An internal solitary wave amplitude prediction method fusing physical mechanism and deep learning
By integrating physical mechanisms and deep learning to predict the amplitude of internal solitary waves, and utilizing multi-source satellite data and the ISW-PI-GAT-KAN model, the problem of insufficient prediction accuracy of traditional models in complex sea areas is solved, and high-precision, stable and physically plausible prediction of internal solitary wave amplitude is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- FIRST INSTITUTE OF OCEANOGRAPHY MNR
- Filing Date
- 2026-06-22
- Publication Date
- 2026-07-24
AI Technical Summary
Existing technologies struggle to achieve high-precision and stable prediction of internal solitary wave amplitudes in complex sea areas. Traditional physical models cannot adapt to large-amplitude and highly nonlinear environments, and purely data-driven models lack physical mechanism constraints, resulting in inconsistent prediction results and weak generalization ability.
An internal solitary wave amplitude prediction method integrating physical mechanisms and deep learning is proposed. By processing multi-source satellite remote sensing data and combining the DJL equation and eKdV equation, an ISW-PI-GAT-KAN model is constructed. Amplitude prediction is performed using graph attention network and Kolmogorov-Arnold network. A physical constraint layer is introduced to ensure the physical rationality and interpretability of the prediction results.
It significantly improves the accuracy and stability of internal solitary wave amplitude prediction, and can accurately predict large-amplitude, strongly nonlinear internal solitary waves in the entire sea area. It has good generalization ability and physical interpretability, and is superior to traditional models.
Smart Images
Figure CN122454440A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of ocean solitary wave prediction, and in particular to a method for predicting the amplitude of solitary waves that integrates physical mechanisms and deep learning. Background Technology
[0002] Internal solitary waves are typical mesoscale dynamic processes in the ocean, widely distributed in major sea areas worldwide, characterized by large amplitude, short period, and high velocity. They can alter the vertical structure of seawater, promote the mixing of water and plankton, and are an important energy source for internal mixing in continental shelf sea areas, significantly impacting marine ecology and the hydrological environment. Simultaneously, large-amplitude internal solitary waves possess strong destructive power, seriously threatening the navigation safety of underwater submarines and the stable operation of marine engineering facilities such as subsea pipelines and offshore drilling platforms. Therefore, conducting research on the amplitude prediction of internal solitary waves has significant theoretical and engineering application value.
[0003] Currently, remote sensing technology, with its advantages of wide-area, all-weather, and non-contact observation, has become an important means of observing and inverting parameters of internal solitary waves. However, existing amplitude inversion methods mostly rely on traditional physical models such as KdV. These models are based on ideal assumptions of weak nonlinearity and weak dispersion, making them difficult to adapt to large-amplitude, strongly nonlinear internal solitary wave environments and unable to meet the needs of dynamic amplitude prediction in complex sea areas. Compared to propagation velocity prediction, research on high-precision amplitude prediction is even more scarce, and there is an urgent need to develop amplitude inversion and prediction methods applicable to all sea areas and strongly nonlinear scenarios.
[0004] The difficulty in amplitude prediction stems from several factors. First, amplitude is a vertical underwater parameter, and remote sensing can only indirectly retrieve it based on sea surface texture information, not through direct observation. Furthermore, on-site observation is costly and yields limited data, making it difficult to obtain large-scale, long-term amplitude samples. Second, compared to propagation speed, amplitude is more sensitive to environmental factors such as seawater stratification, tidal currents, and ocean current disturbances. It exhibits strong multi-factor nonlinear coupling and complex evolutionary patterns. Purely physical models rely on fixed dynamic formulas and empirical parameter corrections, making it difficult to accurately fit the nonlinear abrupt changes in the amplitude of internal solitary waves under complex ocean conditions. This results in weak generalization ability and insufficient prediction accuracy for complex sea states.
