Wavelet-enhanced graph neural network-based sea surface core variable prediction method and system
By employing wavelet-enhanced graph neural networks, the problems of multi-scale coupling and long-term dependency degradation in multivariate spatiotemporal ocean data were solved, enabling efficient and stable prediction of core sea surface variables and improving the accuracy and stability of predictions.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- HARBIN INST OF TECH
- Filing Date
- 2026-04-10
- Publication Date
- 2026-07-07
AI Technical Summary
Existing technologies struggle to effectively address the issues of multi-scale coupling, long-term dependency degradation, and adaptive graph learning error accumulation in multivariate marine spatiotemporal data, leading to a decline in the stability and accuracy of predictions for core sea surface variables.
We employ a wavelet-based enhanced graph neural network approach, utilizing a variable-level multi-scale wavelet gating fusion module, a KAN-LSTM encoder module, and a symbol-adaptive spatial graph convolution module to achieve multi-scale temporal feature enhancement, long-term dependency stability improvement, and sparse adaptive graph learning, thereby constructing the WaveKAN spatiotemporal adaptive graph neural network.
It enhances the ability to perceive trend and fluctuation components in multivariate time series, improves the stability of long-term time series state transitions, and achieves structured spatial dependence modeling without prior graphs, thereby improving the prediction accuracy and stability of core sea surface variables.
Smart Images
Figure CN122347743A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of marine data processing and spatiotemporal sequence prediction technology, and more specifically to a method and system for predicting core sea surface variables based on wavelet-enhanced graph neural networks. Background Technology
[0002] Currently, accurate long-term predictions of core ocean surface elements such as sea surface temperature, salinity, ocean current velocity, and wind stress are crucial for air-sea interaction analysis and operational marine environmental applications. This type of data is typically distributed across irregular grids or discrete sites, exhibiting complex multivariate spatiotemporal coupling characteristics. In recent years, graph neural networks have been widely applied in spatiotemporal prediction due to their natural adaptability to irregular spatial structures.
[0003] However, long-term forecasting for multivariate oceanographic data still faces three major technical challenges: First, in multivariate sequences, long-term trends and short-term disturbances are coupled with each other at multiple scales, and different variables have different sensitivities to different time scales, making it difficult for existing methods to achieve variable-level multi-scale characterization enhancement. Second, as the forecast time increases, time-series dependencies are prone to degradation, and error propagation and accumulation problems become prominent, leading to a decrease in forecast stability. Third, in the absence of a reliable prior spatial graph structure, the adaptive adjacency matrix learned end-to-end from the data often tends to be dense or unstable, easily introducing redundant connections, leading to excessive information propagation, and thus weakening the ability to characterize long-distance spatial dependencies and the accuracy of long-term forecasts.
[0004] Therefore, how to provide a method for predicting core sea surface variables that can solve the problems of multi-scale coupling, long-term dependency degradation, and adaptive graph learning error accumulation in long-term prediction of multivariate spatiotemporal data of the ocean is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention
[0005] In view of the above problems, the present invention is proposed to provide a method and system for predicting core sea surface variables based on wavelet-enhanced graph neural networks to overcome or at least partially solve the above problems.
[0006] To achieve the above objectives, the present invention adopts the following technical solution:
[0007] A method for predicting core sea surface variables based on wavelet-enhanced graph neural networks includes the following steps: S1. Obtain multivariable map sequence data of the target sea surface; S2. Input the multivariate graph sequence data into the pre-trained variable-level multi-scale wavelet gating fusion module, perform multi-level wavelet decomposition and reconstruction on the time series of each variable, and adaptively fuse the decomposition coefficients at different scales through learnable gating parameters to output enhanced multi-scale time series features. S3. The enhanced multi-scale temporal features are input into the pre-trained KAN-LSTM encoder module. The KAN-LSTM encoder module processes the current input and historical state in parallel through the regular convolutional branch and the KAN convolutional branch, and fuses the gated signals of the regular convolutional branch and the KAN convolutional branch based on the learnable fusion coefficients. The output encoder spatiotemporal features are updated recursively. S4. Input the encoder spatiotemporal features into the pre-trained symbolic adaptive spatial graph convolution module, generate a symbolic sparse adaptive adjacency matrix based on trainable node embedding, perform multi-level diffusion aggregation on the encoder spatiotemporal features to obtain aggregated features, perform nonlinear mapping on the aggregated features, and then perform residual connection with the encoder spatiotemporal features to output the prediction results of the target sea surface core variables.
