Regional sea wave forecasting method based on single-point buoy observation and graph neural network

Abstract

This application discloses a regional wave forecasting method based on single-point buoy observations and graph neural networks, belonging to the field of marine environmental forecasting. It innovatively proposes a solution based on graph neural networks (GNNs) and a MeshGraphNet model fused with single-point buoy observations to significantly improve the efficiency, accuracy, and timeliness of significant wave height forecasting. Specifically, the observation sequences from a single buoy station are used to extract temporal features and generate short-term forecasts via an LSTM network. The forecast results output by the LSTM, along with ERA5 spatial wind field features, are then used as node features in a spatial graph neural network. The encoder of the graph neural network encodes the node wind field features and edge geometric features into a multi-dimensional latent space. This space is then updated via a message passing layer, involving edge updates, node aggregation, and global state updates to fuse local neighborhood information with the global sea area state. Finally, the decoder outputs the significant wave height at the forecast time.

Description

Technical Field

[0001] This application relates to the field of marine environmental forecasting, specifically proposing a regional wave forecasting method based on single-point buoy observation and graph neural networks. Background Technology

[0002] Ocean wave forecasting is a key technology in fields such as marine engineering, shipping safety, and disaster prevention and mitigation. Existing numerical wave forecasting methods, such as WAVEWATCH III and SWAN, are based on physical equations and have high computational complexity. They also depend on the accuracy of initial and boundary conditions. Fine-grained forecasts (spatial resolution from meters to hundreds of meters) for local sea areas often take several hours to complete a forecast for the next 7-10 days.

[0003] Currently, data-driven machine learning methods offer new solutions for wave forecasting, such as convolutional neural networks (CNNs) or recurrent neural networks (RNNs) based on regular grids. However, these methods struggle to effectively handle the unstructured and irregularly distributed station / grid point data commonly found in ocean monitoring. Existing, more effective techniques are spatiotemporal prediction models based on graph neural networks (GNNs), such as the "MeshGraphNet" architecture proposed by the DeepMind team (see references: PWBattaglia et al., "Relational inductive biases, deep learning, and graphnetworks", arXiv:1806.01261, 2018; and JB Ham et al., "Learning to Simulate Complex Physics with Graph Networks", arXiv:2002.09405, 2020).

[0004] DeepMind's MeshGraphNet uses graph neural networks (GNNs) for fluid simulations. Its core is building a graph on a triangular mesh and fusing neighborhood information through message passing. However, GNNs have significant limitations in wave forecasting. Specifically: they are only validated on ideal fluid / simple scenarios, including tests on physical simulations such as flow around a cylinder and ball collisions, but not on real ocean wave data; they fail to incorporate ocean observation conditions, with many wave forecasting models driven solely by wind fields, ignoring crucial observational data in ocean forecasting; and they lack operational design methods, such as not considering practical operational constraints like sparse observations (e.g., single-point buoys).

[0005] Therefore, while existing GNN technology has potential, it has not yet been effectively integrated with the operational needs of wave forecasting. In view of this, this application is hereby submitted. Summary of the Invention

[0006] This application proposes a regional wave forecasting method based on single-point buoy observations and graph neural networks. It aims to overcome the technical difficulties of existing technologies, which rely on regularized reanalysis grid data as input and do not deeply couple real-time observation data. The innovative approach is based on graph neural networks (GNNs) and integrates a MeshGraphNet model from single-point buoy observations. This fills the gap in existing technologies and significantly improves the efficiency, accuracy, and timeliness of significant wave height (Hs) forecasting.

[0007] To achieve the above-mentioned objectives, the regional wave forecasting method based on single-point buoy observation and graph neural network proposed in this application extracts time-series features and performs short-term forecasting from the observation sequence of a single buoy station through an LSTM network. Then, the forecasting results output by the LSTM and the ERA5 spatial wind field features are used together as node features of the spatial graph neural network.

[0008] The encoder of the graph neural network encodes the wind field features of nodes and the geometric features of edges into a multidimensional latent space. The message passing layer performs edge updates, node aggregation, and global state updates to fuse local neighborhood information with the global sea state. Finally, the decoder outputs the effective wave height for the forecast time.

[0009] Furthermore, in the messaging layer, single-point buoy data affects adjacent nodes.

[0010] The regional wave forecasting method based on single-point buoy observations and graph neural networks includes the following steps:

[0011] Step (1): Problem modeling and data preprocessing;

[0012] Step (2): Model using LSTM;

[0013] To provide time series forecast results for a single site, a Long Short-Term Memory (LSTM) network is used to model the significant wave height sequence of the site, which is then used to output the single-point forecast value at the target time.

[0014] Step (3), graph neural network processing;

[0015] Step (3.1): Input features and single-point condition constraints;

[0016] The effective wave height at the forecast time is driven by the wind field sequence, and conditional information from a single site is introduced as an external constraint.

[0017] Single-point condition information is provided by LSTM for the station sequence. The predicted value for time is denoted as ,Should The predicted values ​​at each time point are used as conditional inputs in the graphical model and injected with the same value at each node, thereby imposing a consistent constraint on the overall prediction.

[0018] For any node The node input features consist of historical wind field, current wind field, and single-point conditional parameters, expressed as follows: ;

[0019] in, The wind vector at the node is 10 meters.

