Wave height prediction method and device based on physical guidance dynamic graph mamba network

Abstract

The application provides a sea wave height prediction method and device based on a physical guidance dynamic graph Mamba network, belongs to the technical field of sea wave height prediction, adopts a selective scanning mechanism of a state space model, thereby reconstructing a calculation paradigm of time series modeling, enabling the state space model to adaptively determine which historical information to retain and which noise to discard according to current marine environment characteristics, and realizing time series modeling with linear calculation complexity. In the condition of rapidly changing weather, the discrete parameter Δ value increases, the model pays more attention to recent information; in the condition of stability, the Δ value decreases, the model retains more historical information, and thus the purpose of guaranteeing calculation efficiency and improving prediction accuracy is achieved, the technical problem that long sequence modeling efficiency and precision are difficult to consider is overcome, the technical inertia that serial calculation or quadratic complexity calculation must be used in the traditional technology is broken, and a physical perception graph learner is used as a solution mechanism, thereby reconstructing a space relationship modeling method.

Description

Technical Field

[0001] This application relates to the technical field of wave height prediction, and in particular to a method and apparatus for wave height prediction based on a physically guided dynamic graph Mamba network. Background Technology

[0002] In the field of marine meteorological forecasting, the increasing demands for applications such as maritime navigation safety, marine engineering operations, and marine energy development have placed higher requirements on the accuracy and timeliness of wave height prediction. Wave height prediction technology primarily requires processing spatiotemporal series data containing multiple variables such as wind speed, wave period, and wave height. This data originates from various monitoring devices, including ocean buoys, weather stations, and satellite remote sensing, and is characterized by strong spatiotemporal correlation, significant nonlinearity, and strict physical constraints. Under technical scenarios involving long-term series prediction, multivariate coupling relationship modeling, and ensuring consistency of physical laws, existing technologies face technical bottlenecks such as the difficulty in balancing prediction accuracy and computational efficiency, insufficient capture of dynamic coupling relationships, and difficulty in effectively integrating physical constraints. With even higher demands such as long-term predictions exceeding 48 hours, adaptation to extreme weather conditions, and multi-source data fusion, even higher requirements are typically placed on prediction stability, physical rationality, and real-time computation.

[0003] However, existing or mainstream technologies commonly employ recurrent neural networks (RNNs) for time series modeling, static graph neural networks (SNNs) for spatial relationship modeling, and partial differential equation residuals as regularization terms for physical constraints, which can lead to performance defects. RNNs suffer from low inference efficiency due to their serial computation mechanism, making it difficult to capture long-range dependencies when processing long-sequence data, and they are prone to gradient vanishing or exploding problems during training. While the Transformer architecture supports parallel computing and can capture long-range dependencies, the computational complexity of its self-attention mechanism increases quadratically with sequence length, resulting in huge computational resource consumption when processing high-frequency, long-term series data, making it difficult to meet real-time prediction requirements. Static graph neural networks assume that the dependencies between variables are constant, failing to adapt to the time-varying coupling strength between wind speed, wave period, and wave height in marine environments. Especially under extreme weather conditions such as typhoons, the interactions between variables change significantly, and static graph structures cannot accurately capture these dynamic coupling relationships. Physical constraint methods based on partial differential equation residuals only incorporate the physical equations as regularization terms into the loss function, resulting in limited constraint strength. This makes it difficult to guarantee that predictions strictly conform to ocean dynamics, easily leading to results that violate physical realities, such as negative wave heights and anomalous energy surges. Furthermore, general physical equations struggle to accurately describe the wind-wave interaction mechanisms in specific sea areas. In addition, existing data preprocessing methods are simplistic, typically only performing standardization, failing to effectively separate the variation characteristics of wave data across different time scales. This makes it difficult for models to simultaneously capture short-term fluctuations and long-term trends. The optimization strategies during model training are simplistic, prone to getting trapped in local optima, resulting in insufficient generalization ability and unstable performance across different sea area datasets. The lack of a systematic physical plausibility check mechanism in post-processing of prediction results may lead to outputs that do not conform to actual physical laws, affecting the reliability of practical applications.

[0004] Therefore, it is necessary to address the problems in existing wave height prediction technologies, such as the difficulty in balancing efficiency and accuracy in long-sequence modeling, insufficient capture of dynamic coupling relationships, and limited effectiveness of physical constraints, in order to meet the needs of the marine meteorological forecasting field for a high-precision, high-efficiency, and physically reasonable wave height prediction system. Summary of the Invention

[0005] This application provides a method and apparatus for predicting wave height based on a physical guided dynamic graph Mamba network. It adopts a selective scanning mechanism of the state-space model as a solution mechanism, thereby reconstructing the computational paradigm of time series modeling. This enables the state-space model to adaptively decide which historical information to retain and which noise to discard based on the current marine environmental characteristics, achieving time series modeling with linear computational complexity.

[0006] In a first aspect, this application provides a wave height prediction method based on a physically guided dynamic graph Mamba network, the wave height prediction method comprising:

[0007] Multivariate spatiotemporal sequence data containing wind speed, wave period, and wave height are processed using deep learning models. The dependencies between variables are modeled based on graph neural networks, and the evolution of the time series is modeled based on state-space models.

[0008] In the prediction process, prior physical knowledge is injected into graph structure learning, the coupling relationship between variables is dynamically adjusted through a data-driven mechanism, and the model prediction results are optimized through a loss function containing multiple physical constraints.

[0009] A dynamic adjacency matrix is ​​generated through a physical perception graph learner, which is configured to: construct a physical prior adjacency matrix based on ocean dynamics knowledge, learn a data-driven adjacency matrix from data through a self-attention mechanism, and fuse the physical prior adjacency matrix and the data-driven adjacency matrix through learnable gating parameters.

[0010] The time series is modeled by a selective scanning mechanism of a state-space model, in which the discretization parameters of the state-space model are dynamically adjusted according to the input features, so that the state-space model can decide which historical information to retain and which noise data to discard based on the current marine environmental characteristics.

[0011] The prediction results are optimized by a multidimensional physical constraint loss function, which includes energy conservation constraints, physical boundary constraints, and fluid smoothness constraints. The energy conservation constraints are based on the wind-wave interaction theory to limit the wave energy increment to no more than the upper limit of wind energy input. The physical boundary constraints prevent negative predictions through an exponential barrier function. The fluid smoothness constraints ensure time continuity by minimizing the second difference of the prediction sequence.

[0012] Optionally, in the physical perception graph learner, the learnable gating parameter α is a scalar parameter that is automatically optimized through backpropagation to control the contribution ratio of the physical prior adjacency matrix and the data-driven adjacency matrix. The value range of the gating parameter α is [0,1].

[0013] Optionally, the physical prior adjacency matrix is ​​constructed based on the physical principle that wind is the main source of power for ocean waves. The connection weights of wind speed nodes and other nodes are initialized to the first weight, while the connection weights of weakly correlated nodes are initialized to the second weight. The first weight is greater than the second weight.

[0014] Optionally, in the physical perception graph learner, the data-driven adjacency matrix is ​​generated through a self-attention mechanism, specifically: , ,in and Let M be the learnable node embedding matrix, and M be the unnormalized node similarity matrix.

