Method and system for predicting sea surface temperature based on coupling of multi-scale two-dimensional wavelet and physical information

Abstract

This application relates to the field of marine prediction technology and discloses a sea surface temperature prediction method and system that couples multi-scale two-dimensional wavelets and physical information. The method includes the following steps: S1, cross-scale spatiotemporal modeling; S2, physically supervised low-frequency prediction; S3, high-frequency information-guided anomaly structure reconstruction; and S4, dynamic fusion. This invention adopts a multi-scale strategy, using wavelet decomposition to decompose features into multiple frequency components and introducing physical information into the wavelet framework. While separating and reconstructing each frequency component, it improves the physical consistency of low-frequency prediction by using constraints such as the heat budget equation, thereby enhancing the predictive ability of the model.

Description

Technical Field

[0001] This application belongs to the field of marine prediction technology, and relates to the prediction of sea surface temperature, particularly to a sea surface temperature prediction method and system that couples multi-scale two-dimensional wavelets and physical information. Background Technology

[0002] Sea surface temperature (SST) changes are highly nonlinear and nonstationary, and their prediction is crucial for understanding ocean processes, improving the accuracy of climate models, and providing early warnings of marine disasters. Traditional methods typically rely on Fourier transform to perform frequency analysis on SST data to extract its periodic characteristics. However, Fourier transform is based on the assumption of global signal stationarity. Therefore, when faced with real nonstationary SST changes, especially those with abrupt changes, drifts, or local anomalies, it often fails to capture their key local spatiotemporal dynamics, leading to decreased prediction accuracy.

[0003] Wavelet transform is widely used in time-series modeling tasks due to its ability to perform local time-frequency analysis. However, it still relies on predefined fixed filters and lacks the ability to adaptively learn from data. When faced with complex and variable sea surface temperature variations with significant scale differences, this limitation makes wavelet methods significantly inadequate in modeling local changes or extreme events.

[0004] Compared with other spatiotemporal fields, the sea surface temperature field has stronger physical interpretability, that is, the changing trend of the sea surface temperature field can be described by the heat budget equation. However, many small-scale changes in ocean processes are smaller than the spatial resolution of the data and cannot be modeled. Physical constraints cannot accurately describe the changing patterns of the ocean surface.

[0005] Furthermore, sea surface temperature fields exhibit multi-scale variations: low-frequency components reflect large-scale seasonal thermodynamic and dynamic processes, while high-frequency components represent rapid changes such as weather disturbances. Therefore, traditional methods struggle to simultaneously model processes at different scales, limiting their ability to characterize complex ocean mechanisms. This method introduces a physical information-driven approach into a multi-scale framework. It can separate and reconstruct each frequency component while using constraints such as heat budget equations to improve the physical consistency of low-frequency predictions, thereby enhancing the model's predictive power. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a multi-scale, two-dimensional wavelet-physical information coupling method and system for sea surface temperature (SST) prediction, solving the technical problem of "difficulty in simultaneously addressing large-scale physical consistency constraints and small-scale anomaly characterization" in existing SST prediction methods. Unlike technical solutions that only use fixed wavelet bases or empirical wavelets for multi-scale decomposition, this invention constructs learnable one-dimensional wavelet filters in both the longitude and latitude directions, and generates two-dimensional wavelet analysis convolution kernels and corresponding inverse wavelet reconstruction convolution kernels through outer product. This allows the multi-scale decomposition and reconstruction processes to be jointly optimized end-to-end in conjunction with the prediction task, thereby improving the adaptive characterization capability for non-stationary, directional, and regionally differentiated SST variations. Unlike technical solutions that apply unified physical consistency constraints as a physical information loss term to the overall prediction process, this invention does not merely impose physical constraints on the prediction results through a loss function at the network output. Instead, it embeds the heat budget equation into the solution process of low-frequency components, calculates the spatial derivative using an automatic differential framework, and performs numerical integration using time difference to directly generate large-scale sea surface temperature stationarity features under physical information constraints. These features then guide the reconstruction of high-frequency anomaly components, allowing physical information to be injected into the deep learning process as intermediate features, rather than being used for posterior correction only as error penalties. Unlike technical solutions that directly apply unified physical consistency constraints to the overall prediction process, this invention only introduces the heat budget equation into the low-frequency components for numerical solution, obtaining stationarity features characterizing large-scale thermodynamic and dynamic processes. High-frequency components are extracted and reconstructed separately as small-scale anomaly processes. This ensures that physical constraints primarily apply to the low-frequency components that can be stably described by physical mechanisms, avoiding overly strong unified physical assumptions about high-frequency non-stationary disturbances. Furthermore, this invention uses inverse wavelet reconstruction to form multi-scale spatiotemporal integrated features from the low-frequency physical stationarity features and high-frequency anomaly features, and further uses a hierarchical gating mechanism to dynamically fuse them, thereby achieving a synergistic improvement in low-frequency physical consistency and high-frequency anomaly detail characterization, and improving the accuracy, stability and interpretability of sea surface temperature prediction.

[0007] To address the aforementioned technical problems, this invention provides a sea surface temperature prediction method that couples multi-scale two-dimensional wavelets and physical information, comprising the following steps: S1. Cross-scale spatiotemporal modeling: Multi-scale feature decomposition is performed on the input sea surface temperature sequence to extract multi-scale sea surface temperature change features with different physical driving mechanisms. ; S2, Low-frequency prediction under physical supervision: Based on the principle of two-dimensional wavelet transform, learnable one-dimensional low-frequency wavelet filters are constructed in the longitude and latitude directions respectively. A learnable two-dimensional low-frequency wavelet decomposition convolution kernel is then generated through outer product operations. This kernel is used to extract low-frequency components of multi-scale sea surface temperature variation characteristics, obtaining a low-frequency sea surface temperature signal reflecting large-scale, slowly varying thermodynamic and dynamic processes. The low-frequency signal of sea surface temperature As input variables to the heat budget equation, the spatial derivative is calculated using an automatic differential framework, and the temporal derivative is calculated using a forward difference method. Numerical integration is then used to obtain the large-scale sea surface temperature stability characteristics under physical information constraints. ; The heat budget equation applies only to the low-frequency components and not directly to the high-frequency anomaly components. The large-scale sea surface temperature stability characteristics... Not only as a result of physical supervision, but also as a guiding information input for the reconstruction process of abnormal structure reconstruction guided by high-frequency information in step S3, it is used to realize the collaborative fusion of physical information and data information after frequency decoupling; S3. High-frequency information-guided abnormal structure reconstruction: The multi-scale sea surface temperature variation characteristics are subjected to multi-branch high-frequency wavelet decomposition to extract small-scale anomaly information, and the extracted small-scale anomaly information is combined with the large-scale sea surface temperature stability characteristics obtained in step S2. Reconstruction and fusion are performed to generate multi-scale spatiotemporal integrated features. ; S4, Dynamic Fusion: Multi-scale spatiotemporal integrated features of S3 reconstruction Dynamic fusion is performed by constructing multiple gating mechanisms, calculating the fusion weights between each feature, and using element-wise multiplication to dynamically weight and fuse each feature to generate the prediction result G.

