A turbidity current prediction visualization method based on a physically constrained directed spatio-temporal graph neural network

Abstract

The present application relates to the technical field of marine observation, and is a turbidity current prediction visualization method based on a physically constrained directed spatio-temporal graph neural network, comprising: acquiring geometric information and turbidity current historical information of a target sea area; performing grid processing on the target sea area to construct a turbidity current propagation graph and a graph neural network training data set; training the physically constrained directed spatio-temporal graph neural network; updating parameters of the physically constrained directed spatio-temporal graph neural network based on a joint loss function; outputting three-directional flow velocities, sediment concentrations and turbidity current front information at each prediction node at multiple time points within a preset future prediction time window; converting the three-directional flow velocities, sediment concentrations and turbidity current front information into basic parameters, and generating a turbidity current prediction three-dimensional visualization scene of the target sea area based on the basic parameters. The present application constructs a turbidity current propagation graph, predicts the state of each prediction node at a future time point by using a physically constrained directed spatio-temporal graph neural network, and generates a turbidity current prediction three-dimensional visualization scene.

Description

Technical Field

[0001] This invention relates to the field of marine observation technology, and in particular to a method for predicting and visualizing turbidity currents based on a physically constrained directed spatiotemporal graph neural network. Background Technology

[0002] With the increasing demand for marine engineering construction and seabed environmental safety assessment, it is of great significance to conduct turbidity current movement prediction and three-dimensional visualization analysis for specific target sea areas. Existing turbidity current analysis methods mainly include numerical model-based computational methods and data-driven prediction methods. The former usually obtains information such as turbidity current velocity, sediment concentration, and propagation range by solving the fluid-sediment coupling control equations; the latter uses historical monitoring data or existing calculation results to quickly predict the turbidity current state.

[0003] However, numerical calculation methods often require repeated calculations when dealing with different inlet locations, inflow velocities, sediment concentrations, and durations, making it difficult to meet the needs for rapid prediction and dynamic visualization under multiple conditions. While data-driven methods can shorten prediction time, existing methods still have shortcomings in spatial relationship representation, physical constraints, and visualization integration, as detailed below: (1) Insufficient representation of spatial propagation relationships of turbidity currents within the target sea area. Existing methods mostly use regular matrices or single-point time series to organize turbidity current data, which makes it difficult to simultaneously reflect the combined influence of seabed elevation, slope, aspect, node neighborhood relationships, and local flow direction on the turbidity current propagation path. In areas with significant topographic relief and where the propagation direction adjusts with changes in the seabed, it is difficult to accurately describe the interaction relationships between predicted nodes.

[0004] (2) Limited monitoring data is insufficient to support the prediction of turbidity current status across the entire field. In practical applications, monitoring equipment can usually only be deployed in the inlet area, the main propagation channel, or local key locations, while three-dimensional visualization requires obtaining state information such as velocity and concentration at various spatial locations throughout the target sea area. Existing methods lack a mechanism to unify monitoring data, grid nodes, and spatial reconstruction results into a spatiotemporal prediction dataset.

[0005] (3) Insufficient physical consistency of prediction results. Some deep learning methods mainly use velocity error or concentration error as training targets, which can easily lead to negative sediment concentration, abnormal increase or decrease in total sediment mass, sudden changes in local flow field, or mismatch in boundary region conditions. For turbidity flow prediction, relying solely on data fitting is insufficient to ensure that the prediction results conform to basic transport laws and boundary conditions.

[0006] (4) Insufficient ability to predict turbidity fronts at multiple times. Existing methods often focus on predicting the changes in velocity and concentration at a single time or a few locations, making it difficult to continuously output the turbidity state at each node at multiple future times, and also making it difficult to identify the range and evolution process of the turbidity front.

[0007] (5) There is a lack of direct conversion between the prediction results and the 3D visualization. Existing 3D displays usually rely on offline numerical results, post-processing software or preset animations. The predicted node velocity and sediment concentration are difficult to directly convert into visualization parameters such as volumetric cloud transparency, particle motion velocity, particle generation quantity and streamline direction, resulting in the prediction process being disconnected from the 3D scene generation process.

[0008] In summary, the core process of existing methods still mainly relies on offline acquisition of numerical calculation results, prediction of single data forms, and subsequent independent visualization processing. It is difficult to form a complete technical chain for historical information acquisition, propagation map construction, physical constraint prediction, prediction result conversion, and three-dimensional dynamic display for specific target sea areas.

[0009] Therefore, there is a need to propose a turbidity prediction method that can combine seabed topography, turbidity propagation direction and physical constraints, and can directly drive the generation of three-dimensional visualization scenes. Summary of the Invention

[0010] To address the aforementioned technical problems, this invention provides a method for predicting and visualizing turbidity currents based on a physically constrained directed spatiotemporal graph neural network. The invention constructs a turbidity current propagation map, encoding the spatial distances between predicted nodes within the target sea area, seabed elevation differences, slope aspects, and turbidity current direction relationships as directed edge weights. It then uses a physically constrained directed spatiotemporal graph neural network to predict the triaxial flow velocities, sediment concentrations, and turbidity current front information at each predicted node at multiple future time points. Finally, the prediction results are converted into volume rendering parameters, particle motion parameters, and streamline parameters, thereby generating a three-dimensional visualization scene for turbidity current prediction.

[0011] The technical means employed in this invention are as follows: A method for predicting and visualizing turbidity currents based on a physically constrained directed spatiotemporal graph neural network includes: acquiring geometric information and historical turbidity current information of a target sea area; performing gridding processing on the target sea area to generate prediction nodes, and setting monitoring points in the prediction nodes; constructing a turbidity current propagation map based on the spatial relationship between the prediction nodes, seabed topography information, and turbidity current attribute information at the monitoring points; constructing a graph neural network training dataset based on the turbidity current propagation map, historical turbidity current information, and node turbidity current state information at corresponding future times; and inputting the graph neural network training dataset into the physically constrained directed spatiotemporal graph neural network. The network is trained; the parameters of the physically constrained directed spatiotemporal graph neural network are updated based on the joint loss function; after training, the initial parameters of the turbidity current to be simulated are input into the trained physically constrained directed spatiotemporal graph neural network, and the triaxial velocity, sediment concentration and turbidity current front information at each prediction node at multiple time points are output within a preset future prediction time window; the triaxial velocity, sediment concentration and turbidity current front information are converted into basic parameters, including: volume rendering parameters, particle motion parameters and streamline parameters; a three-dimensional visualization scene of turbidity current prediction for the target sea area is generated based on the basic parameters.

