the long- and short-term time-series dependencies of the multi-feature matrices of the stations, and the final output is a preliminary forecast of the storm surge level of the stations. The specific formula is as follows:
[0120] ;
[0121] ;
[0122] ;
[0123] ;
[0124] ;
[0125] ;
[0126] Among them, the Gate of Oblivion This determines which information will be removed from long-term memory; This represents the Sigmoid activation function; It is the weight matrix related to the forget gate; It is the output of the previous time step; It is the input value at the current time step; It is the bias term of the forget gate; input gate Determines the current input The degree of impact on the memory of the updated unit; It is the weight matrix of the input gate. and It is a bias term; It is the weight matrix of the candidate unit states; memory unit Used to store long-term dependencies in data; This represents the multi-feature matrix of a site.
[0127] In a further embodiment, due to the different typhoon paths, the upstream and downstream relationships between stations will inevitably change. Therefore, it is necessary for the model to have the ability to identify causal relationships and infer reasonable connections between stations. This step aims to learn the dynamic causal relationships between stations from the time series of storm surge water levels and output a sparse and efficient dynamic adjacency matrix as the graph structure for subsequent graph convolutional networks. Step 4 includes the following specific steps:
[0128] (a) Temporal matrix concatenation: The water levels at previous times of multiple stations are concatenated with the preliminary forecast results of UNet-LSTM in the time dimension to form a continuous water level change matrix with a more obvious trend. This improves the efficiency of causal structure inference;
[0129] (b) Static Global Structure Learning: The correlations within storm surge systems are influenced by geographical conditions and inherent marine environmental attributes (such as perennial ocean current direction and shoreline constraints), resulting in a stable global correlation structure. Modeling this stable structure provides a foundational framework for dynamic graph structure learning; this is achieved through two learnable node embedding layers. , This maps the stable statistical characteristics of the site to a high-order feature space, while introducing hyperparameters. Control activation function To control the saturation level and avoid excessive saturation of eigenvalues, the formula is expressed as:
[0130] ;
[0131] ;
[0132] in, , This represents the output dimension of the embedding layer, used to encode the core attribute associations of the site.
[0133] Storm surges are characterized by propagation from the open sea to the nearshore, with upstream station signals changing before downstream stations. To accommodate the unidirectional nature of storm surge propagation, it is necessary to calculate... The difference between the outer products of two embedding matrices forms an antisymmetric matrix. The calculation is expressed as:
[0134] ;
[0135] ;
[0136] The sign of the elements in the antisymmetric matrix directly reflects the direction of the edges between stations, while the magnitude of the values reflects the strength of the association. Finally, the values are compressed to the range [-1, 1] using the tanh function, and then the ReLU function is used to filter out invalid negative associations, retaining only positive propagation associations, resulting in a static global adjacency matrix. This matrix is an asymmetric matrix, which can fit the physical characteristics of storm surge "unidirectional propagation" and encode a relatively stable global spatiotemporal relationship between sites;
[0137] (c) Local Dynamic Structure Learning: Static global graph structures cannot capture time-varying correlations during storm surge processes. Therefore, a local dynamic graph structure learning module needs to be constructed. This module aims to learn the local correlations that dynamically change with the storm surge process through time-delay modeling. First, the station time series features are expanded. Conv2D is used to extract the global features of the station time series, and then linear mapping is used to increase the dimensionality to obtain the overall time series feature matrix F. Next, since the propagation of storm surge has a significant time delay, the number of hidden features after dimensionality increase is calculated based on this pattern. Based on the time delay coefficient Decomposed into cause fragments Fruit fragments ; Characteristics representing the triggers of transmission The similarity matrix represents the propagation response characteristics, used to learn the response of early propagation triggers to later sites after dynamic time delays; it calculates the similarity between causal and effect segments using batch matrix multiplication to quantify the time-varying and time-delayed correlation strength between sites throughout the entire time period; the element values of the similarity matrix are dynamically adjusted as the storm surge develops to capture changes in the correlation strength between sites when the typhoon path shifts; the relationship between sites is learned using the similarity of two segments, resulting in a dynamic graph structure, the calculation formula of which is expressed as:
[0138] ;
[0139] ;
[0140] ;
[0141] in, This represents the learnable linear layer parameters. Represents a dynamic graph structure;
[0142] (d) Graph Fusion and Sparsification: To balance the stability of static global associations with the timeliness of local dynamic associations, an additive fusion mechanism is used to fuse the static global adjacency matrix and the local dynamic adjacency matrix. The static global graph provides the basic association framework under geographical constraints, while the local dynamic graph supplements the time-varying propagation characteristics throughout the entire time period, avoiding excessive association fluctuations or deviations from physical laws caused by purely dynamic graphs. The fusion formula is expressed as:
[0143] ;
[0144] In storm surge forecasting scenarios, changes at a single site are typically only affected by a few core sites. Excessive redundant correlations increase computational complexity and introduce noise. Therefore, a Top-k sparsity strategy is adopted to address this issue. For each row, retain the one with the strongest correlation. One value is set to zero, and the rest are set to 0; this process is implemented using a mask matrix, ultimately yielding a dynamic adjacency matrix. ;
[0145] ;
[0146] ;
[0147] Where ⊙ represents the Hadamard product.