[0005] With the deep application of artificial intelligence and big data technologies in marine remote sensing, intelligent algorithms such as machine learning and deep learning have provided new pathways for predicting internal solitary waves. These methods can fully exploit the latent features in massive amounts of remote sensing imagery, compensating for the insufficient nonlinear fitting capabilities of traditional purely physical models. However, current purely data-driven models generally lack physical mechanism constraints, potentially leading to physical inconsistencies in prediction results, as well as weak extrapolation capabilities and poor interpretability. Therefore, how to effectively integrate physical mechanisms with deep learning to improve prediction accuracy while ensuring physical plausibility is a pressing technical challenge in the field of internal solitary wave amplitude prediction. Summary of the Invention
[0006] To address the aforementioned technical problems, this invention provides a method for predicting the amplitude of internal solitary waves that integrates physical mechanisms and deep learning. This method aims to achieve high-precision and high-stability prediction of internal solitary wave amplitudes in complex marine environments, while ensuring that the prediction results conform to the dynamic laws of internal solitary wave propagation, possess good generalization ability, and have physical interpretability.
[0007] To achieve the above objectives, the technical solution of the present invention is as follows: A method for predicting the amplitude of internal solitary waves that integrates physical mechanisms and deep learning includes the following steps: Step 1: Collect and preprocess multi-source satellite remote sensing image data; Step 2: Based on the preprocessed multi-source satellite remote sensing image data, extract the position and propagation velocity information of the inner solitary wave crest line, and invert the amplitude of the inner solitary wave by combining background environmental parameters; Step 3: Based on the internal isolated wave amplitude obtained by inversion and the internal isolated wave amplitude obtained by field observation, and combined with the background environmental parameters, construct an internal isolated wave amplitude prediction dataset, and divide the prediction dataset into a training set and a test set. Step 4: Construct an internal solitary wave amplitude prediction model. The model includes a spatial topology layer, a graph attention network module, a Kolmogorov-Arnold network module, and a physical information constraint layer. Input the training set data into the model for training, and use the test set data to evaluate the trained model and determine the optimal model. Step 5: After processing the remote sensing image data of the internal solitary wave to be predicted, input it into the qualified model to predict the amplitude of the internal solitary wave.
[0008] In the above scheme, the multi-source satellite remote sensing image data mentioned in step 1 includes geostationary meteorological satellite remote sensing data, polar-orbiting optical satellite remote sensing data, and synthetic aperture radar (SAR) remote sensing data.
[0009] In the above scheme, step 2 uses the fully nonlinear DJL equation to perform the amplitude inversion of the internal solitary wave. The DJL equation is as follows: ; in, This represents the vertical displacement of the isodense surface. The propagation speed of the internal solitary wave. For buoyancy frequency, For the Laplace operator, , , These are the horizontal and vertical coordinates, respectively. Internal solitary wave amplitude The calculation formula is: ; in, This represents the vertical displacement of the isodensity surface of the internally isolated wave disturbance that eventually converges.
[0010] In the above scheme, the internal solitary wave amplitude prediction dataset in step 3 consists of 10-dimensional input features and 1-dimensional output labels. The input features include time, longitude, latitude, water depth, tidal current, stratum depth, upper layer density, lower layer density, internal solitary wave propagation speed and direction, and the output label is the internal solitary wave amplitude.
[0011] In the above scheme, the spatial topology layer transforms discrete, unordered observation data into a graph topology structure with physical spatial relationships. The specific method is as follows: The effective observation samples extracted along the propagation path of the internal solitary wave are defined as the graph node set. ; Connect adjacent observation nodes based on the propagation trajectory of the internal solitary wave to construct a set of topological edges. ; Establish the irregular graph structure of the propagation evolution of internal solitary waves .
[0012] In the above scheme, the graph attention network module adopts a dynamic attention mechanism, and the formula for calculating the attention score is: ; in, As the central node For neighboring nodes Attention score For attention vectors, , They are the central nodes. and neighboring nodes The original feature vector, As the central node The transformation matrix, Neighboring nodes The transformation matrix, It is a non-linear activation function.
[0013] In the above scheme, the graph attention network module first focuses on the central node. All neighboring nodes raw attention score Perform masking to obtain the attention score after masking. ; ; in, It is a mask matrix; Then, the Softmax function is used to... Normalization is performed to obtain the attention weights.