[0020] Step (3.2), edge attribute construction;

[0021] Edge attributes are constructed based on the two-dimensional position coordinates of grid nodes; for any pair of adjacent nodes... Set nodes The two-dimensional position coordinates are ,node The two-dimensional position coordinates are ,in and These are the orthogonal coordinate components of the node in the local Cartesian coordinate system, derived from geographic latitude and longitude through a small-area plane approximation, used to uniquely determine the geometric location of the node; an adjacent edge set is generated based on the vertex connection relationships of the triangular mesh cells, and for each directed edge... Construct the corresponding edge attribute vector;

[0022] Step (3.3): Encoding-Processing-Decoding;

[0023] Step (3.3.1), Encoding stage;

[0024] FVCOM unstructured meshes are represented as ;

[0025] Each node With input feature vector Each edge Has geometric edge properties The node coordinates are Festival;

[0026] Point features and edge attributes are first linearly mapped to the latent space dimension. The initial hidden variables are obtained as shown in the following equation:

[0027]

[0028] in, Represents a node The initial node is implicitly represented after encoding. Representing an edge In the initial implicit edge representation after encoding, the superscript is the layer index, which is used to distinguish the feature representations of different layers; This is a learnable linear mapping layer used to project the original node and edge features onto a dimension of 1. The hidden space, this application takes ;

[0029] Step (3.3.2), processing stage;

[0030] The processor is made by The system consists of stacked message passing layers, each layer employing a computational paradigm that first updates the edge representation, then aggregates and updates the node representation.

[0031] The edge update process introduces a gating coefficient based on the consistency between wind direction and edge direction to continuously modulate the edge message intensity. When wind direction information is not representative, the influence of this modulation term on propagation is naturally weakened. This modulation term does not rely on explicit discrimination of sea state type (wind waves or swells), but is a controllable structural prior. It enhances the propagation of neighborhood information along the wind direction when wind direction information is more explanatory, and tends to weaken its influence when wind direction explanatory power is insufficient.

[0032] Step (3.3.3), Decoding stage;

[0033] The processing stage outputs the implicit representation of the final node. The predicted effective wave height of the node is obtained by decoding using the following formula:

[0034]

[0035] Step (1) includes:

[0036] Step (1.1), diagram representation;

[0037] The FVCOM unstructured mesh is represented as an undirected graph G, expressed as: ;

[0038] in, Represents a set of grid nodes. Represents the set of edges formed by spatially adjacent nodes;

[0039] The node set is represented as ,in, For node indexing, This represents the total number of grid nodes.

[0040] edge set It consists of adjacent node pairs in the mesh topology, used to characterize the spatial adjacency relationship on the unstructured mesh, and to provide a structural basis for the subsequent propagation of spatial information;

[0041] Step (1.2), Task Definition;

[0042] The task is defined as a node-level regression problem, which is to predict the spatial distribution of effective wave height at a target time, given wind field information and wave height at a single buoy station.

[0043] For any node At the predicted time Forecast effective wave height The reference significant wave height is denoted as . ;

[0044] Given forecast time Select time interval The wind field sequence within the node is used as input, where, Indicates the length of the historical wind field window;

[0045] Step (1.3), standardization process;

[0046] Both input features and supervised outputs are uniformly processed using Z-core standardization based on training set statistics.

[0047] Step (2) includes:

[0048] Step (2.1), Sample Construction;

[0049] Supervised learning samples are constructed from the effective wave height time series of the stations using a sliding window method.

[0050] Step (2.2), LSTM timing modeling;

[0051] LSTM networks are used to model the time dependence in the significant wave height sequence of a single site. By introducing memory units and gating mechanisms, they can model long-term trend information and short-term fluctuation characteristics.

[0052] For each input sample, the LSTM network sequentially reads a 64-bit sequence of historical valid wave heights. At each time step, based on the valid wave height input value of the current time step and the hidden state of the previous time step, the network performs the following state update process:

[0053] Step (2.3), single-point prediction output;

[0054] The aforementioned temporal features are input into the linear output layer and mapped to generate a one-step leading significant wave height prediction value for the target time, thereby achieving a quantitative forecast of the significant wave height of a single station. This prediction result serves as the station-level forecast output and can also be used as an input feature for boundary forcing information in subsequent regional modeling.

[0055] Step (2.4), model training and parameter update;

[0056] During the training phase, the predicted effective wave height output by the LSTM network is compared with the reference effective wave height at the corresponding target time. The regression error is used as the training objective, and the network parameters are updated through iterative optimization so that the model can gradually learn the temporal evolution of the effective wave height of a single site.

[0057] Step (2.5), inference stage and continuous forecast;

[0058] During the inference phase, the sliding window input method, consistent with that used in the training phase, is employed to predict the historical significant wave height sequence over a continuous time period window by window, outputting the single-point significant wave height value corresponding to the target time, thereby forming a single-site significant wave height forecast sequence on a continuous time scale.

[0059] Step (2.2) includes:

[0060] First, the state of the memory unit at the previous time step is modulated by the forget gate to control the proportion of information that needs to be retained or decayed in historical memory, thereby avoiding irrelevant or outdated information from interfering with the current modeling process.

[0061] Secondly, the input information at the current time step is filtered through the input gate, and the candidate memory content generated from the current input is combined to determine the extent to which new information is written into the memory unit, so as to introduce effective features related to the current wave evolution.

[0062] Subsequently, the historical memories preserved by the forget gate are merged with the new memories introduced by the input gate to update the memory unit state at the current time step, so that the network can continuously accumulate the historical evolution information of the effective wave height during the sequence progression.

[0063] Finally, the current memory cell state is modulated through the output gate to generate the hidden state of the current time step. This hidden state serves as both the output representation of the current time step and the input for the state update of the next time step.

[0064] Once the complete historical window sequence is input, the hidden state corresponding to the last moment of the window is taken as the comprehensive temporal feature representation of the historical sequence, which is used to characterize the integer state of the effective wave height of the station before the target time.

