Inner solitary wave propagation velocity prediction method based on deep learning

Abstract

The invention relates to the technical field of marine environment monitoring and forecasting, and discloses an internal solitary wave propagation velocity prediction method based on deep learning, which comprises the following steps: acquiring multi-source satellite remote sensing image data, extracting a wave crest line of an internal solitary wave front guide wave, and calculating the propagation velocity of the wave crest line; constructing an inner solitary wave propagation velocity prediction data set; according to the method, a prediction model fusing a physical mechanism and deep learning is constructed, the model comprises an STL decomposition module, a TimesNet module, an iTransform module and a gating mechanism fusion module, an internal isolated fluctuation mechanics theory is fused into model training through a physical constraint loss function, and finally a prediction speed is output through the gating mechanism fusion module; and inputting the preprocessed image data of the target sea area into the trained model to realize the prediction of the propagation velocity of the internal solitary wave. According to the method, the prediction precision, stability and physical credibility are effectively improved, and the problems of insufficient generalization ability and poor physical interpretability of a pure data driven model are solved.

Description

Technical Field

[0001] This invention relates to the field of marine environmental monitoring and forecasting technology, and in particular to a method for predicting the propagation velocity of internal solitary waves based on deep learning. Background Technology

[0002] Internal solitary waves are large-amplitude waves occurring near density gradients within the ocean. Their amplitude can reach tens of meters, their propagation distance can reach hundreds of kilometers, and they carry enormous energy. Internal solitary waves have a significant impact on the safety of marine engineering structures, underwater vehicle operations, the marine ecological environment, and military underwater operations. Propagation speed, as one of the core dynamic parameters of internal solitary waves, directly determines their propagation path, energy dissipation, and the intensity and extent of their impact on the marine environment. Therefore, accurate and efficient prediction of the propagation speed of internal solitary waves is of great practical significance for ensuring the safety of marine engineering projects, optimizing marine resource development, supporting national defense and military activities, and deepening physical oceanography research.

[0003] Traditional methods for studying the propagation velocity of internal solitary waves primarily rely on field observations, theoretical analysis, and numerical simulations. Field observation methods (such as moored arrays and shipborne ADCPs) can acquire direct data, but they are costly and have limited spatiotemporal coverage, making them unsuitable for large-scale, continuous monitoring. Theoretical models (such as the KdV equation and eKdV equation) are based on idealized fluid assumptions, and in the complex and variable real ocean environment, they often suffer from significant prediction errors due to their inability to accurately characterize background flow fields, topographic effects, and nonlinear interactions. Numerical models (such as MITgcm and ROMS) can consider more environmental factors, but they consume enormous computational resources, making it difficult to achieve rapid, operational forecasts.

[0004] In recent years, with the rapid development of satellite remote sensing technology and the rise of artificial intelligence methods, the study of internal solitary waves has entered a new stage of data-driven and intelligent prediction. Researchers have begun to use multi-source satellite remote sensing imagery (such as SAR and optical imagery) to extract the spatial characteristics and motion information of internal solitary waves, and combine this with machine learning models (such as support vector machines, random forests, and neural networks) to establish a nonlinear mapping relationship between ocean environmental parameters (such as density profiles, water depth, and tidal currents) and the propagation speed of internal solitary waves. These methods, to a certain extent, complement traditional physical models and can utilize massive amounts of data to mine potential complex patterns.

[0005] However, existing AI-based methods for predicting internal solitary waves still have several limitations. First, most models are purely data-driven, and their performance is highly dependent on the quantity and quality of training data, resulting in insufficient generalization ability in data-scarce sea areas or extreme environmental conditions. Second, the "black box" nature of these models leads to a lack of physical interpretability in the prediction results, making it difficult to corroborate with known ocean dynamics laws and limiting their credibility in scientific research and practical applications. Third, the occurrence and propagation of internal solitary waves is a complex process containing information across multiple time scales (such as seasonal variations, tidal cycles, and short-term disturbances), and existing methods often fail to effectively decouple and utilize these different time-series characteristics, resulting in limited ability to capture long-term trends and periodic patterns. Finally, how to effectively integrate prior physical knowledge (such as governing equations and conservation laws) into data-driven models to constrain model output and improve its physical consistency and extrapolation ability remains a key technical challenge.

[0006] Therefore, there is an urgent need to develop a new prediction method that can fully exploit the temporal information and spatial characteristics in multi-source remote sensing data and effectively integrate the fundamental physical mechanisms of internal solitary waves, so as to overcome the shortcomings of existing technologies and achieve more accurate, reliable and physically credible prediction of the propagation speed of internal solitary waves. Summary of the Invention

[0007] To address the aforementioned technical problems, this invention provides a deep learning-based method for predicting the propagation velocity of internal solitary waves, thereby effectively improving the accuracy and stability of predictions for the propagation velocity of internal solitary waves in the ocean.