[0012] Furthermore, the geometric information of the target sea area includes: water depth data, sea area boundary data, seabed slope data, seabed aspect data, and seabed roughness data. The geometric information is converted into a unified spatial coordinate system. The turbidity current history information includes: turbidity current velocity, sediment concentration, local mixing density, turbulent kinetic energy, and corresponding timestamps at each monitoring location. A digital elevation model of the seabed of the target sea area is obtained. Based on the digital elevation model and the water depth data, a three-dimensional geometric model of the target sea area is generated. The historical turbidity current information is time-aligned according to a preset sampling time interval to obtain turbidity current attribute data for each monitoring location at a unified time series. The sediment concentration data is non-negatively corrected, and the corrected sediment concentration satisfies the following conditions:

[0013] in, Indicates monitoring point At any moment The original sediment concentration, This indicates the corrected sediment concentration; The mean and standard deviation of turbidity attribute data are calculated based on a preset time window centered on the current time. When the difference between the turbidity attribute data and the mean is greater than three times the standard deviation, it is determined to be an outlier. The outlier is replaced by a linear interpolation value from adjacent time points.

[0014] Furthermore, the gridding of the target sea area specifically includes: performing regular three-dimensional gridding of the target sea area based on its three-dimensional geometric model; determining the center position of each grid cell as a prediction node; selecting prediction nodes located in the turbidity current inlet region, main propagation channel region, seabed slope abrupt change region, and turbidity current diffusion region as monitoring points; assigning corresponding seabed topographic attributes and turbidity current attributes to each prediction node to form prediction node features; and configuring the prediction nodes... At any moment The predicted node features are represented as follows:

[0015] in, Indicates the prediction node Three-dimensional spatial coordinates, Indicates seabed elevation. Indicates the slope of the seabed. Indicates the slope of the seabed. Indicates the roughness of the substrate. , and These represent the turbidity velocity components in three directions, Indicates sediment concentration. Indicates local mixing density, Represents turbulent kinetic energy; For prediction nodes without monitoring points, spatial reconstruction is performed based on turbidity attribute data from adjacent monitoring points, wherein the spatial reconstruction satisfies:

[0016]

[0017] in, Indicates the prediction node At any moment The reconstructed turbidity property values, Indicates the number of monitoring points. Indicates the prediction node With monitoring points Spatial distance, Indicates monitoring point For prediction nodes Spatial reconstruction weights, This represents a preset minimum constant to prevent the denominator from being zero.

[0018] Furthermore, the construction of the turbidity propagation graph specifically includes: determining candidate connection edges based on the spatial distance and neighborhood relationship between predicted nodes; the candidate connection edges are determined in the following manner:

[0019] in, Indicates the prediction node With prediction nodes Candidate connection identifiers between them Indicates the prediction node of Nearest neighbor prediction node set and Representing prediction nodes With prediction nodes Spatial position vector, Indicates the preset neighborhood search radius; The downslope propagation relationship is determined based on the seabed elevation difference between the starting and ending points of the candidate connecting edges; the flow direction propagation relationship is determined based on the angle between the spatial direction of the candidate connecting edges and the turbidity current velocity direction at the initial predicted node; a turbidity current propagation map is constructed based on the candidate connecting edges, the downslope propagation relationship, and the flow direction propagation relationship; time... Next prediction node Pointing to the prediction node The weights of directed edges satisfy:

[0020] in, This represents the weight of the directed edge before normalization. Indicates spatial distance weights. Indicates the weight of the terrain slope. Indicates the flow weight. This represents the weighting coefficient for downhill terrain. Indicates the flow direction weighting coefficient; The spatial distance weight Downhill weight of terrain and flow weight They respectively satisfy:

[0021]

[0022]

[0023] in, Indicates the distance attenuation coefficient. and These represent the prediction nodes. With prediction nodes seabed elevation, Indicates the prediction node At any moment The turbidity velocity vector, This represents a preset minimum constant to prevent the denominator from being zero.

[0024] Furthermore, the construction of the graph neural network training dataset specifically includes: dividing the historical turbidity flow information into historical input time windows and future prediction time windows according to time order; extracting the node features and corresponding turbidity flow propagation maps of each prediction node within the historical input time window; extracting the turbidity flow velocity, sediment concentration, and turbidity flow front state of each prediction node within the future prediction time window as prediction labels; combining the node features, turbidity flow propagation maps, initial parameters of the corresponding turbidity flow conditions, and prediction labels within the future prediction time window into graph neural network training samples; and combining the node features, turbidity flow propagation maps, initial parameters of the corresponding turbidity flow conditions, and prediction labels within the future prediction time window into graph neural network training samples; and combining the first... The training samples for a graph neural network are represented as follows:

[0025] in, Indicates from time At that time The sequence of node feature matrices, Indicates from time At that time The adjacency matrix sequence of the turbidity propagation graph. Indicates the first Initial parameters for each turbidity flow condition. Indicates from time At that time Predicted labels, Indicates the length of the historical input time window. Indicates the length of the future forecast time window; The initial parameters of the turbidity flow condition Represented as:

[0026] in, Indicates the location of the turbidity inlet. Indicates the inlet flow rate. Indicates the concentration of sediment at the inlet. Represents the unit vector in the direction of inflow. Indicates the duration of inflow. Indicates inflow rate. This indicates the median particle size of the sediment.