[0148] In a further embodiment, after obtaining the dynamic adjacency matrix, it is necessary to further integrate the temporal features of the stations with the dynamic station connections to realize the information propagation and forecasting of storm surges from different stations; the Graph Convolutional Network does not require the assumption of spatial regularity of the data and can directly use the adjacency matrix to define the relationship between nodes, guiding the propagation and aggregation of features in the graph structure, thereby accurately capturing the dependencies between elements in complex systems; a symmetric normalization strategy is adopted to balance the feature propagation intensity of stations with different degrees, ensuring training stability; step 5 includes the following specific steps:
[0149] First, to ensure that the unique characteristics of each site are not lost during propagation, an identity matrix is added to the adjacency matrix. Add the self-loop terms; then sum the rows to obtain the node degree vector, and finally construct the degree matrix. Then calculate the inverse square root of the degree matrix. Symmetric normalization is achieved through matrix multiplication; this process is expressed as:
[0150] ;
[0151] ;
[0152] ;
[0153] Considering the complexity of the spatiotemporal correlation of storm surges, a multi-layered stacked graph convolutional structure is adopted, with the number of graph convolutional layers set to n. , and These are represented by the preceding time length and the predicted time length, respectively, and the feature dimension sequence is as follows: Each layer represents the hidden layer dimension, and each layer shares the normalized dynamic adjacency matrix. , define the first The input features of the layer are The output features are The hierarchical iteration formula and the final output are expressed as follows:
[0154] ;
[0155] ;
[0156] in, For the first Learnable weights of linear layers For the final forecast results, .
[0157] In a further embodiment, after completing data preprocessing and model structure construction, the model is trained and validated to ensure model convergence stability and generalization ability; step 6 specifically includes:
[0158] The UNet-LSTM-DGCN combined model obtained in step 5 is input with standardized storm surge water level time series data and meteorological grid field data at the preceding time point, and the station water level at the corresponding time point is used as the supervision label. The mean squared error (MSE) is used as the loss function to quantify the deviation between the predicted value and the true value. The calculation formula is as follows:
[0159] ;
[0160] in, The total number of samples, For the first Real-time measured storm surge level The predicted water level output by the model;
[0161] The UNet-LSTM-DGCN combined model training uses the Adam optimizer to update network parameters and minimizes the loss function through the backpropagation algorithm. At the same time, the dataset is divided into training and validation sets in a 7:3 ratio. The training set is used for parameter learning, and the validation set is used to monitor loss changes in real time. An early stopping strategy is used to suppress overfitting.
[0162] In a further embodiment, to intuitively demonstrate the model's prediction effect and verify its accuracy, a visualization analysis is conducted using the causal inference edges output by the graph structure learning module. This is presented from three dimensions: temporal, spatial, and graph structure. Step 7 specifically includes: drawing a comparison curve of the measured water level at a single station, the preliminary prediction sequence, and the final prediction sequence to show the fitting effect on the storm surge's increase, decrease, and peak processes; drawing a multi-station water level spatial heat map using regional geographic information and overlaying causal relationship edges between stations to intuitively show the spatial distribution and propagation path of water levels; and presenting the learned causal relationship matrix in the form of a network graph, with nodes representing stations and weighted directed edges representing the causal influence intensity between stations, clearly presenting the core causal link of storm surge water level propagation.
[0163] In a further embodiment, step 8 specifically includes: quantifying the contribution of meteorological elements and historical water levels to the prediction results through feature importance indicators; quantifying the causal influence weights between different stations based on the causal edges output by the graph structure; identifying key driving stations and their dominant role in water level changes of surrounding stations; explaining the model decision-making basis from the perspective of physical mechanisms; and further locating the prediction bias caused by insufficient correlation capture by combining the prediction residuals and causal structure distribution, thus providing traceable and explainable scientific support for model optimization and business applications.