[0008] To achieve the above objectives, the technical solution of the present invention is as follows:

[0009] A deep learning-based method for predicting the propagation velocity of internal solitary waves includes the following steps: Step 1: Collect multi-source satellite remote sensing image data, extract the wave crest of the inner solitary wave after preprocessing the data, and calculate the propagation speed of the inner solitary wave; Step 2: Combine the propagation velocity of internal solitary waves with background hydrological parameters to construct a dataset for predicting the propagation velocity of internal solitary waves, and divide it into a training set and a test set; Step 3: Construct an internal solitary wave propagation velocity prediction model integrating physical mechanisms and deep learning. The model includes an STL decomposition module, a TimesNet module, an iTransformer module, and a gating mechanism fusion module. The STL decomposition module decomposes the internal solitary wave time series data into trend, seasonal, and residual terms through local weighted regression. The trend and seasonal terms output by the STL decomposition module are input into the TimesNet module, and the residual term is input into the iTransformer module for internal solitary wave propagation velocity prediction. The gating mechanism fusion module adaptively and dynamically fuses the propagation velocities predicted by the TimesNet and iTransformer modules using learnable gating weights, and outputs the final predicted propagation velocity. The model is trained using a training set and validated using a test set. Step 4: Acquire satellite remote sensing image data of the target sea area, preprocess it, and input it into the qualified model to predict the propagation speed of internal solitary waves.

[0010] In the above scheme, the decomposition formula of the STL decomposition module is as follows: ; ; ; in, This contains the original time series data of the solitary wave at time t; The trend component at time t; The seasonal component at time t; The residual component at time t; The degree of the polynomial used to represent the fitted trend; Indicates a time index; The low-pass smoothing window is at time t; This is a locally weighted regression.

[0011] In the above scheme, the STL decomposition module introduces a cross-scale attention mechanism, which weights the trend term, seasonal term, and residual term using the following formula: ; ; ; in, Represents the function for cross-scale attention mechanisms; It is a trend term extracted from the original time series data; It is a seasonal term extracted from the original time-series data; These are the residual terms extracted from the original time-series data; The trend term feature vector is weighted by a cross-scale attention mechanism. This is the seasonal feature vector after being weighted by a cross-scale attention mechanism. This is the feature vector of the residual term after being weighted by the cross-scale attention mechanism.

[0012] In the above scheme, the TimesNet module includes an embedding layer, a temporal folding module, a TimesBlock module, a spatiotemporal attention module, a temporal unfolding module, and a prediction layer; The embedding layer transforms the trend and seasonal terms of the internal solitary wave time series data from low-dimensional features to high-dimensional features through linear transformation; The time-series folding module extracts the significant periodicity of the internal solitary wave time series through fast Fourier transform and converts the one-dimensional sequence into a two-dimensional tensor to make the time series variation patterns within and between periods explicit. The TimesBlock module uses multi-scale convolution kernels to extract local multi-scale features of the internal solitary wave time series from the two-dimensional tensor, and achieves feature filtering and information retention through gating mechanism and residual connection. The spatiotemporal attention module captures the global correlation between different variables of the internal isolated wave trend term and the seasonal term through a self-attention mechanism, thereby enhancing the model’s attention to key physical driving factors. The temporal unrolling module restores the two-dimensional tensor that has undergone temporal folding and feature extraction into a one-dimensional sequence, thereby realizing the inverse mapping of the temporal features of internal solitary waves from image-like structures to time series. The prediction layer maps the time-expanded high-dimensional features into predicted values ​​of the propagation velocity of the internal solitary wave, completing the final output from the feature space to the target variable.

[0013] In a further technical solution, the spatiotemporal attention module generates a query, key, and value matrix, and calculates the attention weights between different variables of the internal solitary wave trend term and the seasonal term, using the following formula: ; in, The output represents spatiotemporal attention; To obtain attention weights through normalization; For query matrix; The key matrix; It is a value matrix; This is the scaling factor.

[0014] In the above scheme, the iTransformer module includes an embedding layer, a local physical attention module, a feedforward network, layer normalization, and a prediction layer. The embedding layer maps the low-dimensional temporal features of the internal solitary wave residual term to a high-dimensional space through a linear transformation, thereby enhancing the feature representation capability. The local physical attention module calculates physically weighted attention weights within a temporal / spatial local window to accurately capture feature associations related to the dynamics of internal isolated waves. The feedforward network performs nonlinear transformation and dimensionality reduction on the features output by the local physical attention module to achieve refined feature extraction and dimensionality adaptation. The layer normalization involves performing a residual connection between the local physical attention and the output of the feedforward network, and then stabilizing the training process through layer normalization. The prediction layer maps the processed high-dimensional features into predicted values ​​of the propagation velocity of the internal solitary wave, completing the final output of the module.

[0015] In a further technical solution, the local physical attention module is implemented using the following formula: ; in, This represents the output of the local physics attention module; To obtain attention weights through normalization; For query matrix; The key matrix; It is a value matrix; This is the scaling factor; This is the matrix transpose.