[0027] Further, the graph neural network training dataset is input into the physically constrained directed spatiotemporal graph neural network for training, specifically including: inputting the graph neural network training dataset into the physically constrained directed spatiotemporal graph neural network; extracting spatial propagation features between each prediction node using a directed graph spatial encoding module; the directed graph spatial encoding module performs feature aggregation on the outgoing and incoming neighborhoods of the prediction nodes respectively, and the prediction node feature update process satisfies:

[0028]

[0029]

[0030] in, Indicates time Next The node feature matrix of the layer This represents the updated node feature matrix. This represents the adjacency matrix of the turbidity propagation graph, consisting of the initial weights of the directed edges. express The corresponding out-degree matrix, express The corresponding in-degree matrix, Indicates the first Outward propagation parameter matrix, Indicates the first The forward propagation parameter matrix, This indicates the order of graph convolution propagation. Indicates the activation function; The temporal evolution characteristics of turbidity velocity and sediment concentration are extracted using a time series encoding module. This module employs a gated cyclic unit to temporally encode the spatial propagation characteristics of each prediction node, and the state update process satisfies the following:

[0031]

[0032]

[0033]

[0034] in, Indicates time The spatial propagation characteristics, namely the node spatial propagation characteristic matrix output by the directed graph spatial encoding module, Indicates the current hidden state. This indicates the hidden state in the previous moment. This represents the candidate hidden state at the current moment. Indicates an update to the door. This indicates that the door is being reset. This represents element-wise multiplication; , and These represent the input feature weight matrices corresponding to the update gate, reset gate, and candidate hidden state, respectively. , and These represent the weight matrices of the cyclic hidden states corresponding to the update gate, reset gate, and candidate hidden states, respectively. , and These represent the bias vectors corresponding to the update gate, reset gate, and candidate hidden state, respectively. This represents the hyperbolic tangent activation function.

[0035] The multi-task prediction and decoding module is used to output the triaxial flow velocity, sediment concentration and turbidity front state at each prediction node at multiple future time points.

[0036] Furthermore, the joint loss function includes: velocity prediction error loss, sediment concentration prediction error loss, sediment mass conservation constraint loss, concentration non-negativity constraint loss, flow field continuity constraint loss, and boundary condition constraint loss; the sediment mass conservation constraint loss... Concentration non-negative constraint loss Flow field continuity constraint loss and boundary condition constraint loss They respectively satisfy:

[0037]

[0038]

[0039]

[0040]

[0041] in, Indicates time The predicted total mass of sediment, Indicates time Predicted inlet sediment flux, Indicates time Predicted export sediment flux, Indicates the prediction time step. Indicates the prediction node At any moment Predicted sediment concentration, Indicates the prediction node Corresponding to the volume of the mesh cell, Indicates the number of predicted nodes. Indicates the length of the future forecast time window. Indicates the first The set of boundary surfaces of each grid cell. Indicates time Lower mesh cell face The predicted velocity vector at that location, Represents the mesh cell surface The outer normal vector, Represents the mesh cell surface The area of. Among them, This represents the set of prediction nodes corresponding to the turbidity inlet region. This represents the set of predicted nodes corresponding to the seabed boundary and the marine side boundary. Indicates the prediction node At any moment The predicted velocity vector, Indicates time Set the velocity vector in the lower inlet region. This indicates the set sediment concentration in the inlet region at time t. Indicates the prediction node The outer normal vector of the boundary. This indicates the predicted number of nodes in the turbidity inlet region. This indicates the number of predicted nodes for the seabed boundary and the marine side boundary. The joint loss function is expressed as:

[0042] in, Denotes the joint loss function. This indicates the loss due to speed prediction error. This represents the weighting coefficient for the speed prediction error loss. This indicates the loss in sediment concentration prediction error. This represents the weighting coefficient for the prediction error of sediment concentration. This represents the weighting coefficient for the loss due to the conservation constraint on sediment mass. This represents the concentration non-negative constraint loss weighting coefficient. This represents the weighting coefficient for the flow field continuity constraint loss. This represents the weighting coefficient of the boundary condition constraint loss.

[0043] Further, the initial parameters of the turbidity flow to be simulated include inlet location, inlet velocity, inlet sediment concentration, inflow direction, inflow duration, inflow flow rate, and median sediment particle size. These initial parameters are input into a trained physically constrained directed spatiotemporal graph neural network. The velocity and sediment concentration of the predicted nodes in the inlet region are initialized based on the inlet location and inflow direction. Based on the initialized state of the predicted nodes in the inlet region, the trained physically constrained directed spatiotemporal graph neural network outputs the triaxial velocity, sediment concentration, and turbidity front information of each predicted node at multiple future time points within a preset future prediction time window. The turbidity front information is determined by the sediment concentration and velocity modulus at the predicted nodes, satisfying the following conditions:

[0044] in, Indicates time The turbidity front region, Indicates the prediction node Spatial position vector, Indicates the prediction node At any moment Predicted sediment concentration, Indicates the prediction node At any moment The predicted velocity vector, Indicates the threshold for sediment concentration. Indicates the flow rate threshold; When it is necessary to make predictions for a period of time that exceeds the future prediction time window, the prediction node state at the end of the current prediction time window is used as the initial state of the next prediction time window, and rolling predictions are performed.

[0045] Furthermore, the step of generating a 3D visualization scene for turbidity current prediction of the target sea area based on basic parameters specifically includes: resampling the sediment concentration and velocity information at each prediction node to a regular 3D volumetric data grid; for the coordinates in the regular 3D volumetric data grid... The resampling results of the voxels, sediment concentration, and velocity vectors satisfy:

[0046]

[0047]

[0048] in, Indicates the voxel at time The resampling sediment concentration, Indicates the voxel at time The resampling velocity vector, Indicates the prediction node voxels Spatial interpolation weights, This represents the voxel resampling scale parameter; Turbidity volume rendering parameters are generated based on the resampled sediment concentration; the transparency of the turbidity volume rendering is determined by the voxel sediment concentration, satisfying the following:

[0049] in, Voxel representation At any moment transparency, Indicates minimum transparency. Indicates maximum transparency. Indicates the lower limit of concentration mapping. Indicates the upper limit of concentration mapping. This represents the truncation function; This represents a preset minimum constant to prevent the denominator from being zero; Particle motion parameters and streamline parameters are generated based on the resampled velocity vector; the particle velocity and the number of particles generated satisfy the following conditions:

[0050]

[0051] in, Voxel representation At any moment Corresponding to the particle's velocity, The particle velocity display shows the scaling factor. Voxel representation At any moment The number of particles generated, Indicates the maximum number of particles generated. Indicates reference sediment flux; Streamlines are generated by successive integration of voxel velocity vectors, satisfying:

[0052] in, Indicates the first The first streamline Each sampling location Indicates the first The next sampling position of the streamline, Indicates the streamline integration step size. Indicates sampling position The resampled velocity vector at the location; when the streamline integration position exceeds the boundary of the target sea area, the corresponding velocity modulus is less than the preset velocity threshold, the corresponding sediment concentration is less than the preset concentration threshold, or the streamline integration step reaches the preset maximum integration step, the integration generation of the corresponding streamline stops; The turbidity volume rendering parameters, particle motion parameters, and streamline parameters are updated according to the prediction sequence of multiple future time points to generate a 3D visualization scene of turbidity prediction. The turbidity volume rendering parameters, particle motion parameters, and streamline parameters are loaded into the visualization system, and the turbidity volume cloud is generated through the 3D texture rendering module of the visualization system. The turbidity particle motion state is updated through the particle module, and the spatial propagation direction of the turbidity velocity field is displayed through the streamline rendering module.