[0008] Furthermore, in step S1, the cross-scale modeling generates multi-scale sea surface temperature change features by alternating feature extraction and downsampling operations on the original sea surface temperature sequence X. The feature extraction process includes four steps: normalization, convolution, channel attention, residual connection, and convolution. Downsampling is achieved using stride convolution, thereby obtaining large-scale and small-scale feature maps corresponding to different spatial resolutions, which serve as multi-scale features of sea surface temperature changes. Multiscale sea surface temperature variation characteristics Including large-scale sea surface temperature variation characteristics Small-scale sea surface temperature variation characteristics Among them, the large-scale sea surface temperature change characteristics correspond to the change trend dominated by large-scale thermodynamic and dynamic processes, while the small-scale sea surface temperature change characteristics are change processes dominated by short-term, small-scale, complex non-stationary disturbance processes that cannot be described by traditional physical constraints.

[0009] Furthermore, in step S3, based on the principle of two-dimensional wavelet transform, learnable one-dimensional high-frequency wavelet filters are constructed in the longitude and latitude directions respectively. These one-dimensional high-frequency wavelet filters are then combined through outer product operations to obtain three learnable high-frequency wavelet decomposition convolution kernels, including: a vertical high-frequency filter. Horizontal high-frequency filter and diagonal high frequency filter The final high-frequency filter is obtained by aggregating all the filters. Using high-frequency filters Multiscale sea surface temperature variation features extracted from S1 Perform wavelet decomposition separately to extract vertical high-frequency information. Horizontal high-frequency information and diagonal high-frequency information directional high-frequency decoupling characteristics were obtained. It contains three components, represented as: ; Where i represents the scale, i = 0 or 1. Represents a vertical high-frequency filter The vertical high-frequency information of the filtered output. Represents a horizontal high-frequency filter The high-frequency information of the filtered output, Represents a diagonal high-frequency filter The filtered output is high-frequency information in the diagonal direction, and [;] represents the splicing of multiple components.

[0010] Furthermore, the directional high-frequency decoupling feature Large-scale sea surface temperature stability characteristics under the constraints of the physical information extracted in step S2 By combining these features, multi-frequency decoupling characteristics can be obtained. , is represented as: ; Where i represents the scale, i = 0 or 1, and concat represents the aggregation operation; The learnable two-dimensional low-frequency wavelet decomposition convolution kernel and three learnable two-dimensional high-frequency wavelet decomposition convolution kernels constitute a complete learnable wavelet convolution kernel. , construct a set with The corresponding complete learnable inverse wavelet convolution kernel Using a fully learnable inverse wavelet convolution kernel Multi-frequency decoupling features Inverse wavelet reconstruction is performed to fuse low-frequency and high-frequency information, as well as physical and data information, to obtain multi-scale spatiotemporal integrated features. The learnable inverse wavelet reconstruction convolution kernel and the learnable two-dimensional wavelet analysis convolution kernel are jointly trained to ensure the consistency of the frequency decomposition and reconstruction process, so that low-frequency physical features can be injected into the high-frequency anomaly modeling process in a reconstruction-guided manner. Then, a set of corresponding learnable inverse wavelet convolution kernels is used to decouple the directional high-frequency features. Large-scale sea surface temperature stability characteristics under the constraints of the three components and the physical information obtained from S2. Reconstruction is performed to obtain multi-scale spatiotemporal integrated features. .

[0011] Furthermore, in S4, the multi-scale spatiotemporal integrated features extracted in S3 are dynamically fused. A bottom-up approach is adopted, using upsampling and gating mechanisms to calculate the fusion weights between each layer, and element-wise multiplication is used to perform weighted fusion of the features from each layer. When i=1, the fusion features at this scale Equal to the spatiotemporal integrated characteristics at this scale The activation output is represented as: ; in, Represents the activation function; When i=0, the upsampling mechanism and the gating mechanism are fused together. and The fusion feature G at this scale is obtained and expressed as: ; in This outputs small-scale fusion features. For the local spatiotemporal integrated features at the current scale, For the weights of the gating network, This represents the offset of the gated network. [;] represents an upsampling operation, and [;] represents the concatenation of two features. This represents the activation function, and G is ultimately used as the model's output.

[0012] This invention also provides a sea surface temperature prediction system that couples multi-scale two-dimensional wavelet and physical information, the prediction system comprising: The cross-scale spatiotemporal modeling module is used to extract multi-scale ocean features: it performs multi-scale feature decomposition on the input sea surface temperature sequence to extract multi-scale sea surface temperature change features with different physical driving mechanisms. The low-frequency prediction module of physical supervision is used to predict the low-frequency component of sea surface temperature: the multi-scale sea surface temperature change characteristics are subjected to low-frequency filtering, and the filtered low-frequency signal of sea surface temperature is used as the parameter input of the heat budget equation. The large-scale sea surface temperature stability characteristics under physical information constraints are obtained by solving the equation. The high-frequency information-guided anomaly structure reconstruction module is used to extract multi-scale spatiotemporal integrated features: multi-branch high-frequency wavelet decomposition is performed on the multi-scale sea surface temperature change features to extract small-scale anomaly information. This extracted small-scale anomaly information is then reconstructed and fused with the large-scale sea surface temperature stability features obtained in step S2 to generate multi-scale spatiotemporal integrated features. ; The dynamic fusion module is used for dynamic fusion: it dynamically fuses the extracted multi-scale spatiotemporal comprehensive features, constructs multiple gating mechanisms, calculates the fusion weights between each feature, and uses element-wise multiplication to dynamically weight and fuse each feature to generate prediction results.