[0008] Preferably, the process of acquiring multivariate graphical sequence data includes: Obtain ocean feature data for multiple spatial nodes across multiple variable dimensions within a preset historical time window, construct a tensor of shape (B, T, N, V) as multivariate graph sequence data, where B is the batch size, T is the historical time step, N is the number of nodes, and V is the number of variables.
[0009] Preferably, the processing procedure of the variable-level multi-scale wavelet-gated fusion module for multivariable graph sequence data includes: For the v For time series of variables, perform several levels of Haar discrete wavelet transform to generate low-frequency trend coefficients and high-frequency fluctuation coefficients in each level of decomposition. Interpolation operators are used to align the low-frequency trend coefficients and high-frequency fluctuation coefficients at each level to the length of the original time series; We introduce learnable gating parameters for each variable at each decomposition level and use the tanh function to restrict the weights of the gating parameters to the range of (-1, 1). Based on the weights of the gating parameters, the aligned low-frequency trend coefficients and high-frequency fluctuation coefficients at each level are weighted and summed, and then fused with the original input sequence corresponding to the original time series in the form of residuals to output enhanced multi-scale time series features.
[0010] Preferably, when performing Haar discrete wavelet transform, if the time length of the current sequence to be decomposed is odd, the data from the last time step is copied to fill the gap, thus ensuring the parity pairing in the decomposition process.
[0011] Preferably, the KAN-LSTM encoder module's processing of enhanced multi-scale temporal features includes: At each time step, the enhanced multi-scale temporal features of the current time step are concatenated with the hidden state of the previous time step in the channel dimension. The concatenated tensor is input into the regular convolution branch and the KAN convolution branch respectively to generate gated preactivation tensors for the two branches. Learnable fusion coefficients are introduced for each output channel and constrained to the (0, 1) interval by the Sigmoid function to perform weighted fusion of the gated preactivation tensors of the two branches; The fused gated pre-activation tensor is segmented along the channel dimension, and activation functions are applied to generate input gates, forget gates, output gates, and candidate states. Update the current memory state and hidden state based on the input gate, forget gate, output gate, and candidate states.
[0012] Preferably, the KAN convolution branch is specifically used to extract neighborhood patches along the node dimension from the concatenated input tensor; each patch is input into the Fourier parameterized KAN map for processing; the Fourier parameterized KAN map contains learnable frequencies, phases and Fourier coefficients, which are used to perform nonlinear transformations on the input.
[0013] Preferably, the process by which the sign-adaptive spatial graph convolution module generates a sign-sparse adaptive adjacency matrix includes: Two sets of trainable node embedding matrices are introduced, and the original correlation matrix is generated by bilinear pooling and applying the ReLU activation function. For each target node, select the set of strong connections from the row vectors of its corresponding original association matrix, and select the set of weak connections from the row vectors of the strong connections. The weights in the set of strong connections are normalized to obtain positive weights; The weights in the weak connection set are reverse-emphasized and then normalized to obtain negative weights. The positive and negative weights are combined to form a signed sparse adaptive adjacency matrix.
[0014] Preferably, the spatiotemporal features of the encoder are subjected to multi-order diffusion aggregation based on the signed sparse adaptive adjacency matrix, including: Based on the signed sparse adaptive adjacency matrix, a diffusion representation from order 0 to a preset order is constructed; The diffusion representations of each order are concatenated along the feature dimension; The concatenated features are mapped back to the original feature dimensions through a linear layer, and residual connections are made with the spatiotemporal features of the encoder in the input symbolic adaptive spatial graph convolution module to output the final prediction result.