[0015] Optionally, the weight coefficients of each constraint in the multidimensional physical constraint loss function are set based on dimensional analysis, wherein the proportional relationship between the energy conservation constraint weight λ1, the boundary constraint weight λ2, and the smoothing constraint weight λ3 is 10. -6 10 -8 10 -4 Magnitude.

[0016] Optionally, the formula for calculating the energy conservation constraint is: T is the length of the predicted sequence. Indicates time difference, Indicates the effective wave height at time t. This represents the wind speed at a depth of 10 meters above the sea surface at time t. The wind energy conversion coefficient, The value range is 0.1-0.5.

[0017] Optionally, the physical boundary constraints employ an exponential barrier function: Where T is the length of the predicted sequence, and t indicates that the current calculation is at time t in the predicted sequence. This represents the predicted effective wave height at time t. The upper limit of the wave height. It is the barrier steepness coefficient. The value range is 0.1-10; when the effective wave height prediction value When the exponential function approaches zero or a negative value, it generates a rapidly increasing loss, forming a "soft barrier" that pushes the predicted value back to the physically permissible range. .

[0018] Optionally, the total loss calculation formula for the multidimensional physical constraint loss function is as follows: ,in, It is the mean squared error loss. It is an energy constraint. It is a physical boundary constraint. It is a smoothing constraint. For energy conservation constraint weights, For boundary constraint weights, To smooth out constraint weights.

[0019] Secondly, this application provides a wave height prediction device based on a Physically Guided Dynamic Graph (Mamba) network, the wave height prediction device based on the Physically Guided Dynamic Graph (Mamba) network comprising:

[0020] The physical perception graph learning module is configured to process multivariate spatiotemporal sequence data containing wind speed, wave period, and wave height through a deep learning model, model the dependencies between variables based on graph neural networks, and model the evolution of time series based on a state space model.

[0021] The coupling processing module is configured to inject physical prior knowledge into graph structure learning during the prediction process, dynamically adjust the coupling relationship between variables through a data-driven mechanism, and optimize the model prediction results through a loss function containing multiple physical constraints.

[0022] The spatiotemporal coding module is configured to generate a dynamic adjacency matrix through a physical perception graph learner. The physical perception graph learner is configured to: construct a physical prior adjacency matrix based on ocean dynamics knowledge, learn a data-driven adjacency matrix from data through a self-attention mechanism, and fuse the physical prior adjacency matrix and the data-driven adjacency matrix through learnable gating parameters.

[0023] The physical modeling module is configured to model time series data through a selective scanning mechanism of a state-space model, wherein the discretization parameters of the state-space model are dynamically adjusted according to the input features, so that the state-space model can decide which historical information to retain and which noise data to discard based on the current marine environmental characteristics.

[0024] The physical constraint optimization module is configured to optimize the prediction results through a multidimensional physical constraint loss function. The multidimensional physical constraint loss function includes energy conservation constraints, physical boundary constraints, and fluid smoothness constraints. The energy conservation constraints are based on the wind-wave interaction theory to limit the wave energy increment to no more than the upper limit of wind energy input. The physical boundary constraints prevent negative predictions through an exponential barrier function. The fluid smoothness constraints ensure time continuity by minimizing the second difference of the prediction sequence.

[0025] Thirdly, this application provides a wave height prediction device based on a Physically Guided Dynamic Graph (Mamba) network, wherein the wave height prediction device based on the Physically Guided Dynamic Graph (Mamba) network is configured to perform the above-described wave height prediction method based on the Physically Guided Dynamic Graph (Mamba) network.

[0026] The beneficial technical effects of this application are as follows:

[0027] This application provides a wave height prediction method and apparatus based on a physics-guided dynamic graph Mamba network. It employs a selective scanning mechanism of the state-space model as a solution mechanism, thereby reconstructing the computational paradigm of time series modeling. This allows the state-space model to adaptively decide which historical information to retain and which noise to discard based on current ocean environmental characteristics, achieving time series modeling with linear computational complexity. Under rapidly changing weather conditions, the discretized parameter Δ increases, and the model focuses more on recent information; under stable conditions, the Δ value decreases, and the model retains more historical information, thus achieving both computational efficiency and improved prediction accuracy. This overcomes the technical problem of balancing efficiency and accuracy in long-sequence modeling, breaking the technical inertia of traditional techniques that require serial computation or quadratic complexity calculations. It uses a physics-aware graph learner as a solution mechanism, thereby reconstructing the method of spatial relationship modeling, overcoming the technical problem of mismatch between dynamic coupling relationships and static modeling, and breaking the technical inertia of traditional techniques that use fixed graph structures. Furthermore, it employs a multi-dimensional physical constraint loss function as a solution mechanism, thereby reconstructing the model optimization objective, overcoming the technical problem of balancing physical consistency and data-driven accuracy, and breaking the technical inertia of traditional techniques that only use general physical equations as regularization terms. Attached Figure Description

[0028] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0029] Figure 1 A flowchart illustrating a wave height prediction method based on a physically guided dynamic graph Mamba network provided in this application;

[0030] Figure 2 The block diagram of the physically guided dynamic graph mamba network model PG-DyMamba provided in this application;

[0031] Figure 3 A block diagram of the physical perception learner provided in this application;

[0032] Figure 4 The structural block diagram of the spatiotemporal Graph-Mamba encoder provided in this application;

[0033] Figure 5 MSE trends for different forecast time ranges;

[0034] Figure 6 The prediction results for the Australia and NDBC datasets within a 1-hour time frame.

[0035] Figure 7 This is a schematic diagram illustrating the trend changes of each indicator on the Australia dataset.

[0036] Figure 8 This is a schematic diagram illustrating the trend changes of each indicator on the NDBC dataset.

[0037] Figure 9 The verification results of the quasi-static test evaluation method of the shipborne marine gravimeter provided in this application on the measured data of the North China Sea Bureau;

[0038] Figure 10 A framework diagram of a wave height prediction device based on a physically guided dynamic graph Mamba network provided in this application;

[0039] Figure 11 This is a schematic diagram of the structure of an electronic device provided in this application. Detailed Implementation

[0040] To make the objectives, technical solutions, and advantages of this application clearer, the application will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0041] It should be understood that in the various embodiments of this application, the sequence number of each process does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0042] It should be understood that in this application, "comprising" and "having" and any variations thereof are intended to cover non-exclusive inclusion, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are explicitly listed, but may include other steps or units that are not explicitly listed or that are inherent to such process, method, product or device.

[0043] The technical solutions of this application will be described in detail below with specific embodiments. The following specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments.

[0044] In the technical framework of marine meteorological forecasting, wave height prediction technology primarily needs to process spatiotemporal series data containing multiple variables such as wind speed, wave period, and wave height. These variables exhibit complex nonlinear coupling relationships, and the marine environment displays highly dynamic characteristics. Existing technologies typically employ recurrent neural networks or Transformer architectures for time series modeling, static graph neural networks for spatial relationship modeling, and soft constraint methods based on partial differential equation residuals for physical constraints. Under this modular technical framework, three interrelated technical bottlenecks exist: the difficulty in balancing computational efficiency and prediction accuracy for long-sequence modeling, the mismatch between dynamic coupling relationships and static modeling, and the challenge of balancing physical consistency and data-driven accuracy.