[0013] The present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, is used to implement the method described above.

[0014] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) This invention achieves a deep integration of "multi-scale decomposition" and "physical driving mechanism", significantly improving the physical consistency and accuracy of the prediction. By using the cross-scale spatiotemporal modeling module, the original complex sea surface temperature field is separated into components of different scales in the time domain. This invention constructs a physical information-guided collaborative prediction mechanism: low-frequency component physical prediction. The extracted low-frequency components are explicitly input into the heat budget equation of the mixing layer, and physical calculations are performed through an automatic differential framework, forcing the core prediction module of the model to comply with basic physical laws such as energy conservation.

[0015] (2) The present invention adopts a learnable two-dimensional wavelet decomposition convolution kernel and a corresponding inverse wavelet reconstruction convolution kernel to jointly construct a multi-scale decomposition-reconstruction framework. Unlike the static decomposition method based on fixed wavelet basis or empirical wavelet, it can combine sea surface temperature prediction target to jointly optimize the frequency decomposition boundary and reconstruction process, thereby improving the adaptive characterization ability of complex non-stationary ocean processes, regional differences and directional anomalies.

[0016] (3) This invention selectively applies the heat budget equation to the low-frequency components, performing physical solutions only on low-frequency information reflecting large-scale, slowly varying thermodynamic and dynamic processes. This yields large-scale sea surface temperature stability characteristics under physical constraints, and these characteristics are used as guiding information for subsequent high-frequency anomaly structure reconstruction. Compared to schemes that directly apply unified physical consistency constraints to the overall prediction network, this invention can ensure large-scale physical consistency while avoiding excessive unified physical assumptions on high-frequency anomaly disturbances.

[0017] (4) This invention significantly improves the effectiveness of multi-scale spatiotemporal integrated feature fusion through a dynamic fusion strategy based on a gating mechanism. By utilizing bottom-up upsampling and gating networks to calculate the fusion weights between features at each layer, dynamic weighted fusion of multi-scale spatiotemporal integrated features is achieved. This method can dynamically and adaptively adjust the contribution of information at different scales according to real-time sea surface temperature changes, effectively solving the problem of information mutual exclusion or loss. Attached Figure Description

[0018] The accompanying drawings, which form part of this application, are used to provide a further understanding of the application. The illustrative embodiments and descriptions of the application are used to explain the application, but do not constitute an undue limitation of the application. Obviously, the drawings described below are merely some embodiments, and those skilled in the art can obtain other drawings based on these drawings without creative effort.

[0019] Figure 1 This is a flowchart illustrating the sea surface temperature prediction method in this specific embodiment; Figure 2 This is a schematic diagram of the cross-scale spatiotemporal modeling module of the sea surface temperature prediction method in this specific embodiment; Figure 3 This is a schematic diagram of the low-frequency prediction module for physical supervision of the sea surface temperature prediction method in this specific embodiment. Figure 4 This is a schematic diagram of the high-frequency information-guided anomaly structure reconstruction module of the sea surface temperature prediction method in this specific embodiment. Figure 5 This is a schematic diagram of the dynamic fusion module of the sea surface temperature prediction method in this specific embodiment. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions in the embodiments will be clearly and completely described below with reference to the accompanying drawings. The following embodiments are used to illustrate this application, but are not intended to limit the scope of this application.

[0021] It should be noted that the execution entity of the prediction method in this embodiment is a sea surface temperature prediction device, which can be an electronic device, a component of an electronic device, an integrated circuit, or a chip. The electronic device can be a mobile electronic device or a non-mobile electronic device. For example, mobile electronic devices can be mobile phones, tablets, laptops, PDAs, in-vehicle electronic devices, wearable devices, etc., while non-mobile electronic devices can be servers and personal computers, etc., and this application does not impose specific limitations. The following description uses a server as the execution entity to illustrate the sea surface temperature prediction method in this embodiment.

[0022] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of the embodiments of this application, "multiple" means two or more, unless otherwise explicitly specified.

[0023] like Figure 1 As shown, the sea surface temperature prediction method coupling multi-scale two-dimensional wavelet and physical information includes the following steps: S1. Cross-scale spatiotemporal modeling: Multi-scale feature decomposition is performed on the input sea surface temperature sequence to extract multi-scale sea surface temperature change features with different physical driving mechanisms. .

[0024] S2, Low-frequency prediction under physical supervision: The multi-scale sea surface temperature variation characteristics Low-frequency filtering is performed, and the resulting low-frequency sea surface temperature signal is used as a parameter input to the heat budget equation. By solving the equation, the large-scale sea surface temperature stability characteristics under physical information constraints are obtained. .

[0025] S3. High-frequency information-guided abnormal structure reconstruction: The multi-scale sea surface temperature variation characteristics are subjected to multi-branch high-frequency wavelet decomposition to extract small-scale anomaly information, and the extracted small-scale anomaly information is combined with the large-scale sea surface temperature stability characteristics obtained in step S2. Reconstruction and fusion are performed to generate multi-scale spatiotemporal integrated features. .

[0026] S4, Dynamic Fusion: Multi-scale spatiotemporal integrated features of S3 reconstruction (i=0 or 1) Dynamic fusion is performed by constructing multiple gating mechanisms, calculating the fusion weights between each feature respectively, and using element-wise multiplication to dynamically weight and fuse each feature to generate the prediction result G.