[0065] Step (3.2) includes:

[0066] Step (3.2.1), distance calculation and standardization;

[0067] Calculate nodes using the following formula With nodes Geometric distance:

[0068]

[0069] The set of distances to all edges Calculate the mean and standard deviation, and obtain the standardized distance using the standardized formula. ;

[0070] Step (3.2.2): Direction angle calculation and direction coding;

[0071] The side direction angle is calculated from the node coordinate difference using the following formula:

[0072]

[0073] in, Indicates from node Pointing to node The direction angle of the side, This represents the arctangent function, and its range is typically 1 / 2. ;

[0074] Then construct the direction code as follows:

[0075]

[0076] in, , It is a sine and cosine encoding of the direction angle, used to avoid angles in... Discontinuous at the point;

[0077] Step (3.2.3), edge attribute splicing;

[0078] The standardized distance and direction code are concatenated in a fixed order to form an edge attribute vector. The completed edge attributes As the geometric descriptor of the edges in the graph, it is input into the edge encoder and mapped to the latent space to participate in the message passing and feature update process.

[0079] Step (3.3.2) includes:

[0080] Determine the modulation coefficients for directional consistency: Let the nodes Forecast time wind vector ,node The wind vector at the predicted time is First, the local wind speed vector on the side is obtained by averaging the wind speed vectors at both ends using the following formula:

[0081]

[0082] Then proceed as follows: Normalization yields its unit wind direction vector:

[0083]

[0084] in, This represents the 2-norm (Euclidean norm), which is the Euclidean length.

[0085] The edge direction vector is obtained by subtracting the geometric coordinates of the nodes using the following formula:

[0086]

[0087] Normalize to the unit direction vector of the edge using the following formula:

[0088]

[0089] in, Determined by static mesh geometry, and independent of time;

[0090] Finally, the side-level wind direction unit vector is adopted. unit vector of edge direction The dot product measures directional consistency, and the gating weights of the edge messages are obtained through the Sigmoid mapping as follows:

[0091]

[0092] in, A fixed scaling factor is used to adjust the weight discrimination. It is the Sigmoid function. It is a scalar weight obtained by aligning wind direction with edge direction, used to modulate edge message strength;

[0093] Perform edge update: at the In layer message passing, edge updates take the implicit representations of the two endpoints and the current edge implicit representation as input, and are processed by the update function. The candidate edge representations are obtained, and then directional consistency gating weights are introduced. The candidate edge representations are multiplicatively modulated to obtain the updated hidden edge representations, calculated as follows:

[0094]

[0095] in, They represent the first Layer nodes With nodes The hidden vectors of the nodes. Indicates the first Layer nodes Pointing to node The implicit edge vector is for the node The aggregation and edge feature update provide information. The hidden vector of the candidate edge is obtained by updating the edge. This is the gated weighted implicit edge vector. Implemented by a multilayer perceptron, it consists of several linear transformation layers and nonlinear activation functions connected in a fixed order, and its general form is expressed as:

[0096]

[0097] in, Represents the input vector. For learnable parameters, The nonlinear activation function is represented by the ReLU function. Through this nonlinear mapping, the original node features and edge attributes are projected onto a unified latent space representation, thereby enhancing the feature expression capability while maintaining the integrity of physical information, and providing a unified representation basis for subsequent graph-based message passing and feature updates.

[0098] Perform node aggregation and node update: in the first stage In layer message passing, for each node Gather all its inbound edges The edge information it carries;

[0099] To distinguish incoming edge aggregation, each undirected edge is typically aggregated during implementation. Expand into two directed edges and ;make For nodes If the neighboring region is , then the aggregation vector is defined as

[0100]

[0101] in, Indicates from node Pointing to node The directed edge representation, ;

[0102] The node's own representation is then concatenated with the aggregated message, and the node update is completed through a multilayer perceptron.

[0103]

[0104] in, This represents a vector concatenation operation;

[0105] right From 1 to Perform the following operations in sequence: Calculate the gating weights for consistency between wind direction and edge direction. ; Perform edge updates to obtain candidate edge representations and then... Perform multiplicative weighting to obtain the edge representation ; Execute the node's incoming edge message aggregation and complete the node update to obtain .

[0106] In summary, the advantages of this application compared with the prior art are as follows:

[0107] 1. This application constructs a wave forecasting method that combines LSTM with graph neural networks based on "wind field driving + observation constraints". It can effectively combine real ocean wave data and observation conditions. The forecasting model is based on important observation data while taking into account the operational constraints of sparse observations (such as single-point) buoys, thus filling the gap in the field of wave forecasting of graph neural networks (GNN) at home and abroad, and has high forecasting efficiency and timeliness.

[0108] 2. This application retains the high-precision temporal evolution characteristics of buoy observations and effectively propagates station information to unobserved sea areas through the spatial message passing mechanism of GNN, thereby significantly improving the accuracy of wave forecasting under sparse observation conditions. Attached Figure Description

[0109] The present application will now be further described in conjunction with the following figures;

[0110] Figure 1 A schematic diagram of the sea conditions in the area;

[0111] Figure 2 This is an FVCOM triangular mesh diagram;

[0112] Figure 3 The flowchart shows the regional wave forecasting method based on single-point buoy observation and graph neural network. Detailed Implementation

[0113] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to specific examples. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0114] Example 1: This application proposes a regional ocean wave forecasting system based on a cascaded architecture of "LSTM and graph neural network". The system includes:

[0115] (1) Graph construction module;

[0116] The graph construction module is used to discretize a regional sea area into an unstructured grid map, including:

[0117] A node is obtained by dividing the area of ​​the sea into N grid points, and each node corresponds to a geographical location.

[0118] Edges: Undirected edges are constructed based on the connection relationships between adjacent grid points in the triangulation, with a total of E edges;

[0119] Edge features: The features of each edge consist of the normalized geometric distance between nodes and the direction information, where the direction information is represented in sine and cosine form to avoid the problem of angle discontinuity;

[0120] (2) Input feature construction module;

[0121] The input feature construction module describes the temporal wind field forcing of each grid node and the constraint information of individual stations. Its total dimension is 483 to adapt to regional wave forecasting scenarios under sparse perspectives; it includes:

[0122] Historical wind field characteristics: Dimensions are 240×2=480, representing the wind speed time series within 240 hours prior to the prediction start time;

[0123] Current wind field characteristics: dimension is 1×2=2, representing the wind speed at the start of the prediction;

[0124] Constraint features of a single site: dimension 1, representing the effective wave height Hs at the predicted target time, which is used to propagate future boundary forcing information into the region;

[0125] The above input features are concatenated along the node dimension and then used as the node input of the graph neural network.