[0016] In a further technical solution, the feedforward network is implemented using the following formula: ; in, The input features are from the output of the local physics attention module. and The weights and biases are for the first-level linear transformation; and The weights and biases for the second-level linear transformation; For activation function, This is the output of the feedforward network.

[0017] In a further technical solution, both the TimesNet module and the iTransformer module introduce physical constraints on the loss function to ensure that the model output conforms to the dynamics of internal isolated waves; the physical constraints on the loss function are implemented through the following formula: ; ; ; in, For loss function, For data-driven loss, For physical constraint loss, , For hyperparameters; This is a predicted value for the propagation velocity of an internal solitary wave. The propagation velocity of the internal solitary wave is calculated using remote sensing. This represents the theoretical value of the propagation velocity of an internal solitary wave calculated under continuous density stratification conditions.

[0018] In the above scheme, the gating mechanism fusion module outputs the final propagation speed of the internal solitary wave using the following formula: ; in, This is the final predicted propagation speed; This is the propagation speed predicted by the TimesNet module; It is the propagation speed predicted by the iTransformer module; , and These are weights obtained through learning; It represents the residual.

[0019] Through the above technical solution, the deep learning-based method for predicting the propagation velocity of internal solitary waves provided by this invention has the following beneficial effects: 1. Improved Prediction Accuracy and Stability: By constructing a collaborative prediction model integrating physical mechanisms and deep learning, and utilizing high spatiotemporal resolution geostationary satellite remote sensing data, this method significantly improves the prediction accuracy of internal solitary wave propagation velocity. Comparative experiments show that its root mean square error (RMSE) and mean absolute error (MAE) are significantly better than traditional mainstream time series prediction models such as Transformer, TCN, and CNN-LSTM, demonstrating superior performance and stronger stability. 2. Enhancing the physical credibility and generalization ability of the model: The innovative approach introduces the theory of internal isolated wave dynamics into the model training process as a physical constraint loss function, forcing the model to learn data patterns that conform to physical laws. This effectively corrects the "spurious correlation" fitting problem that may exist in purely data-driven models. This mechanism not only improves the physical rationality of the prediction results but also enhances the model's generalization and inference capabilities in areas outside the data distribution or sparsely observed sea areas. 3. Effective decoupling and modeling of multi-scale time series features: The STL decomposition strategy is adopted to decouple the complex original time series data into trend, seasonal, and residual terms. Improved TimesNet and iTransformer modules are designed for specialized processing based on the characteristics of different components. This "decomposition-coordination" architecture effectively solves the modeling problem of multi-scale feature aliasing in internal solitary wave time series, and can capture long-term trends, periodic patterns, and random disturbances more precisely. 4. Enhanced Feature Interaction and Key Information Extraction: Cross-scale attention and local physical attention mechanisms were introduced into the model. The former promotes information interaction and modulation between temporal components at different scales; the latter weights attention based on physical relationships within a local window, precisely focusing on features strongly correlated with the dynamic process. These mechanisms collectively improve the model's efficiency in identifying and utilizing key driving factors. 5. Adaptive Fusion and Dynamic Weight Allocation: Through a gated fusion module, the model can adaptively and dynamically fuse the prediction results and residuals of the TimesNet and iTransformer sub-modules in a learnable manner. This mechanism can automatically adjust the contribution weights of each component according to different time points and environmental conditions, thereby achieving a more flexible and robust final prediction.

[0020] In summary, this invention not only achieves a deep integration of data-driven and physical mechanisms in terms of methodology, but also effectively improves the accuracy, robustness, and physical interpretability of predicting the propagation velocity of internal solitary waves in engineering applications, providing a more reliable technical tool for marine environmental monitoring, engineering safety assurance, and scientific research. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below.

[0022] Figure 1 This is a schematic diagram of a deep learning-based method for predicting the propagation velocity of an internal solitary wave, as disclosed in an embodiment of the present invention. Figure 2 This is a schematic diagram of the deep learning model structure for predicting the propagation velocity of internal solitary waves. Detailed Implementation

[0023] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0024] This invention provides a deep learning-based method for predicting the propagation velocity of internal solitary waves, such as... Figure 1 As shown, it includes the following steps:

[0025] Step 1: Collect multi-source satellite remote sensing image data and calculate the propagation speed of internal solitary waves; The collected multi-source satellite remote sensing image data is preprocessed with denoising, geometric correction, mosaicking and cropping; the wave crest of the inner solitary wave is extracted based on the preprocessed multi-source satellite remote sensing image data, and the propagation speed of the inner solitary wave is calculated based on this;

[0026] (1) Calculation of the propagation velocity of the internal solitary wave Based on preprocessed multi-source satellite remote sensing image data, pixel offset tracking technology was used to calculate the propagation velocity of internal solitary waves. Feature points in the image were located by normalizing the peak cross-correlation coefficient. Pixel displacement within The propagation velocity of internal solitary waves is calculated. The accuracy of internal solitary wave propagation velocity extraction is affected by the time interval, template window size, and window overlap, and needs to be dynamically adjusted in conjunction with image resolution and the brightness-dark spacing of internal solitary waves.