[0015] A sea surface core variable prediction system based on wavelet-enhanced graph neural network includes a data acquisition module, a variable-level multi-scale wavelet-gated fusion module, a KAN-LSTM encoder module, and a symbol-adaptive spatial graph convolution module. The data acquisition module is used to acquire multivariate graph sequence data of the target sea surface; The variable-level multi-scale wavelet gating fusion module is used to perform multi-level wavelet decomposition and reconstruction on the time series of each variable, and adaptively fuses the decomposition coefficients of different scales through learnable gating parameters to output enhanced multi-scale time series features. The KAN-LSTM encoder module is used to recursively update the enhanced multi-scale temporal features by gating the fusion of regular convolution and KAN convolution branches, and output the encoder spatiotemporal features. The symbolic adaptive spatial graph convolution module generates a signed sparse adaptive adjacency matrix based on trainable node embeddings, performs multi-level diffusion aggregation on the spatiotemporal features of the encoder, and outputs the prediction results of the core variables of the target sea surface.
[0016] As can be seen from the above technical solutions, compared with the prior art, the present invention discloses a method and system for predicting core sea surface variables based on wavelet-enhanced graph neural networks. The beneficial effects of the above technical solutions provided by the embodiments of the present invention include at least the following: ① By employing a variable-level multi-scale decomposition and adaptive fusion strategy, the model's ability to perceive trend and fluctuation components in multivariate time series is enhanced.
[0017] ②The stability of long-term state transitions is improved by using a recursive update mechanism that enhances nonlinear expression capabilities.
[0018] ③ By using sparse symbolic adaptive graph learning and multi-order propagation paradigm, structured spatial dependency modeling can be achieved without prior graphs. Attached Figure Description
[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.
[0020] Figure 1 This is a structural diagram of the WaveKAN spatiotemporal adaptive graph neural network model provided in an embodiment of the present invention. Detailed Implementation
[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0022] This invention discloses a method for predicting core sea surface variables based on wavelet-enhanced graph neural networks, comprising the following steps: S1. Obtain multivariable map sequence data of the target sea surface; S2. Input the multivariate graph sequence data into the pre-trained variable-level multi-scale wavelet gating fusion module, perform multi-level wavelet decomposition and reconstruction on the time series of each variable, and adaptively fuse the decomposition coefficients at different scales through learnable gating parameters to output enhanced multi-scale time series features. S3. The enhanced multi-scale temporal features are input into the pre-trained KAN-LSTM encoder module. The KAN-LSTM encoder module processes the current input and historical state in parallel through the regular convolutional branch and the KAN convolutional branch, and fuses the gated signals of the regular convolutional branch and the KAN convolutional branch based on the learnable fusion coefficients. The output encoder spatiotemporal features are updated recursively. S4. Input the encoder spatiotemporal features into the pre-trained symbolic adaptive spatial graph convolution module, generate a symbolic sparse adaptive adjacency matrix based on trainable node embedding, perform multi-level diffusion aggregation on the encoder spatiotemporal features to obtain aggregated features, perform nonlinear mapping on the aggregated features, and then perform residual connection with the encoder spatiotemporal features to output the prediction results of the target sea surface core variables.
[0023] The technical solution of this invention is described in detail through specific embodiments. For long-term prediction tasks of core ocean variables such as SST / SSS, seawater current velocity, and sea surface wind stress, this paper proposes the WaveKAN spatiotemporal adaptive graph neural network. Figure 1 As shown, the network consists of three core modules: a variable-level multi-scale wavelet gating fusion module, a KAN-LSTM encoder module, and a symbolic adaptive spatial graph convolution module.