[0027] As a specific implementation method, cross-scale spatiotemporal modeling involves using alternating feature extraction and downsampling operations on the original sea surface temperature sequence X to generate multi-scale sea surface temperature variation features. (i=0 or 1), where feature extraction includes steps such as normalization, convolution, channel attention, residual connection, and convolution. Downsampling is achieved using stride convolution, thereby obtaining large-scale and small-scale feature maps corresponding to different spatial resolutions, which serve as multi-scale sea surface temperature change features. Multiscale characteristics of sea surface temperature variation Including large-scale sea surface temperature variation characteristics Small-scale sea surface temperature variation characteristics Among them, the large-scale sea surface temperature change characteristics correspond to the change trend dominated by large-scale thermodynamic and dynamic processes, while the small-scale sea surface temperature change characteristics are change processes dominated by short-term, small-scale, and complex non-stationary disturbance processes that cannot be described by traditional physical constraints. The small-scale sea surface temperature change characteristic components mostly show change trends dominated by non-stationary disturbances.

[0028] Specifically, the dimension of the n time points is... The sea surface temperature data is named As input to the model, sea surface temperature information within the region is extracted, then downsampled and extracted again, repeated three times to obtain multi-scale sea surface temperature variation characteristics. The specific calculation process is as follows: ;

[0029] Where i represents the scale, i = 0 or 1, and FE represents the feature embedding operation. This represents the sea surface temperature variation characteristics at the i-th scale. This represents a downsampling operation; specifically, the downsampling operation uses a size of... A convolutional layer with a stride of 2 reduces the length and width of the feature map to half. The specific process of feature embedding includes four steps: layer normalization, convolution, channel attention, residual connection, and convolution. The specific steps are as follows: ; Where LN represents layer normalization, Conv represents convolution, and GAP represents global average pooling. W represents the activation function, and W represents the learnable weight matrix. Represents matrix multiplication. Represents the Hadamah altar; As a specific implementation method, S2, physically supervised low-frequency prediction: Based on the principle of two-dimensional wavelet transform, learnable one-dimensional low-frequency wavelet filters are constructed in the longitude and latitude directions respectively, and learnable two-dimensional low-frequency wavelet decomposition convolution kernels are generated through outer product operation. The learnable two-dimensional low-frequency wavelet decomposition convolution kernel is used to extract low-frequency components of multi-scale sea surface temperature variation features, thereby obtaining low-frequency sea surface temperature signals that mainly reflect large-scale, slowly varying thermal and dynamic processes. The low-frequency signal As input variables to the heat budget equation, the spatial derivative is calculated using an automatic differential framework, and the temporal derivative is calculated using a forward difference method. Numerical integration is then used to obtain the large-scale sea surface temperature stability characteristics under physical information constraints. The heat budget equation applies only to the low-frequency components, not directly to the high-frequency anomaly components, so that physical constraints can prioritize characterizing large-scale change trends with clear physical significance, while retaining the flexible characterization capability of high-frequency anomaly processes. The large-scale sea surface temperature stability characteristics not only serve as physical monitoring results, but also as guiding information input for subsequent high-frequency anomaly structure reconstruction, enabling the synergistic fusion of physical and data information after frequency decoupling.

[0030] In practical applications, a one-dimensional learnable low-frequency wavelet filter is constructed in S2 to extract the low-frequency components of the signal, thereby capturing the periodic large-scale stationary features in the sea surface temperature signal and reflecting the macroscopic trend dominated by large-scale, long-term thermodynamic and dynamic processes. The one-dimensional learnable low-frequency wavelet filter can be represented as: ; in, This represents a one-dimensional learnable low-frequency wavelet filter. Indicates time, This represents the translation parameter of the wavelet transform. and These represent the scaling function and the wavelet function, respectively. The initial value is selected using the low-frequency filtering of the traditional Haar wavelet, which can be gradually optimized by learning.

[0031] In practical applications, to obtain a two-dimensional filtering effect, the above-mentioned one-dimensional low-frequency wavelet filters are combined by outer product to obtain a learnable two-dimensional low-frequency wavelet decomposition convolution kernel, including a two-dimensional low-frequency filter. This method extracts components from ocean signals that exhibit low-frequency characteristics in both the horizontal and vertical directions, essentially approximating the image portion obtained after applying low-pass filtering in both directions. This component represents smooth regions and global trends in sea surface temperature variations, often corresponding to large-scale, slowly varying thermodynamic processes. These low-frequency processes are typically driven by large-scale energy transfer, propagating slowly but with far-reaching impacts; therefore, low-frequency filters are crucial. This helps to better understand the overall evolution trend of sea surface temperature, and is represented as: ; use Characteristics of multi-scale sea surface temperature variation Filtering was performed to obtain the low-frequency signal of sea surface temperature. , is represented as: ; Where i represents the scale, i = 0 or 1. This represents the low-frequency signal of sea surface temperature at the i-th scale.

[0032] Then, the low-frequency signal of sea surface temperature As a physical characteristic, let This is used to substitute into the heat budget equation of the ocean mixing layer to achieve a combination of physical laws and data; an automatic differentiation framework (PyTorch is selected in this embodiment) is used to... Calculate the partial derivatives in the x and y directions. and To fit and Thus using and Fitting and , among which Indicates ocean surface temperature, , express Latitude and longitude information and Represents momentum flux Components and Quantity; Will and replace and Substituting into the heat budget equation for the mixed layer, it can be expressed as: ; in , This represents the average zonal and meridional current velocities at the depth of the mixed layer. This represents the average ocean temperature of the mixed layer. Indicates the depth of the mixing layer. and These represent the specific heat capacity and density of seawater, respectively. and The vertical current velocity and seawater temperature below the mixed layer. Represent the algebraic expression formed by the other variables in the equation; Finally, Discretization is performed using the forward integration method to obtain the desired prediction field. , is represented as: ; in, The predicted field can be obtained by integrating the time steps. ; make The large-scale sea surface temperature stability characteristics under physical information constraints were obtained. .

[0033] As a specific implementation method, S3, high-frequency information-guided anomaly structure reconstruction: Based on the principle of two-dimensional wavelet transform, learnable one-dimensional high-frequency wavelet filters are constructed in the longitude and latitude directions respectively. These one-dimensional high-frequency wavelet filters are then combined through outer product operations to obtain three learnable high-frequency wavelet decomposition convolution kernels, including: a vertical high-frequency filter. Horizontal high-frequency filter and diagonal high frequency filter The final high-frequency filter is obtained by aggregating all the filters. Using high-frequency filters Multiscale sea surface temperature variation features extracted from S1 Perform wavelet decomposition separately to extract vertical high-frequency information. Horizontal high-frequency information and diagonal high-frequency information directional high-frequency decoupling characteristics were obtained. It contains three components, represented as: ; Where i represents the scale, i = 0 or 1. Represents a vertical high-frequency filter The vertical high-frequency information of the filtered output. Represents a horizontal high-frequency filter The high-frequency information of the filtered output, Represents a diagonal high-frequency filter The filtered output is high-frequency information in the diagonal direction, and [;] represents the splicing of multiple components.