[0053] Compared with the prior art, the present invention has the following advantages: This invention provides a three-dimensional visualization method for turbidity current prediction based on a physically constrained directed spatiotemporal graph neural network. It encodes the seabed elevation, slope, aspect, spatial distance, and turbidity current direction of the target sea area into a directed graph structure, which can express the spatial pattern of turbidity current propagation from upstream to downstream and from high-elevation areas to low-elevation areas under complex seabed topography conditions.

[0054] This invention provides a three-dimensional visualization method for turbidity flow prediction based on a physically constrained directed spatiotemporal graph neural network. By jointly extracting spatial propagation features and temporal evolution features through a directed graph spatial encoding module and a time series encoding module, it can simultaneously predict the triaxial flow velocity and sediment concentration at multiple future time points and multiple prediction nodes, rather than just predicting the turbidity flow state at a single location or a single depth.

[0055] This invention provides a three-dimensional visualization method for turbidity flow prediction based on a physically constrained directed spatiotemporal graph neural network. By incorporating sediment mass conservation, concentration non-negativity, flow field continuity, and boundary condition constraints during model training, the possibility of negative concentration, abnormal mass changes, local velocity abrupt changes, and inlet boundary mismatch in the prediction results can be reduced, thereby improving the physical rationality of the prediction results.

[0056] This invention provides a 3D visualization method for turbidity flow prediction based on a physically constrained directed spatiotemporal graph neural network. The method resamples the prediction node results into regular 3D volume data, maps sediment concentration to volume rendering parameters, and maps velocity vectors to particle motion parameters and streamline parameters, thereby achieving direct linkage between prediction data and 3D visualization scene.

[0057] This invention provides a three-dimensional visualization method for turbidity flow prediction based on a physically constrained directed spatiotemporal graph neural network. After model training is completed, the turbidity flow state at multiple future times can be quickly output directly based on the new initial turbidity flow parameters, without having to repeat the complete numerical solution process in each simulation, thereby improving the prediction and visualization efficiency for turbidity flow scenarios under multiple operating conditions. Attached Figure Description

[0058] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0059] Figure 1 This is a flowchart of the method of the present invention.

[0060] Figure 2 This is a schematic diagram of the gridding of the target sea area, the layout of prediction nodes and monitoring points according to the present invention.

[0061] Figure 3 This is a schematic diagram of the turbidity propagation diagram constructed according to the present invention.

[0062] Figure 4 This is a schematic diagram of the physically constrained directed spatiotemporal graph neural network structure of the present invention.

[0063] Figure 5 This is a schematic diagram illustrating the conversion of the prediction results of this invention into a Unity3D 3D visualization scene. Detailed Implementation

[0064] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0065] 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 the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0066] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0067] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps described in these embodiments do not limit the scope of the invention. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters in the following figures denote similar items; therefore, once an item is defined in one figure, it need not be further discussed in subsequent figures.

[0068] like Figure 1 As shown, this invention provides a turbidity current prediction and visualization method based on a physically constrained directed spatiotemporal graph neural network, including: acquiring geometric information and historical turbidity current information of a target sea area; in a preferred embodiment of this invention, the geometric information of the target sea area includes: water depth data, sea area boundary data, seabed slope data, seabed aspect data, and seabed roughness data, and the geometric information is converted into a unified spatial coordinate system; the historical turbidity current information includes: turbidity current velocity, sediment concentration, local mixing density, turbulent kinetic energy, and corresponding timestamps at each monitoring location; A digital elevation model (DEM) of the seabed is acquired for the target sea area. During implementation, the DEM describes the spatial undulations of the seabed surface; water depth data is used to determine the spatial extent of the water body; sea area boundary data is used to define the calculation area; and seabed slope, aspect, and substrate roughness are used to describe the influence of seabed topography on the direction and velocity variations of turbidity current propagation and sediment transport processes. Specifically, seabed topographic data, monitoring location data, and historical turbidity current data from different sources are converted to the same local three-dimensional coordinate system. Let the original coordinates be... The transformed target coordinates are The coordinate transformation relationship is as follows:

[0069] in, Represents the coordinate rotation matrix. This represents the coordinate translation vector.

[0070] Based on the digital elevation model of the seabed and water depth data, a three-dimensional geometric model of the target sea area is generated; let the seabed elevation function be... The water surface elevation function is Then any valid spatial location in the target sea area satisfies:

[0071] in, , Represents planar coordinates, Represents the vertical coordinate.

[0072] Turbidity flow historical information is time-aligned according to a preset sampling time interval to obtain turbidity flow attribute data for each monitoring location under a unified time series. In practice, the preset sampling time interval can be determined based on the sampling frequency of the monitoring equipment or the predicted time step. For monitoring data that do not fall within a unified time series, time interpolation or time matching is used for alignment so that the turbidity flow attributes at different monitoring locations can constitute the node state at the same time.

[0073] The sediment concentration data were non-negatively corrected, and the corrected sediment concentrations satisfied the following:

[0074] in, Indicates monitoring point At any moment The original sediment concentration, This indicates the corrected sediment concentration; this process effectively avoids negative concentration values ​​caused by monitoring noise, data transmission errors, or interpolation from being used in subsequent graph construction and model training.

[0075] The mean and standard deviation of turbidity attribute data are calculated based on a preset time window centered on the current moment. When the difference between the turbidity attribute data and the mean is greater than three times the standard deviation, it is considered an outlier. During implementation, monitoring points are set up. At any moment The turbidity property value is In time Within the preset time window centered on the center, the mean value of the turbidity property is The standard deviation is When satisfied At that time, It was determined to be an outlier.