[0024] Specifically, the variable-level multi-scale wavelet-gated fusion module enhances the representation of multi-scale temporal features through variable-level multi-scale decomposition and gating fusion to decouple trend and fluctuation components; the KAN-LSTM encoder module employs a dual-branch gating mechanism to achieve nonlinear state updates, mitigating temporal dependency degradation in long-term prediction; and the symbolic adaptive spatial graph convolution module learns structured spatial dependencies without prior graphs, combining multi-order diffusion aggregation to strengthen long-distance interaction modeling. The synergistic effect of these three components comprehensively improves the WaveKAN spatiotemporal adaptive graph neural network in terms of multi-scale temporal perception, long-term dependency preservation, and spatial relationship stability, effectively alleviating the performance degradation problem of existing graph neural networks in long-term ocean prediction.
[0025] Variable-level multi-scale wavelet gating fusion module Figure 1It includes an enhanced spatiotemporal adaptive graph neural network for multi-scale time series representation in multivariate graph sequences, and introduces a variable-level multi-scale wavelet gating fusion module. This module performs multi-level Haar wavelet decomposition on a "variable-by-variable" basis on the time series, and fuses the data in a residual manner through learnable gating with tanh limiting, thereby achieving enhanced dynamic and cross-scale variable coupling.
[0026] The variable-level multi-scale wavelet-gated fusion module takes a multivariable graph sequence as input. Where B is the batch size, T is the historical time step, N is the number of nodes, and V is the number of variables (such as sea surface salinity, sea surface temperature, and seawater velocity). u / v Sea surface wind stress u / v The outputs of the variable-level multi-scale wavelet-gated fusion module have the same shape: For the first v Given a variable, take its subsequence: .
[0027] The processing steps of the variable-level multi-scale wavelet-gated fusion module for multivariable graph sequence data include: For the v For a time series of variables, perform several levels of Haar discrete wavelet transform, generating low-frequency trend coefficients and high-frequency fluctuation coefficients in each level of decomposition. When performing Haar discrete wavelet transform, if the time length of the current sequence to be decomposed is odd, fill it by copying the data from the last time step to ensure odd-even pairing in the decomposition process.
[0028] Interpolation operators are used to align the low-frequency trend coefficients and high-frequency fluctuation coefficients at each level to the length of the original time series. Learnable gating parameters corresponding to each variable at each decomposition level are introduced, and the weights of the gating parameters are restricted to the interval (-1, 1) using the tanh function. The aligned low-frequency trend coefficients and high-frequency fluctuation coefficients at each level are weighted and summed according to the weights of the gating parameters, and then fused with the original input sequence corresponding to the original time series in the form of residuals to output enhanced multi-scale time series features.
[0029] The variable-level multi-scale wavelet-gated fusion module performs an L-level Haar discrete wavelet transform on each variable along the time dimension. Let the 0th-level approximation coefficients be:
[0030] In the l ( In level ) sampling, sampling is first performed according to odd and even time steps:
[0031] in, This indicates the sampling results based on even-numbered time steps. l Indicates the firstl Level decomposition, This indicates the sampling results based on odd-numbered time steps. L Let be the number of decomposition levels, and satisfy . .
[0032] When the current time step is odd, the end is copied and padded once to ensure odd-even pairing, that is, the last time step is copied once and spliced to the end.
[0033] The low-frequency trend coefficient of Haar was then calculated. and high-frequency fluctuation coefficient :
[0034] in, and The time step is Both maintain the node dimension N unchanged.
[0035] Since the time lengths of the coefficients at different scales are different, the variable-level multi-scale wavelet-gated fusion module uses one-dimensional linear interpolation to align them with the original time step T and records the aligned interpolation operator. ,but:
[0036] in, .
[0037] To adaptively select the contribution of "variable-scale", the variable-level multi-scale wavelet gating fusion module performs a multi-scale wavelet gating fusion for each variable. v With each scale l Introducing learnable scalar gating parameters and use activation function Limit the weights to the range (-1, 1):
[0038] in, It is an initialization parameter that automatically learns weights based on the network and is then weighted and coupled with low-frequency trend coefficients after passing through an activation function. It is also an initialization parameter. The weights are automatically learned by the network and then weighted and coupled with the high-frequency fluctuation coefficients after passing through the activation function. for After activation function The subsequent weights, for After activation function The weights after that.
