A Sea Surface Temperature Spatiotemporal Prediction Method Based on GCN-LSTM

Abstract

The present invention discloses a sea surface temperature spatio-temporal prediction method based on GCN-LSTM, belonging to the technical field of spatio-temporal prediction for sea surface temperature, and comprising the following steps: selecting a sea surface temperature spatio-temporal data set and defining a sea surface temperature spatio-temporal data prediction task; constructing a sea surface temperature spatio-temporal prediction model based on GCN-LSTM; the spatio-temporal prediction model STFTIG of the sea surface temperature based on GCN-LSTM includes three modules: a dynamic graph module DGM, a time dependence module TDM, and a spatio-temporal fusion module STFM; the spatio-temporal prediction model STFTIG of the sea surface temperature is constructed based on a graph convolutional network and a long short-term memory network. The present invention improves the accuracy and reliability of sea surface temperature prediction by fusing the spatio-temporal features of data.

Description

Technical Field

[0001] The present invention relates to the technical field of spatio-temporal prediction of sea surface temperature, and in particular to a spatio-temporal prediction method of sea surface temperature based on GCN-LSTM. Background Technique

[0002] Marine fishery aquaculture plays a decisive role in the national economic and social development. For example, in June 2022, the salmon aquaculture in the Yellow Sea of China achieved a bumper harvest, which not only gave birth to a deep-sea cold-water fish aquaculture industry with a production value of hundreds of billions of yuan, but also was of great significance for helping to build China's marine blue granary. However, green and efficient fishery aquaculture is also a high-risk production activity. Especially under the influence of global climate anomalies, when the sea surface temperature undergoes sudden / abnormal changes, it will not only cause a large number of shellfish to "escape" or fish to die, resulting in serious economic losses; it may also cause ecological disasters such as jellyfish blooms, resulting in casualties, etc. Therefore, it is urgent to achieve accurate prediction of the spatio-temporal changes of sea surface temperature, provide decision-making support for the environmental warning of China's offshore aquaculture industry, and also be of great significance for promoting the implementation of the national strategy based on smart ocean.

[0003] The spatio-temporal prediction of sea surface temperature is mainly divided into methods driven by theoretical / physical mechanisms and data-driven methods. Among them, the methods driven by theory mainly construct physical process equations based on dynamics and thermodynamics, and then use numerical models, etc. to achieve prediction. Such methods have problems such as complex models, long calculation time, and high parameter errors, and their limited non-linear processing ability restricts the prediction performance. With the continuous accumulation of spatio-temporal big data of sea surface temperature and the rapid development of artificial intelligence technology, data-driven prediction models can predict the sea surface temperature in the future for a period of time by learning the spatio-temporal dependence relationships and characteristics in the sea surface temperature data. Especially, Ham et al. published a research on the prediction of ENSO (El -Southern Oscillation) based on a convolutional neural network model in the journal Nature, and its prediction effect for one and a half years is better than that of most dynamic and linear statistical models, providing new methods and ideas for the spatio-temporal prediction of sea surface temperature.

[0004] Existing sea surface temperature (SST) spatio-temporal prediction models mainly include prediction methods based on long short-term memory network (LSTM), convolutional long short-term memory network (ConvLSTM), diffusion convolutional recurrent neural network (DCRNN), spatio-temporal graph convolutional network (STGCN), and attention-based spatio-temporal graph convolutional network (ASTGCN). However, existing research mainly conducts SST prediction based on time-dependent relationships, without effectively integrating spatio-temporal features and dependencies. Existing research usually constructs a static graph with historical data as a whole, but the static graph cannot reflect the differences and dynamic change characteristics among SST data at different times. Existing research mainly considers the topological dependence relationship of SST at adjacent positions, ignoring implicit influencing factors and weights in space, such as the time (presence of extreme weather, seasonal differences) or functional (nearshore or offshore) correlations of SST. Therefore, how to extract the dynamic change characteristics of SST, fuse the topological relationship of adjacent points and the spatial dependence presented by implicit information, and how to learn the weights of various spatio-temporal characteristics are the keys to improving the accuracy and effectiveness of SST spatio-temporal prediction. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a SST spatio-temporal prediction method based on GCN-LSTM, which not only considers the spatial correlation between adjacent nodes, but also learns the correlation hidden between non-adjacent nodes, and also considers the influence of time redundancy, and improves the accuracy and reliability of SST prediction by fusing the spatio-temporal features of data.

[0006] To solve the above technical problems, the technical solution adopted by the present invention is:

[0007] A SST spatio-temporal prediction method based on GCN-LSTM includes the following steps:

[0008] S1. Select a SST spatio-temporal data set and define a SST spatio-temporal data prediction task;

[0009] S2. Construct a SST spatio-temporal prediction model based on GCN-LSTM; the spatio-temporal prediction model STFTIG of SST based on GCN-LSTM includes three modules: a dynamic graph module (DGM), a time dependence module (TDM), and a spatio-temporal fusion module (STFM); the spatio-temporal prediction model STFTIG of SST is constructed based on a graph convolutional network and a long short-term memory network.