Claims
1. A storm surge intelligent forecasting method integrating causal structure and graph neural network, characterized in that, Includes the following steps: Step 1. Multi-source data fusion: Collect water level data from multiple hydrological stations, meteorological stations, and authoritative global weather forecasting systems. The station water level data includes historical and real-time water level changes; the meteorological station and weather forecasting system data includes wind speed, wind direction, and air pressure. Step 2. Data preprocessing and standardization; Step 3. Use UNet-LSTM to achieve the fusion modeling of storm surge meteorological spatiotemporal features and water level temporal features; use the UNet-LSTM combined model to complete the preliminary water level prediction, extract the spatial features of the meteorological field through UNet, model the water level temporal dependence through LSTM, and deeply fuse the two types of features to output the preliminary forecast results; Step 4. Causal structure inference and graph structure learning; Step 5. Use a graph convolutional neural network to obtain a combined UNet-LSTM-DGCN model for the final storm surge water level forecast; Step 6. Training and validation of the UNet-LSTM-DGCN combined model; Step 7. Visualize the prediction results; Step 8. Interpretability analysis; Step 4 includes the following specific steps: (a) Temporal matrix concatenation: The water levels at previous times of multiple stations are concatenated with the preliminary forecast results of UNet-LSTM in the time dimension to form a continuous water level change matrix. ; (b) Static global structure learning: through two learnable node embedding layers , This maps the stable statistical characteristics of the site to a high-order feature space, while introducing hyperparameters. Control activation function To control the saturation level and avoid excessive saturation of eigenvalues, the formula is expressed as: ； ； in, , This represents the output dimension of the embedding layer, used to encode the core attribute associations of the site. calculate The difference between the outer products of two embedding matrices forms an antisymmetric matrix. The calculation is expressed as: ； ； The sign of the elements in the antisymmetric matrix directly reflects the direction of the edges between stations, while the magnitude of the values reflects the strength of the association. Finally, the values are compressed to the range [-1, 1] using the tanh function, and then the ReLU function is used to filter out invalid negative associations, retaining only positive propagation associations, resulting in a static global adjacency matrix. ; (c) Local Dynamic Structure Learning: Through time-delay modeling, the focus is on learning the local correlations that dynamically change with the storm surge process. First, the site time series features are expanded. Conv2D is used to extract the global features of the site time series, and then linear mapping is used to increase the dimensionality to obtain the overall time series feature matrix F. Then, the number of hidden features after dimensionality increase is... Based on the time delay coefficient Decomposed into cause fragments Fruit fragments ; Characteristics representing the triggers of transmission, The similarity matrix represents the propagation response characteristics, used to learn the response of early propagation triggers to later sites after dynamic time delays; it calculates the similarity between causal and effect segments using batch matrix multiplication to quantify the time-varying and time-delayed correlation strength between sites throughout the entire time period; the element values of the similarity matrix are dynamically adjusted as the storm surge develops to capture changes in the correlation strength between sites when the typhoon path shifts; the relationship between sites is learned using the similarity of two segments, resulting in a dynamic graph structure, the calculation formula of which is expressed as: ； ； ； in, This represents the learnable linear layer parameters. Represents a dynamic graph structure; (d) Graph fusion and sparsification: The fusion formula is expressed as: ； Using a Top-k sparsity strategy, for For each row, retain the one with the strongest correlation. One value is set to zero, and the rest are set to 0; this process is implemented using a mask matrix, ultimately yielding a dynamic adjacency matrix. ; ； ； Where ⊙ represents the Hadamard product.
2. The storm surge intelligent forecasting method integrating causal structure and graph neural network as described in claim 1, characterized in that step 2 includes the following specific steps: (a) Outlier Detection and Removal: Anomalies were identified and cleaned in the time-series data of water level, wind speed, and air pressure. Outlier detection was performed using a method based on the time-series rate of change and local neighborhood consistency test. Let the water level time series be... The corresponding time is Define the rate of change of water level between adjacent time points: ； Based on the statistical analysis of historical storm surge events in the studied sea area, a reasonable threshold range for water level change rate was determined: [ , For moments when the rate of change exceeds this interval, the average rate of change within its local neighborhood is further calculated. If the rate of change at a point deviates significantly from the overall trend of the neighborhood and is not supported by physical continuous evolution, it is determined to be an outlier caused by equipment failure or transmission error, and is removed and marked as missing. (b) Missing value interpolation: For a one-dimensional water level time series, linear time series interpolation is used to fill in missing points; let time be... water level Missing, with the valid observations before and after being respectively , The corresponding time is , The interpolation formula is: ； For two-dimensional meteorological gridded field data of wind speed and air pressure, bilinear interpolation is used to complete spatial missing data, maintaining the rationality of the spatial distribution of the meteorological field while ensuring the spatiotemporal continuity and integrity of multi-source data; let the coordinates of the points to be interpolated be... The values of its four surrounding known grid points are respectively First Directional interpolation, and then in The final value is obtained by directional interpolation, using the following formula: ； ； ； (c) Data Standardization: The Z-score standardization method is used to normalize the preprocessed data, mapping it to a standard normal distribution with a mean of 0 and a standard deviation of 1; let a certain feature sequence be... Its mean and standard deviation The calculation is as follows: ； ； ； in, These are the standardized feature values.