[0039] The final fusion uses a residual form, fusing the original input with the weighted reconstruction coefficients at each level to obtain the enhanced features of the variable:
[0040] When the high-frequency fluctuation coefficient is not enabled, in the formula The V variables are removed, and the resulting concatenation yields the final output of the enhanced multi-scale temporal features. :
[0041] This gate is related to the number of variables V and the number of decomposition levels. L It is related to the number of nodes N. By initializing the gating parameters to values close to 0, the modules are approximately identically mapped in the early stages of training, which is beneficial for stable training.
[0042] The following is the pseudocode for the computation process of the variable-level multi-scale wavelet gating fusion module.
[0043]
[0044] KAN gated convolutional long short-term memory timing encoder module The KAN-LSTM encoder module is used to enhance the nonlinear representation of spatiotemporal state transitions in long-term prediction. At each time step, the KAN-LSTM encoder module performs convolutional interactive modeling of the node dimension and propagates information along the time dimension through recursive state updates. Gating is generated jointly by "regular convolutional branches" and "KAN convolutional branches," and bounded fusion is performed using channel-level fusion coefficients limited by the sigmoid activation function to balance expressive power and training stability.
[0045] The KAN-LSTM encoder module's processing of enhanced multi-scale temporal features includes: At each time step, the enhanced multi-scale temporal features of the current time step are concatenated with the hidden state of the previous time step in the channel dimension.
[0046] The concatenated tensor is input into the regular convolution branch and the KAN convolution branch respectively to generate gated pre-activation tensors for the two branches. The KAN convolution branch is specifically used to extract neighborhood patches along the node dimension of the input concatenated tensor. Each patch is input into the Fourier parameterized KAN map for processing. The Fourier parameterized KAN map contains learnable frequencies, phases and Fourier coefficients, which are used to perform nonlinear transformations on the input.
[0047] Learnable fusion coefficients are introduced for each output channel and constrained to the (0, 1) interval by the Sigmoid function to perform weighted fusion of the gated pre-activation tensors of the two branches; the fused gated pre-activation tensors are split in the channel dimension and activation functions are applied to generate input gate, forget gate, output gate and candidate state; the memory state and hidden state at the current time step are updated according to the input gate, forget gate, output gate and candidate state.
[0048] The input characteristics of the KAN-LSTM encoder module are set as follows: ,and .in, Enhanced multi-scale temporal features output by the variable-level multi-scale wavelet-gated fusion module , C For feature dimensions, the values are typically taken as follows: The features output by the KAN-LSTM encoder module are the encoder's spatiotemporal features. ,and .in For the hidden layer dimension.
[0049] Specifically, at time step t, let
[0050] in, This indicates that the tensor is from Replace with , Indicates taking The t-th time step.
[0051] Hidden state and memory state are respectively This means that it refers to the previous moment.
[0052] First, the hidden state of the current input and the previous time frame are concatenated in the channel dimension:
[0053] in, This represents the result of splicing the information from the current frame and the previous frame along the time dimension.
[0054] Subsequently, two parallel branches, including a regular convolution branch and a KAN convolution branch, are used to generate a gated activation tensor, which is then computed by merging the branches through four gates: ;
[0055] in, Indicates to One-dimensional convolution operation performed, Indicates to The Fourier KAN operation was performed.
[0056] To limit the impact of KAN branches on gating and enhance training stability, channel-level learnable fusion coefficients u are introduced, satisfying the following conditions: Furthermore, the sigmoid function is used to constrain the channel-level learnable fusion coefficients to the range of (0, 1):
[0057] in, It will broadcast on both the batch and node dimensions. The two branch gates are fused as follows to obtain the fused features. :
[0058] Fusion features Each channel is divided into four groups: input gate, forget gate, output gate, and candidate state.
[0059] in, Indicates the input gate. Represents the Gate of Oblivion Indicates the output gate. Indicates a candidate state.