[0126] (3) LSTM network;

[0127] The LSTM network is used to predict the effective wave height time series of a single site to form the future forced input of the regional model. The LSTM network takes the historical observation sequence of the site as input, extracts the long-term and short-term dependencies of wave height evolution over time in chronological order, and outputs the single-site effective wave height Hs at the target time.

[0128] The LSTM network consists of a sequence input layer, an LSTM recurrent layer, and an output mapping layer. First, the historical wave height sequence of a station is input into one or more stacked LSTM recurrent layers to encode time-dependent features. Then, the hidden state of the LSTM recurrent layer at the last time step (or the aggregated representation of the last few time steps) is input into the fully connected output mapping layer to obtain the single-site effective wave height prediction value at the target prediction time. This prediction value serves as a single-site constraint feature with a dimension of 1, representing the single-point effective wave height Hs at the target prediction time, and is used to propagate future forcing information into the region.

[0129] (4) MeshGraphNet model;

[0130] The MeshGraphNet model is used to model the spatial propagation of ocean waves on unstructured meshes. It improves upon the basic message passing structure by introducing a physically-aware edge attention mechanism based on dynamic calculation of node spatial coordinates. This mechanism adaptively modulates edge information transmission with wind direction-edge alignment, thereby enhancing the physical consistency of wave propagation modeling. It includes:

[0131] The encoder includes a node encoder: which uses a linear mapping to map the node input features from 483 dimensions to 128 dimensions to obtain the node hidden representation; and an edge encoder: which uses a linear mapping to map the edge features from 3 dimensions to 128 dimensions to obtain the edge hidden representation.

[0132] A multi-layered message passing module, consisting of multiple iterative layers, with each layer including:

[0133] The edge update model is used to update edge features based on the hidden representations of the two connected nodes and the hidden representation of the current edge. Specifically...

[0134] The source node hidden representation, destination node hidden representation, and edge hidden representation are concatenated and input into the edge update network (multilayer perceptron) to obtain the updated edge hidden representation. Furthermore, a physical awareness edge attention mechanism is introduced, which dynamically calculates the edge direction vector based on the node spatial coordinates and calculates the alignment between the wind direction and the edge direction by combining the current wind field components at both ends of the node, thereby obtaining the edge attention weight. The edge hidden representation is then weighted to enhance the physical consistency of information propagation.

[0135] The node update model is used to aggregate the hidden representations of adjacent edges and update the node state. Specifically, the hidden representations of edges are first subjected to a nonlinear transformation to obtain aggregateable edge representations. Then, these representations are accumulated and aggregated according to the target end nodes of the edges. The aggregated result is then concatenated with the node's own hidden representation and input into the node update network (multilayer perceptron) to obtain the updated node hidden representation. Through multilayer iterations, information in the graph is propagated and fused layer by layer among adjacent nodes.

[0136] The decoder uses a linear mapping to map the 128-dimensional hidden representation of a node into a 1-dimensional output, which is used to obtain the normalized effective wave height Hs prediction value corresponding to the node.

[0137] like Figure 1 A map showing the sea conditions in the area, including single-point buoy stations:

[0138] The wind field data source is based on the ERA5 reanalysis dataset from the European Centre for Medium-Range Weather Forecasts (ECMWF), and includes the following variables: 10-meter U-wind component (U10, m / s) and 10-meter V-wind component (V10, m / s).

[0139] The spatiotemporal resolution includes: time: hourly, space: 0.25° × 0.25° global grid, time range: 2021–2024; spatial alignment is adopted in the processing flow, that is, interpolation is performed to the FVCOM triangular grid resolution;

[0140] Wave height data, based on FVCOM numerical simulation results; data source: hindcast results of the FVCOM (Finite Volume Community Ocean Model); variable: significant wave height; grid type: unstructured triangular mesh; spatiotemporal resolution includes: time: hourly; space: triangular mesh nodes (approximately 5845 internal nodes); time range: 2021–2024.

[0141] like Figure 3 As shown, the regional wave forecasting method based on single-point buoy observation and graph neural network extracts time-series features and performs short-term forecasting from the observation sequence of a single buoy station through an LSTM network. Then, the forecasting results output by the LSTM and the ERA5 spatial wind field features are used together as node features of the spatial graph neural network (GNN).

[0142] The encoder of a graph neural network (GNN) encodes the wind field features of nodes and the geometric features of edges into a multidimensional latent space. The message passing layer performs edge updates, node aggregation, and global state updates to fuse local neighborhood information with the global sea state. Finally, the decoder outputs the effective wave height for the forecast time.

[0143] In the messaging layer, single-point buoy data affects adjacent nodes.

[0144] Specifically, the regional wave forecasting method based on single-point buoy observations and graph neural networks includes the following steps:

[0145] Step (1): Problem modeling and data preprocessing;

[0146] Step (1.1), diagram representation;

[0147] The FVCOM unstructured mesh is represented as an undirected graph G, expressed as: ;

[0148] in, Represents a set of grid nodes. Represents the set of edges formed by spatially adjacent nodes;

[0149] The node set is represented as ,in, For node indexing, This represents the total number of grid nodes.

[0150] edge set It consists of adjacent node pairs in the mesh topology, used to characterize the spatial adjacency relationship on the unstructured mesh, and to provide a structural basis for the subsequent propagation of spatial information;

[0151] Step (1.2), Task Definition;

[0152] The task is defined as a node-level regression problem, which is to predict the spatial distribution of effective wave height at a target time, given wind field information and wave height at a single buoy station.