[0076] Outliers are replaced with linear interpolated values ​​from adjacent time points. In implementation, let the time of the outlier be denoted as . The previous valid time was The next valid time is Then, linear interpolation is used to replace outliers:

[0077] in, This represents the replaced turbidity property value. Through time alignment, non-negativity correction, and outlier handling, the historical turbidity information is made to meet the data input requirements of subsequent spatiotemporal prediction models.

[0078] The target sea area is gridded to generate prediction nodes, and monitoring points are set in the prediction nodes; in specific implementation, as a preferred embodiment of the present invention, such as... Figure 2 As shown, based on the three-dimensional geometric model of the target sea area, the target sea area is processed into a regular three-dimensional mesh; the center position of each mesh cell is determined as the prediction node; during implementation, the preset mesh spacing is followed. , and The target sea area is processed into a regular three-dimensional grid. The center position of each effective grid cell is determined as the prediction node. The positions of the prediction nodes are represented as follows:

[0079] The set of predicted nodes is represented as:

[0080] in, This indicates the total number of predicted nodes.

[0081] Monitoring points were selected from the predicted nodes located in the turbidity current inlet region, the main propagation channel region, the seabed slope abrupt change region, and the turbidity current diffusion region. During implementation, the monitoring points in the turbidity current inlet region were used to obtain information on the velocity and sediment concentration of the turbidity current when it enters the target sea area; the monitoring points in the main propagation channel region were used to obtain information on the state changes of the turbidity current along the main propagation path; the monitoring points in the seabed slope abrupt change region were used to obtain information on the flow direction deflection, velocity changes, and concentration changes caused by topographic changes; and the monitoring points in the turbidity current diffusion region were used to obtain information on the expansion of the turbidity current front and the concentration decay.

[0082] Each prediction node is assigned corresponding seabed topography and turbidity current attributes to form prediction node features; the prediction nodes are then... At any moment The predicted node features are represented as follows:

[0083] in, Indicates the prediction node Three-dimensional spatial coordinates, Indicates seabed elevation. Indicates the slope of the seabed. Indicates the slope of the seabed. Indicates the roughness of the substrate. , and These represent the turbidity velocity components in three directions, Indicates sediment concentration. Indicates local mixing density, Represents turbulent kinetic energy; For prediction nodes without monitoring points, spatial reconstruction is performed based on turbidity attribute data from adjacent monitoring points. The spatial reconstruction satisfies the following:

[0084]

[0085] in, Indicates the prediction node At any moment The reconstructed turbidity property values, Indicates the number of monitoring points. Indicates the prediction node With monitoring points Spatial distance, Indicates monitoring point For prediction nodes Spatial reconstruction weights, This represents a preset minimum constant to prevent the denominator from being zero. Monitoring points closer to the prediction node have a larger reconstruction weight, thus making the reconstruction results more reflective of the actual turbidity flow state near the prediction node.

[0086] like Figure 3 As shown, a turbidity propagation map is constructed based on the spatial relationships between predicted nodes, seabed topography information, and turbidity current attribute information at monitoring points. In a preferred embodiment of this invention, candidate connection edges are determined based on the spatial distance and neighborhood relationships between predicted nodes. During implementation, at any given time... The turbidity propagation diagram below is shown as follows:

[0087] in, Represents the set of predicted nodes. Indicates time The set of directed edges, This represents the adjacency matrix of the turbidity propagation graph. This represents the feature matrix of the predicted node. If the predicted node... Belongs to prediction node of Nearest neighbor prediction node set And predicted nodes With prediction nodes The spatial distance between them is no greater than the preset neighborhood search radius. Then, candidate connection edges are established:

[0088] in, Indicates the prediction node With prediction nodes Candidate connection identifiers between them Indicates the prediction node of Nearest neighbor prediction node set and These represent the prediction nodes. With prediction nodes Spatial position vector, Indicates the preset neighborhood search radius; The downslope propagation relationship is determined based on the seabed elevation difference between the starting and ending points of the candidate connection edge; during implementation, the seabed downslope weight is:

[0089] in, Indicates the prediction node Pointing to the prediction node The weight of the terrain downslope. When Greater than At that time, predict the node Located at the prediction node The downhill direction has a terrain downhill weight greater than zero; when Less than or equal to At that time, the weight of the downhill slope is zero.

[0090] The flow direction propagation relationship is determined based on the angle between the spatial direction of the candidate connection edge and the direction of the turbidity velocity at the initial prediction node; during implementation, the flow direction weight is:

[0091] in, Indicates the prediction node At any moment Pointing to the prediction node The flow weight, Indicates the prediction node At any moment The turbidity velocity vector, "" represents the vector dot product. When predicting nodes When the node is located in front of the current turbidity flow, the flow direction weight increases; when the prediction node... When located in the counter-current direction of the turbidity flow, the flow direction weight tends to zero.

[0092] Based on candidate connecting edges, downslope propagation relationships, and flow direction propagation relationships, a turbidity propagation map is constructed; during implementation, the spatial distance weight is:

[0093] in, This represents the distance attenuation coefficient.

[0094] time Next prediction node Pointing to the prediction node The weights of directed edges satisfy:

[0095] in, This represents the weight of the directed edge before normalization. Indicates spatial distance weights. Indicates the weight of the terrain slope. Indicates the flow weight. This represents the weighting coefficient for downhill terrain. Indicates the flow direction weighting coefficient; The normalized directed edge weights are:

[0096] in, This represents the weighting coefficient for downhill terrain. This represents the terrain downslope weighting coefficient. Through the above mapping method, the turbidity propagation map simultaneously represents the spatial proximity relationship between predicted nodes, the propagation relationship along the terrain downslope direction, and the propagation relationship along the local flow direction, enabling the map structure to dynamically change with the turbidity state at different times.