[0034] In practical applications, S3 constructs a one-dimensional learnable high-frequency wavelet filter to extract the high-frequency features of the signal, thereby capturing short-term and temporary anomalous features in the sea surface temperature signal and reflecting the anomalous features dominated by non-stationary disturbances. The designed one-dimensional learnable high-frequency wavelet filter can be expressed as: ; in, This represents a one-dimensional learnable high-frequency filter. Indicates time, This represents the translation parameter of the wavelet transform. and These represent the scaling function and the wavelet function, respectively. The initial value is selected using the high-frequency filtering of the traditional Haar wavelet, which can be gradually optimized by learning.

[0035] Specifically, to achieve a two-dimensional filtering effect, the constructed one-dimensional filters are combined to obtain three learnable high-frequency wavelet decomposition convolution kernels, including: a vertical high-frequency filter. Horizontal high-frequency filter and diagonal high frequency filter Vertical high-frequency information, horizontal high-frequency information, and high-frequency-to-high-frequency information are extracted respectively and represented as follows: ; ; ; in This indicates that high-frequency filtering is performed in the horizontal direction. This indicates that high-frequency filtering is performed in the vertical direction. This indicates that low-frequency filtering is performed in the horizontal direction. This indicates that low-frequency filtering is performed in the vertical direction.

[0036] By aggregating all the filters, a final learnable two-dimensional high-frequency filter is obtained. , is represented as: ; Here, concat represents the aggregation operation.

[0037] Using a learnable two-dimensional high-frequency filter Characteristics of multi-scale sea surface temperature variations Filtering is performed to obtain high-frequency characteristics. , is represented as: ; Where i represents the scale, i = 0 or 1. The high-frequency decoupling characteristics obtained after filtering consist of three components, as shown below: ; Where i represents the scale, i = 0 or 1. Represents a vertical high-frequency filter The vertical high-frequency information of the filtered output. Represents a horizontal high-frequency filter The high-frequency information of the filtered output, Represents a diagonal high-frequency filter The high-frequency information of the filtered output, [;] indicates the splicing of multiple components.

[0038] Then, the directional high-frequency decoupling feature is... Large-scale sea surface temperature stability characteristics under the constraints of the physical information extracted in step S2 By combining these features, multi-frequency decoupling characteristics can be obtained. , is represented as: ; Where i represents the scale, i = 0 or 1, and concat represents the aggregation operation.

[0039] The learnable two-dimensional low-frequency wavelet decomposition convolution kernel and three learnable two-dimensional high-frequency wavelet decomposition convolution kernels constitute a complete learnable wavelet convolution kernel. , construct a set with The corresponding complete learnable inverse wavelet convolution kernel Using a fully learnable inverse wavelet convolution kernel Multi-frequency decoupling features Inverse wavelet reconstruction is performed to fuse low-frequency and high-frequency information, as well as physical and data information, to obtain multi-scale spatiotemporal integrated features. (i=0 or 1); wherein, the learnable inverse wavelet reconstruction convolution kernel and the learnable two-dimensional wavelet analysis convolution kernel are jointly trained to ensure the consistency of the frequency decomposition and reconstruction process, so that low-frequency physical features can be injected into the high-frequency anomaly modeling process in a reconstruction-guided manner, thereby improving the accuracy and stability of anomaly structure recovery in complex non-stationary sea surface temperature fields.

[0040] Then, a set of corresponding learnable inverse wavelet convolution kernels is used to decouple the directional high-frequency features. Large-scale sea surface temperature stability characteristics under the constraints of the three components and the physical information obtained from S2. Reconstruction is performed to obtain multi-scale spatiotemporal integrated features. .

[0041] In S4, the multi-scale spatiotemporal integrated features extracted in S3 are dynamically fused. A bottom-up approach is adopted, and the fusion weights between each layer are calculated through upsampling and gating mechanisms. The features of each layer are weighted and fused using element-wise multiplication.

[0042] As a specific implementation method, the final step involves integrating multi-scale spatiotemporal comprehensive features. Obtain the fusion feature G, where the fusion feature at this scale is when i=1. Equal to the spatiotemporal integrated characteristics at this scale The activation output is represented as: ; in, This represents the activation function.

[0043] When i=0, the upsampling mechanism and the gating mechanism are fused together. and The fusion feature G at this scale is obtained and expressed as: ; in This outputs small-scale fusion features. For the local spatiotemporal integrated features at the current scale, For the weights of the gating network, This represents the offset of the gated network. [;] represents an upsampling operation, and [;] represents the concatenation of two features. G represents the activation function, and G is ultimately used as the output of the model, i.e., the sea surface temperature prediction result.

[0044] In practical applications, the mean squared error (MSE) is used to measure the error between the sea surface temperature prediction results output by the model and the actual observed values. It is expressed as: ; Where m represents the batch size and l represents the number of scales. This represents the true sea surface temperature at the next time step on the j-th scale in the i-th sample. This represents the predicted sea surface temperature at the next time step at the j-th scale in the i-th sample; To verify the technical effectiveness of the proposed method in sea surface temperature prediction, historical sea surface temperature data from a certain sea area was selected as the input dataset. The training data spanned from January 1, 2009 to December 31, 2020; the validation data spanned from January 1, 2021 to December 31, 2021; and the test data spanned from January 1, 2022 to December 31, 2022. The spatial resolution of all data was 0.25° × 0.25°. All data sources were officially released and included daily sea surface temperature data.

[0045] The input data includes sea surface temperature data for the past 10 days, and the model task is to predict sea surface temperature changes for the next day.