[0153] For any node At the predicted time Forecast effective wave height The reference significant wave height is denoted as . ;

[0154] Given forecast time Select time interval The wind field sequence within the node is used as input, where This represents the length of the historical wind field window and is fixed to a preset constant of 240 in the implementation.

[0155] Step (1.3), standardization process;

[0156] To reduce the differences in wind field variables (U10, V10) and significant wave height across numerical scales, and to improve the numerical stability and convergence consistency of network training, this step uniformly applies Z-core standardization based on training set statistics to both input features and supervised outputs; specifically,

[0157] The mean and standard deviation of U10, V10, and node wave height were calculated on the training data. Then, the corresponding variables at any time point and any node were standardized. Specifically, the mean of the variable on the training set was subtracted to center it, and then it was divided by the standard deviation of the training set to normalize the scale. To avoid numerical instability caused by the standard deviation approaching zero, a stabilization term was added to the denominator. The value is 10. -6 .

[0158] The same principle applies to the wave height of a single station: the boundary wave height vector at the target time is standardized according to its training statistics and then used as the constraint input.

[0159] The aforementioned mean and standard deviation are fixed and saved during the training phase and strictly reused during the inference or testing phase to ensure the consistency of data distribution between the training and application phases, thereby ensuring the reproducibility and comparability of the model output across time periods.

[0160] In evaluation and engineering applications, network forecast results can be de-standardized using the same set of statistics according to the following formula to restore the original physical dimensions, facilitating interpretation and comparison:

[0161] Step (2): Model using LSTM;

[0162] To provide time series forecast results for a single site, a Long Short-Term Memory (LSTM) network is used to model the significant wave height sequence of the site, which is then used to output the single-point forecast value at the target time; specifically,

[0163] Step (2.1), Sample Construction;

[0164] Supervised learning samples are constructed from the effective wave height time series of the stations using a sliding window method.

[0165] The historical window length is set to 64, for any predicted target time. The effective wave height data of the first 64 moments are selected and arranged in chronological order to form a historical input sequence. The effective wave height at the target moment is used as the output label for this sample. By sliding a window with a fixed step size along the time axis, a sample set covering the entire time series is constructed, thereby realizing single-site forecast modeling at continuous moments.

[0166] Step (2.2), LSTM timing modeling;

[0167] LSTM networks are used to model the time dependence in the significant wave height sequence of a single site. By introducing memory units and gating mechanisms, they can model long-term trend information and short-term fluctuation characteristics.

[0168] For each input sample, the LSTM network sequentially reads a 64-bit sequence of historical valid wave heights. At each time step, based on the valid wave height input value of the current time step and the hidden state of the previous time step, the network performs the following state update process:

[0169] First, the state of the memory unit at the previous time step is modulated by the forget gate to control the proportion of information that needs to be retained or decayed in historical memory, thereby avoiding irrelevant or outdated information from interfering with the current modeling process.

[0170] Secondly, the input information at the current time step is filtered through the input gate, and the candidate memory content generated from the current input is combined to determine the extent to which new information is written into the memory unit, so as to introduce effective features related to the current wave evolution.

[0171] Subsequently, the historical memories preserved by the forget gate are merged with the new memories introduced by the input gate to update the memory unit state at the current time step, so that the network can continuously accumulate the historical evolution information of the effective wave height during the sequence progression.

[0172] Finally, the current memory cell state is modulated through the output gate to generate the hidden state of the current time step. This hidden state serves as both the output representation of the current time step and the input for the state update of the next time step.

[0173] Through the synergistic effect of the forget gate, input gate, output gate and memory unit, the LSTM network can effectively model the long-term dependence and short-term dynamic characteristics of the effective wave height over time during the reading of historical sequences, thereby overcoming the problem of historical information decay that is prone to occur in the modeling of long-term sequences in ordinary recurrent structures.

[0174] Once the complete historical window sequence is input, the hidden state corresponding to the last moment of the window is taken as the comprehensive temporal feature representation of the historical sequence, which is used to characterize the integer state of the effective wave height of the station before the target time.

[0175] Step (2.3), single-point prediction output;

[0176] The aforementioned temporal features are input into a linear output layer and mapped to generate a one-step leading significant wave height prediction value for the target time, achieving quantitative forecasting of significant wave heights at a single site. This prediction result serves as the site-level forecast output and can also be used as input features for boundary forcing information in subsequent regional modeling.

[0177] Step (2.4), model training and parameter update;

[0178] During the training phase, the predicted effective wave height output by the LSTM network is compared with the reference effective wave height at the corresponding target time. The regression error is used as the training objective, and the network parameters are updated through iterative optimization so that the model can gradually learn the temporal evolution of the effective wave height of a single site.

[0179] Step (2.5), inference stage and continuous forecast;

[0180] During the inference phase, the sliding window input method, consistent with that used in the training phase, is adopted to predict the historical significant wave height sequence of continuous time periods window by window, and output the single-point significant wave height value corresponding to the target time, thereby forming a single-site significant wave height forecast sequence on a continuous time scale.

[0181] Step (3), graph neural network processing;

[0182] Step (3.1): Input features and single-point condition constraints;

[0183] To perform node-level regression, the effective wave height at the forecast time is driven by the wind field sequence, and conditional information of a single site is introduced as an external constraint.

[0184] Single-point condition information is provided by LSTM for the station sequence. The predicted value for time is denoted as ,Should The predicted values ​​at each time point are used as conditional inputs in the graphical model and injected with the same value at each node, thereby imposing a consistent constraint on the overall prediction.

[0185] For any node The node input features consist of historical wind field, current wind field, and single-point conditional parameters, expressed as follows: ;

[0186] in, The wind vector at the node is 10 meters.

[0187] In the specific implementation, the historical wind field sequence, current wind field information and single-point effective wave height constraint features are standardized and then spliced ​​to form a 483-dimensional node feature vector, which is used as the input of the graph neural network encoder.