[0027] To ensure the reliability of the results, the original velocity field is filtered. First, low-reliability vectors with a normalized cross-correlation coefficient peak value < 0.3 are removed; then, Reciprocal filtering is applied (to remove...). outliers, For displacement vectors, (where σ is the neighborhood mean and σ is the neighborhood standard deviation) and direction consistency filtering (based on the normal direction of the inner solitary wave frontguide, eliminating...) outliers, Median_ is the projection of the velocity vector onto the normal direction. MAD_ is the median of the neighborhood. The data is further purified by using the median absolute deviation of the neighborhood. Finally, based on pixel offset, time interval, and image spatial resolution, the pixel displacement is converted into actual displacement components, and the propagation velocity of the internal solitary wave is calculated. The normalized cross-correlation coefficient is: ; ; Where ρ is the normalized cross-correlation coefficient. and These are the pixels in the i-th row and j-th column of the main image, the image template window, and the search window, respectively. , Here, M and N represent the average pixel value within the window, and M and N are the dimensions of the template window. and This is the pixel offset. Let V be the time interval, and V be the propagation speed of the internal solitary wave.

[0028] (2) Extraction of the propagation direction of the internal solitary wave

[0029] The propagation direction of the internal solitary wave is calculated based on morphological analysis. Using true north as the baseline (0°), the direction increases clockwise. The angle between the morphologically derived propagation direction and true north is the final propagation direction, ranging from 0° to 360°. The wave crests of the internal solitary wave leader are manually extracted from the preprocessed multi-source satellite remote sensing images. Several sampling points are selected along each wave crest, and the minimum bounding rectangle and convex hull direction of the crest curve between adjacent sampling points are calculated. The minimum bounding rectangle is the smallest rectangle that can completely enclose the crest curve, and the convex hull direction is the overall trend direction fitted along the convex direction of the crest curve.

[0030] Step 2: Combine the propagation velocity of internal solitary waves with background hydrological parameters to construct an internal solitary wave propagation velocity prediction dataset; divide the constructed internal solitary wave propagation velocity prediction dataset into a training set and a test set;

[0031] Based on the propagation velocity of internal solitary waves extracted from multi-source satellite remote sensing imagery (the propagation velocity includes both magnitude and direction), and matching the corresponding environmental parameters at different times, an internal solitary wave propagation velocity prediction dataset was constructed. Each sample in the dataset includes eight parameters: propagation velocity (v), propagation direction (d), time (t), longitude (lon), latitude (lat), water depth (depth), density (ρ), and tidal current (u), totaling 14,862 samples. To ensure model training stability and generalization ability, the following data partitioning strategy was adopted: 80% of the samples in the constructed internal solitary wave prediction dataset were divided into a training set and 20% into a test set. The resulting training set contains 11,889 data points, and the test set contains 2,973 data points. Simultaneously, it was strictly ensured that complete time-series data for the same internal solitary wave event belonged to only a single dataset. This setting effectively avoids overfitting problems caused by dataset homogenization, thereby improving the model's predictive ability for unknown internal solitary wave events.

[0032] Step 3: Construct an internal solitary wave propagation velocity prediction model that integrates physical mechanisms and deep learning;

[0033] The model decomposes the time-series data of internal solitary waves into trend, seasonal, and residual terms using an STL decomposition strategy. The trend term includes water depth, longitude, and latitude; the seasonal term includes propagation speed, density, tidal current, and time; and the residual term includes the differences in all the above input features (water depth, longitude, latitude, propagation speed, propagation direction, density, tidal current, and time). An improved collaborative architecture of TimesNet and iTransformer is employed. TimesNet excels at capturing structured, regular features to adapt to the changing patterns of the trend and seasonal terms, while iTransformer focuses on modeling nonlinear, dynamic features to match the random perturbation characteristics of the residual term. The two technologies have clear divisions of labor and are complementary, effectively improving the accurate adaptation of different scale components of internal solitary waves. Simultaneously, the model retains the core components of TimesNet and iTransformer and adds physical constraints to the loss function to enhance data-driven accuracy and improve the physical accuracy and rationality of the model.

[0034] Model structure as follows Figure 2 As shown, the constructed model includes an improved STL decomposition module, a TimesNet module, an iTransformer module, and a gating mechanism fusion module. A cross-scale attention mechanism is added to the STL decomposition module to enhance the correlation of temporal features of internal solitary waves; the core components of TimesNet are retained, and a spatiotemporal sequence attention mechanism and physical constraints on the loss function are added to enhance the model's attention to key physical driving factors; the core components of iTransformer are retained, and a local physical attention mechanism and physical constraints on the loss function are added to accurately capture physically relevant features.

[0035] I. STL Decomposition Module The STL decomposition module decomposes internal solitary wave time series data into trend, seasonal, and residual terms through local weighted regression, thereby decoupling the patterns of internal solitary wave time series data.