[0046] The model performance was evaluated using commonly used metrics in sea surface temperature prediction: Root Mean Squared Error (RMSE), Mean Squared Error (MSE), Mean Absolute Error (MAE), and Coefficient of Determination (R²). Specifically: RMSE measures the standard deviation between predicted and actual values; a smaller value indicates lower error. MSE measures the average squared error between predicted and actual values; a smaller value indicates lower error. MAE measures the average magnitude of the error between predicted and actual values. R² represents the model's ability to explain the variation in real data; a value closer to 1 indicates a better fit.

[0047] The formulas for calculating RMSE, MSE, MAE, and R² are as follows: ; ; ; ; in, Represents the total number of samples. Indicates the first Index of prediction points, This represents the true value of that point. Indicates the model's prediction; The experiments in this embodiment were conducted on a single NVIDIA RTX 4090 GPU, using the Adam optimizer to train the network for 300 epochs with a minimum batch size of 64. During training, the learning rate was adjusted to 1e-3.

[0048] To demonstrate the effectiveness of the proposed solution, this embodiment selected LSTM, Conv-LSTM, Swin-Transformer, and U-Net for comparative experiments with the proposed method. All models were trained with the goal of inputting sea surface temperature data from the past 10 days and predicting sea surface temperature changes for the next day. Subsequently, they were tested using test data. Detailed information on the experimental results is shown in Table 1 below, which compares the predictions over a period of one day.

[0049] Table 1. Comparison of the proposed method with existing methods when the prediction duration is 1 day.

[0050] Among all evaluation metrics, the method proposed in this embodiment consistently demonstrates superior results. For instance, when predicting 1-day variations, the RMSE value of the method proposed in this embodiment is 0.156208, which is better than existing methods such as LSTM (0.27378), Conv-LSTM (0.158721), Swin-Transformer (0.162184), and U-Net (0.168988). This indicates that the method proposed in this embodiment has higher accuracy in sea surface temperature prediction compared to existing methods.

[0051] When predicting 1-day variations, the method proposed in this embodiment consistently exhibits the lowest MSE value (0.024401), which is superior to existing methods such as LSTM (0.074956), Conv-LSTM (0.025511), Swin-Transformer (0.026304), and U-Net (0.028558). This indicates that the method proposed in this embodiment has a smaller error in sea surface temperature prediction compared to existing methods.

[0052] When predicting 1-day variations, the method proposed in this embodiment also exhibits a low MAE value (0.10846), which is better than existing LSTM (0.209282), Conv-LSTM (0.110432), Swin-Transformer (0.112318) and U-Net (0.117799). This shows that the method proposed in this embodiment is more effective than existing methods in reducing the average prediction error in sea surface temperature prediction, and demonstrates stability and reliability at different time scales.

[0053] When predicting 1-day variations, the method proposed in this embodiment also exhibits the highest R² value (0.984547), which is better than existing LSTM (0.952531), Conv-LSTM (0.983844), Swin-Transformer (0.983342) and U-Net (0.981915). This indicates that the method proposed in this embodiment has a stronger interpretability for the variation of observed data.

[0054] To further verify the effectiveness and stability of the proposed method in continuous prediction scenarios, a recursive prediction approach was used. This involved predicting the result for one day in the future, then using the predicted result as part of the input sequence, replacing the earliest actual data in the input sequence to form a new input sequence, and then predicting again. This method achieves multi-step rolling prediction. Detailed experimental results are shown in Tables 2-5 below, which compare prediction durations of 2, 3, 4, and 5 days.

[0055] Table 2 compares the method proposed in this embodiment with existing methods when the prediction duration is 2 days.

[0056] Table 3. Comparison of the proposed method with existing methods when the prediction duration is 3 days.

[0057] Table 4. Comparison of the proposed method with existing methods when the prediction duration is 4 days.

[0058] Table 5. Comparison of the proposed method with existing methods when the prediction duration is 5 days.

[0059] In tests using recursive prediction, our model consistently outperformed existing representative methods across all prediction days in terms of RMSE, MSE, MAE, and R². This demonstrates that our method is superior to existing methods in capturing long-term dependencies and model stability, fully showcasing its potential and advantages in practical applications such as marine forecasting.

[0060] To further verify the necessity of the learnable two-dimensional wavelet decomposition and reconstruction in this invention, the following ablation comparison scheme was set up: fixed Haar wavelet kernel, fixed db4 wavelet kernel, empirical wavelet decomposition, and the learnable two-dimensional wavelet convolution kernel scheme of this invention. Tests were conducted using the same experimental conditions as the experiments described above. Detailed information on the experimental results is shown in Table 6 below, which compares prediction times over a period of one day.

[0061] RMSE MSE MAE <![CDATA[R 2 ]]> This invention 0.243847 0.059461 0.180682 0.962408 Fixed Haar wavelet kernel 0.266153 0.070837 0.191044 0.953024 Fixed db4 wavelet kernel 0.251041 0.065114 0.184233 0.951376 Empirical wavelet decomposition 0.249424 0.062212 0.182257 0.960411 In all evaluation metrics, the learnable two-dimensional wavelet convolution kernel of this invention consistently outperforms the fixed Haar wavelet kernel, the fixed db4 wavelet kernel, and empirical wavelet decomposition. This indicates that this invention is not a simple replacement of existing wavelet decomposition methods, but rather improves the characterization and recovery capabilities of multi-scale non-stationary features of sea surface temperature through the synergistic optimization of the learnable analysis kernel and the inverse reconstruction kernel.

[0062] Based on the same inventive concept, this application also provides a sea surface temperature prediction system that couples multi-scale two-dimensional wavelets and physical information.

[0063] As another embodiment of the present invention, a sea surface temperature prediction system coupled with multi-scale two-dimensional wavelet and physical information is designed to implement the sea surface temperature prediction method coupled with multi-scale two-dimensional wavelet and physical information as described above. Figure 1 As shown, it includes: The cross-scale spatiotemporal modeling module is used to extract multi-scale ocean features. It performs multi-scale feature decomposition on the input sea surface temperature (SST) sequence to extract multi-scale SST variation features with different physical driving mechanisms. Operations such as convolution and downsampling are used to decompose and extract multi-scale SST variation features from the input SST sequence. The large-scale SST variation feature components correspond to trends dominated by large-scale thermodynamic and dynamic processes, while the small-scale SST variation feature components are mostly changes that are difficult to describe using traditional physical constraints and are dominated by short-term, small-scale, and complex non-stationary perturbation processes.