[0010] A further improvement of the technical solution of the present invention is that: S1 specifically includes the following steps:

[0011] S11. Obtain data to form a SST spatio-temporal data set;

[0012] Select the SST data within the grid range of the target sea area as the research object, and the SST spatio-temporal data set is denoted as X;

[0013] S12. Construct a topological graph based on the sea surface temperature spatio-temporal dataset

[0014] Construct a topological graph based on the grid after removing land. The intersection points in the grid are regarded as nodes, and the topological graph is represented as a binary tuple where V represents the node set and E S represents the edge set; A S represents the weight matrix of the edges, as shown in Equation (1):

[0015]

[0016] where If (v i , v j ) belongs to the direct connection edges E S1 in the network, then A S (v i , v j ) = 1; if (v i , v j ) belongs to the diagonal connection edges E S2 in the network, then Otherwise, A S (v i , v j ) = 0;

[0017] S13. Construct an implicit graph according to the topological graph Construct an implicit graph

[0018] Given the topological graph representing the sea surface temperature data of the t-th sliding window, the implicit graph corresponding to the t-th sliding window is denoted as where V is the node set in, represents the edges learned based on the sea surface temperature data between nodes in the t-th sliding window using the function L; represents the implicit correlation matrix of the sea surface temperature between nodes in the t-th sliding window learned using the function Fun; if this implicit graph is constructed based on time or functional correlation, it is called a time-correlated implicit graph or a function-correlated implicit graph and their correlation matrices are respectively denoted as

[0019] S14. Define the sea surface temperature spatio-temporal data prediction task;

[0020] Given the dataset of sea surface temperature spatio-temporal data where N = |V| represents the number of nodes and M is the total time, Denote the sea surface temperature data of N nodes at the m-th moment; in the topological graph Fused with the implicit graph Based on the fusion, learn a function f according to the sea surface temperature data of w historical time steps to predict the sea surface temperature data of the next k time steps, as shown in Equation (2):

[0021]

[0022] Where is the topological graph, is the implicit graph, V is the node set, E S is the edge set of the topological graph, E I is the edge set of the implicit graph, is the implicit graph of functional correlation, is the implicit graph of temporal correlation, and X is the sea surface temperature data set.

[0023] A further improvement of the technical solution of the present invention lies in: S2 specifically includes the following steps:

[0024] S21 Construct a dynamic graph module;

[0025] In the construction of the dynamic graph module, first construct the implicit graph of temporal correlation and the implicit graph of functional correlation based on the embedding representations of the nodes learned from the sea surface temperature data in segments, then use the self-attention mechanism to learn the weights of the topological graph and the implicit graph, and further use the fused graph as the input of the GCN to learn the spatial features of the sea surface temperature;

[0026] S22 Construct a time dependence module;

[0027] Downsample the original time series into odd and even sequences; use the LSTM model / temporal feature extractor to learn the temporal features of the subsequences respectively;

[0028] S23 Construct a spatio-temporal fusion module;

[0029] Fuse the sea surface temperature spatial features extracted by the dynamic graph module and the sea surface temperature temporal features extracted by the time dependence module;

[0030] S24 Construct a sea surface temperature spatio-temporal prediction model based on GCN-LSTM based on the dynamic graph module, the time dependence module and the spatio-temporal fusion module;

[0031] Among them, in the dynamic graph module, first construct an implicit graph of temporal correlation and an implicit graph of functional correlation respectively based on the embedded representations of nodes learned from the sea surface temperature data in different time periods, then use the self-attention mechanism to learn the weights of the topological graph and the implicit graph, and further use the fused graph as the input of the GCN to learn the spatial features of the sea surface temperature; in the time dependence module, first divide the data set into odd sequences and even sequences, and then use LSTM to learn the temporal features of the sea surface temperature; finally, fuse the learned temporal and spatial features based on STFM to achieve the prediction of the spatio-temporal data of the sea surface temperature.

[0032] A further improvement of the technical solution of the present invention lies in: S21 specifically includes the following steps:

[0033] S211 Learn the embedded representation of nodes based on the sea surface temperature data in the time-division / sliding window;

[0034] During the node embedding process, use a sliding window to divide the given sea surface temperature data set into different time periods; if the size of the sliding window is w and the step length is L, divide the data set into segments of windows, denoted as For each time window data Construct a fully connected layer MLP to extract the sea surface temperature features of each node within the time window, so as to obtain the embedded representation of N nodes in d dimensions, denoted as As shown in Equation (3):

[0035] H(t) = σ([X(wt + 1),..., X(wt + w)] × W1 + b1) (3)

[0036] where the sliding window K t = {X(wt + 1),..., X(wt + w)}, σ() represents the Tanh function, and W1 and b1 represent learnable parameters; it can be seen that a set of vector representations H(t) of nodes will be obtained based on each sliding window;

[0037] S212 Fuse the implicit graph constructed based on this embedded representation with the topological graph into a dynamic graph;

[0038] In the t-th sliding window, the implicit graph of temporal correlation based on the embedded representation of the sea surface temperature between nodes, denoted as The temporal correlation matrix of the sea surface temperature between all nodes is denoted as Given two nodes v i and v j , H i (t) and H j (y) respectively represent the embedded representations of v i and v j in the t-th sliding window; use the Euclidean distance to characterize the temporal correlation of the sea surface temperature between nodes As shown in Equation (4):

[0039]

[0040] In the t-th sliding window, the implicit graph based on the functional correlation of sea surface temperature embeddings between nodes is denoted as The functional correlation matrix of sea surface temperature between all nodes is denoted as Given two nodes v i and v j , the functional similarity is characterized based on the cosine function As shown in Equation (5):