[0036] The STL decomposition module decomposes time-series data using the following formula: ; ; ; in, for Raw time series data of the solitary wave within a given time period; for Time-trend component; for Time and season components; for Time-dependent residual components; for Low-pass smoothing window at all times; The degree of the polynomial used to represent the fitted trend; This indicates a time index; LOESS represents locally weighted regression.

[0037] The STL decomposition module introduces a cross-scale attention mechanism to obtain weighted feature vectors through cross-branch attention. , , This allows the timing characteristics of internal solitary waves at different scales to interact with each other and extract relevant modulation information.

[0038] The cross-scale attention mechanism is implemented through the following formula: ; ; ; in, Represents the function for cross-scale attention mechanisms; It is a trend term extracted from the original time series data; It is a seasonal term extracted from the original time-series data; These are the residual terms extracted from the original time-series data; The trend term feature vector is weighted by a cross-scale attention mechanism. This is the seasonal feature vector after being weighted by a cross-scale attention mechanism. This is the feature vector of the residual term after being weighted by the cross-scale attention mechanism.

[0039] The trend and seasonal terms output by STL decomposition are input into the improved TimesNet module, and the residual terms are input into the improved iTransformer module to predict the propagation velocity of internal solitary waves.

[0040] II. TimesNet Module The TimesNet module includes an embedding layer, a temporal folding module, a TimesBlock module, a spatiotemporal attention module, a temporal unrolling module, and a prediction layer.

[0041] 1. Embedded layer By using linear transformation, the trend and seasonal terms of the internal solitary wave time series data are transformed from low-dimensional features to high-dimensional features, which improves the feature representation capability, uncovers the subtle features hidden in the original data, and provides more representative input for subsequent time series folding and feature extraction modules, avoiding the problem of insufficient low-dimensional feature representation.

[0042] The embedding layer achieves high-dimensional feature transformation using the following formula: ; ; in, High-dimensional features output for trend terms; High-dimensional features output for seasonal terms; Embed a weight matrix for the trend term; Embed the weight matrix for the seasonal terms; The trend term feature vector is weighted by a cross-scale attention mechanism; The seasonal feature vector is weighted by a cross-scale attention mechanism. Embed a bias vector for the trend term; Embed the bias vector for the seasonal term.

[0043] 2. Timing folding module Significant periods of the internal solitary wave time series are extracted using Fast Fourier Transform (FFT), and the one-dimensional sequence is converted into a two-dimensional tensor to make the temporal variation patterns within and between periods explicit. Specifically, the frequency domain signals of the trend and seasonal terms of the internal solitary wave time series data are calculated using FFT, and the top k significant periods are selected by analyzing the frequency intensity. Then, each selected period (with zeros padded if less than one period) is converted into a two-dimensional tensor, where the rows and columns correspond to the changes within and between periods, respectively, thus making the two-dimensional temporal variations originally hidden in the one-dimensional sequence explicit.

[0044] 3. TimesBlock module Multi-scale convolutional kernels are used to extract local multi-scale features of the temporal sequence of internal solitary waves from a two-dimensional tensor, and feature filtering and information preservation are achieved through gating mechanisms and residual connections. Specifically, multi-scale convolution is used to process the two-dimensional tensor. Multiple convolutional kernels of different sizes (such as 1×3, 3×1, and 3×3) are used simultaneously to capture local patterns at different scales. This extracts short-term changes in the seasonal and trend terms of internal solitary waves within the period, while also capturing long-term trends between periods, efficiently mining local dependencies in the two-dimensional tensor. The gating mechanism is used to filter the extracted two-dimensional features of the seasonal and trend terms of internal solitary waves, retaining effective information valuable to the task, filtering noise interference, improving feature quality, and ensuring the effectiveness of subsequent processing. Finally, residual connections are used to preserve the original input features.

[0045] 4. Spatiotemporal Attention Module By employing a self-attention mechanism to capture the global correlation between different variables of the internal isolated wave trend term and the seasonal term, the model's focus on key physical driving factors is enhanced. Specifically, by generating a query, key, and value matrix, attention weights are calculated between different variables of the internal isolated wave trend term and the seasonal term, capturing the global correlation between different variables and enhancing the model's focus on key physical driving factors.

[0046] The spatiotemporal attention module is implemented using the following formula: ; The output represents spatiotemporal attention; To obtain attention weights through normalization; For query matrix; The key matrix; It is a value matrix; This is the scaling factor; This is the matrix transpose.

[0047] 5. Timing Deployment Module By restoring the two-dimensional tensor after temporal folding and feature extraction to a one-dimensional sequence, the temporal features of internal solitary waves are inversely mapped from image-like structures to time series. Specifically, through periodic pattern mining and two-dimensional unfolding, the temporal features of internal solitary waves are transformed into image-like two-dimensional matrices, thereby effectively capturing periodic patterns and long-term dependencies in the time series.

[0048] 6. Prediction layer The high-dimensional features, after time-series expansion, are mapped to predicted values ​​of the propagation velocity of internal solitary waves, completing the final output from the feature space to the target variable. Specifically, the time-series features of internal solitary waves, after being physically constrained by the loss function and output by the time-series expansion module, are mapped to the final predicted propagation velocity of ocean internal solitary waves, completing the mapping from high-dimensional features to predicted values ​​in the target dimension and solving the adaptation problem between the feature dimension and the prediction target.