[0014] ; Finally, the neighborhood features are weighted and aggregated to obtain the node output feature vector of the graph attention network module: ; in, The node outputs feature vectors for the graph attention network module; As the central node The original feature vector; Neighboring nodes A set of.
[0015] In the above scheme, the Kolmogorov-Arnold network module adopts a learnable B-spline activation function and introduces an edge activation function regularization term: ; in, For normal loss, For the KAN network Layer nodes With nodes B-spline mapping function between Represents the network layer index. Enter the node number. This is to output the node number.
[0016] In the above scheme, the physical information constraint layer introduces the solitary wave dynamics equation within eKdV to construct the physical residual. : ; in, For the amplitude of the internal solitary wave, For linear phase velocity, Represents the first-order nonlinear coefficients. Represents the second-order nonlinear coefficients. Represents the dispersion coefficient. Indicates time, Represents horizontal spatial coordinates; The physical constraint loss function is: ; in, Indicates physical loss. For the number of points, For the first A spatial location.
[0017] In the above scheme, the total loss function of the internal solitary wave amplitude prediction model for: ; in, For data loss, For physical constraint loss, For normal loss, , , These are the corresponding weights.
[0018] Through the above technical solution, the internal solitary wave amplitude prediction method that integrates physical mechanisms and deep learning provided by the present invention has the following beneficial effects: 1. Construct a deep learning prediction architecture that integrates GAT and KAN: This invention employs a collaborative design of a Graph Attention Network (GAT) and a Kolmogorov-Arnold Network (KAN) at both the front and back ends. The front-end GAT module accurately captures the spatial dependencies and historical evolution characteristics of internal solitary waves along their propagation paths through spatial topology layers and dynamic attention mechanisms. The back-end KAN module utilizes the strong nonlinear approximation capability of learnable B-spline activation functions to resolve the implicit nonlinear mapping between complex ocean environments and internal solitary wave amplitudes in a high-dimensional feature space. This collaborative approach overcomes the shortcomings of traditional models, such as weak spatial modeling capabilities and insufficient nonlinear analytical accuracy, significantly improving prediction accuracy and generalization performance.
[0019] 2. Introduce eKdV physical constraints to enhance model interpretability: This invention incorporates physical constraint terms based on the extended Korteweg-de Vries (eKdV) equations into the loss function, ensuring that the model training process follows the dispersion characteristics and nonlinear equilibrium mechanism of internal solitary waves. The prediction results not only match the statistical characteristics of remote sensing observation data but also satisfy the dynamic laws of internal solitary wave propagation. This effectively improves upon the shortcomings of purely data-driven models, such as lack of physical priors, weak extrapolation ability, and poor interpretability, thereby enhancing the physical accuracy of the prediction results.
[0020] 3. Improve the accuracy of solitary wave amplitude inversion across the entire sea area: Compared to traditional physical models based on weakly nonlinear and weakly dispersion assumptions such as KdV, this invention introduces the fully nonlinear DJL equation, overcoming the limitations of small amplitude and long waves. By combining multi-source satellite remote sensing data and using the propagation velocity of internal solitary waves to invert amplitude, it effectively solves the problem that traditional models struggle to accurately characterize large-amplitude, strongly nonlinear internal solitary waves, significantly improving the accuracy and reliability of solitary wave amplitude inversion across the entire ocean area.
[0021] 4. Improve the dynamic attention mechanism of GAT: This invention dynamically improves the static attention mechanism of native graph attention networks, abandoning the traditional method of concatenating the central node and neighboring nodes for computation, and adopting a phased transformation and feature fusion computation strategy. Each node can adaptively determine the importance of its surrounding neighboring nodes based on its own characteristics and the propagation scenario of internal solitary waves, accurately capturing the differences in spatial correlation of internal solitary waves, thus enhancing the network's feature representation ability and generalization performance.
[0022] 5. Introduce a marginal activation function regularization term to suppress overfitting: To address the issue of overfitting caused by the large number of control points and high degree of freedom in the learnable B-spline activation function in KAN networks, this invention introduces a marginal activation function regularization term. This regularization term, on the one hand, constrains the output amplitude of the B-spline function, suppressing overfitting of the model to training set noise; on the other hand, it achieves network sparsity, automatically selecting effective feature transmission paths and improving the interpretability of the model's response surface to internal isolated wave features.