[0041]

[0042] and are obtained by calculating the embedding representation through a function, and the values in the matrix represent the degree of correlation between nodes;

[0043] Introduce Gumble Softmax to learn and the extreme value distributions in, to retain the minimum value in and the maximum value in, in order to achieve the purpose of and sparsification; let σ be the activation function, s IT and s IF is a temperature coefficient, and the sparse adjacency matrices and are as shown in Equation (6):

[0044]

[0045] and represent and the temporal correlation matrix and the functional correlation matrix of sea surface temperature in respectively; in Equation (7), if then if then In Equation (8), if then if then

[0046] Fuse the above three graphs; the dynamic graph module learns weights by using the self-attention mechanism, that is, assigns weights according to the influence of different features on sea surface temperature;

[0047] Fusion Graph Correlation Matrix Based on Attention Network As shown in Equation (9):

[0048]

[0049] Among them, f a represents the self-attention network, and θ a , θ b and θ c are the weight parameters corresponding to three types of graphs respectively;

[0050] Taking the fusion graph as the input, use GCN to extract the spatial features of the t-th window As shown in Equation (10):

[0051]

[0052] Among them, is the dynamic fusion graph correlation matrix, D is the degree matrix, is the original input data of the t-th window, and W FG and b FG are learnable weight and bias parameters.

[0053] A further improvement of the technical solution of the present invention lies in: S22 specifically includes the following steps:

[0054] S221 In the time-dependent module, first divide the data set into odd sequences and even sequences;

[0055] Utilize the low-rank characteristics of the existing sea surface temperature data to downsample the original time series into odd sequences and even sequences;

[0056] S222 Use LSTM to learn the time features of the sea surface temperature;

[0057] Then use the LSTM model / time feature extractor to learn the time features of the subsequences respectively, and finally merge them in the original order to obtain the time features of the t-th window As shown in Equation (11):

[0058]

[0059] Among them, K t represents the original sea surface temperature data to be sampled, K t,1 represents the odd sequence of the sea surface temperature after sampling, and K t,2 represents the even sequence of the sea surface temperature after sampling; represents the result learned after inputting the sampled sequence K t,i into the LSTM model; represents the result of merging the learned and .

[0060] A further improvement of the technical solution of the present invention lies in that: S23 specifically includes:

[0061] Input the t-th window, and each window contains sea surface temperature data of w historical time steps. In order to more accurately predict the sea surface temperature data of the next k time steps, it is necessary to fuse the spatial features of the sea surface temperature extracted by the dynamic graph module and the temporal features of the sea surface temperature extracted by the temporal dependence module, and learn the sea surface temperature of the next k time steps through constructing a fully connected layer As shown in Equation (12):

[0062]

[0063] where and are the spatial feature and temporal feature of the t-th window respectively, σ() represents the Tanh function, and W2 and b2 represent learnable weight and bias parameters;

[0064] In order to effectively measure the average deviation between the predicted value and the true value, the mean absolute error is introduced as the loss function of the model, as shown in Equation (13):

[0065]

[0066] where W θ are all learnable parameters in the prediction model STFTIG.

[0067] Due to the adoption of the above technical solution, the technical progress achieved by the present invention is:

[0068] The present invention constructs a dynamic graph module based on the embedded representation of sea surface temperature data, fuses the topological graph, the implicit graph of temporal correlation and the implicit graph of functional correlation, and better captures the dynamically changing spatial features in the sea surface temperature data; constructs a temporal dependence module of odd and even sequences through downsampling to avoid the influence of temporal redundancy on the prediction effect; further fuses the spatio-temporal features to achieve spatio-temporal prediction of the sea surface temperature. Ablation experiments have confirmed the effectiveness of graph fusion and the odd and even sequence temporal dependence module. Compared with the classical baseline model, the STFTIG model constructed based on GCN-LSTM shows better prediction effect in the sea surface temperature spatio-temporal prediction task. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 is the topological graph in the present invention;

[0070] Figure 2(a) is the framework diagram of the sea surface temperature spatio-temporal prediction model based on GCN-LSTM, and Figure 2(b) is the formation process diagram of the fusion graph;

[0071] Figure 3(a) is a schematic diagram of the 12-month correlation of sea surface temperature between nodes, and Figure 3(b) is a schematic diagram of the correlation of sea surface temperature between nodes in February, May, August, and November;

[0072] Figure 4 It is a schematic diagram of time redundancy in the present invention;

[0073] Figure 5(a) shows the MAE and RMSE values for the first day in the next 2 days; Figure 5(b) shows the MAE and RMSE values for the second day in the next 2 days;

[0074] Figure 6(a) shows the true value of the sea surface temperature for the first day in the 2-day prediction of 8 days; Figure 6(b) shows the predicted value of the sea surface temperature for the first day in the 2-day prediction of 8 days; Figure 6(c) shows the difference in the sea surface temperature for the first day in the 2-day prediction of 8 days;

[0075] Figure 7(a) shows the MAE results of the ablation experiment, and Figure 7(b) shows the RMSE results of the ablation experiment;

[0076] Figure 8(a) shows the MAE results of different models predicting for 2 days, and Figure 8(b) shows the RMSE results of different models predicting for 2 days;