[0188] Step (3.2), edge attribute construction;

[0189] To characterize the geometric relationships between adjacent nodes in an unstructured triangular mesh, edge attributes are constructed in this step based on the two-dimensional position coordinates of the mesh nodes; specifically,

[0190] For any pair of adjacent nodes Set nodes The two-dimensional position coordinates are ,node The two-dimensional position coordinates are ,in and These are the orthogonal coordinate components of the node in the local Cartesian coordinate system, approximated by mapping geographical latitude and longitude through a small-area plane, used to uniquely determine the geometric location of the node. An adjacent edge set is generated based on the vertex connection relationships of the triangular mesh cells, and for each directed edge... Construct the corresponding edge attribute vector; including,

[0191] Step (3.2.1), distance calculation and standardization;

[0192] Calculate nodes using the following formula With nodes Geometric distance:

[0193]

[0194] The set of distances to all edges Calculate the mean and standard deviation, and obtain the standardized distance using the standardized formula. ;

[0195] Step (3.2.2): Direction angle calculation and direction coding;

[0196] The side direction angle is calculated from the node coordinate difference using the following formula:

[0197]

[0198] in, Indicates from node Pointing to node The direction angle of the side, This represents the arctangent function, and its range is typically 1 / 2. ;

[0199] Then construct the direction code as follows:

[0200]

[0201] in, , It is a sine and cosine encoding of the direction angle, used to avoid angles in... Discontinuous at the point;

[0202] Step (3.2.3), edge attribute splicing;

[0203] The standardized distance and direction code are concatenated in a fixed order to form an edge attribute vector. The completed edge attributes As the geometric description of the edges in the graph, it is input into the edge encoder and mapped to the latent space to participate in the message passing and feature update process;

[0204] Step (3.3): Encoding-Processing-Decoding;

[0205] Step (3.3.1), Encoding stage;

[0206] FVCOM unstructured meshes are represented as ;

[0207] Each node With input feature vector Each edge Has geometric edge properties The node coordinates are Festival;

[0208] Point features and edge attributes are first linearly mapped to the latent space dimension. The initial hidden variables are obtained as shown in the following equation:

[0209]

[0210] in, Represents a node The initial node is implicitly represented after encoding. Representing an edge In the initial implicit edge representation after encoding, the superscript is the layer index, which is used to distinguish the feature representations of different layers; This is a learnable linear mapping layer used to project the original node and edge features onto a dimension of 1. The hidden space, this application takes ;

[0211] Step (3.3.2), processing stage;

[0212] The processor is made by The system consists of stacked message passing layers, each layer employing a computational paradigm that first updates the edge representation, then aggregates and updates the node representation.

[0213] To enhance the model's ability to represent potential anisotropic spatial dependencies, a gating coefficient based on the consistency between wind direction and edge direction is introduced in the edge update stage to continuously modulate the edge message intensity. When wind direction information is not representative, the influence of this modulation term on propagation is naturally weakened. This modulation term does not rely on explicit discrimination of sea state type (wind waves or swells), but rather serves as a controllable structural prior. It enhances the propagation of neighborhood information along the wind direction when wind direction information is more explanatory, and tends to weaken its influence when wind direction explanatory power is insufficient. This includes:

[0214] Determine the modulation coefficients for directional consistency: Let the nodes Forecast time wind vector ,node The wind vector at the predicted time is First, the local wind speed vector on the side is obtained by averaging the wind speed vectors at both ends using the following formula:

[0215]

[0216] Then proceed as follows: Normalization yields its unit wind direction vector:

[0217]

[0218] in, This represents the 2-norm (Euclidean norm), which is the Euclidean length.

[0219] The edge direction vector is obtained by subtracting the geometric coordinates of the nodes using the following formula:

[0220]

[0221] Normalize to the unit direction vector of the edge using the following formula:

[0222]

[0223] in, Determined by static mesh geometry, and independent of time;

[0224] Finally, the side-level wind direction unit vector is adopted. unit vector of edge direction The dot product measures directional consistency, and the gating weights of the edge messages are obtained through the Sigmoid mapping as follows:

[0225]

[0226] in, A fixed scaling factor is used to adjust the weight discrimination. It is the Sigmoid function. It is a scalar weight obtained by aligning wind direction with edge direction, used to modulate edge message strength;

[0227] Perform edge update: at the In layer message passing, edge updates take the implicit representations of the two endpoints and the current edge implicit representation as input, and are processed by the update function. The candidate edge representations are obtained, and then directional consistency gating weights are introduced. The candidate edge representations are multiplicatively modulated to obtain the updated hidden edge representations, calculated as follows:

[0228]

[0229] in, They represent the first Layer nodes With nodes The hidden vectors of the nodes. Indicates the first Layer nodes Pointing to node The implicit edge vector is for the node The aggregation and edge feature update provide information. The hidden vector of the candidate edge is obtained by updating the edge. This is the gated weighted implicit edge vector. Implemented by a multilayer perceptron, it consists of several linear transformation layers and nonlinear activation functions connected in a fixed order, and its general form is expressed as:

[0230]

[0231] in, Represents the input vector. For learnable parameters, The nonlinear activation function is represented by ReLU. Through this nonlinear mapping, the original node features and edge attributes are projected onto a unified latent space representation, thereby enhancing feature expressiveness while maintaining the integrity of physical information, and providing a unified representation basis for subsequent graph-based message passing and feature updates.

[0232] Perform node aggregation and node update: in the first stage In layer message passing, for each node Gather all its inbound edges The edge information it carries;

[0233] To distinguish incoming edge aggregation, each undirected edge is typically aggregated during implementation. Expand into two directed edges and ;make For nodes If the neighboring region is , then the aggregation vector is defined as

[0234]

[0235] in, Indicates from node Pointing to node The directed edge representation, ;

[0236] The node's own representation is then concatenated with the aggregated message, and the node update is completed through a multilayer perceptron.