[0045] Existing technologies suffer from several drawbacks. Firstly, time series modeling is often limited to serial or quadratic computations. While recurrent neural networks can capture time dependencies, their computational efficiency is low. Secondly, although Transformers support parallel computation, their computational complexity increases quadratically with sequence length, resulting in significant resource consumption when processing high-frequency, long-sequence ocean wave data. Thirdly, traditional graph neural networks, which assume static dependencies, fail to capture the time-varying coupling strength between wind speed, wave period, and wave height in the ocean environment, especially under extreme weather conditions such as typhoons, where interactions between variables can change significantly. Furthermore, existing physical constraint methods cannot guarantee that predictions strictly conform to ocean dynamics, easily leading to results that violate physical realities, such as negative wave heights and anomalous energy surges.

[0046] To overcome the technical challenge of balancing efficiency and accuracy in long sequence modeling, and breaking away from the traditional inertia of requiring serial or quadratic complexity calculations, this invention provides a wave height prediction method and apparatus based on a physically guided dynamic graph Mamba network. It applies the Mamba state-space model to wave prediction, using its selective scanning mechanism to efficiently model long historical sequences collected by buoys, effectively solving the problem of balancing computational efficiency and prediction accuracy in long sequence spatiotemporal modeling. A Physics-Aware Graph Learner is proposed, overcoming the limitations of traditional methods that rely on static graph structures. Considering the temporal evolution of the marine environment, the model can dynamically adjust the graph structure based on data, adaptively capturing the time-varying dependencies between meteorological variables. Combining constraints such as energy conservation, fluid smoothness, and physical boundaries, a multidimensional physical constraint loss function is designed. This significantly improves the model's robustness and physical consistency under extreme weather conditions, a key advantage in the field of physical information machine learning.

[0047] refer to Figure 1 , Figure 2 As shown, this embodiment of the invention provides a wave height prediction method based on a physically guided dynamic graph Mamba network, including:

[0048] Step 100: Process multivariate spatiotemporal sequence data containing wind speed, wave period, and wave height using a deep learning model, model the dependencies between variables based on a graph neural network, and model the evolution of the time series based on a state-space model.

[0049] The PG-DyMamba model in this embodiment of the invention adopts an end-to-end encoder-decoder framework, such as... Figure 2 As shown, the overall process can be divided into four parts: data preprocessing, graph structure learning, spatiotemporal feature encoding, and physical-guided optimization.

[0050] First, historical wave data is organized into an input tensor. Due to the inherent non-stationarity and distribution variations of wave data, the raw data undergoes VMD decomposition to separate variations across different time scales. Then, RevIN is used to standardize the data, eliminating the effects of distribution shifts. The standardized data is then projected onto a higher-dimensional feature space through a linear projection layer.

[0051] Meanwhile, the physical perception graph learner operates in parallel. On one hand, it utilizes prior relationships built upon ocean physics knowledge; on the other hand, it directly extracts node representations from input data features to capture the dynamic relationships between variables. After weighted fusion, the two generate a time-varying graph structure to characterize the dependencies between variables such as wind speed and wave height.

[0052] Next, the features are fed into the core of the model—a spatiotemporal encoder composed of multiple stacked layers. Within each layer, a sequential spatiotemporal modeling structure is employed, incorporating residual connections. First, the spatial GCN aggregates information from different variables on the generated dynamic graph structure, capturing spatial correlations, and then fuses the input features through residual connections. Subsequently, the aggregated features enter the Mamba module. This module combines one-dimensional convolution (Conv1d) and a state-space model (SSM), utilizing a gating mechanism to efficiently capture trends over long time periods. The output of Mamba is again added to the input through residual connections, completing the spatiotemporal feature update for the current layer.

[0053] In the decoding stage, the encoded features are decoded to obtain the prediction results, and then restored to the original physical scale through the inverse transform of RevIN, outputting the final wave prediction value. To ensure that the prediction results conform to the real physical laws, we incorporated a physics-guided optimization strategy during training. The final loss function not only includes the prediction error (MSE) but also incorporates physical constraints such as energy conservation, boundary constraints, and smoothness. These constraints work together to guide the model to output more reasonable and stable prediction results while maintaining accuracy.

[0054] Variational mode decomposition (VMD) is performed on the raw wave data to separate variations at different time scales. Then, reversible instance normalization (RMS) is used to standardize the data, reducing the impact of distribution shift. By employing VMD and RMS data preprocessing, the non-stationarity and distribution variation issues of wave data are addressed, further separating variation features at different time scales and reducing the impact of distribution shift. This results in more stable feature extraction and more accurate prediction.

[0055] Step 200: During the prediction process, physical prior knowledge is injected into graph structure learning, the coupling relationship between variables is dynamically adjusted through a data-driven mechanism, and the model prediction results are optimized through a loss function containing multiple physical constraints.

[0056] According to graph signal processing theory, wave prediction is essentially a typical multivariate spatiotemporal sequence prediction problem. In this invention, the ocean observation system is abstracted into a graph structure. ,in represent One physical observation variable; Edges represent interactions between variables; It is a weighted adjacency matrix, used to quantify the dependence strength between different physical variables.

[0057] set up For a moment The feature matrix is ​​given by , where D is the feature dimension. The length of the given historical backtracking window is... Our research goal is to learn a nonlinear mapping function. (in, (Represents the set of learnable parameters of the model). Utilizing the historical observation tensor. and the dynamic graph structure generated by the model To predict the future Effective wave height at time ,Right now: .

[0058] This definition differs from the traditional method in that the traditional method uses the adjacency matrix... Instead of considering static priors, this invention proposes the concept of an adaptive adjacency matrix. This matrix dynamically adjusts the dependency weights between variables through a data-driven approach, no longer limited to a fixed physical topology, thereby capturing the non-stationary coupling characteristics in the marine environment.

[0059] Step 300: Generate a dynamic adjacency matrix through a physical perception graph learner, wherein the physical perception graph learner is configured to: construct a physical prior adjacency matrix based on ocean dynamics knowledge, learn a data-driven adjacency matrix from data through a self-attention mechanism, and fuse the physical prior adjacency matrix and the data-driven adjacency matrix through learnable gating parameters.

[0060] In the physical perception graph learner of this invention, the learnable gating parameter α is a scalar parameter that is automatically optimized through backpropagation. It is used to control the contribution ratio of the physical prior adjacency matrix and the data-driven adjacency matrix, and the value range of the gating parameter α is [0,1]. By using a learnable gating parameter α, the model can automatically adjust the balance ratio of physical priors and data features according to different marine environmental conditions. This solves the problem that fixed weights in traditional methods cannot adapt to different weather conditions. Furthermore, it enhances the stability of physical prior weights during typhoon passage and enhances the accuracy of data feature weights during calm weather, thereby achieving the technical effect of adaptive optimization of prediction performance.