[0097] Based on the turbidity propagation diagram, historical turbidity information, and node turbidity state information at corresponding future moments, a graph neural network training dataset is constructed; in specific implementations, as a preferred embodiment of the present invention, such as... Figure 4 As shown, the historical turbidity flow information is divided into historical input time windows and future prediction time windows according to time sequence; node features and corresponding turbidity flow propagation maps of each prediction node within the historical input time window are extracted; turbidity flow velocity, sediment concentration, and turbidity flow front state of each prediction node within the future prediction time window are extracted as prediction labels; the node features, turbidity flow propagation maps, initial parameters of the corresponding turbidity flow conditions, and prediction labels within the future prediction time window are combined into graph neural network training samples; the 1st... The training samples for a graph neural network are represented as follows:

[0098] in, Indicates from time At that time The sequence of node feature matrices, Indicates from time At that time The adjacency matrix sequence of the turbidity propagation graph. Indicates the first Initial parameters for each turbidity flow condition. Indicates from time At that time Predicted labels, Indicates the length of the historical input time window. Indicates the length of the future forecast time window; The initial parameters of the turbidity flow condition Represented as:

[0099] in, Indicates the location of the turbidity inlet. Indicates the inlet flow rate. Indicates the concentration of sediment at the inlet. Represents the unit vector in the direction of inflow. Indicates the duration of inflow. Indicates inflow rate. This indicates the median particle size of the sediment.

[0100] The triaxial flow velocity, sediment concentration, and turbidity front state of each prediction node within the future prediction time window together constitute the prediction label. The turbidity front state can be represented using a binary state: when the prediction node meets the preset concentration threshold and preset flow velocity threshold, the front state is recorded as 1; otherwise, it is recorded as 0.

[0101] The graph neural network training dataset is input into the physically constrained directed spatiotemporal graph neural network for training. Specifically, in a preferred embodiment of this invention, the graph neural network training dataset is input into the physically constrained directed spatiotemporal graph neural network; the directed graph spatial encoding module extracts the spatial propagation features between each prediction node; the directed graph spatial encoding module performs feature aggregation on the outgoing and incoming neighbors of the prediction nodes respectively, and the prediction node feature update process satisfies:

[0102]

[0103]

[0104] in, Represent the outward propagation matrix. Represents the incoming propagation matrix. Indicates time Next The node feature matrix of the layer, This represents the updated node feature matrix. This represents the adjacency matrix of the turbidity propagation graph, consisting of the initial weights of the directed edges. express The corresponding out-degree matrix, express The corresponding in-degree matrix, Indicates the first Outward propagation parameter matrix, Indicates the first The forward propagation parameter matrix, This indicates the order of graph convolution propagation. Indicates the activation function; The temporal evolution characteristics of turbidity velocity and sediment concentration are extracted using a time series encoding module. The time series encoding module employs a gated cyclic unit to temporally encode the spatial propagation characteristics of each prediction node, and the state update process satisfies the following:

[0105]

[0106]

[0107]

[0108] in, Indicates time The spatial propagation characteristics, namely the node spatial propagation characteristic matrix output by the directed graph spatial encoding module, Indicates the current hidden state. This indicates the hidden state in the previous moment. This represents the candidate hidden state at the current moment. Indicates an update to the door. This indicates that the door is being reset. This represents element-wise multiplication; , and These represent the input feature weight matrices corresponding to the update gate, reset gate, and candidate hidden state, respectively. , and These represent the weight matrices of the cyclic hidden states corresponding to the update gate, reset gate, and candidate hidden states, respectively. , and These represent the bias vectors corresponding to the update gate, reset gate, and candidate hidden state, respectively. This represents the hyperbolic tangent activation function.

[0109] The multi-task prediction and decoding module outputs the triaxial flow velocity, sediment concentration, and turbidity front state at each prediction node at multiple future time points. During implementation, the... The prediction results for each future moment are expressed as follows:

[0110] in, Indicates future time Predicted triaxial velocity; Indicates future time Predicted sediment concentration; Indicates future time The predicted state of the turbidity front.

[0111] The parameters of a physically constrained directed spatiotemporal graph neural network are updated based on a joint loss function. Specifically, in a preferred embodiment of this invention, the joint loss function includes: velocity prediction error loss, sediment concentration prediction error loss, sediment mass conservation constraint loss, concentration non-negativity constraint loss, flow field continuity constraint loss, and boundary condition constraint loss. The sediment mass conservation constraint loss... Concentration non-negative constraint loss Flow field continuity constraint loss and boundary condition constraint loss They respectively satisfy:

[0112]

[0113]

[0114]

[0115]

[0116] in, Indicates time The predicted total mass of sediment, Indicates time Predicted inlet sediment flux, Indicates time The predicted export sediment flux Indicates the prediction time step. Indicates the prediction node At any moment Predicted sediment concentration, Indicates the prediction node Corresponding to the volume of the mesh cell, Indicates the number of predicted nodes. Indicates the length of the future forecast time window. Indicates the first The set of boundary surfaces of each grid cell. Indicates time Lower mesh cell face The predicted velocity vector at that location, Represents the mesh cell surface The outer normal vector, Represents the mesh cell surface The area of. Among them, This represents the set of prediction nodes corresponding to the turbidity inlet region. This represents the set of predicted nodes corresponding to the seabed boundary and the marine side boundary. Indicates the prediction node At any moment The predicted velocity vector, Indicates time Set the velocity vector in the lower inlet region. This indicates the set sediment concentration in the inlet region at time t. Indicates the prediction node The outer normal vector of the boundary, This indicates the predicted number of nodes in the turbidity inlet region. This indicates the number of predicted nodes for the seabed boundary and the marine side boundary. The joint loss function is expressed as:

[0117] in, Denotes the joint loss function. This indicates the loss due to speed prediction error. This represents the weighting coefficient for the speed prediction error loss. This indicates the loss in sediment concentration prediction error. This represents the weighting coefficient for the prediction error of sediment concentration. This represents the weighting coefficient for the loss due to the conservation constraint on sediment mass. This represents the concentration non-negative constraint loss weighting coefficient. This represents the weighting coefficient for the flow field continuity constraint loss. This represents the weighting coefficient of the boundary condition constraint loss.

[0118] After training, the initial parameters of the turbidity flow to be simulated are input into the trained physical constraint directed spatiotemporal graph neural network. Within a preset future prediction time window, the network outputs triaxial flow velocity, sediment concentration, and turbidity flow front information at each prediction node at multiple time points. In a preferred embodiment of the present invention, the initial parameters of the turbidity flow to be simulated include: inlet location, inlet velocity, inlet sediment concentration, inflow direction, inflow duration, inflow flow rate, and median sediment particle size. The initial parameters of the turbidity flow to be simulated are input into the trained physical constraint directed spatiotemporal graph neural network. The velocity and sediment concentration of the prediction nodes in the inlet region are initialized according to the inlet location and inflow direction.