[0023] 6. Deep synergy among GAT spatial memory, eKdV physical constraints, and KAN nonlinear fitting: The superior predictive performance of this invention's model is not a simple stacking of modules, but rather the result of deep synergy between spatial topological memory, physical constraints, and high-precision nonlinear fitting. The GAT module provides spatial propagation feature memory, the eKdV physical constraints inject the dynamic mechanism of ocean internal waves, and the KAN network achieves high-precision nonlinear mapping. All three are indispensable, collectively addressing the shortcomings of traditional pure data-driven models, such as lack of physical constraints, weak environmental adaptability, low prediction accuracy, and poor stability. This enables high-precision, high-stability, long-term time-series prediction of the amplitude of isolated waves in the ocean.
[0024] 7. The prediction accuracy is significantly better than that of existing mainstream models: Through comparative experiments with various representative baseline models (including XGBoost, LSTM, GRU, Transformer, and CNN-LSTM), the model of this invention achieves the minimum prediction error in both short-time step prediction and long-time step prediction tasks in complex terrain, and has the best prediction anti-attenuation ability, which fully proves the technical practical value of this invention. Attached Figure Description
[0025] 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.
[0026] Figure 1 This is a schematic diagram of a method for predicting the amplitude of an internal solitary wave that integrates physical mechanisms and deep learning, as disclosed in an embodiment of the present invention. Figure 2 This is a diagram of the architecture of the internal solitary wave amplitude prediction model constructed in this invention. Detailed Implementation
[0027] 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.
[0028] This invention provides a method for predicting the amplitude of internal solitary waves that integrates physical mechanisms and deep learning, such as... Figure 1 As shown, it includes the following steps.
[0029] Step 1: Collection and Preprocessing of Multi-Source Satellite Remote Sensing Image Data Multi-source satellite remote sensing imagery data is collected, including high temporal resolution geostationary meteorological satellite remote sensing data, wide-swath polar-orbiting optical satellite remote sensing data, and synthetic aperture radar (SAR) remote sensing data unaffected by clouds and fog. These three data sources complement each other, effectively improving the accuracy and completeness of spatiotemporal coverage.
[0030] The above remote sensing images are preprocessed as follows: Geometric correction: Eliminates sensor distortion and geometric deformation, ensuring accurate matching between image coordinates and geographic coordinates.
[0031] Image cropping: Cropping out the effective region containing the features of internal solitary waves based on the study area.
[0032] Image enhancement: Histogram equalization and filtering are used to enhance the texture features of isolated waves within the sea surface and reduce background noise.
[0033] Step 2: Amplitude Inversion of Internal Solitary Waves Based on preprocessed multi-source satellite remote sensing images, the position of the inner solitary wave crest is extracted using a human-computer interactive method. Then, using the multi-temporal imagery (MTI) method, the propagation speed is calculated based on the geographical location difference and time interval of the same inner solitary wave in different remote sensing images. And the direction of dissemination.
[0034] Amplitude inversion is performed using the fully nonlinear DJL (Dubreil-Jacotin-Long) equations. The DJL equations do not assume small amplitudes or long waves, making them suitable for solitary wave amplitude inversion across the entire ocean. The DJL equations under continuous stratification conditions are as follows: ; In the formula, This represents the vertical displacement of the isodense surface; The propagation speed of an internal solitary wave; For buoyancy frequency; For the Laplace operator, , , These are the horizontal and vertical coordinates, respectively.
[0035] buoyancy frequency Calculations based on ocean density profiles: ; in, It is the acceleration due to gravity. Background vertical density profile, For reference density.
[0036] Propagation velocity of internal solitary waves calculated using remote sensing images By combining marine environmental parameters (density profile, water depth), the half-width of the horizontal computational domain (taken as 5000 m based on the characteristic width of internal solitary waves), and effective potential energy, the vertical displacement of the isodense surface of the final perturbation field is obtained through iterative convergence and energy matching. , the internal solitary wave amplitude Take the maximum absolute value: ; Step 3: Construction of the Internal Solitary Wave Amplitude Prediction Dataset Based on the amplitude retrieved in step 2 and the amplitude obtained from on-site observations, a prediction dataset is constructed by combining background environmental parameters.