[0061] The physical prior adjacency matrix is ​​constructed based on the physical principle that wind is the primary source of power for ocean waves. The connection weights between wind speed nodes and other nodes are initialized to a first weight, while the connection weights of weakly correlated nodes are initialized to a second weight, with the first weight being greater than the second weight. In other words, in the physics-aware graph learner, the physical prior adjacency matrix is ​​constructed based on the physical principle that wind is the primary source of power for ocean waves, initializing the connection weights between wind speed nodes and other nodes to higher values, while initializing the connection weights of weakly correlated nodes to lower values. By adopting an initialization strategy based on the physical principle of wind-wave interaction, a reasonable initial search space is provided for model optimization, solving the problem of traditional random initialization easily getting trapped in local optima. This further accelerates model convergence and improves physical interpretability, thereby achieving better predictive performance and stronger generalization ability.

[0062] In the physics-aware graph learner, the data-driven adjacency matrix is ​​generated through a self-attention mechanism, specifically: , ,in and Let M be the learnable node embedding matrix, and M be the unnormalized node similarity matrix. By employing a self-attention mechanism to generate a data-driven adjacency matrix, the problem of traditional methods requiring a predefined fixed graph structure is solved. Furthermore, by learning node embeddings, potential dependencies between variables are automatically discovered, thereby achieving more accurate spatial relationship modeling.

[0063] The performance of graph convolutional networks largely depends on the quality of their adjacency matrices. Existing data-driven methods typically learn the graph structure from random initialization, which is not only slow to converge but also easily captures spurious correlations. To address this issue, this invention proposes a graph learning strategy that incorporates domain knowledge. The physical perception graph learner architecture of this invention is as follows: Figure 3 As shown, it mainly consists of three parts: physical prior injection, data-driven generation, and gating fusion mechanism.

[0064] Physics-based prior input: Ocean dynamics provides a clear causal graph of relationships between variables. For example, wind is the primary driving force behind wave generation. Based on this, a causal graph of relationships between variables is first constructed, such as... Figure 3 As shown on the left, it is mapped to a prior adjacency matrix. Specifically, if the variable It is a variable The direct physical driving factors, we will Set it to 1 otherwise, set it to 0. This sparse physical graph structure provides a reasonable initial search space and inductive bias for model optimization.

[0065] Adaptive generation of dynamic graphs: Although physical priors provide the basic framework, the coupling strength between variables is not constant. To capture this nonlinear, time-varying dependency, a method such as... Figure 3 The data-driven generation module shown on the right directly extracts node representations from the input features at the current time step. Through a linear mapping layer, the input feature tensor is projected into source node embeddings. Embedding the target node These are dynamic features that are generated in real time as the input data changes. Then, a self-attention mechanism is used to dynamically infer data-driven dependencies. :

[0066] ;

[0067] ;

[0068] Where M represents the unnormalized node similarity matrix. Finally, a learnable gating parameter is used. To balance physical priors and data characteristics: ;when When the size is small, the model relies more on physical priors; when When the data is large, the relationships learned from the data are given more weight. This ensures the model doesn't deviate from fundamental physical laws and can adaptively adjust the coupling strength between variables under extreme weather or abnormal sea conditions. The final result... It is sent to the GCN module to guide the propagation of information among multiple variables.

[0069] Step 400: The time series is modeled using a selective scanning mechanism of the state-space model, wherein the discretization parameters of the state-space model are dynamically adjusted according to the input features, so that the state-space model can decide which historical information to retain and which noise data to discard based on the current marine environmental characteristics.

[0070] In the selective scanning mechanism of the state-space model, the discretization parameters are dynamically generated based on the input features through linear transformation. Because of this dynamically generated discretization parameter approach, the state-space model can adaptively adjust its information retention strategy according to the current marine environmental characteristics. This solves the problem that traditional fixed parameters cannot adapt to changes at different time scales. Furthermore, it enhances recent information retention under rapidly changing weather conditions and long-term memory retention under stable conditions, thus achieving more accurate temporal evolution modeling. In the selective scanning mechanism of the state-space model, when the input features contain high-frequency changing components, the discretization parameters... The value of increases, causing the state-space model to focus more on recent information; when the input features change steadily, the discretization parameter... Decreasing the value of allows the state-space model to retain more historical information. Adaptively adjusting the discretization parameters based on the changing characteristics of the input features solves the problem of traditional state-space models using the same retention strategy for all time scales. This further enhances the sensitivity to recent information under rapidly changing conditions and strengthens the ability to capture long-term trends under stable conditions, thus achieving more accurate time series modeling results.

[0071] like Figure 4 As shown, the Graph-Mamba layer mainly consists of a GCN module and a Mamba module connected in series, responsible for feature extraction in the spatial and temporal dimensions, respectively. Traditional RNN models are difficult to parallelize when processing long sequences, but the computational complexity of the Transformer is... This limits the Transformer's ability to process long-term historical data. To address this issue, this invention introduces the state-space model Mamba and builds a spatiotemporal encoder based on it. The computational complexity of this structure is O(n log n). It can process long sequence data more efficiently.

[0072] Spatial Feature Aggregation: To simulate the transfer of ocean energy between different physical variables, this embodiment of the invention uses graph convolutional (GCN) operations in each encoder layer. Input features are first normalized by the layers, and then based on the generated dynamic graph... Perform graph convolution operations. To facilitate gradient flow, this embodiment of the invention employs a residual connection structure. The spatial aggregation process of layers can be represented as:

[0073] ;

[0074] in, This represents the output features of the previous layer. It is a learnable weight matrix. It is an activation function. Each node in this process can aggregate the features of its neighboring nodes, achieving the fusion of multivariate information.

[0075] Temporal Evolution Based on Mamba: Obtaining Spatial Features Subsequently, this embodiment of the invention uses the Mamba module to capture the changing patterns in the time dimension. To process all observation nodes in parallel, this embodiment of the invention will... Remodeling In the form of. For example... Figure 4 As shown, the input features are first normalized by a layer, and then local contextual features are extracted through one-dimensional convolution before entering the core SSM layer. The core of Mamba is the Selective Scan mechanism, whose mathematical form is based on the Continuous State-Space Equation (SSM):

[0076] ;

[0077] ;

[0078] in, Let be the input features at time t. For implicit state variables, For output features, It is the state evolution matrix. and These are the projection matrices of the input and output, respectively. To perform computations on discrete time-series data, Mamba discretizes the above continuous equation using a time-scale parameter:

[0079] ;

[0080] ;

[0081] in, and These are the discretized transfer parameters. It is an identity matrix.

[0082] Finally, the output of the SSM is multiplied by the gated branch and connected via residuals to output the final feature tensor. Unlike traditional SSM, the parameters are discretized in Mamba. and projection matrix and It is no longer fixed, but depends on the input. Dynamic adjustments are made. This allows the model to determine which historical information to retain and which noise to discard based on the current characteristics of the ocean environment. This not only achieves efficient linear computation but also meets the need to remember key historical events during wave evolution.

[0083] Step 500: Optimize the prediction results using a multidimensional physical constraint loss function, which includes energy conservation constraints, physical boundary constraints, and fluid smoothness constraints. The energy conservation constraints are based on the wind-wave interaction theory to limit the wave energy increment to no more than the upper limit of wind energy input. The physical boundary constraints prevent negative predictions through an exponential barrier function. The fluid smoothness constraints ensure time continuity by minimizing the second difference of the prediction sequence.