[0049] III. iTransformer Module The iTransformer module includes an embedding layer, a local physical attention module, a feedforward network, layer normalization, and a prediction layer.

[0050] 1. Embedded layer The low-dimensional temporal features of the internal solitary wave residuals are mapped to a high-dimensional space through a linear transformation, enhancing the feature representation capability. Specifically, the residuals of the internal solitary wave time series data are transformed from low-dimensional features to high-dimensional features through a linear transformation, uncovering subtle features hidden in the original data and providing input for the subsequent local physics attention module, thus avoiding the problem of insufficient representation by low-dimensional features.

[0051] 2. Local Physical Attention Module Within a temporal / spatial local window, physically weighted attention weights are calculated to accurately capture feature correlations related to the dynamics of the internal solitary wave. Specifically, attention weights between different variables in the internal solitary wave residual term are calculated using physical weighting, allowing the model to accurately capture the physically relevant features of each variable within the temporal / spatial local window and suppress physically meaningless noise correlations. Attention weights between different variables in the internal solitary wave trend and seasonal terms are also calculated.

[0052] Local physical attention is achieved through the following formula: ; This represents the output of the local physical attention mechanism; To obtain attention weights through normalization; For query matrix; The key matrix; It is a value matrix; This is the scaling factor; This is the matrix transpose.

[0053] 3. Feed-Forward Network (FFN) The features output by the Local Physical Attention (LPA) module undergo nonlinear transformation and dimensionality reduction to achieve refined feature extraction and dimensionality adaptation. Specifically, the temporal correlation features of internal solitary waves captured by the LPA module are transformed into high-dimensional nonlinear features for refined feature extraction, and then dimensionality is reduced back to the original dimension. The high-dimensional space provides richer feature representation capabilities, allowing the model to distinguish more subtle temporal differences, while dimensionality reduction ensures that the output dimension is consistent with the LPA layer, facilitating subsequent residual connections and layer normalization.

[0054] Feedforward networks are implemented using the following formula: ; in, The input features are from the output of the local physics attention module. and The weights and biases are for the first-level linear transformation; and The weights and biases for the second-level linear transformation; For activation function, This is the output of the feedforward network.

[0055] 4. Layer Normalization The local physical attention and the output of the feedforward network are residually connected, and then the training process is stabilized through layer normalization.

[0056] 5. Prediction layer The processed high-dimensional features are mapped to predicted values ​​of the propagation velocity of the internal solitary wave, completing the module's final output.

[0057] Both the TimesNet and iTransformer modules introduce physical constraints on the loss function to ensure that the model output conforms to the dynamics of internal solitary waves, thereby improving the rationality and physical reliability of the prediction results.

[0058] The physical constraints of the loss function are achieved through the following formula: ; ; ; in, For loss function, For data-driven loss, For physical constraint loss, , For hyperparameters; This is a predicted value for the propagation velocity of an internal solitary wave. The propagation velocity of the internal solitary wave is calculated using remote sensing. This represents the theoretical value of the propagation velocity of the internal solitary wave, calculated under continuous density stratification conditions. Density was obtained from WOA data, total water depth from GEBCO data, and the vertical density profile was input as a two-dimensional sequence of data, in the form of... The water depth at the i-th sampling point is calculated from the temperature and salinity data in the WOA data. The corresponding density value at that depth .

[0059] IV. Gating Mechanism Integration Module The gating mechanism fusion module adaptively and dynamically fuses the propagation speeds predicted by the TimesNet and iTransformer modules using learnable gating weights. It automatically adjusts the weights by learning the relative importance of different components under different time and environmental conditions.

[0060] The gating mechanism fusion module outputs the final propagation velocity of the internal solitary wave using the following formula: ; in, This is the final predicted propagation speed; This is the propagation speed predicted by the TimesNet module; It is the propagation speed predicted by the iTransformer module; , and These are weights obtained through learning; It represents the residual.

[0061] Model training and testing: The training set is used to train the model, and the test set is used to test the model.

[0062] The training set (including propagation speed, direction, time, longitude, latitude, water depth, density, and tidal current) is input into the constructed model for training. The propagation speed and direction of the internal solitary wave are used as the model output. The model is input with the speed and direction at different times and predicts the speed and direction at a certain time in the future (the prediction of a future time is set by the time step).

[0063] During model training, the initial learning rate was set to 0.001, and the training process included 5800 iterations, with each batch of training data containing 10 samples. The model employed an early stopping strategy, determining the optimal training state by monitoring changes in the test set error. The results showed that the prediction model reached its best performance at the 37th epoch, at which point training was stopped and the optimal model parameters were saved. At this point, the mean absolute error (MAE) of the predicted internal solitary wave propagation velocity was 0.09 m / s, and the root mean square error (RMSE) was 0.15 m / s.