[0237]

[0238] in, This represents a vector concatenation operation;

[0239] Therefore, the processing stage is the process of... From 1 to Perform the following operations in sequence: Calculate the gating weights for consistency between wind direction and edge direction. ; Perform edge updates to obtain candidate edge representations and then... Perform multiplicative weighting to obtain the edge representation ; Execute the node's incoming edge message aggregation and complete the node update to obtain ;

[0240] Step (3.3.3), Decoding stage;

[0241] The processing stage outputs the implicit representation of the final node. The predicted effective wave height of the node is obtained by decoding using the following formula:

[0242]

[0243] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A regional ocean wave forecasting method based on single-point buoy observation and graph neural network, characterized in that: The observation sequence of a single buoy station is used to extract time-series features and make short-term forecasts through an LSTM network. Then, the forecast results output by the LSTM and the ERA5 spatial wind field features are used together as the node features of the spatial graph neural network. The encoder of the graph neural network encodes the wind field features of nodes and the geometric features of edges into a multidimensional latent space. The message passing layer performs edge updates, node aggregation, and global state updates to fuse local neighborhood information with global sea state. Finally, the decoder outputs the effective wave height at the forecast time. Includes the following steps, Step (1): Problem modeling and data preprocessing; Step (2): Model using LSTM; To provide time series forecast results for a single site, a Long Short-Term Memory (LSTM) network is used to model the significant wave height sequence of the site, which is then used to output the single-point forecast value at the target time. Step (3), graph neural network processing; Step (3.1): Input features and single-point condition constraints; The effective wave height at the forecast time is driven by the wind field sequence, and conditional information from a single site is introduced as an external constraint. Single-point condition information is provided by LSTM for the station sequence. The predicted value for time is denoted as ,Should The predicted values ​​at each time point are used as conditional inputs in the graphical model and injected with the same value at each node, thereby imposing a consistent constraint on the overall prediction. For any node The node input features consist of historical wind field, current wind field, and single-point conditional parameters, expressed as follows: ; in, The wind vector at the node is 10 meters. Step (3.2), edge attribute construction; Edge attributes are constructed based on the two-dimensional position coordinates of grid nodes; for any pair of adjacent nodes... Set nodes The two-dimensional position coordinates are ,node The two-dimensional position coordinates are ,in and These are the orthogonal coordinate components of the node in the local Cartesian coordinate system, derived from geographic latitude and longitude through a small-area plane approximation, used to uniquely determine the geometric location of the node; an adjacent edge set is generated based on the vertex connection relationships of the triangular mesh cells, and for each directed edge... Construct the corresponding edge attribute vector; Step (3.3): Encoding-Processing-Decoding; Step (3.3.1), Encoding stage; FVCOM unstructured meshes are represented as ; Each node With input feature vector Each edge Has geometric edge properties The node coordinates are Festival; Point features and edge attributes are first linearly mapped to the latent space dimension. The initial hidden variables are obtained as shown in the following equation: in, Represents a node The initial node is implicitly represented after encoding. Representing an edge In the initial implicit edge representation after encoding, the superscript is the layer index, which is used to distinguish the feature representations of different layers; This is a learnable linear mapping layer used to project the original node and edge features onto a dimension of 1. The hidden space, this application takes ; Step (3.3.2), processing stage; The processor is made by The system consists of stacked message passing layers, each layer employing a computational paradigm that first updates the edge representation, then aggregates and updates the node representation. The edge update process introduces a gating coefficient based on the consistency between wind direction and edge direction to continuously modulate the edge message intensity. When wind direction information is not representative, the influence of this modulation term on propagation is naturally weakened. This modulation term does not rely on explicit discrimination of sea state type (wind waves or swells), but is a controllable structural prior. It enhances the propagation of neighborhood information along the wind direction when wind direction information is more explanatory, and tends to weaken its influence when wind direction explanatory power is insufficient. Step (3.3.3), Decoding stage; The processing stage outputs the implicit representation of the final node. The predicted effective wave height of the node is obtained by decoding using the following formula:

2. The regional wave forecasting method based on single-point buoy observation and graph neural network according to claim 1, characterized in that: In the message passing layer, data from a single buoy affects neighboring nodes.

3. The regional wave forecasting method based on single-point buoy observation and graph neural network according to claim 1, characterized in that: Step (1) includes, Step (1.1), diagram representation; The FVCOM unstructured mesh is represented as an undirected graph G, expressed as: ; in, Represents a set of grid nodes. Represents the set of edges formed by spatially adjacent nodes; The node set is represented as ,in, For node indexing, This represents the total number of grid nodes. edge set It consists of adjacent node pairs in the mesh topology, used to characterize the spatial adjacency relationship on the unstructured mesh, and to provide a structural basis for the subsequent propagation of spatial information; Step (1.2), Task Definition; The task is defined as a node-level regression problem, which is to predict the spatial distribution of effective wave height at a target time, given wind field information and wave height at a single buoy station. For any node At the predicted time Forecast effective wave height The reference significant wave height is denoted as . ; Given forecast time Select time interval The wind field sequence within the node is used as input, where, Indicates the length of the historical wind field window; Step (1.3), standardization process; Both input features and supervised outputs are uniformly processed using Z-core standardization based on training set statistics.