[0060] By applying a gated activation function, the following results were obtained:
[0061] in, This indicates that the input gate has undergone activation function operation. This indicates that the forget gate has undergone activation function operation. This indicates that the output gate has undergone an activation function operation. This indicates that the tanh activation function operation is added to the fused features.
[0062] The final recursive update is as follows: ,
[0063] In the KAN convolution branch Along the node dimension N Perform local receptive field modeling. The preset convolutional kernel size is K, where K is an odd number, and the padding is... Then, construct a patch vector for each node position n:
[0064] The output of the KAN convolution at each node can be written as:
[0065] in, It is a Fourier-parameterized KAN mapping.
[0066] The specific steps are as follows: Given an input graph sequence data x, and satisfying First, the input graph sequence data is normalized and scaled dimension by dimension:
[0067] in, It is a learnable, dimension-wise scale.
[0068] KAN mapping uses A frequency grid, for each input dimension With frequency index Define learnable frequency parameters With learnable phase parameters :
[0069] And introduce a frequency attenuation factor ,in, The decay exponent is a constant. For the output channel... The response can be written as:
[0070] in, and For learnable Fourier coefficients, For linear residual shortcuts, This is a bias term.
[0071] Gated convolutional long short-time memory sequential encoder module by time step Perform recursion, perform initialization operations, and obtain... .
[0072] And on Repeating the above equation yields Finally, all time-step outputs are stacked and transposed back. Obtain the spatiotemporal features of the encoder :
[0073] This indicates that the hidden states of the KAN-LSTM encoder module at each time step are stacked. Furthermore, when using a multi-layer structure, random deactivation operations can be applied between layers.
[0074] Symbolic Adaptive Spatial Graph Convolution Module The spatiotemporal features of the encoder are input into the pre-trained symbolic adaptive spatial graph convolutional module. The current symbolic adaptive spatial graph convolutional module aims to learn structured node dependencies from data without the need for a predefined spatial graph, and enhance the ability to model long-distance spatial interactions through multi-level diffusion message passing.
[0075] The process by which the sign-adaptive spatial graph convolution module generates a sign-sparse adaptive adjacency matrix includes: Two sets of trainable node embedding matrices are introduced. The original association matrix is generated by bilinear pooling and applying the ReLU activation function. For each target node, the sets of connections with the largest values are selected from the row vectors of its corresponding original association matrix as strong connections, and the sets of connections with the smallest values are selected as weak connections. The weights in the strong connection set are normalized to obtain positive weights. The weights in the weak connection set are reverse-emphasized and then normalized to obtain negative weights. The positive and negative weights are combined to form a signed sparse adaptive adjacency matrix.
[0076] A signed sparse adaptive adjacency matrix performs multi-order diffusion aggregation on the spatiotemporal features of the encoder, including: Based on the signed sparse adaptive adjacency matrix, a diffusion representation from order 0 to a preset order is constructed; the diffusion representations of each order are concatenated on the feature dimension; the concatenated features are mapped back to the original feature dimension through a linear layer, and residual connections are made with the spatiotemporal features of the encoder of the input signed adaptive spatial graph convolution module to output the final prediction result.
[0077] The module consists of two parts: (i) a signed sparse adaptive adjacency matrix generated by trainable node embedding; and (ii) a multi-order diffusion graph convolution based on the adjacency matrix, which concatenates information of different propagation orders and performs nonlinear mapping to improve the ability to model long-distance spatial interactions and the robustness of long-term prediction.
[0078] Specifically, let the encoder spatiotemporal characteristics output by the KAN-LSTM encoder module be... Marked as And satisfy , Output after sign-adaptive convolution module And satisfy ,in This indicates the predicted results of the target sea surface core variables.
[0079] The trainable node embedding parameters, E1 and E2, are introduced into the symbolic sparse adaptive adjacency matrix. The original incidence matrix is generated in a bilinear form, and a ReLU activation function is applied to obtain:
[0080] Where E1 and E2 satisfy , For embedded dimensions.