[0064] The low-frequency prediction module under physical supervision constructs one-dimensional learnable low-frequency wavelet filters along both the longitude and latitude directions based on the principle of two-dimensional wavelet transform. These filters are then subjected to an outer product operation to obtain a convolution kernel for two-dimensional low-frequency signal decomposition. This convolution kernel is used to extract low-frequency components from multi-scale sea surface temperature data, yielding a low-frequency sea surface temperature signal reflecting large-scale, slowly varying thermal and dynamic processes. The extracted results are then incorporated into the heat budget equation for numerical calculation. The specific steps are as follows: the low-frequency signal of the sea surface temperature... As input variables to the heat budget equation, the spatial derivative is calculated using the PyTorch automatic differentiation framework, and the temporal derivative is calculated using the forward difference method. Numerical integration is then used to obtain the large-scale sea surface temperature stability characteristics under physical information constraints. .

[0065] The heat budget equation applies only to the low-frequency components and not directly to the high-frequency anomaly components. The large-scale sea surface temperature stability characteristics... It serves not only as a result of physical supervision, but also as a guiding information input for the reconstruction process of abnormal structures guided by high-frequency information in step S3, in order to achieve the collaborative fusion of physical information and data information after frequency decoupling.

[0066] The high-frequency information-guided anomaly structure reconstruction module is used to extract multi-scale spatiotemporal integrated features: the multi-branch high-frequency wavelet decomposition is performed on the multi-scale sea surface temperature change features to extract small-scale anomaly information, and the extracted small-scale anomaly information is reconstructed and fused with the large-scale sea surface temperature stability features obtained in step S2 to generate multi-scale spatiotemporal integrated features.

[0067] One-dimensional learnable high-frequency wavelet filters are constructed in the longitude and latitude directions respectively, and a set of learnable high-frequency wavelet decomposition convolution kernels are generated by performing outer product operations on them. These two-dimensional wavelet kernels are used to perform wavelet decomposition on the multi-scale sea surface temperature change features extracted by S1 to extract small-scale anomaly information. Then, the small-scale anomaly information and the large-scale sea surface temperature stability features under the constraints of physical information are reconstructed using a set of corresponding learnable inverse wavelet convolution kernels to obtain multi-scale spatiotemporal comprehensive features.

[0068] The dynamic fusion module is used for dynamic fusion: it dynamically fuses the extracted multi-scale spatiotemporal comprehensive features, constructs multiple gating mechanisms, calculates the fusion weights between each feature, and uses element-wise multiplication to dynamically weight and fuse each feature to generate prediction results.

[0069] Optimization module: Calculates the mean square error (MSE) between the multi-scale sea surface temperature prediction results output by the model and the corresponding actual observations, in order to optimize the overall prediction accuracy of the model.

[0070] The data processing procedures and loss calculations for each module can be found in the previous descriptions and will not be repeated here. It should be noted that the model mentioned in this invention refers to the multi-scale two-dimensional wavelet and physical information coupled sea surface temperature prediction system constructed in this invention, which is used for sea surface temperature prediction. It includes a cross-scale spatiotemporal modeling module, a multi-scale feature decoupling module, a physically guided structure reconstruction module, and a dynamic fusion module.

[0071] Based on the same inventive concept, this application also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the method as described above.

[0072] The program product of this application for implementing the above method may employ a portable compact disk read-only memory and include program code, and may run on a terminal device, such as a personal computer. However, the program product of this application is not limited thereto. In this application, the readable storage medium may be any tangible medium containing or storing a program that may be used by or in conjunction with an instruction execution system, apparatus, or device.

[0073] It should be noted that a computer-readable storage medium may include data signals propagated in baseband or as part of a carrier wave, carrying readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A readable storage medium may also be any readable medium other than a readable storage medium, capable of transmitting, propagating, or transmitting programs for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the readable storage medium may be transmitted using any suitable medium, including but not limited to wireless, wired, optical fiber, RF, etc., or any suitable combination thereof.

[0074] The above are merely preferred embodiments of this application and are not intended to limit this application in any way. Although this application has disclosed preferred embodiments as described above, it is not intended to limit this application. Any person skilled in the art can make some modifications or alterations to the above-mentioned technical content to create equivalent embodiments without departing from the scope of the technical solution of this application. The implementation schemes in the above embodiments can also be further combined or replaced. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of this application without departing from the content of the technical solution of this application shall still fall within the scope of this application.

Claims

1. A method for predicting sea surface temperature using multi-scale two-dimensional wavelet and physical information coupling, characterized by, Includes the following steps: S1. Cross-scale spatiotemporal modeling: Multi-scale feature decomposition is performed on the input sea surface temperature sequence to extract multi-scale sea surface temperature change features with different physical driving mechanisms. ; S2, Low-frequency prediction under physical supervision: Based on the principle of two-dimensional wavelet transform, learnable one-dimensional low-frequency wavelet filters are constructed in the longitude and latitude directions respectively. A learnable two-dimensional low-frequency wavelet decomposition convolution kernel is then generated through outer product operations. This kernel is used to extract low-frequency components of multi-scale sea surface temperature variation characteristics, obtaining a low-frequency sea surface temperature signal reflecting large-scale, slowly varying thermodynamic and dynamic processes. ; The low-frequency signal of sea surface temperature As input variables to the heat budget equation, the spatial derivative is calculated using an automatic differential framework, and the temporal derivative is calculated using a forward difference method. Numerical integration is then used to obtain the large-scale sea surface temperature stability characteristics under physical information constraints. ; The heat budget equation applies only to the low-frequency components and not directly to the high-frequency anomaly components. The large-scale sea surface temperature stability characteristics... Not only as a result of physical supervision, but also as a guide information input for the reconstruction process of abnormal structure reconstruction guided by high-frequency information in step S3, it is used to realize the collaborative fusion of physical information and data information after frequency decoupling; S3. High-frequency information-guided abnormal structure reconstruction: The multi-scale sea surface temperature variation characteristics are subjected to multi-branch high-frequency wavelet decomposition to extract small-scale anomaly information, and the extracted small-scale anomaly information is combined with the large-scale sea surface temperature stability characteristics obtained in step S2. Reconstruction and fusion are performed to generate multi-scale spatiotemporal integrated features. ; S4, Dynamic Fusion: Multi-scale spatiotemporal integrated features of S3 reconstruction Dynamic fusion is performed by constructing multiple gating mechanisms, calculating the fusion weights between each feature, and using element-wise multiplication to dynamically weight and fuse each feature to generate the prediction result G.