[0084] The weight coefficients of each constraint in the multidimensional physical constraint loss function are set based on dimensional analysis. Among them, the proportional relationship between the weights of energy conservation constraints (λ1), boundary constraints (λ2), and smoothing constraints (λ3) is 10. -6 10 -8 10 -4 Scale. By adopting a weighting coefficient setting strategy based on dimensional analysis, the problem of training instability caused by excessive differences in the numerical scale of different physical constraints is solved. This further balances the relationship between prediction accuracy and physical consistency, avoids a single constraint from dominating the training process, and thus achieves a technical effect of stable convergence and balanced optimization results.

[0085] The formula for calculating the energy conservation constraint is: T is the length of the predicted sequence. Indicates time difference, Indicates the effective wave height at time t. This represents the wind speed at a depth of 10 meters above the sea surface at time t. The wind energy conversion coefficient, The value range is 0.1-0.5. Setting a reasonable range for the wind energy conversion coefficient γ solves the problem of unstable training caused by improper physical parameter settings in the energy conservation constraint. Furthermore, when the value of γ is too large, the constraint is too strong and may limit the model's fitting ability, while when the value of γ is too small, the constraint is too weak and cannot guarantee physical consistency. A balance is achieved by using a reasonable range of 0.1-0.5, thereby achieving a stable and effective physical constraint technique.

[0086] The physical boundary constraints employ an exponential barrier function: Where T is the length of the predicted sequence, and t indicates that the current calculation is at time t in the predicted sequence. This represents the predicted effective wave height at time t. The upper limit of the wave height. It is the barrier steepness coefficient. The value range is 0.1-10; when the effective wave height prediction value When the exponential function approaches zero or a negative value, it generates a rapidly increasing loss, forming a "soft barrier" that pushes the predicted value back to the physically permissible range. Set the parameters of the exponential barrier function within a reasonable range. This solves the balance problem between the effect of soft boundary constraints and training stability, and further... When the value is too small, the constraint effect is insufficient and it cannot effectively prevent negative value prediction. When the value is too large, the gradient changes too drastically, leading to unstable training. A reasonable range of 0.1-10 is used to achieve a balance, thereby achieving an effective and stable boundary constraint technique.

[0087] The formula for calculating the total loss of the multidimensional physical constraint loss function is as follows: ,in, It is the mean squared error loss. It is an energy constraint. It is a physical boundary constraint. It is a smoothing constraint. For energy conservation constraint weights, For boundary constraint weights, To smooth out the constraint weights, multidimensional physical constraints are combined with traditional mean squared error loss, solving the problem that a single loss function cannot simultaneously consider prediction accuracy and physical consistency. Furthermore, multi-objective optimization is achieved through weighted combination, which forces the model to obey physical laws while ensuring prediction accuracy, thus achieving a technical effect that balances accuracy and physical consistency.

[0088] Deep learning models are often considered "black boxes," and their predictions often lack physical explanation and may violate basic physical laws such as energy conservation. To improve the credibility of the model in scientific computing, inspired by the idea of ​​PINN

[31] , we designed a composite loss function that combines three physical constraints:

[0089] ;in, , , It is a non-negative tradeoff coefficient used to balance the order-of-magnitude difference between data-driven loss and physical constraint terms, and to adjust the constraint strength of physical rules on model optimization. It is the mean squared error loss. It is an energy constraint. It is a physical boundary constraint. It is a smoothing constraint.

[0090] Wave growth and decay follow an energy balance, according to the wind-wave interaction theory, wave energy density. It is proportional to the square of the significant wave height ( The growth rate will be limited by the energy provided by the wind farm. To prevent the model from predicting unreasonable physical phenomena, this embodiment of the invention defines an energy penalty term (energy conservation constraint): Where T is the length of the predicted sequence. Indicates time difference, Indicates the effective wave height at time t. This represents the wind speed at a depth of 10 meters above the sea surface at time t. It should be noted that for observational datasets that do not include meteorological driving variables (such as wind speed), since the upper limit of wind energy input cannot be calculated, we reduce the weight of this constraint during training. Set to 0 to retain only smoothness and boundary constraints. When the increment of wave energy exceeds the physical upper limit of wind energy input, a gradient penalty is applied, forcing the model to learn the correct wind-wave energy transfer mechanism.

[0091] Significant wave height is a non-negative physical quantity, but traditional regression models may predict negative values ​​when there are numerical oscillations. If a simple cutoff is used, such as ReLU, the gradient will vanish near zero, making it difficult for the model to self-correct. To solve this problem, an exponential term is introduced. A "soft barrier" was constructed, with physical boundary constraints as follows: Where T is the length of the predicted sequence, and t indicates that the current calculation is at time t in the predicted sequence. This represents the predicted effective wave height at time t. The upper limit of the wave height. It is the kurtosis coefficient of the potential barrier. When the predicted value of the significant wave height approaches 0 or is negative, the exponential function will generate a rapidly increasing loss, forming a "soft barrier" that pushes the predicted value back to the physically permissible range. .

[0092] Considering the inertia and viscosity of seawater, the change in wave height should be smooth. To suppress high-frequency noise and non-physical oscillations, a second-order difference of the prediction sequence is minimized, forming an object smoothness constraint: This constraint term is essentially an application of Tikhonov regularization to time series. From a physical perspective, seawater is a fluid with mass and inertia; according to Newton's second law, its state change cannot occur abruptly in an extremely short time. The second-order difference term in the formula... Mathematically, this term approximates the second derivative over continuous time, reflecting the "acceleration" of wave height changes. Minimizing this term effectively suppresses high-frequency jitter, a common phenomenon in deep learning models, and avoids violent oscillations that do not conform to physical laws. Ultimately, this constraint ensures the smoothness and continuity of the prediction curve in the time dimension, making the results more consistent with real fluid dynamics characteristics.

[0093] When the predicted value exceeds the physically permissible range, a truncation operation restricts the predicted value to the range [0, H_max], where H_max is the maximum significant wave height threshold determined based on historical data statistics. Adding a post-processing step to the prediction results addresses the issue of the model potentially outputting non-physical values ​​under extreme conditions. Furthermore, the truncation operation ensures that the final output conforms to physical reality, avoiding unreasonable predictions in practical applications and achieving a more reliable prediction system. The learnable gating parameter α is adaptively adjusted according to marine environmental conditions. Under typhoon conditions, the α value decreases to enhance the weight of physical priors, while under calm and stable weather conditions, the α value increases to enhance the weight of data features. Adaptively adjusting the gating parameter α according to marine environmental conditions solves the problem that fixed gating parameters cannot adapt to changes in different weather conditions. This further enhances the stability of physical priors under extreme weather conditions and improves the accuracy of data-driven predictions under normal conditions, thus achieving a more robust prediction performance.

[0094] This invention differs from existing technologies that rely on static graph structures to capture time-varying coupling relationships. It cleverly utilizes prior knowledge of ocean dynamics, employing a physical-aware graph learner to fuse physical priors with data-driven features, thus solving the problem of balancing computational efficiency and prediction accuracy in long-sequence modeling. By dynamically adjusting discretization parameters through a selective scanning mechanism in the state-space model, it overcomes the low efficiency of traditional RNN serial computation and the high complexity of Transformer quadratic computation. Furthermore, through a multi-dimensional physical constraint loss function, it addresses the issue of purely data-driven models outputting results that violate physical laws. In 48-hour long-term predictions, it further reduces MSE by approximately 29.7% compared to the basic Mamba model, and R... 2 The value was increased from 0.6467 to 0.7220, achieving better stability and physical consistency.