[0119] During implementation, based on the location of the turbidity inlet... and inflow direction Determine the set of predicted nodes in the entry area. For predicted nodes within the inlet region, initialization is performed using inlet velocity and inlet sediment concentration:

[0120]

[0121] in, .

[0122] Based on the initialized state of the predicted nodes in the inlet region, a trained physically constrained directed spatiotemporal graph neural network outputs the triaxial velocity, sediment concentration, and turbidity front information of each predicted node at multiple future time points within a preset future prediction time window. The turbidity front information is determined by the sediment concentration and velocity modulus at the predicted nodes, satisfying the following conditions:

[0123] in, Indicates time The turbidity front region, Indicates the prediction node Spatial position vector, Indicates the prediction node At any moment Predicted sediment concentration, Indicates the prediction node At any moment The predicted velocity vector, Indicates the sediment concentration threshold. Indicates the flow rate threshold; When it is necessary to make predictions for periods exceeding the future prediction time window, the state of the prediction node at the end of the current prediction time window is used as the initial state for the next prediction time window, and rolling predictions are performed.

[0124] The three-dimensional flow velocity, sediment concentration, and turbidity front information are converted into basic parameters, including volume rendering parameters, particle motion parameters, and streamline parameters. A three-dimensional visualization scene of turbidity current prediction for the target sea area is generated based on these basic parameters. In specific implementation, as a preferred embodiment of this invention, such as... Figure 5 The sediment concentration and velocity information at each prediction node is resampled to a regular three-dimensional volumetric data grid; for the coordinates in the regular three-dimensional volumetric data grid are... The resampling results of the voxels, sediment concentration, and velocity vectors satisfy:

[0125]

[0126]

[0127] in, Indicates the voxel at time The resampling sediment concentration, Indicates the voxel at time The resampling velocity vector, Indicates the prediction node voxels Spatial interpolation weights, This represents the voxel resampling scale parameter.

[0128] In practice, the spatial interpolation weights are:

[0129] in, This represents the voxel resampling scale parameter. Through resampling, the discrete turbidity states at the prediction nodes are transformed into continuous voxel states on a regular three-dimensional volumetric data grid.

[0130] Turbidity volume rendering parameters are generated based on the resampled sediment concentration; the transparency of the turbidity volume rendering is determined by the voxel sediment concentration, satisfying the following:

[0131] in, Voxel representation At any moment transparency, Indicates minimum transparency. Indicates maximum transparency. Indicates the lower limit of concentration mapping. Indicates the upper limit of concentration mapping. This represents the truncation function; This represents a preset minimum constant to prevent the denominator from being zero; Particle motion parameters and streamline parameters are generated based on the resampled velocity vector; the particle velocity and the number of particles generated satisfy the following conditions:

[0132]

[0133] in, Voxel representation At any moment Corresponding to the particle's velocity, The particle velocity display shows the scaling factor. Voxel representation At any moment The number of particles generated, Indicates the maximum number of particles generated. Indicates reference sediment flux; Streamlines are generated by successive integration of voxel velocity vectors, the first... The first streamline The positions are The next sampling position is:

[0134] in, Indicates the first The first streamline Each sampling location Indicates the first The next sampling position of the streamline, Indicates the streamline integration step size. Indicates sampling position The resampled velocity vector at the location; when the streamline integration position exceeds the boundary of the target sea area, the corresponding velocity modulus is less than the preset velocity threshold, the corresponding sediment concentration is less than the preset concentration threshold, or the streamline integration step reaches the preset maximum integration step, the integration generation of the corresponding streamline stops; The turbidity current volume rendering parameters, particle motion parameters, and streamline parameters are updated sequentially according to predictions at multiple future time points to generate a 3D visualization scene for turbidity current prediction. During implementation, the turbidity current volume rendering parameters, particle motion parameters, and streamline parameters are loaded into the Unity3D engine. A 3D texture rendering module generates a turbidity current volume cloud; the particle system updates the generation location, particle quantity, motion direction, and velocity of turbidity current particles; and the streamline rendering module displays the spatial propagation direction of the turbidity current velocity field. By sequentially updating the volume rendering parameters, particle motion parameters, and streamline parameters according to the prediction sequence at multiple future time points, the 3D visualization scene continuously displays the changes in turbidity current velocity, concentration diffusion, and frontal advance within the target sea area.

[0135] During implementation, the target sea area can be a region with a turbidity current inlet area, a slope propagation area, and a downstream diffusion area. Based on the geometric information and historical turbidity current information of the target sea area, a turbidity current propagation map and training dataset are constructed. After the model training is completed, inputting new inlet location, inlet velocity, inlet sediment concentration, inlet direction, inlet duration, inlet flow rate, and median sediment particle size will output turbidity current state information for each predicted node at multiple future time points, generating corresponding dynamic 3D visualization results in a Unity3D scene.

[0136] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting and visualizing turbidity flow based on a physically constrained directed spatiotemporal graph neural network, characterized in that, include: Obtain geometric information and historical turbidity current information of the target sea area; The target sea area is gridded to generate prediction nodes, and monitoring points are set in the prediction nodes; Based on the spatial relationship between the predicted nodes, seabed topography information, and turbidity current attribute information at the monitoring points, a turbidity current propagation map is constructed. Based on the turbidity propagation diagram, historical turbidity information, and node turbidity state information at corresponding future moments, a graph neural network training dataset is constructed. The graph neural network training dataset is input into the physically constrained directed spatiotemporal graph neural network for training. The parameters of the physically constrained directed spatiotemporal graph neural network are updated based on the joint loss function; After training, the initial parameters of the turbidity flow to be simulated are input into the trained physical constraint directed spatiotemporal graph neural network, and the triaxial flow velocity, sediment concentration and turbidity flow front information at each prediction node at multiple time points are output within a preset future prediction time window. The triaxial flow velocity, sediment concentration and turbidity front information are converted into basic parameters, which include: volume rendering parameters, particle motion parameters and streamline parameters. Based on the aforementioned fundamental parameters, a 3D visualization scene for predicting turbidity currents in the target sea area is generated.