[0064] Step 4: Acquire satellite remote sensing image data of the target sea area. After preprocessing the satellite remote sensing image data, input it into the qualified model to predict the propagation speed of internal solitary waves.

[0065] The time step was set, and the model was run to predict the propagation speed of the internal solitary wave. The predicted location of the internal solitary wave was calculated based on the time step and propagation speed. The model's prediction was compared with satellite observations of the internal solitary wave location. It was found that the prediction error was small over short time periods (average RMSE of 1.21 km for 2 hours), while the error increased over longer time periods (average RMSE of 4.7 km for 28 hours). This characteristic is consistent with the general law of model error accumulation over time. Furthermore, the model exhibits good robustness and can effectively predict the propagation of the internal solitary wave.

[0066] Ablation experiments: To quantitatively evaluate the necessity and contribution of each module in the STL-iTransformer-TimesNet fusion framework, three sets of ablation runs and two sets of replacement runs were designed. The results of the ablation experiments are shown in Table 1. The baseline complete model is STL+iTransformer+TimesNet. All models are trained on the same training set (80%) and evaluated on the same independent test set (20%). The input features, hyperparameters, number of iterations, and batch size are kept completely consistent; only the network structure is changed.

[0067] Table 1 Ablation Experiment Results

[0068] The ablation experiments show that the baseline full model STL+iTransformer+TimesNet performs best. The iTransformer-TimesNet model shows a 26.1% increase in MAE and a 22.9% increase in RMSE, but its performance is significantly lower, confirming the important role of STL. The STL-LSTM-TimesNet model shows a 13.0% increase in MAE and a 12.0% increase in RMSE, but its performance is lower, indicating that iTransformer outperforms traditional LSTM in capturing long-term temporal dependencies. iTransformer, based on a self-attention mechanism, can model global temporal correlations in parallel, avoiding the problem of insufficient long-sequence modeling ability caused by the "gradient vanishing" phenomenon in LSTM. The STL-LSTM-CNN model shows a 50.0% increase in MAE and a 45.8% increase in RMSE, indicating that TimesNet can accurately capture multi-scale periodic patterns in temporal data, while CNN is only good at local feature extraction and cannot model global temporal dynamics, leading to a significant increase in prediction error. The STL-Fully Connected model shows the worst performance, with an 84.8% increase in MAE and a 78.3% increase in RMSE. Fully connected networks lack time-series modeling capabilities and cannot capture the time dependency of internal solitary wave propagation, indicating that iTransformer and TimesNet work together to support prediction accuracy through complementary mechanisms.

[0069] To comprehensively evaluate the performance of the proposed model in predicting the propagation velocity of internal solitary waves, Transformer, TCN, CNN+LSTM, LSTM, and RNN were selected as comparison models, as shown in Table 2. The model of this invention predicts the propagation velocity of internal solitary waves with an RMSE of 0.15 m / s, which is significantly better than Transformer (0.18 m / s), TCN (0.21 m / s), CNN+LSTM (0.24 m / s), LSTM (0.29 m / s), and RNN (0.37 m / s). The prediction model of this invention has better performance and higher accuracy, proving that the method used in this invention is indeed feasible and effective.

[0070] Table 2. Experimental Results of Model Comparison

[0071] 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 the propagation velocity of an internal solitary wave based on deep learning, characterized in that, Includes the following steps: Step 1: Collect multi-source satellite remote sensing image data, extract the wave crest of the inner solitary wave after preprocessing the data, and calculate the propagation speed of the inner solitary wave; Step 2: Combine the propagation velocity of internal solitary waves with background hydrological parameters to construct a dataset for predicting the propagation velocity of internal solitary waves, and divide it into a training set and a test set; Step 3: Construct an internal solitary wave propagation velocity prediction model integrating physical mechanisms and deep learning. The model includes an STL decomposition module, a TimesNet module, an iTransformer module, and a gating mechanism fusion module. The STL decomposition module decomposes the internal solitary wave time series data into trend, seasonal, and residual terms through local weighted regression. The trend and seasonal terms output by the STL decomposition module are input into the TimesNet module, and the residual term is input into the iTransformer module for internal solitary wave propagation velocity prediction. The gating mechanism fusion module adaptively and dynamically fuses the propagation velocities predicted by the TimesNet and iTransformer modules using learnable gating weights, and outputs the final predicted propagation velocity. The model is trained using a training set and validated using a test set. Step 4: Acquire satellite remote sensing image data of the target sea area, preprocess it, and input it into the qualified model to predict the propagation speed of internal solitary waves.

2. The method for predicting the propagation velocity of an internal solitary wave based on deep learning according to claim 1, characterized in that, The decomposition formula of the STL decomposition module is as follows: ； ； ； in, This contains the original time series data of the solitary wave at time t; The trend component at time t; The seasonal component at time t; The residual component at time t; The degree of the polynomial used to represent the fitted trend; Indicates a time index; The low-pass smoothing window is at time t; This is a locally weighted regression.