4. The regional wave forecasting method based on single-point buoy observation and graph neural network according to claim 1, characterized in that: Step (2) includes, Step (2.1), Sample Construction; Supervised learning samples are constructed from the effective wave height time series of the stations using a sliding window method. Step (2.2), LSTM timing modeling; LSTM networks are used to model the time dependence in the significant wave height sequence of a single site. By introducing memory units and gating mechanisms, they can model long-term trend information and short-term fluctuation characteristics. For each input sample, the LSTM network sequentially reads a 64-bit sequence of historical valid wave heights. At each time step, based on the valid wave height input value of the current time step and the hidden state of the previous time step, the network performs the following state update process: Step (2.3), single-point prediction output; The aforementioned temporal features are input into the linear output layer and mapped to generate a one-step leading significant wave height prediction value for the target time, thereby achieving a quantitative forecast of the significant wave height of a single station. This prediction result serves as the station-level forecast output and can also be used as an input feature for boundary forcing information in subsequent regional modeling. Step (2.4), model training and parameter update; During the training phase, the predicted effective wave height output by the LSTM network is compared with the reference effective wave height at the corresponding target time. The regression error is used as the training objective, and the network parameters are updated through iterative optimization so that the model can gradually learn the temporal evolution of the effective wave height of a single site. Step (2.5), inference stage and continuous forecast; During the inference phase, the sliding window input method, consistent with that used in the training phase, is employed to predict the historical significant wave height sequence over a continuous time period window by window, outputting the single-point significant wave height value corresponding to the target time, thereby forming a single-site significant wave height forecast sequence on a continuous time scale.

5. The regional wave forecasting method based on single-point buoy observation and graph neural network according to claim 4, characterized in that: Step (2.2) includes, First, the state of the memory unit at the previous time step is modulated by the forget gate to control the proportion of information that needs to be retained or decayed in historical memory, thereby avoiding irrelevant or outdated information from interfering with the current modeling process. Secondly, the input information at the current time step is filtered through the input gate, and the candidate memory content generated from the current input is combined to determine the extent to which new information is written into the memory unit, so as to introduce effective features related to the current wave evolution. Subsequently, the historical memories preserved by the forget gate are merged with the new memories introduced by the input gate to update the memory unit state at the current time step, so that the network can continuously accumulate the historical evolution information of the effective wave height during the sequence progression. Finally, the current memory cell state is modulated through the output gate to generate the hidden state of the current time step. This hidden state serves as both the output representation of the current time step and the input for the state update of the next time step. Once the complete historical window sequence is input, the hidden state corresponding to the last moment of the window is taken as the comprehensive temporal feature representation of the historical sequence, which is used to characterize the integer state of the effective wave height of the station before the target time.

6. The regional wave forecasting method based on single-point buoy observation and graph neural network according to claim 1, characterized in that: Step (3.2) includes, Step (3.2.1), distance calculation and standardization; Calculate nodes using the following formula With nodes Geometric distance: The set of distances to all edges Calculate the mean and standard deviation, and obtain the standardized distance using the standardized formula. ; Step (3.2.2): Direction angle calculation and direction coding; The side direction angle is calculated from the node coordinate difference using the following formula: in, Indicates from node Pointing to node The direction angle of the side, This represents the arctangent function, and its range is typically 1 / 2. ; Then construct the direction code as follows: in, , It is a sine and cosine encoding of the direction angle, used to avoid angles in... Discontinuous at the point; Step (3.2.3), edge attribute splicing; The standardized distance and direction code are concatenated in a fixed order to form an edge attribute vector. The completed edge attributes As the geometric descriptor of the edges in the graph, it is input into the edge encoder and mapped to the latent space to participate in the message passing and feature update process.

7. The regional wave forecasting method based on single-point buoy observation and graph neural network according to claim 1, characterized in that: The aforementioned step (3.3.2) includes, Determine the modulation coefficients for directional consistency: Let the nodes Forecast time wind vector ,node The wind vector at the predicted time is First, the local wind speed vector on the side is obtained by averaging the wind speed vectors at both ends using the following formula: Then proceed as follows: Normalization yields its unit wind direction vector: in, This represents the 2-norm (Euclidean norm), which is the Euclidean length. The edge direction vector is obtained by subtracting the geometric coordinates of the nodes using the following formula: Normalize to the unit direction vector of the edge using the following formula: in, Determined by static mesh geometry, and independent of time; Finally, the side-level wind direction unit vector is adopted. unit vector of edge direction The dot product measures directional consistency, and the gating weights of the edge messages are obtained through the Sigmoid mapping as follows: in, A fixed scaling factor is used to adjust the weight discrimination. It is the Sigmoid function. It is a scalar weight obtained by aligning wind direction with edge direction, used to modulate edge message strength; Perform edge update: at the In layer message passing, edge updates take the implicit representations of the two endpoints and the current edge implicit representation as input, and are processed by the update function. The candidate edge representations are obtained, and then directional consistency gating weights are introduced. The candidate edge representations are multiplicatively modulated to obtain the updated hidden edge representations, calculated as follows: in, They represent the first Layer nodes With nodes The hidden vectors of the nodes. Indicates the first Layer nodes Pointing to node The implicit edge vector is for the node The aggregation and edge feature update provide information. The hidden vector of the candidate edge is obtained by updating the edge. This is the gated weighted implicit edge vector. Implemented by a multilayer perceptron, it consists of several linear transformation layers and nonlinear activation functions connected in a fixed order, and its general form is expressed as: in, Represents the input vector. For learnable parameters, The nonlinear activation function is represented by the ReLU function. Through this nonlinear mapping, the original node features and edge attributes are projected onto a unified latent space representation, thereby enhancing the feature expression capability while maintaining the integrity of physical information, and providing a unified representation basis for subsequent graph-based message passing and feature updates. Perform node aggregation and node update: in the first stage In layer message passing, for each node Gather all its inbound edges The edge information it carries; To distinguish incoming edge aggregation, each undirected edge is typically aggregated during implementation. Expand into two directed edges and ;make For nodes If the neighboring region is , then the aggregation vector is defined as in, Indicates from node Pointing to node The directed edge representation; The node's own representation is then concatenated with the aggregated message, and the node update is completed through a multilayer perceptron. in, This represents a vector concatenation operation; right From 1 to Perform the following operations in sequence: Calculate the gating weights for consistency between wind direction and edge direction. ; Perform edge updates to obtain candidate edge representations and then... Perform multiplicative weighting to obtain the edge representation ; Execute the node's incoming edge message aggregation and complete the node update to obtain .

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