3. The storm surge intelligent forecasting method integrating causal structure and graph neural network as described in claim 2, characterized in that, Step 3 includes the following specific steps: (a) For meteorological gridded field data such as wind speed and air pressure, the UNet network is used to capture their spatial distribution and evolution patterns; let the input meteorological gridded field be... ,in, Divided into the height and width of the region matrix, For meteorological features, spatial features are extracted using a UNet encoder-decoder structure. In the encoding stage, multi-scale spatial features are extracted through convolutional layer downsampling; in the decoding stage, the spatial dimension is restored through upsampling and skip connections, ultimately outputting meteorological spatial features. ,in, For feature dimensions; (b) Use The convolution kernel will capture the spatial features of meteorology. Mapped to each station, the data is concatenated with the time-series water level data of each station along the feature dimension to form a multi-feature matrix of stations that integrates meteorological spatiotemporal information. ,in, For the number of sites, For time step, For feature dimensions; (c) An LSTM network is used to model the long- and short-term time-series dependencies of the multi-feature matrices of the stations, and the final output is a preliminary forecast of the storm surge level of the stations. The specific formula is as follows: ； ； ； ； ； ； Among them, the Gate of Oblivion This determines which information will be removed from long-term memory; This represents the Sigmoid activation function; It is the weight matrix related to the forget gate; It is the output of the previous time step; It is the input value at the current time step; It is the bias term of the forget gate; input gate Determines the current input The degree of impact on the memory of the updated unit; It is the weight matrix of the input gate. and It is a bias term; It is the weight matrix of the candidate unit states; memory unit Used to store long-term dependencies in data; This represents the multi-feature matrix of a site.
4. The storm surge intelligent forecasting method integrating causal structure and graph neural network as described in claim 3, characterized in that step 5 includes the following specific steps: First, to ensure that the unique characteristics of each site are not lost during propagation, an identity matrix is added to the adjacency matrix. Add the self-loop terms; then sum the rows to obtain the node degree vector, and finally construct the degree matrix. Then calculate the inverse square root of the degree matrix. Symmetric normalization is achieved through matrix multiplication; this process is expressed as: ； ； ； Considering the complexity of the spatiotemporal correlation of storm surges, a multi-layered stacked graph convolutional structure is adopted, with the number of graph convolutional layers set to n. , and These are represented by the preceding time length and the predicted time length, respectively, and the feature dimension sequence is as follows: Each layer represents the hidden layer dimension, and each layer shares the normalized dynamic adjacency matrix. , define the first The input features of the layer are The output features are The hierarchical iteration formula and the final output are expressed as follows: ； ； in, For the first Learnable weights of linear layers For the final forecast results, .
5. The storm surge intelligent forecasting method integrating causal structure and graph neural network as described in claim 4, characterized in that, Step 6 specifically includes: The UNet-LSTM-DGCN combined model takes standardized storm surge water level time series data and meteorological gridded field data as input, and station water levels at corresponding times as supervision labels. It uses mean squared error (MSE) as the loss function to quantify the deviation between predicted and actual values. The calculation formula is as follows: ； in, The total number of samples, For the first Real-time measured storm surge level The predicted water level output by the model; The UNet-LSTM-DGCN combined model training uses the Adam optimizer to update network parameters and minimizes the loss function through the backpropagation algorithm. At the same time, the dataset is divided into training and validation sets in a 7:3 ratio. The training set is used for parameter learning, and the validation set is used to monitor loss changes in real time. An early stopping strategy is used to suppress overfitting.
6. The storm surge intelligent forecasting method integrating causal structure and graph neural network as described in claim 5, characterized in that, Step 7 specifically includes: drawing a comparison curve of the measured water level at a single station, the preliminary prediction sequence, and the final prediction sequence to present the fitting effect on the storm surge increase, decrease, and peak process; drawing a multi-station water level spatial heat map in combination with regional geographic information, and overlaying causal relationship edges between stations to intuitively show the spatial distribution and propagation path of water level; and presenting the learned causal relationship matrix in the form of a network graph, with nodes representing stations and weighted directed edges representing the causal influence intensity between stations, clearly presenting the core causal link of storm surge water level propagation.
7. The storm surge intelligent forecasting method integrating causal structure and graph neural network as described in claim 6, characterized in that, Step 8 specifically includes: quantifying the contribution of meteorological elements and historical water levels to the prediction results through feature importance indicators; quantifying the causal influence weights between different stations based on the causal edges output by the graph structure; identifying key driving stations and their dominant role in water level changes of surrounding stations; explaining the model decision-making basis from the perspective of physical mechanisms; and further locating the prediction bias caused by insufficient correlation capture by combining the prediction residuals and causal structure distribution, thus providing traceable and explainable scientific support for model optimization and business applications.