[0081] At the same time, the "strongest / weakest" connection is preserved for sparsity reduction, for each node (i.e., matrix number) (Lines), selecting the Top-k as the set of strong connections. Bottom-k is selected as the set of weak connections. Define the mask:
[0082] Perform symbolic normalization and apply it to strong connections. Row normalization yields positive weights :
[0083] For weak connections To achieve reverse emphasis, after parallel normalization, a negative sign is applied to obtain negative weights. :
[0084] Final signed sparse adaptive adjacency matrix for:
[0085] Only about 100% of each line is retained Each connection is normalized within the strong / weak sets, and its contribution direction is distinguished by a symbol.
[0086] The symbolic adaptive spatial graph convolution module employs a linear propagation operator in the node dimension:
[0087] Let the diffusion order be Constructing order 0 to Diffusion representation of order:
[0088] Concatenate the results of each order along the feature dimension:
[0089] in, This is the prediction result after processing by the concat function.
[0090] Then, a nonlinear layer was used to map back. Dimension, and connect ReLU activation function and random deactivation layer:
[0091] Specifically, the overall module adopts a residual connection method to obtain the final prediction result. :
[0092] Based on the above signed sparse adaptive adjacency matrix, the spatiotemporal features of the encoder are subjected to multi-level diffusion aggregation to output the final prediction results of the core variables of the target sea surface.
[0093] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.
[0094] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims
1. A method for predicting core sea surface variables based on wavelet-enhanced graph neural networks, characterized in that, Includes the following steps: S1. Obtain multivariable map sequence data of the target sea surface; S2. Input the multivariate graph sequence data into the pre-trained variable-level multi-scale wavelet gating fusion module, perform multi-level wavelet decomposition and reconstruction on the time series of each variable, and adaptively fuse the decomposition coefficients at different scales through learnable gating parameters to output enhanced multi-scale time series features. S3. The enhanced multi-scale temporal features are input into the pre-trained KAN-LSTM encoder module. The KAN-LSTM encoder module processes the current input and historical state in parallel through the regular convolutional branch and the KAN convolutional branch, and fuses the gated signals of the regular convolutional branch and the KAN convolutional branch based on the learnable fusion coefficients. The output encoder spatiotemporal features are updated recursively. S4. Input the encoder spatiotemporal features into the pre-trained symbolic adaptive spatial graph convolution module, generate a symbolic sparse adaptive adjacency matrix based on trainable node embedding, perform multi-level diffusion aggregation on the encoder spatiotemporal features to obtain aggregated features, perform nonlinear mapping on the aggregated features, and then perform residual connection with the encoder spatiotemporal features to output the prediction results of the target sea surface core variables.
2. The method for predicting core sea surface variables based on wavelet-enhanced graph neural networks according to claim 1, characterized in that, The process of obtaining multivariate graphical sequence data includes: Obtain ocean feature data for multiple spatial nodes across multiple variable dimensions within a preset historical time window, construct a tensor of shape (B, T, N, V) as multivariate graph sequence data, where B is the batch size, T is the historical time step, N is the number of nodes, and V is the number of variables.
3. The method for predicting core sea surface variables based on wavelet-enhanced graph neural networks according to claim 1, characterized in that, The processing steps of the variable-level multi-scale wavelet-gated fusion module for multivariable graph sequence data include: For the v For time series of variables, perform several levels of Haar discrete wavelet transform to generate low-frequency trend coefficients and high-frequency fluctuation coefficients in each level of decomposition. Interpolation operators are used to align the low-frequency trend coefficients and high-frequency fluctuation coefficients at each level to the length of the original time series; We introduce learnable gating parameters for each variable at each decomposition level and use the tanh function to restrict the weights of the gating parameters to the range of (-1, 1). Based on the weights of the gating parameters, the aligned low-frequency trend coefficients and high-frequency fluctuation coefficients at each level are weighted and summed, and then fused with the original input sequence corresponding to the original time series in the form of residuals to output enhanced multi-scale time series features.