[0095] To verify the technical effects of the embodiments of the present invention, experiments were conducted on three publicly available datasets with different geographical and climatic characteristics: the Australian dataset (collected from Gold Coast buoys in 2021-2022), the NDBC dataset (2020 and 2023), and the North Sea dataset (provided by the North Sea Forecasting and Disaster Reduction Center of the Ministry of Natural Resources, 2022).

[0096] All experiments were conducted on a Linux server environment equipped with an NVIDIA GeForce RTX 3080 GPU. The model input length was 48, and evaluation was performed at multiple prediction step sizes ranging from 1 to 48. The AdamW optimizer was used during training with an initial learning rate of 0.0005, weight decay of 0.01, and cosine annealing scheduling. The batch size was set to 64. Specifically, the model employed a dual loss function incorporating MSE physics constraints to ensure the physical consistency of the predictions.

[0097] To avoid excessively large numerical discrepancies between the data-driven term (MSE) and the physical constraint term in the loss function, weighting coefficients for each term were empirically set based on dimensional analysis. Specifically, the wind energy input term is proportional to the cube of the wind speed (…). Its value is usually in The magnitude is [missing information], while the normalized MSE loss is typically [missing information]. Order of magnitude. To eliminate this approximately 10... 6 With a difference of several times, we will adjust the weight of energy constraints. Set as .

[0098] For boundary constraint weights and smoothing constraint weights Considering that they are auxiliary regularization terms, in order not to affect the learning of the main task, they are set to... and To find a balance between physical consistency and prediction accuracy.

[0099] To comprehensively evaluate the performance of the PG-DyMamba model provided in this embodiment of the invention under different prediction step sizes, four commonly used statistical metrics were used, which can be divided into two categories: error measurement and goodness of fit.

[0100] Error metrics: Mean squared error (MSE) and mean absolute error (MAE) are used to measure the difference between predicted and true values. MSE is more sensitive to outliers and reflects the stability of the model; MAE visually displays the average level of prediction error. In addition, we have included mean absolute relative error (MARE) to assess the proportion of prediction bias relative to the true wave height.

[0101] Goodness of fit: using the coefficient of determination To evaluate the model's ability to fit the trend of wave height changes. The closer the value is to 1, the more accurately the model can capture the temporal fluctuation pattern of the effective wave height.

[0102] In the ablation experiments, the main focus was on the impact of model structural changes on predictive stability and trend fitting ability; therefore, MSE, MAE, and As an evaluation metric, in the comparative experiments, since the sea state and wave height magnitudes corresponding to different datasets are different, using only the absolute error metric may not be comprehensive enough. Therefore, we additionally introduce MARE to measure the relative prediction error of the model at different scales, so as to more fairly evaluate the model's generalization ability.

[0103] The formula for calculating the above indicators is as follows:

[0104] ;

[0105] ;

[0106] ;

[0107] ;

[0108] in, The total number of test samples, and Representing time respectively The actual value and the predicted value, This represents the mean of the true values.

[0109] To more clearly analyze the role of each module of PG-DyMamba provided by the method of this invention embodiment, and to verify the actual effect of the physical guidance strategy in complex marine environments, a systematic ablation experiment was conducted on the model. This invention designed three progressively advanced model versions for comparative analysis, where Mamba-Base serves as the base model, DyMamba adds a physical perception map learning module to the base model, and PG-DyMamba is the complete model provided by this invention embodiment.

[0110] The experimental results for different prediction step sizes are shown in Table 1. MSE and The visualization results of the changing trends are as follows Figure 5 As shown.

[0111] Table 1: Experimental results under different prediction step sizes

[0112]

[0113] By comparing the three model variants—Mamba-Base, DyMamba, and PG-DyMamba—the following conclusions can be drawn:

[0114] (1) Advantages of spatial modeling using dynamic graph mechanisms

[0115] Unlike Mamba-Base, which focuses only on temporal features, DyMamba, with its dynamic graph module, achieved performance improvements across all prediction steps. Particularly in short-term predictions (Horizon 1), the MSE decreased from 0.0132 to 0.0098, a reduction of 25.7%. This indicates that wave evolution is not only influenced by historical conditions but also closely related to physical factors such as wind speed and wave period. The dynamic graph module successfully captures the interrelationships between these variables, thus significantly improving the model's performance.

[0116] (2) The decisive role of physical constraints in medium-term forecasting

[0117] With the addition of physical constraints, PG-DyMamba achieved its best performance. The effect of physical constraints was particularly evident in mid-term predictions (Horizon 6): compared to DyMamba, PG-DyMamba's R² improved from 0.9051 to 0.9298. This indicates that, in the stage where short-term memory gradually fades and long-term chaotic effects have not yet become dominant, physical conservation laws corrected the non-physical biases of purely data-driven models.

[0118] (3) Robustness and resistance to decay in long-term prediction

[0119] As the prediction step size increases, the performance of Mamba-Base drops sharply (R² is only 0.6467 at Horizon 48), indicating that its error gradually accumulates. In contrast, PG-DyMamba maintains a higher R² (0.7220) at Horizon 48, and its MSE is reduced by approximately 29.7% compared to Mamba-Base. This demonstrates that physical constraints not only serve a regularization function but also improve the long-term stability and robustness of the model by limiting the search range of the state space and preventing model divergence during long-sequence predictions.

[0120] To verify the effectiveness of the wave height prediction method based on a physically guided dynamic graph Mamba network according to an embodiment of the present invention, it was compared with two types of baseline models: one type is a general time series prediction model, including Informer, Autoformer, and Reformer; the other type is a specialized model optimized for wave prediction, including SWH-CLSTM, Wave-S2S, SWH-Trans, ATL-Net, and the latest MFET. The prediction results for the two datasets are as follows: Figure 6 As shown.

[0121] Table 2: MSE, MAE, and MARE results of each model on the Australia dataset with different prediction step sizes.

[0122]

[0123] Table 3: MSE, MAE, and MARE results of each model on the NDBC dataset with different prediction step sizes.

[0124]

[0125] From Table 2, Table 3 and Figure 7 as well as Figure 8 Experimental results show that our model has a significant advantage in prediction error compared to traditional RNN-type models (such as SWH-CLSTM and Wave-S2S). This is mainly due to the more efficient sequence modeling capability of the Mamba structure. Compared with general Transformer-based models (such as Informer and Autoformer), PG-DyMamba performs better in long sequence prediction. Especially on the Australia dataset, its MSE is significantly lower than that of Autoformer. This indicates that the dynamic graph structure designed for ocean data is more suitable for characterizing the spatiotemporal relationships of waves than general self-attention mechanisms.

[0126] In short-term prediction (Horizon 1–6h), PG-DyMamba demonstrates strong ability to extract key features. Taking the Australia dataset as an example, its MSE is 0.0156 in Horizon 6, significantly outperforming most general-purpose models. In Horizon 1, PG-DyMamba's MSE further decreases to 0.0065, also outperforming methods such as MFET.