3. The method for predicting the propagation velocity of an internal solitary wave based on deep learning according to claim 1, characterized in that, The STL decomposition module introduces a cross-scale attention mechanism, which weights the trend term, seasonal term, and residual term using the following formula: ； ； ； in, Represents the function for cross-scale attention mechanisms; It is a trend term extracted from the original time series data; It is a seasonal term extracted from the original time-series data; These are the residual terms extracted from the original time-series data; The trend term feature vector is weighted by a cross-scale attention mechanism. This is the seasonal feature vector after being weighted by a cross-scale attention mechanism. This is the feature vector of the residual term after being weighted by the cross-scale attention mechanism.

4. The method for predicting the propagation velocity of an internal solitary wave based on deep learning according to claim 1, characterized in that, The TimesNet module includes an embedding layer, a temporal folding module, a TimesBlock module, a spatiotemporal attention module, a temporal unrolling module, and a prediction layer; The embedding layer transforms the trend and seasonal terms of the internal solitary wave time series data from low-dimensional features to high-dimensional features through linear transformation; The time-series folding module extracts the significant periodicity of the internal solitary wave time series through fast Fourier transform and converts the one-dimensional sequence into a two-dimensional tensor to make the time series variation patterns within and between periods explicit. The TimesBlock module uses multi-scale convolution kernels to extract local multi-scale features of the internal solitary wave time series from the two-dimensional tensor, and achieves feature filtering and information retention through gating mechanism and residual connection. The spatiotemporal attention module captures the global correlation between different variables of the internal isolated wave trend term and the seasonal term through a self-attention mechanism, thereby enhancing the model’s attention to key physical driving factors. The temporal unrolling module restores the two-dimensional tensor that has undergone temporal folding and feature extraction into a one-dimensional sequence, thereby realizing the inverse mapping of the temporal features of internal solitary waves from image-like structures to time series. The prediction layer maps the time-expanded high-dimensional features into predicted values ​​of the propagation velocity of the internal solitary wave, completing the final output from the feature space to the target variable.

5. The method for predicting the propagation velocity of an internal solitary wave based on deep learning according to claim 4, characterized in that, The spatiotemporal attention module generates a query, key, and value matrix, and calculates the attention weights between different variables of the internal solitary wave trend term and the seasonal term, using the following formula: ； in, The output represents spatiotemporal attention; To obtain attention weights through normalization; For query matrix; The key matrix; It is a value matrix; This is the scaling factor.

6. The method for predicting the propagation velocity of an internal solitary wave based on deep learning according to claim 1, characterized in that, The iTransformer module includes an embedding layer, a local physical attention module, a feedforward network, layer normalization, and a prediction layer. The embedding layer maps the low-dimensional temporal features of the internal solitary wave residual term to a high-dimensional space through a linear transformation, thereby enhancing the feature representation capability. The local physical attention module calculates physically weighted attention weights within a temporal / spatial local window to accurately capture feature associations related to the dynamics of internal isolated waves. The feedforward network performs nonlinear transformation and dimensionality reduction on the features output by the local physical attention module to achieve refined feature extraction and dimensionality adaptation. The layer normalization involves performing a residual connection between the local physical attention and the output of the feedforward network, and then stabilizing the training process through layer normalization. The prediction layer maps the processed high-dimensional features into predicted values ​​of the propagation velocity of the internal solitary wave, completing the final output of the module.

7. The method for predicting the propagation velocity of an internal solitary wave based on deep learning according to claim 6, characterized in that, The local physical attention module is implemented using the following formula: ； in, This represents the output of the local physics attention module; To obtain attention weights through normalization; For query matrix; The key matrix; It is a value matrix; Scaling factor This is the matrix transpose.

8. The method for predicting the propagation velocity of an internal solitary wave based on deep learning according to claim 6, characterized in that, The feedforward network is implemented using the following formula: ； in, The input features are from the output of the local physics attention module. and The weights and biases are for the first-level linear transformation; and The weights and biases for the second-level linear transformation; For activation function, This is the output of the feedforward network.

9. A method for predicting the propagation velocity of an internal solitary wave based on deep learning according to claim 4 or 6, characterized in that, Both the TimesNet and iTransformer modules incorporate physical constraints on the loss function to ensure that the model output conforms to the dynamics of internal isolated waves. These physical constraints are implemented using the following formula: ； ； ； in, For loss function, For data-driven loss, For physical constraint loss, , For hyperparameters; This is a predicted value for the propagation velocity of an internal solitary wave. The propagation velocity of the internal solitary wave is calculated using remote sensing. This represents the theoretical value of the propagation velocity of an internal solitary wave calculated under continuous density stratification conditions.

10. The method for predicting the propagation velocity of an internal solitary wave based on deep learning according to claim 1, characterized in that, The gating mechanism fusion module outputs the final propagation speed of the internal solitary wave using the following formula: ； in, This is the final predicted propagation speed; This is the propagation speed predicted by the TimesNet module; It is the propagation speed predicted by the iTransformer module; , and These are weights obtained through learning; It represents the residual.

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