[0077] Figure 9(a) shows the MAE results of different models predicting for 10 days, and Figure 9(b) shows the RMSE results of different models predicting for 10 days. Detailed implementation manners

[0078] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments:

[0079] A sea surface temperature spatio-temporal prediction method based on GCN-LSTM includes the following steps:

[0080] S1. Select a sea surface temperature spatio-temporal data set and define a sea surface temperature spatio-temporal data prediction task;

[0081] S1 specifically includes the following steps:

[0082] S11. Obtain data to form a sea surface temperature spatio-temporal data set;

[0083] The data is from NOAA (National Oceanic and Atmospheric Administration), and it is a series of global SST (Sea Surface Temperature, hereinafter referred to as sea surface temperature) data products after super-resolution collation of multi-sensor grids. The time range is from 2000 to the present, the time resolution is 1 day, the spatial horizontal resolution is 0.02°, and the download website is https: / / coastwatch.noaa.gov / cwn / index.htmlThe sea temperature data within a certain target sea area grid range from 2000 to 2023 are selected as the research object, and the sea temperature spatiotemporal dataset is denoted as X.

[0084] S12. Construct a topological map based on the SST spatiotemporal dataset

[0085] The topological graph is constructed based on the grid after removing the land, and the intersections in the grid are regarded as nodes, such as Figure 1 As shown; the topology graph is represented as a two-tuple Among them, V represents the node set, E S represents the edge set; A S Represents the edge weight matrix, as shown in formula (1):

[0086]

[0087] in, If (v i ,v j ) belongs to the direct edge E in the network S1 (such as the edge of the red circle and the purple rectangle), then A S (v i ,v j )=1; if (v i ,v j ) belongs to the edge E between diagonals in the network S2 (such as the edge of the red circle and the green triangle), then Otherwise A S (v i ,v j )=0;

[0088] S13. According to the topology diagram Constructing an implicit graph

[0089] The above topology can only reflect the static correlation between adjacent nodes; however, there may be certain correlations between non-adjacent nodes near the coast, such as higher sea temperatures near the coast in summer than in the open sea, and lower sea temperatures near the coast in winter than in the open sea; this also reflects that there are different correlations between sea temperature data in different time periods. Therefore, it is necessary to learn the correlations between non-adjacent nodes hidden in the data through sea temperature in a given time period.

[0090] Given a topology graph represents the sea temperature data of the t-th sliding window, and the corresponding implicit graph of the t-th sliding window is Where V is The node set in denotes the edge learned by using function L based on the sea surface temperature data between nodes in the t-th sliding window; denotes the implicit correlation matrix of the sea surface temperature between nodes in the t-th sliding window learned by using function Fun; if this implicit graph is constructed based on time or functional correlation, it is called a time-correlated implicit graph or a functional-correlation implicit graph and their correlation matrices are respectively denoted as

[0091] S14. Define the sea surface temperature spatio-temporal data prediction task;

[0092] Given a dataset of sea surface temperature spatio-temporal data where N = |V| represents the number of nodes, M is the total time, represents the sea surface temperature data of N nodes at the m-th moment; on the basis of the fusion of the topological graph and the implicit graph learn a function f according to the sea surface temperature data of w historical time steps to predict the sea surface temperature data of the next k time steps, as shown in Equation (2):

[0093]

[0094] where, is the topological graph, is the implicit graph, V is the node set, E S is the edge set of the topological graph, E I is the edge set of the implicit graph, is the functional-correlation implicit graph, is the time-correlated implicit graph, and X is the sea surface temperature dataset.

[0095] S2. Construct a sea surface temperature spatio-temporal prediction model based on GCN-LSTM;

[0096] To better learn the implicit correlation, dynamic change characteristics, and time dependence affecting sea surface temperature prediction, fuse the topological graph and the implicit graph Construct a spatio-temporal forecasting model of SST, STFTIG (Spatio-Temporal Forecasting model of SST based on the Fusion of Topological graph and Implicit Graph), based on GCN (Graph Convolutional Network) and LSTM (Long Short Term Memory), as shown in Figure 2(a); the spatio-temporal forecasting model of SST based on GCN-LSTM, STFTIG, includes three modules: a dynamic graph module DGM (Dynamic graph module), a time-dependent module TDM (Time-dependent module), and a spatio-temporal fusion module STFM (Spatio-temporal fusion module).

[0097] S21 Construct the dynamic graph module;

[0098] In the construction of the dynamic graph module, first construct an implicit graph of temporal correlation and an implicit graph of functional correlation based on the embedded representations of nodes learned from the sea surface temperature data in different time periods, then use the self-attention mechanism to learn the weights of the topological graph and the implicit graph, and further use the fused graph as the input of the GCN to learn the spatial features of the sea surface temperature;

[0099] Existing studies usually learn a static graph based on historical data to represent the correlation between nodes; however, in fact, the correlation between nodes changes over time. Taking the sea surface temperature data of 20 nodes as an example, the correlation between nodes is the Pearson correlation of the sea surface temperature between nodes within 12 months of a certain year, as shown in Figure 3(a); at the same time, the correlation of the sea surface temperature between nodes in four time periods of February in winter, May in spring, August in summer, and November in autumn of that year, as shown in Figure 3(b); it can be seen from Figure 3(a) and Figure 3(b) that there are obvious differences in the sea surface temperature correlation in different time periods. Therefore, a single static graph cannot reflect the time-varying characteristics. In order to more realistically reflect the time-varying characteristics of the sea surface temperature, it is necessary to construct a dynamic graph by considering the sea surface temperature correlation between nodes in different time periods, so as to improve the prediction effect of the sea surface temperature.