2. The method according to claim 1, characterized in that, In step S1, the cross-scale modeling generates multi-scale sea surface temperature change features by using alternating feature extraction and downsampling operations on the original sea surface temperature sequence X. The feature extraction process includes four steps: normalization, convolution, channel attention, residual connection, and convolution. Downsampling is achieved using stride convolution, thereby obtaining large-scale and small-scale feature maps corresponding to different spatial resolutions, which serve as multi-scale features of sea surface temperature changes. Multiscale sea surface temperature variation characteristics Including large-scale sea surface temperature variation characteristics Small-scale sea surface temperature variation characteristics Among them, the large-scale sea surface temperature change characteristics correspond to the change trend dominated by large-scale thermodynamic and dynamic processes, while the small-scale sea surface temperature change characteristics are change processes dominated by short-term, small-scale, complex non-stationary disturbance processes that cannot be described by traditional physical constraints.

3. The method according to claim 1, characterized in that, In step S3, based on the principle of two-dimensional wavelet transform, learnable one-dimensional high-frequency wavelet filters are constructed in the longitude and latitude directions respectively. These one-dimensional high-frequency wavelet filters are then combined through an outer product operation to obtain three learnable high-frequency wavelet decomposition convolution kernels, including: a vertical high-frequency filter. Horizontal high-frequency filter and diagonal high frequency filter The final high-frequency filter is obtained by aggregating all the filters. Using high-frequency filters Multiscale sea surface temperature variation features extracted from S1 Perform wavelet decomposition separately to extract vertical high-frequency information. Horizontal high-frequency information and diagonal high-frequency information directional high-frequency decoupling characteristics were obtained. It contains three components, represented as: ； Where i represents the scale, i = 0 or 1. Represents a vertical high-frequency filter The vertical high-frequency information of the filtered output. Represents a horizontal high-frequency filter The high-frequency information of the filtered output, Represents a diagonal high-frequency filter The filtered output is high-frequency information in the diagonal direction, and [;] represents the splicing of multiple components.

4. The method according to claim 3, characterized in that, The directional high-frequency decoupling feature Large-scale sea surface temperature stability characteristics under the constraints of the physical information extracted in step S2 By combining these features, multi-frequency decoupling characteristics can be obtained. , is represented as: ； Where i represents the scale, i = 0 or 1, and concat represents the aggregation operation; The learnable two-dimensional low-frequency wavelet decomposition convolution kernel and three learnable two-dimensional high-frequency wavelet decomposition convolution kernels constitute a complete learnable wavelet convolution kernel. , construct a set with The corresponding complete learnable inverse wavelet convolution kernel Using a fully learnable inverse wavelet convolution kernel Multi-frequency decoupling features Inverse wavelet reconstruction is performed to fuse low-frequency and high-frequency information, as well as physical and data information, to obtain multi-scale spatiotemporal integrated features. The learnable inverse wavelet reconstruction convolutional kernel and the learnable two-dimensional wavelet analysis convolutional kernel are jointly trained to ensure consistency between the frequency decomposition and reconstruction processes, enabling low-frequency physical features to be injected into the high-frequency anomaly modeling process in a reconstruction-guided manner. Subsequently, a set of corresponding learnable inverse wavelet convolutional kernels is used to decouple directional high-frequency features. Large-scale sea surface temperature stability characteristics under the constraints of the three components and the physical information obtained from S2. Reconstruction is performed to obtain multi-scale spatiotemporal integrated features. .

5. The method according to claim 1, characterized in that, In S4, the multi-scale spatiotemporal comprehensive features extracted in S3 are dynamically fused. A bottom-up approach is adopted, using upsampling and gating mechanisms to calculate the fusion weights between each layer, and element-wise multiplication is used to perform weighted fusion of the features from each layer. When i=1, the fusion features at this scale Equal to the spatiotemporal integrated characteristics at this scale The activation output is represented as: ； in, Represents the activation function; When i=0, the upsampling mechanism and the gating mechanism are fused together. and The fusion feature G at this scale is obtained and expressed as: ； in This outputs small-scale fusion features. For the local spatiotemporal integrated features at the current scale, For the weights of the gating network, This represents the offset of the gated network. [;] represents an upsampling operation, and [;] represents the concatenation of two features. This represents the activation function, and G is ultimately used as the model's output.

6. A sea surface temperature prediction system coupled with multi-scale two-dimensional wavelet and physical information, characterized in that, The prediction system includes: The cross-scale spatiotemporal modeling module is used to extract multi-scale ocean features: it performs multi-scale feature decomposition on the input sea surface temperature sequence to extract multi-scale sea surface temperature change features with different physical driving mechanisms. The low-frequency prediction module of physical supervision is used to predict the low-frequency component of sea surface temperature: the multi-scale sea surface temperature change characteristics are subjected to low-frequency filtering, and the filtered low-frequency signal of sea surface temperature is used as the parameter input of the heat budget equation. The large-scale sea surface temperature stability characteristics under physical information constraints are obtained by solving the equation. The high-frequency information-guided anomaly structure reconstruction module is used to extract multi-scale spatiotemporal integrated features: the multi-branch high-frequency wavelet decomposition is performed on the multi-scale sea surface temperature change features to extract small-scale anomaly information, and the extracted small-scale anomaly information is reconstructed and fused with the large-scale sea surface temperature stability features obtained in step S2 to generate multi-scale spatiotemporal integrated features. The dynamic fusion module is used for dynamic fusion: it dynamically fuses the extracted multi-scale spatiotemporal comprehensive features, constructs multiple gating mechanisms, calculates the fusion weights between each feature, and uses element-wise multiplication to dynamically weight and fuse each feature to generate prediction results.

7. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it is used to implement the method as described in any one of claims 1-5.

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