[0037] First, spatial encoding is performed on latitude and longitude, transforming discrete geographic coordinates into standardized three-dimensional feature vectors to eliminate scale differences: ; ; ; in, Latitude Longitude.
[0038] The dataset consists of 10-dimensional input features and 1-dimensional output labels: Input features: time, longitude, latitude, water depth, tidal current, strata depth, upper layer density, lower layer density, internal solitary wave propagation speed, and propagation direction.
[0039] Output label: Internal solitary wave amplitude.
[0040] The dataset is divided into training and test sets in an 8:2 ratio, and the single-event attribution principle is followed to ensure that complete time-series data of the same isolated wave event are assigned to only the training or test set to avoid data leakage. In this embodiment, the training set contains 1029 samples and the test set contains 258 samples.
[0041] Step 4: Construction, training, and evaluation of the internal solitary wave amplitude prediction model (I) Model Construction The structure of the internal solitary wave amplitude prediction model (named ISW-PI-GAT-KAN) constructed in this embodiment is as follows: Figure 2 As shown, it includes, in sequence: input layer, spatial topology construction layer, graph attention network module, Kolmogorov-Arnold network module, physical information constraint layer and output layer.
[0042] (1) Spatial topology layer Transform discrete, unordered observation data into a graph topology with physical spatial relationships: The effective observation samples extracted along the propagation path of the internal solitary wave are defined as the graph node set. Each node contains parameters such as time, latitude and longitude, water depth, tidal current, depth of the superstructure, density of the upper and lower layers, propagation speed and direction.
[0043] Connect adjacent observation nodes based on the propagation trajectory of the internal solitary wave to construct a set of topological edges. .
[0044] Establish the irregular graph structure of the propagation evolution of internal solitary waves .
[0045] This structure fully preserves the spatial continuity of the propagation of internal isolated waves along the path, laying a data foundation for the model to capture the "historical memory" features brought about by topographic undulations and stratification changes.
[0046] (2) Graph Attention Network Module A Graph Attention Network (GAT) is employed, utilizing an adaptive attention mechanism to learn the importance relationships between spatial nodes. This embodiment dynamically improves upon the native static attention mechanism, abandoning the method of concatenating the center node with its neighbors for calculation, and instead adopting a phased transformation and feature fusion strategy. The formula for calculating the dynamic attention score is as follows: ; in, As the central node For neighboring nodes Attention score For attention vectors, As the central node The transformation matrix, Neighboring nodes The transformation matrix, As the central node The original feature vector, Neighboring nodes The original feature vector, It is a non-linear activation function.
[0047] First, the central node All neighboring nodes raw attention score Perform masking to obtain the attention score after masking. ; ; in, It is a mask matrix; Then, the Softmax function is used to... Normalization is performed to obtain the attention weights.
[0048] ; Finally, the neighborhood features are weighted and aggregated to obtain the node output feature vector of the graph attention network module: ; in, The node outputs feature vectors for the graph attention network module; As the central node The original feature vector; Neighboring nodes A set of.
[0049] This module outputs a high-dimensional feature vector that incorporates spatial topological information, which is then passed to the KAN module.
[0050] (3) Kolmogorov-Arnold network module Using a KAN network and taking the spatial topological features output by GAT as input, a learnable B-spline activation function is used to adaptively fit the strong nonlinear and multi-coupled mapping relationship between ocean stratification, topography, propagation velocity and direction and internal solitary wave amplitude.
[0051] The KAN network computes layer by layer, and the final output features are: ; in, For the KAN network Layer The final output feature of a node is the result of fusing all input features into that node; For the KAN network Layer nodes With nodes The B-spline mapping function between them. After being passed layer by layer, the final output is the predicted amplitude of the internal solitary wave.
[0052] To prevent overfitting due to the high degrees of freedom of B-splines, a regularization term using an edge activation function is introduced: ; in, For normal loss, For the KAN network Layer nodes With nodes B-spline mapping function between Represents the network layer index. Enter the node number. This is to output the node number.