[0100] The specific steps for constructing the dynamic graph module DGM are as follows:

[0101] S211 Learn the embedded representation of nodes based on the sea surface temperature data in the time-sliced / sliding window;

[0102] In the process of node embedding, use a sliding window to divide the given sea surface temperature data set into different time periods; if the size of the sliding window is w and the step length is L, the data set can be divided into Segment window, denoted as For each time window data Construct a fully connected layer MLP to extract the sea surface temperature features of each node within the time window, thereby obtaining an embedded representation of d dimensions for N nodes, denoted as As shown in Equation (3):

[0103] H(t) = σ([X(wt+1),...,X(wt+w)] × W1 + b1) (3)

[0104] Among them, the sliding window K t = {X(wt+1),...,X(wt+w)}, σ() represents the Tanh function, and W1 and b1 represent learnable parameters; it can be seen that based on each sliding window, a set of vector representations H(t) of nodes will be obtained, and a series of implicit graphs that change with time can be constructed based on each different H(t), as shown in Figure 2(b).

[0105] S212 fuses the implicit graph constructed based on this embedded representation with the topological graph into a dynamic graph;

[0106] When constructing a graph based on sea surface temperature spatio-temporal data, not only the topological dependence relationship between nodes needs to be considered, but also the dynamic implicit information in the sea surface temperature spatio-temporal data. However, existing research mainly considers the topological dependence relationship between nodes, or fuses with a simple implicit graph through beta distribution for sea surface temperature prediction. But there are still the following problems: 1) Ignore other implicit correlation factors that affect sea surface temperature prediction; 2) The beta distribution based on empirical values may have artificial cognitive biases; 3) Data in different sea areas may have different characteristics, and using empirical values to set the weights between the topological graph and the implicit graph is not universal. Therefore, how to construct an implicit graph based on the correlation of sea surface temperature and how to allocate the weights between the topological graph and the implicit graph have a crucial impact on the prediction effect of sea surface temperature, which are also two important problems to be solved in this section. Therefore, it is necessary to construct an implicit graph based on the time correlation and functional correlation of grid points / nodes in the target sea area, and the formal definitions are given as follows respectively.

[0107] In the t-th sliding window, the implicit graph based on the time correlation of the sea surface temperature embedded representation between nodes, denoted as The time correlation matrix of the sea surface temperature between all nodes is denoted as Given two nodes v i and v j , H i (t) and H j (t) respectively represent the embedded representations of v i and v j in the t-th sliding window; the Euclidean distance is used to characterize the time correlation of the sea surface temperature between nodes As shown in Equation (4):

[0108]

[0109] If the sea surface temperature is similar in the same time period, the smaller the value, the stronger the similarity between v i and v j , and vice versa, the weaker the similarity;

[0110] In the t-th sliding window, the implicit graph based on the functional correlation of the sea surface temperature embedding representation between nodes is denoted as The functional correlation matrix of the sea surface temperature between all nodes is denoted as Given two nodes v i and v j , the functional similarity is characterized based on the cosine function As shown in Equation (5):

[0111]

[0112] where the larger the value, the stronger the similarity between v i and v j , and vice versa, the weaker the similarity;

[0113] and are obtained by calculating the embedding representation through a function, and the values in the matrix represent the degree of correlation between nodes; however, some smaller values may be due to data errors rather than the actual correlation between nodes; these errors may affect the prediction accuracy of the sea surface temperature. To solve this problem, Gumble Softmax is introduced to learn and the extreme value distributions in, to retain the minimum value in and the maximum value in, in order to achieve the purpose of sparsifying and ; let σ be the activation function, s IT and s IF is a temperature coefficient, and the sparse adjacency matrices and are as shown in Equation (6):

[0114]

[0115]

[0116] and represent and the temporal correlation matrix and the functional correlation matrix of the sea surface temperature in respectively; in Equation (7), if Then If Then In Equation (8), if Then If Then

[0117] The node topology graph, the time-correlation implicit graph, and the function-correlation implicit graph respectively reflect different characteristics of the sea surface temperature between nodes from different perspectives; in order to obtain richer graph information, the above three graphs are fused. However, the information contained in these three graphs is different, and their impacts on the sea surface temperature are also different, so how to assign weights to the three graphs is particularly important. Different from the weighting coefficients in the traditional beta distribution, the dynamic graph module learns weights by using the self-attention mechanism, that is, assigns weights according to the impacts of different characteristics on the sea surface temperature;

[0118] Fusion graph correlation matrix based on the attention network As shown in Equation (9):

[0119]

[0120] Among them, f a represents the self-attention network, and θ a , θ b and θ c are the weight parameters corresponding to the three types of graphs respectively.

[0121] Taking the fusion graph as the input, use GCN to extract the spatial features of the t-th window As shown in Equation (10):

[0122]

[0123] Among them, is the dynamic fusion graph correlation matrix, D is the degree matrix, is the original input data of the t-th window, and W FG and b FG are learnable weight and bias parameters.