[0127] However, at extremely short timescales such as H=1 and H=2, PG-DyMamba's error is slightly higher than some purely data-driven Transformer models, such as SWH-Trans. We believe this is due to the influence of physical constraints. In such ultra-short-term predictions, the data often contains a lot of noise, and pure data models can gain an advantage by fitting these local fluctuations. But PG-DyMamba is constrained by physical rules and cannot arbitrarily fit these "jitters," so its local accuracy is slightly lower.

[0128] This limitation actually proved beneficial when the prediction step size increased. Figure 7 and Figure 8 As can be seen, the performance of most baseline models declines rapidly with increasing step size, especially Autoformer and Wave-S2S. This is typically because pure data models are prone to error accumulation during repeated predictions. In contrast, the PG-DyMamba curve is more stable. At Horizon 48, its MSE is 0.1217, approximately 19.2% lower than the suboptimal MFET model. This indicates that PG-DyMamba is more stable in long-term predictions. This stability is mainly due to the inclusion of physical constraints; PG-DyMamba requires predictions to satisfy physical laws such as energy conservation and smooth changes, thus preventing numerical divergence over time and making long-term predictions more consistent with real ocean changes.

[0129] On the more complex NDBC dataset, the dynamic graph mamba network PG-DyMamba of this invention still maintains good performance, showing a significant advantage in the MARE metric. This demonstrates that the model is not only suitable for relatively stable sea areas, but also can cope with wave fluctuations caused by drastic wind field changes, reflecting the model's strong generalization ability and practical application potential.

[0130] In addition to its excellent performance on public datasets, the practical application value of PG-DyMamba was further evaluated on the North China Sea Bureau dataset. Validation on the North China Sea Bureau's measured data is as follows: Figure 9 As shown, the model achieves MSE 0.0111 and The high-precision prediction of 0.9226 indicates that, thanks to physical constraints and dynamic graph mechanisms, PG-DyMamba can still accurately capture wind-wave coupling characteristics under complex sea conditions influenced by monsoons and with limited samples, demonstrating strong robustness and verifying its practical deployment potential in China's offshore engineering.

[0131] This invention presents a wave height prediction method based on a physics-guided dynamic graph Mamba network (PG-DyMamba). The PG-DyMamba network addresses two core issues in significant wave height prediction: the difficulty of long-term dependency modeling and the lack of physical consistency. By combining the Mamba architecture's state-space selection mechanism with a physics-aware graph learner, the model can track the temporal evolution of long sequences and adaptively simulate the dynamic coupling relationship between multivariate meteorological and oceanographic elements. Multidimensional constraints such as energy conservation, fluid smoothness, and physical boundaries are introduced into the loss function to ensure that the prediction results conform to the fundamental laws of ocean dynamics. The PG-DyMamba framework, based on a linear complexity design using a selective scanning mechanism, exhibits superior stability compared to the Transformer in long-sequence modeling. This characteristic aligns with the continuous temporal variation of ocean dynamic processes, indicating the potential of using this state-space model to analyze time-series data in the physical domain.

[0132] Based on the same inventive concept, and referring to Figure 10 As shown in the illustration, this application also provides a wave height prediction device based on a physically guided dynamic graph Mamba network, comprising:

[0133] The physical perception graph learning module 101 is configured to process multivariate spatiotemporal sequence data containing wind speed, wave period and wave height through a deep learning model, model the dependencies between variables based on graph neural networks, and model the evolution of time series based on state space models.

[0134] The coupling processing module 102 is configured to inject physical prior knowledge into graph structure learning during the prediction process, dynamically adjust the coupling relationship between variables through a data-driven mechanism, and optimize the model prediction results through a loss function containing multiple physical constraints.

[0135] The spatiotemporal coding module 103 is configured to generate a dynamic adjacency matrix through a physical perception graph learner. The physical perception graph learner is configured to: construct a physical prior adjacency matrix based on ocean dynamics knowledge, learn a data-driven adjacency matrix from data through a self-attention mechanism, and fuse the physical prior adjacency matrix and the data-driven adjacency matrix through learnable gating parameters.

[0136] The physical modeling module 104 is configured to model time series through a selective scanning mechanism of a state-space model, wherein the discretization parameters of the state-space model are dynamically adjusted according to the input features, so that the state-space model can decide which historical information to retain and which noise data to discard based on the current marine environmental characteristics.

[0137] The physical constraint optimization module 105 is configured to optimize the prediction results through a multidimensional physical constraint loss function. The multidimensional physical constraint loss function includes energy conservation constraints, physical boundary constraints, and fluid smoothness constraints. The energy conservation constraints limit the wave energy increment to no more than the upper limit of wind energy input based on the wind-wave interaction theory. The physical boundary constraints prevent negative predictions through an exponential barrier function. The fluid smoothness constraints ensure time continuity by minimizing the second difference of the prediction sequence.

[0138] Thirdly, this application provides a wave height prediction device based on a Physically Guided Dynamic Graph (Mamba) network, wherein the wave height prediction device based on the Physically Guided Dynamic Graph (Mamba) network is configured to perform the above-described wave height prediction method based on the Physically Guided Dynamic Graph (Mamba) network.

[0139] It should be noted that the division of the various modules in the above device is merely a logical functional division. In actual implementation, they can be fully or partially integrated into a single physical entity, or they can be physically separated. Furthermore, these modules can be implemented entirely in software via processing element calls; they can be fully implemented in hardware; or some modules can be implemented by processing element calls to software, while others are implemented in hardware. Additionally, these modules can be fully or partially integrated together, or implemented independently. The processing element mentioned here can be an integrated circuit with signal processing capabilities. In the implementation process, each step of the above method or each of the above modules can be completed through the integrated logic circuits in the hardware of the processor element or through software instructions.

[0140] Figure 11 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Figure 9 As shown, the electronic device may include: a processor 21, a memory 22, and computer program instructions stored in the memory 22 and executable on the processor 21. When the processor 21 executes the computer program instructions, it implements a wave height prediction method based on a physically guided dynamic graph Mamba network provided in any of the foregoing embodiments.

[0141] Optionally, the various components of the electronic device can be connected via a system bus.

[0142] The memory 22 can be a separate memory unit or a memory unit integrated into the processor. The number of processors can be one or more.

[0143] Optionally, the electronic device may also include a communication interface for interacting with other devices.

[0144] It should be understood that the processor 21 can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), etc. A general-purpose processor can be a microprocessor or any conventional processor. The steps of the method disclosed in this application can be directly manifested as being executed by a hardware processor, or executed by a combination of hardware and software modules within the processor.

[0145] The system bus can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. The system bus can be divided into address bus, data bus, control bus, etc. For ease of representation, only one thick line is used in the diagram, but this does not indicate that there is only one bus or one type of bus. Memory may include random access memory (RAM) and may also include non-volatile memory (NVM), such as at least one disk storage device.

[0146] All or part of the steps of the above method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a readable memory. When the program is executed, it performs the steps of the above method embodiments; and the aforementioned memory (storage medium) includes: read-only memory (ROM), RAM, flash memory, hard disk, solid-state drive, magnetic tape, floppy disk, optical disk, and any combination thereof.