[0053] This regularization term constrains the output amplitude of the B-spline and achieves network sparsity, improving the interpretability of the model for the feature response surface.
[0054] (4) Physical Information Constraint Layer By introducing the eKdV internal solitary wave dynamics equation to construct physical residual constraints, the network output follows the internal solitary wave evolution law. The physical residual expression of the eKdV equation is: ; in, To predict the amplitude of internal solitary waves, For linear phase velocity, Represents the first-order nonlinear coefficients. Represents the second-order nonlinear coefficients. Represents the dispersion coefficient. Indicates time, Represents horizontal spatial coordinates (direction of wave propagation).
[0055] The physical constraint loss function is defined as the mean square value of the residuals at the collocation points: ; in, Indicates physical loss. For the number of points, Represents physical residuals. For the first The spatial location represents the first position. At that time.
[0056] The total loss function is a weighted average of three components: data loss, physical constraint loss, and regularization loss. ; in, This is the total loss function; For data loss; Loss due to physical constraints; For regular loss; Weight the data loss; Weights for physical constraint loss; For regularization, the loss weight is adjusted.
[0057] In this embodiment, the weights are respectively set as , , .
[0058] (II) Model Training The training set data (time, longitude, latitude, water depth, tidal current, strata depth, upper layer density, lower layer density, propagation speed, and direction) are input into the model, and the internal solitary wave amplitude is used as the output for training.
[0059] Training strategy: The Adam optimizer is used for initial global optimization, with an initial learning rate set to... The batch size is 256, and the maximum number of iterations is 2000.
[0060] As iterations continue, the learning rate smoothly decreases to .
[0061] After Adam optimization is completed, switch to L-BFGS optimizer for high-precision physical residual approximation, with a maximum of 500 iterations.
[0062] The overall model performance is evaluated every 100 iterations. If the validation set error does not decrease within 500 consecutive evaluation periods (threshold), the model is considered successful. If the training is terminated early and the optimal model parameters are saved, then the training will be terminated early.
[0063] (III) Model Evaluation The optimal model was evaluated using test set data. The initial location information of the internal solitary wave (time, latitude and longitude, water depth, tidal current, strata depth, density of upper and lower layers, propagation speed, and direction) was used as input, and the iteration time step was set to 1 hour. The model was run to predict the amplitude sequence of the internal solitary wave.
[0064] Four model structures were set up in the ablation experiment to verify the effectiveness of the three core modules: GAT, KAN, and physical constraints (PI). Model 1 (ISW-PI-GAT-KAN): Complete model.
[0065] Model 2 (ISW-GAT-KAN): Remove the physical constraint layer.
[0066] Model 3 (ISW-PI-KAN): Remove the GAT spatial topology layer.
[0067] Model 4 (ISW-PI-GAT-MLP): Replace KAN with MLP.
[0068] The comparative experimental results are shown in Table 1. The complete model performs best in both short-time step and long-time step prediction, demonstrating the necessity of the synergy of GAT spatial memory, eKdV physical constraints, and KAN high-precision nonlinear fitting.
[0069] Table 1 Comparison of amplitude prediction errors for different module combinations
[0070] Using the model of this invention as the baseline model (Experiment 1), a comparison with the pure data-driven GAT-KAN network (Experiment 2) reveals that the short-term prediction error of the pure data-driven model is 4.52 m, which is relatively close to the accuracy of 3.34 m of the baseline model; however, the long-term prediction error surges to 19.85 m, indicating a significant performance degradation. This model relies solely on data statistical regularity fitting, which can meet short-term prediction requirements, but errors accumulate continuously in long-term extrapolation. Due to the lack of eKdV wave physical constraints, the model cannot fit the internal solitary wave propagation dynamics mechanism, resulting in a significant failure of long-term generalization ability. This indicates that eKdV physical constraints can effectively suppress long-term error divergence and overfitting, and are key to ensuring accurate long-term predictions.