[0124] S22 constructs a time-dependent module;

[0125] The spatio-temporal prediction of sea surface temperature is affected by both spatial dependence and time dependence factors. The DGM module mainly extracts the spatial features of sea surface temperature, and the TDM module mainly extracts the time features of sea surface temperature. However, affected by the variation law of sea surface temperature and the sampling frequency, there is time redundancy in sea surface temperature data, as Figure 4 shown. Given the sea surface temperature dataset (N is the number of nodes, and w represents the time length), there usually exists rank(K t ) < min(N, w), that is, K t generally has a low-rank property, which indicates that there is redundancy in the sea surface temperature data. Therefore, the problem of time redundancy needs to be considered when extracting the time dependence of the sea surface temperature.

[0126] Constructing the Time Dependence Module (TDM) specifically includes the following steps:

[0127] S221 In the time dependence module, first divide the data set into odd (O) sequences and even (E) sequences;

[0128] Utilize the low-rank property of the existing sea surface temperature data to downsample the original time series into odd and even sequences.

[0129] S222 Use LSTM to learn the time features of the sea surface temperature;

[0130] Then use the LSTM model / time feature extractor to learn the time features of the subsequences respectively, and finally merge them in the original order to obtain the time features of the t-th window As shown in Equation (11):

[0131]

[0132] Among them, K t represents the original sea surface temperature data to be sampled, K t,1 represents the odd (O) sequence of the sea surface temperature after sampling, K t,2 represents the even (E) sequence of the sea surface temperature after sampling; represents the result learned after inputting the sampled sequence K t,i into the LSTM model; represents the result of merging the learned and together.

[0133] S23 Construct the spatio-temporal fusion module;

[0134] As shown in Figure 2(a), input the sea surface temperature data of the t-th window (including w historical time steps). In order to more accurately predict the sea surface temperature data of the next k time steps, it is necessary to fuse the sea surface temperature spatial features extracted by the DGM and the sea surface temperature time features extracted by the TDM, and learn the sea surface temperature of the next k time steps through constructing a fully connected layer As shown in Equation (12):

[0135]

[0136] Among them, and They are the spatial feature and temporal feature of the t-th window respectively, σ() represents the Tanh function, and W2 and b2 represent the learnable weight and bias parameters.

[0137] To effectively measure the average deviation between the predicted value and the true value, the mean absolute error (MAE) is introduced as the loss function of the model, as shown in Equation (13):

[0138]

[0139] where W θ are all the learnable parameters in the prediction model STFTIG.

[0140] S24 constructs a sea surface temperature spatio-temporal prediction model based on GCN-LSTM based on the dynamic graph module, time dependence module and spatio-temporal fusion module;

[0141] Among them, in the DGM, the embedded representations of the nodes learned from the sea surface temperature data in different time periods are used to construct the time-correlation implicit graph and the functional-correlation implicit graph respectively. Then, the self-attention mechanism is used to learn the weights of the topological graph and the implicit graph, and the fused graph is further used as the input of the GCN to learn the spatial features of the sea surface temperature; in the TDM, the data set is first divided into odd (O) sequences and even (E) sequences, and then the LSTM is used to learn the temporal features of the sea surface temperature; finally, based on the STFM, the learned temporal and spatial features are fused to realize the prediction of the sea surface temperature spatio-temporal data.

[0142] S3 Experimental result analysis

[0143] S31 Experimental settings

[0144] The sea surface temperature data set is divided into a training set, a validation set and a test set in the ratio of 8:1:1; the historical data of w consecutive time steps are used to predict the data of the next k consecutive time steps.

[0145] The experiment is carried out in an environment of a server with a GPU of GeForce RTX3090 24G and the Pytorch deep learning framework. The Adam optimizer is used to train the model, and the learning rate is 0.003. The batch size is 32, and the number of training times is 100.

[0146] Four baseline models are selected, namely: STFGNN, RGSL, DLinear and Transformer, for comparative experiments. Among them, both STFGNN and RGSL are models based on graph neural networks, and DLinear is a linear model.

[0147] Evaluation metrics: The mean absolute error (MAE) and the root mean square error (RMSE) are used to measure the performance of the model.

[0148] S32 Experimental Results and Analysis

[0149] 1) In the sea surface temperature spatio-temporal dataset, the STFTIG model was used to predict the next two days. Among them, the input lengths were set from 2 to 15 respectively, the output length was set to 2, and MAE and RMSE were used as evaluation indicators. The prediction results are shown in Figures 5(a) and 5(b). As can be seen from Figures 5(a) and 5(b), as the number of historical days increases, the prediction effect first gradually improves and then deteriorates; when the number of historical days is 8, the prediction effect for the next two days is the best. Among them, the prediction effect of the 8-day prediction for the first day is shown in Figures 6(b) and 6(c). Compared with the true value in Figure 6(a), the distribution of isotherms is relatively consistent and the overall effect is good.