[0147] The electronic device provided in this application embodiment can be used to execute a wave height prediction method based on a physical guided dynamic graph Mamba network provided in any of the above method embodiments. Its implementation principle and technical effect are similar, and will not be described again here.

[0148] This application provides a computer-readable storage medium storing computer-executable instructions. When these instructions are executed on a computer, the computer performs the aforementioned quasi-static test evaluation method for a shipborne marine gravimeter.

[0149] The aforementioned computer-readable storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory, electrically erasable programmable read-only memory, erasable programmable read-only memory, programmable read-only memory, read-only memory, magnetic storage, flash memory, magnetic disk, or optical disk. The readable storage medium can be any available medium accessible to a general-purpose or special-purpose computer.

[0150] Optionally, a readable storage medium can be coupled to the processor, enabling the processor to read information from and write information to the readable storage medium. Alternatively, the readable storage medium can be an integral part of the processor. The processor and the readable storage medium can reside in an Application Specific Integrated Circuit (ASIC). Alternatively, the processor and the readable storage medium can exist as discrete components in the device.

[0151] It should be understood that this application is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of this application is limited only by the appended claims.

Claims

1. A wave height prediction method based on a physically guided dynamic graph Mamba network, characterized in that, The wave height prediction method includes: Multivariate spatiotemporal sequence data containing wind speed, wave period, and wave height are processed using deep learning models. The dependencies between variables are modeled based on graph neural networks, and the evolution of the time series is modeled based on state-space models. In the prediction process, prior physical knowledge is injected into graph structure learning, the coupling relationship between variables is dynamically adjusted through a data-driven mechanism, and the model prediction results are optimized through a loss function containing multiple physical constraints. A dynamic adjacency matrix is ​​generated through a physical perception graph learner, which is configured to: construct a physical prior adjacency matrix based on ocean dynamics knowledge, learn a data-driven adjacency matrix from data through a self-attention mechanism, and fuse the physical prior adjacency matrix and the data-driven adjacency matrix through learnable gating parameters. The time series is modeled by a selective scanning mechanism of a state-space model, in which the discretization parameters of the state-space model are dynamically adjusted according to the input features, so that the state-space model can decide which historical information to retain and which noise data to discard based on the current marine environmental characteristics. The prediction results are optimized by a multidimensional physical constraint loss function, which includes energy conservation constraints, physical boundary constraints, and fluid smoothness constraints. The energy conservation constraints are based on the wind-wave interaction theory to limit the wave energy increment to no more than the upper limit of wind energy input. The physical boundary constraints prevent negative predictions through an exponential barrier function. The fluid smoothness constraints ensure time continuity by minimizing the second difference of the prediction sequence.

2. The wave height prediction method according to claim 1, characterized in that: In the physical perception graph learner, the learnable gating parameter α is a scalar parameter that is automatically optimized through backpropagation. It is used to control the contribution ratio of the physical prior adjacency matrix and the data-driven adjacency matrix. The value range of the gating parameter α is [0,1].

3. The wave height prediction method according to claim 2, characterized in that: The physical prior adjacency matrix is ​​constructed based on the physical principle that wind is the main source of power for ocean waves. The connection weights between wind speed nodes and other nodes are initialized to the first weight, while the connection weights of weakly correlated nodes are initialized to the second weight. The first weight is greater than the second weight.

4. The wave height prediction method according to claim 2, characterized in that: In the physical perception graph learner, the data-driven adjacency matrix is ​​generated through a self-attention mechanism, specifically: , ,in, and Let M be the learnable node embedding matrix, and M be the unnormalized node similarity matrix. This is a data-driven dependency.

5. The wave height prediction method according to claim 1, characterized in that: The weight coefficients of each constraint in the multidimensional physical constraint loss function are set based on dimensional analysis. The proportional relationships between the energy conservation constraint weight λ1, the boundary constraint weight λ2, and the smoothing constraint weight λ3 are as follows: Magnitude.

6. The wave height prediction method according to claim 5, characterized in that: The formula for calculating the energy conservation constraint is as follows: , It is an energy constraint, where T is the length of the predicted sequence. Indicates time difference, Indicates the effective wave height at time t. This represents the wind speed at a depth of 10 meters above the sea surface at time t. The wind energy conversion coefficient, The value range is 0.1-0.

5.

7. The wave height prediction method according to claim 6, characterized in that: The physical boundary constraints employ an exponential barrier function: ,in, These are physical boundary constraints, where T is the length of the prediction sequence, and t indicates that the current calculation is at time t in the prediction sequence. This represents the predicted effective wave height at time t. The upper limit of the wave height. It is the barrier steepness coefficient. The value range is 0.1-10; when the effective wave height prediction value When the exponential function approaches zero or a negative value, it generates a rapidly increasing loss, forming a "soft barrier" that pushes the predicted value back to the physically permissible range. .

8. The wave height prediction method according to claim 7, characterized in that: The formula for calculating the total loss of the multidimensional physical constraint loss function is as follows: ,in, It is the mean squared error loss. It is an energy constraint. It is a physical boundary constraint. It is a smoothing constraint. For energy conservation constraint weights, For boundary constraint weights, To smooth out constraint weights.

9. A wave height prediction device based on a physically guided dynamic graph Mamba network, characterized in that, The wave height prediction device based on the physical guided dynamic graph Mamba network includes: The physical perception graph learning module is configured to process multivariate spatiotemporal sequence data containing wind speed, wave period, and wave height through a deep learning model, model the dependencies between variables based on graph neural networks, and model the evolution of time series based on a state space model. The coupling processing module is configured to inject physical prior knowledge into graph structure learning during the prediction process, dynamically adjust the coupling relationship between variables through a data-driven mechanism, and optimize the model prediction results through a loss function containing multiple physical constraints. The spatiotemporal coding module is configured to generate a dynamic adjacency matrix through a physical perception graph learner. The physical perception graph learner is configured to: construct a physical prior adjacency matrix based on ocean dynamics knowledge, learn a data-driven adjacency matrix from data through a self-attention mechanism, and fuse the physical prior adjacency matrix and the data-driven adjacency matrix through learnable gating parameters. The physical modeling module is configured to model time series data through a selective scanning mechanism of a state-space model, wherein the discretization parameters of the state-space model are dynamically adjusted according to the input features, so that the state-space model can decide which historical information to retain and which noise data to discard based on the current marine environmental characteristics. The physical constraint optimization module is configured to optimize the prediction results through a multidimensional physical constraint loss function. The multidimensional physical constraint loss function includes energy conservation constraints, physical boundary constraints, and fluid smoothness constraints. The energy conservation constraints are based on the wind-wave interaction theory to limit the wave energy increment to no more than the upper limit of wind energy input. The physical boundary constraints prevent negative predictions through an exponential barrier function. The fluid smoothness constraints ensure time continuity by minimizing the second difference of the prediction sequence.

10. A wave height prediction device based on a physically guided dynamic graph Mamba network, characterized in that, The wave height prediction device based on a physical guided dynamic graph Mamba network is configured to perform the wave height prediction method based on a physical guided dynamic graph Mamba network as described in any one of claims 1 to 8.

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