[0071] In Experiment 3, after removing the graph attention network module, the model's short-term and long-term prediction errors reached 5.86 m and 24.12 m, respectively, which were the highest values among all groups. The evolution of isolated internal waves is influenced by the cumulative modulation of environmental factors such as seabed shallowing, and is not an independent evolution at a single point. After removing the graph topology, the model loses its spatial memory of topographic and stratification changes, failing to characterize the cumulative evolution of wavefields under complex terrain. The prediction results deviate significantly from the actual physical process, quantitatively confirming the core role and necessity of the GAT spatial topology module.
[0072] Experiment 4 replaced the KAN network with an MLP, and even with the eKdV physical constraints retained, the model performance still significantly decreased. Because the eKdV equation contains a third-order spatial derivative of amplitude, traditional MLPs are prone to spectral bias and gradient vanishing problems when solving higher-order derivatives, making it difficult for the physical loss to converge. In contrast, the model of this invention relies on the higher-order differentiability of the B-spline function of the KAN network, enabling high-precision fitting of complex nonlinear response relationships and adapting to the requirements of solving higher-order physical equations.
[0073] In summary, the superior performance of the ISW-PI-GAT-KAN model is not a simple stacking of modules, but rather the result of deep collaboration among GAT spatial memory, eKdV physical constraints, and KAN high-precision nonlinear fitting. Each module is indispensable, and together they achieve high-precision, high-stability, long-term prediction of the amplitude of internal solitary waves.
[0074] Step 5: Prediction of internal solitary wave amplitude The remote sensing image data of the internal solitary wave to be predicted is preprocessed according to step 1 to extract parameters such as wave crest position, propagation speed, and direction. Combined with the background environmental parameters (water depth, tidal current, strata depth, upper and lower layer density, etc.) of the corresponding spatiotemporal location, the data is input into the ISW-PI-GAT-KAN model that has passed the evaluation in step 4. The model outputs the predicted value of the internal solitary wave amplitude.
[0075] Comparative experiment To verify the technical effectiveness of the model of this invention, five representative baseline models—XGBoost, LSTM, GRU, Transformer, and CNN-LSTM—were selected for comparison. All models were trained and evaluated on the same training and test sets. The experimental results are shown in Table 2.
[0076] Table 2 Comparison of Amplitude Prediction Errors of Different Models
[0077] As shown in Table 2, the absolute amplitude error of the model in this invention for short-time step-length prediction is only 3.34 m, which is superior to the XGBoost (6.52 m), LSTM (5.18 m), GRU (5.45 m), Transformer (4.12 m), and CNN-LSTM (4.75 m) models. In long-time step-length prediction scenarios with complex terrain, the absolute amplitude error of this model is 10.95 m, which is also significantly better than the error results of 28.45 m, 23.6 m, 24.15 m, 18.85 m, and 19.50 m corresponding to the five baseline models. Therefore, the model in this invention achieves the smallest absolute error in both short-time and long-time step-length prediction, and the prediction error decays the least with the increase of step length, proving the superior accuracy and stability of this method for predicting the amplitude of internal solitary waves in complex marine environments.
[0078] 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 in this invention 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 amplitude of internal solitary waves that integrates physical mechanisms and deep learning, characterized in that, Includes the following steps: Step 1: Collect and preprocess multi-source satellite remote sensing image data; Step 2: Based on the preprocessed multi-source satellite remote sensing image data, extract the position and propagation velocity information of the inner solitary wave crest line, and invert the amplitude of the inner solitary wave by combining background environmental parameters; Step 3: Based on the internal isolated wave amplitude obtained by inversion and the internal isolated wave amplitude obtained by field observation, and combined with the background environmental parameters, construct an internal isolated wave amplitude prediction dataset, and divide the prediction dataset into a training set and a test set. Step 4: Construct an internal solitary wave amplitude prediction model. The model includes a spatial topology layer, a graph attention network module, a Kolmogorov-Arnold network module, and a physical information constraint layer. Input the training set data into the model for training, and use the test set data to evaluate the trained model and determine the optimal model. Step 5: After processing the remote sensing image data of the internal solitary wave to be predicted, input it into the qualified model to predict the amplitude of the internal solitary wave.