[0150] 2) To verify the effectiveness of the proposed STFTIG model, ablation experiments were set up, and the components x ∈ {FG, TD, GT} were given; among them, FG and TD represent the fusion graph module and the time dependence model respectively, GT represents having both of these two modules, and (STFTIG-x) is used to represent the experimental control group without embedding the corresponding component. In the experiment, the input sequence length was set to 2 - 15, and the output sequence length was set to 2; the prediction results are shown in Figures 7(a) and 7(b). As can be seen from the figure, STFTIG-TD is better than STFTIG-FG. Since the graph neural network itself considers the spatial structure, the superposition of time features has a more significant effect on improving sea surface temperature prediction; the prediction effect of STFTIG-GT is the worst, indicating that the superposition of spatio-temporal dependence plays a positive role in the prediction accuracy of the final model.

[0151] 3) To further verify the prediction effect of the STFTIG model, four classic baseline models, namely Transformer, DLinear, STFGNN, and RGSL, were selected. Comparative experiments were carried out on predicting the next two days and ten days respectively. The prediction results are shown in Figures 8(a), 8(b), 9(a), and 9(b). It can be seen that the STFTIG model has good prediction effects in both cases, especially showing better prediction effects in longer-term predictions; compared with the optimal effects of each model, the prediction effects for two days are improved by 0.88% - 3.48% and 1.14% - 4.95% respectively in terms of MAE and RMSE indicators; the prediction effects for ten days are improved by 1.38% - 3.53% and 2.46% - 5.32% respectively in terms of MAE and RMSE indicators. It can be seen that GCN based on the fusion of implicit graph and topological graph and LSTM based on data decomposition can better learn the spatio-temporal features of data, thereby improving the prediction effect of sea surface temperature spatio-temporal data.

[0152] In summary, to solve the problem of low accuracy in spatio-temporal prediction of sea surface temperature, the present invention proposes a spatio-temporal prediction method STFTIG of sea surface temperature based on GCN-LSTM. First, an implicit graph of temporal similarity and an implicit graph of functional similarity are respectively constructed based on the embedding representations of nodes learned from sea surface temperature data in different time periods. Then, the self-attention mechanism is used to learn the weights of the topological graph and the implicit graph, and the fused graph is further used as the input of GCN to learn the spatial features of sea surface temperature. Secondly, the data set is divided into odd (O) sequences and even (E) sequences, and LSTM is used to learn the temporal features of sea surface temperature. Then, based on STFM, the learned temporal and spatial features are fused to realize the prediction of spatio-temporal data of sea surface temperature. This model fully considers the spatial and temporal dependencies of sea surface temperature data, can accurately reflect the dynamic change relationship between sea surface temperatures, and effectively solves the problems such as insufficient information contained in static graph models. By comparing with 4 baseline models on a real sea surface temperature data set, the superiority of the proposed model over the baseline models and the importance of the DGM and TDM modules are verified. In the future, how to more accurately predict sea surface temperature under the influence of noise and uncertainty in sea surface temperature data is the focus of the next research.

Claims

1. A sea surface temperature spatio-temporal prediction method based on GCN-LSTM, characterized in that: It includes the following steps: S1. Select the sea surface temperature (SST) spatio-temporal dataset and define the SST spatio-temporal data prediction task; S1 specifically includes the following steps: S11. Obtain data to form the SST spatio-temporal dataset; Select the SST data within the grid range of the target sea area as the research object, and denote the SST spatio-temporal dataset as X; S12. Construct a topological graph based on the sea surface temperature spatio-temporal dataset Construct a topological graph based on the grid after removing the land. The intersection points in the grid are regarded as nodes, and the topological graph is represented as a binary tuple where V represents the set of nodes, and E S represents the set of edges; S13. According to the topological graph Construct an implicit graph S14. Define the SST spatio-temporal data prediction task; Dataset of given sea surface temperature spatio-temporal data where N = |V| represents the number of nodes, and M is the total amount of time, represents the sea surface temperature data of N nodes at the m-th moment; in the topological graph and the implicit graph Based on the fusion, learn a function f according to the sea surface temperature data of w historical time steps to predict the sea surface temperature data of the next k time steps, as shown in Equation (2): Among them, is a topological graph, is an implicit graph, V is a node set, and X is a sea surface temperature data set; S2. Construct an SST spatio-temporal prediction model based on GCN-LSTM; the spatio-temporal prediction model STFTIG of SST based on GCN-LSTM includes three modules: a dynamic graph module DGM, a time dependence module TDM, and a spatio-temporal fusion module STFM; the spatio-temporal prediction model STFTIG of SST is constructed based on a graph convolutional network and a long short-term memory network; S2 specifically includes the following steps: S21 Construct the dynamic graph module; In the construction of the dynamic graph module, first construct an implicit graph of time correlation and an implicit graph of functional correlation based on the embedded representations of nodes learned from the SST data in different time periods, then use the self-attention mechanism to learn the weights of the topological graph and the implicit graph, and further use the fused graph as the input of the GCN to learn the spatial features of SST; S22 Construct the time dependence module; Downsample the original time series into odd and even sequences; use the LSTM model / time feature extractor to learn the time features of the subsequences respectively; S23 Construct the spatio-temporal fusion module; Fuse the SST spatial features extracted by the dynamic graph module and the SST time features extracted by the time dependence module; S24 Construct an SST spatio-temporal prediction model based on GCN-LSTM based on the dynamic graph module, the time dependence module, and the spatio-temporal fusion module.