4. The method for predicting core sea surface variables based on wavelet-enhanced graph neural networks according to claim 3, characterized in that, When performing Haar discrete wavelet transform, if the time length of the current sequence to be decomposed is odd, it is filled by copying the data from the last time step to ensure odd-even pairing in the decomposition process.
5. The method for predicting core sea surface variables based on wavelet-enhanced graph neural networks according to claim 1, characterized in that, The KAN-LSTM encoder module's processing of enhanced multi-scale temporal features includes: At each time step, the enhanced multi-scale temporal features of the current time step are concatenated with the hidden state of the previous time step in the channel dimension. The concatenated tensor is input into the regular convolution branch and the KAN convolution branch respectively to generate gated preactivation tensors for the two branches. Learnable fusion coefficients are introduced for each output channel and constrained to the (0, 1) interval by the Sigmoid function to perform weighted fusion of the gated preactivation tensors of the two branches; The fused gated pre-activation tensor is segmented along the channel dimension, and activation functions are applied to generate input gates, forget gates, output gates, and candidate states. Update the current memory state and hidden state based on the input gate, forget gate, output gate, and candidate states.
6. The method for predicting core sea surface variables based on wavelet-enhanced graph neural networks according to claim 5, characterized in that, The KAN convolution branch is specifically used to concatenate the input tensor and extract neighborhood patches along the node dimension; each patch is then input into a Fourier-parameterized KAN map for processing; the Fourier-parameterized KAN map contains learnable frequencies, phases, and Fourier coefficients, which are used to perform nonlinear transformations on the input.
7. The method for predicting core sea surface variables based on wavelet-enhanced graph neural networks according to claim 1, characterized in that, The process by which the sign-adaptive spatial graph convolution module generates a sign-sparse adaptive adjacency matrix includes: Two sets of trainable node embedding matrices are introduced, and the original correlation matrix is generated by bilinear pooling and applying the ReLU activation function. For each target node, select the set of strong connections from the row vectors of its corresponding original association matrix, and select the set of weak connections from the row vectors of the strong connections. The weights in the set of strong connections are normalized to obtain positive weights; The weights in the weak connection set are reverse-emphasized and then normalized to obtain negative weights. The positive and negative weights are combined to form a signed sparse adaptive adjacency matrix.
8. The method for predicting core sea surface variables based on wavelet-enhanced graph neural networks according to claim 7, characterized in that, Multi-order diffusion aggregation of encoder spatiotemporal features is performed based on a signed sparse adaptive adjacency matrix, including: Based on the signed sparse adaptive adjacency matrix, a diffusion representation from order 0 to a preset order is constructed; The diffusion representations of each order are concatenated along the feature dimension; The concatenated features are mapped back to the original feature dimensions through a linear layer, and residual connections are made with the spatiotemporal features of the encoder in the input symbolic adaptive spatial graph convolution module to output the final prediction result.
9. A sea surface core variable prediction system based on wavelet-enhanced graph neural network, characterized in that, The sea surface core variable prediction method based on wavelet-enhanced graph neural network as described in any one of claims 1-8 includes a data acquisition module, a variable-level multi-scale wavelet gating fusion module, a KAN-LSTM encoder module, and a symbol-adaptive spatial graph convolution module. The data acquisition module is used to acquire multivariate graph sequence data of the target sea surface; The variable-level multi-scale wavelet gating fusion module is used to perform multi-level wavelet decomposition and reconstruction on the time series of each variable, and adaptively fuses the decomposition coefficients of different scales through learnable gating parameters to output enhanced multi-scale time series features. The KAN-LSTM encoder module is used to recursively update the enhanced multi-scale temporal features by gating the fusion of regular convolution and KAN convolution branches, and output the encoder spatiotemporal features. The symbolic adaptive spatial graph convolution module generates a signed sparse adaptive adjacency matrix based on trainable node embeddings, performs multi-level diffusion aggregation on the spatiotemporal features of the encoder, and outputs the prediction results of the core variables of the target sea surface.