2. The method for predicting the amplitude of an internal solitary wave by integrating physical mechanisms and deep learning according to claim 1, characterized in that, The multi-source satellite remote sensing image data mentioned in step 1 includes geostationary meteorological satellite remote sensing data, polar-orbiting optical satellite remote sensing data, and synthetic aperture radar (SAR) remote sensing data.
3. The method for predicting the amplitude of an internal solitary wave by integrating physical mechanisms and deep learning according to claim 1, characterized in that, Step 2 employs the fully nonlinear DJL equations for internal solitary wave amplitude inversion. The DJL equations are as follows: ； in, This represents the vertical displacement of the isodense surface. The propagation speed of the internal solitary wave. For buoyancy frequency, For the Laplace operator, , , These are the horizontal and vertical coordinates, respectively. Internal solitary wave amplitude The calculation formula is: ； in, This represents the vertical displacement of the isodensity surface of the internally isolated wave disturbance that eventually converges.
4. The method for predicting the amplitude of an internal solitary wave by integrating physical mechanisms and deep learning according to claim 1, characterized in that, The internal solitary wave amplitude prediction dataset mentioned in step 3 consists of 10-dimensional input features and 1-dimensional output labels. The input features include time, longitude, latitude, water depth, tidal current, stratum depth, upper layer density, lower layer density, internal solitary wave propagation speed and direction, and the output label is the internal solitary wave amplitude.
5. The method for predicting the amplitude of an internal solitary wave by integrating physical mechanisms and deep learning according to claim 1, characterized in that, The spatial topology layer transforms discrete, unordered observation data into a graph topology structure with physical spatial relationships. The specific method is as follows: The effective observation samples extracted along the propagation path of the internal solitary wave are defined as the graph node set. ; Connect adjacent observation nodes based on the propagation trajectory of the internal solitary wave to construct a set of topological edges. ; Establish the irregular graph structure of the propagation evolution of internal solitary waves .
6. The method for predicting the amplitude of an internal solitary wave by integrating physical mechanisms and deep learning according to claim 1, characterized in that, The graph attention network module employs a dynamic attention mechanism, and the formula for calculating the attention score is as follows: ； in, As the central node For neighboring nodes Attention score For attention vectors, , They are the central nodes. and neighboring nodes The original feature vector, As the central node The transformation matrix, Neighboring nodes The transformation matrix, It is a non-linear activation function.
7. The method for predicting the amplitude of an internal solitary wave by integrating physical mechanisms and deep learning according to claim 1, characterized in that, In the graph attention network module, the central node is first... All neighboring nodes raw attention score Perform masking to obtain the attention score after masking. ; ； in, It is a mask matrix; Then through Softmax function pairs Normalization is performed to obtain the attention weights. : ； Finally, the neighborhood features are weighted and aggregated to obtain the node output feature vector of the graph attention network module: ； in, The node outputs feature vectors for the graph attention network module; As the central node The original feature vector; For nodes Neighboring nodes A set of.
8. The method for predicting the amplitude of an internal solitary wave by integrating physical mechanisms and deep learning according to claim 1, characterized in that, The Kolmogorov-Arnold network module employs a learnable B-spline activation function and introduces an edge activation function regularization term: ； in, For normal loss, For the KAN network Layer nodes With nodes B-spline mapping function between Represents the network layer index. Enter the node number. To output the node number, The node output feature vector of the graph attention network module.
9. The method for predicting the amplitude of an internal solitary wave by integrating physical mechanisms and deep learning according to claim 1, characterized in that, The physical information constraint layer introduces the isolated wave dynamics equation within eKdV to construct the physical residual. : ； in, For the amplitude of the internal solitary wave, For linear phase velocity, Represents the first-order nonlinear coefficients. Represents the second-order nonlinear coefficients. Represents the dispersion coefficient. Indicates time, Represents horizontal spatial coordinates; The physical constraint loss function is: ； in, Indicates physical loss. For the number of points, For the first A spatial location.
10. The method for predicting the amplitude of an internal solitary wave by integrating physical mechanisms and deep learning according to claim 1, characterized in that, The total loss function of the internal solitary wave amplitude prediction model for: ； in, For data loss, For physical constraint loss, For normal loss, , , These are the corresponding weights.