2. The sea surface temperature spatio-temporal prediction method based on GCN-LSTM according to claim 1, characterized in that: In S12, use A S to represent the edge weight matrix, as shown in Equation (1): Among them, if (v i , v j ) belongs to the direct edge E in the network S1 , then A S (v i , v j ) = 1; if (v i , v j ) belongs to the diagonal edge E in the network S2 , then otherwise A S (v i , v j ) = 0.

3. The sea surface temperature spatio-temporal prediction method based on GCN-LSTM according to claim 2, characterized in that: In S13, given a topological graph represents the sea surface temperature data of the t-th sliding window, and the implicit graph corresponding to the t-th sliding window is denoted as where V is the node set in, represents the edge learned based on the sea surface temperature data between nodes in the t-th sliding window using function L; represents the implicit correlation matrix of the sea surface temperature between nodes in the t-th sliding window learned using function Fun; if this implicit graph is constructed based on temporal or functional correlation, it is called a temporal correlation implicit graph or a functional correlation implicit graph and their correlation matrices are respectively denoted as 4. The sea surface temperature spatio-temporal prediction method based on GCN-LSTM according to claim 1, characterized in that: S21 specifically includes the following steps: S211 Learn the embedded representations of nodes based on the SST data in different time periods / sliding windows; During the node embedding process, a sliding window is used to divide the given sea surface temperature dataset into different time periods; if the size of the sliding window is w and the step length is L, the dataset is divided into segments of windows, denoted as For each time window data a fully connected layer MLP is constructed to extract the sea surface temperature features of each node within the time window, thereby obtaining the embedding representation of N nodes with d dimensions, denoted as As shown in Equation (3): H(t) = σ([X(wt+1),...,X(wt+w)]×W1 + b1) (3) Among them, the sliding window K t ={X(wt + 1),..., X(wt + w)}, σ() represents the Tanh function, and W1 and b1 represent learnable parameters; it can be seen that a vector representation H(t) of a group of nodes is obtained based on each sliding window; S212 Fuse the implicit graph constructed based on the embedded representation with the topological graph into a dynamic graph; In the t-th sliding window, the time-correlated implicit graph based on the SST embedding representation between nodes is denoted as The time-correlation matrix of all SSTs between nodes is denoted as Given two nodes v i and v j , H i (t) and H j (t) respectively represent the embedding representations of v i and v j in the t-th sliding window; the Euclidean distance is used to characterize the time correlation of SSTs between nodes As shown in Equation (4): In the t-th sliding window, the implicit graph based on the functional correlation of SST embeddings between nodes is denoted as The functional correlation matrix of all SSTs between nodes is denoted as Given two nodes v i and v j , the functional similarity is characterized based on the cosine function As shown in Equation (5): and is obtained by embedding representation through function calculation, and the values in the matrix represent the degree of correlation between nodes; Introduce Gumble Softmax to learn and the extreme value distribution in to retain the minimum value in and the maximum value in and for the purpose of sparsification; let σ be the activation function, s IT and s IF is a temperature coefficient, and the sparse adjacency matrix and are shown in Equation (6): and respectively represent and the temporal correlation matrix and the functional correlation matrix of the SST; in Equation (7), if then if then in Equation (8), if then if then Fuse the above three graphs; the dynamic graph module uses the self-attention mechanism to learn the weights, that is, allocate weights according to the influence of different features on SST; Attention Network-Based Fusion Graph Correlation Matrix As shown in Equation (9): Among them, f a represents the self-attention network, and θ a , θ b and θ c are weight parameters corresponding to three types of graphs, respectively; Taking the fusion graph as the input, the spatial features of the t-th window are extracted by GCN As shown in Equation (10): Among them, is the dynamic fusion graph correlation matrix, D is the degree matrix, is the original input data of the t-th window, W FG and b FG are learnable weight and bias parameters.

5. The sea surface temperature spatio-temporal prediction method based on GCN-LSTM according to claim 1, characterized in that: S22 specifically includes the following steps: S221 In the time dependence module, first divide the dataset into odd and even sequences; Utilize the low-rank property of the existing SST data to downsample the original time series into odd and even sequences; S222 Use LSTM to learn the time features of SST; Then, the LSTM model / temporal feature extractor is used to learn the temporal features of the subsequences respectively, and finally they are merged in the original order to obtain the temporal features of the $t$-th window. As shown in Equation (11): Among them, K t represents the original sea surface temperature data to be sampled, and K t,1 represents the odd sequence of the sea surface temperature after sampling, and K t,2 represents the even sequence of the sea surface temperature after sampling; represents the result learned after inputting the sampled sequence K t,i into the LSTM model; represents the result of combining the learned and .

6. The sea surface temperature spatio-temporal prediction method based on GCN-LSTM according to claim 1, characterized in that: S23 specifically includes: Input the t-th window, where each window contains sea surface temperature (SST) data of w historical time steps. To more accurately predict the SST data of the next k time steps, it is necessary to fuse the spatial features of SST extracted by the dynamic graph module and the temporal features of SST extracted by the temporal dependence module, and learn the SST of the next k time steps through constructing a fully connected layer. As shown in Equation (12): Among them, and are the spatial feature and the temporal feature of the t-th window respectively, σ() represents the Tanh function, and W2 and b2 represent the learnable weight and bias parameters; To effectively measure the average deviation between the predicted value and the true value, introduce the mean absolute error as the loss function of the model, as shown in Equation (13): Among them, W θ are all the learnable parameters in the prediction model STFTIG.

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