2. The turbidity flow prediction and visualization method based on a physically constrained directed spatiotemporal graph neural network according to claim 1, characterized in that, The geometric information of the target sea area includes: water depth data, sea area boundary data, seabed slope data, seabed aspect data, and seabed roughness data. The geometric information is converted into a unified spatial coordinate system. The turbidity current history information includes: turbidity current velocity, sediment concentration, local mixing density, turbulent kinetic energy, and corresponding timestamp at each monitoring location. A digital elevation model of the seabed of the target sea area is obtained. Based on the digital elevation model and the water depth data, a three-dimensional geometric model of the target sea area is generated. The historical turbidity current information is time-aligned according to a preset sampling time interval to obtain turbidity current attribute data for each monitoring location at a unified time series. The sediment concentration data is non-negatively corrected, and the corrected sediment concentration satisfies the following conditions: in, Indicates monitoring point At any moment The original sediment concentration, This indicates the corrected sediment concentration; The mean and standard deviation of turbidity attribute data are calculated based on a preset time window centered on the current time. When the difference between the turbidity attribute data and the mean is greater than three times the standard deviation, it is determined to be an outlier. The outlier is replaced by a linear interpolation value from adjacent time points.

3. The turbidity flow prediction and visualization method based on a physically constrained directed spatiotemporal graph neural network according to claim 1, characterized in that, The gridding process for the target sea area specifically includes: Based on the three-dimensional geometric model of the target sea area, the target sea area is processed into a regular three-dimensional grid; the center position of each grid cell is determined as a prediction node; from the prediction nodes, prediction nodes located in the turbidity current inlet area, the main propagation channel area, the seabed slope abrupt change area, and the turbidity current diffusion area are selected as monitoring points; each prediction node is assigned corresponding seabed topographic attributes and turbidity current attributes to form prediction node features; the prediction nodes are then... At any moment The predicted node features are represented as follows: in, Indicates the prediction node Three-dimensional spatial coordinates, Indicates seabed elevation. Indicates the slope of the seabed. Indicates the slope of the seabed. Indicates the roughness of the substrate. , and These represent the turbidity velocity components in three directions, Indicates sediment concentration. Indicates local mixing density, Represents turbulent kinetic energy; For prediction nodes without monitoring points, spatial reconstruction is performed based on turbidity attribute data from adjacent monitoring points, wherein the spatial reconstruction satisfies: in, Indicates the prediction node At any moment The reconstructed turbidity property values, Indicates the number of monitoring points. Indicates the prediction node With monitoring points Spatial distance, Indicates monitoring point For prediction nodes Spatial reconstruction weights, This represents a preset minimum constant to prevent the denominator from being zero.

4. The turbidity flow prediction and visualization method based on a physically constrained directed spatiotemporal graph neural network according to claim 1, characterized in that, The construction of the turbidity propagation map specifically includes: Candidate connection edges are determined based on the spatial distance and neighborhood relationship between predicted nodes; the candidate connection edges are determined in the following manner: in, Indicates the prediction node With prediction nodes Candidate connection identifiers between them Indicates the prediction node of Nearest neighbor prediction node set and These represent the prediction nodes. With prediction nodes Spatial position vector, Indicates the preset neighborhood search radius; The downslope propagation relationship is determined based on the seabed elevation difference between the starting and ending points of the candidate connecting edges; the flow direction propagation relationship is determined based on the angle between the spatial direction of the candidate connecting edges and the turbidity current velocity direction at the initial predicted node; a turbidity current propagation map is constructed based on the candidate connecting edges, the downslope propagation relationship, and the flow direction propagation relationship; time... Next prediction node Pointing to the prediction node The weights of directed edges satisfy: in, This represents the weight of the directed edge before normalization. Indicates spatial distance weights. Indicates the weight of the terrain slope. Indicates the flow weight. This represents the weighting coefficient for downhill terrain. Indicates the flow direction weighting coefficient; The spatial distance weight Downhill weight of terrain and flow weight They respectively satisfy: in, Indicates the distance attenuation coefficient. and These represent the prediction nodes. With prediction nodes seabed elevation, Indicates the prediction node At any moment The turbidity velocity vector, This represents a preset minimum constant to prevent the denominator from being zero.

5. The turbidity flow prediction and visualization method based on a physically constrained directed spatiotemporal graph neural network according to claim 1, characterized in that, The construction of the graph neural network training dataset specifically includes: The historical information of turbidity flow is divided into historical input time windows and future prediction time windows according to time sequence; the node features and corresponding turbidity flow propagation maps of each prediction node within the historical input time window are extracted; the turbidity flow velocity, sediment concentration, and turbidity flow front state of each prediction node within the future prediction time window are extracted as prediction labels; the node features, turbidity flow propagation maps, initial parameters of the corresponding turbidity flow conditions, and prediction labels within the future prediction time window are combined into training samples for a graph neural network; the twentieth... The training samples for a graph neural network are represented as follows: in, Indicates from time At that time The sequence of node feature matrices, Indicates from time At that time The adjacency matrix sequence of the turbidity propagation graph. Indicates the first Initial parameters for each turbidity flow condition. Indicates from time At that time Predicted labels, Indicates the length of the historical input time window. Indicates the length of the future forecast time window; The initial parameters of the turbidity flow condition Represented as: in, Indicates the location of the turbidity inlet. Indicates the inlet flow rate. Indicates the concentration of sediment at the inlet. Represents the unit vector in the direction of inflow. Indicates the duration of inflow. Indicates inflow rate. This indicates the median particle size of the sediment.

6. The turbidity flow prediction and visualization method based on a physically constrained directed spatiotemporal graph neural network according to claim 1, characterized in that, The graph neural network training dataset is input into the physically constrained directed spatiotemporal graph neural network for training, specifically including: The training dataset of the graph neural network is input into the physically constrained directed spatiotemporal graph neural network; the spatial propagation features between each prediction node are extracted using the directed graph spatial encoding module; the directed graph spatial encoding module performs feature aggregation on the outgoing and incoming neighborhoods of the prediction nodes respectively, and the feature update process of the prediction nodes satisfies: in, Indicates time Next The node feature matrix of the layer This represents the updated node feature matrix. This represents the adjacency matrix of the turbidity propagation graph, consisting of the initial weights of the directed edges. express The corresponding out-degree matrix, express The corresponding in-degree matrix, Indicates the first Outward propagation parameter matrix, Indicates the first The forward propagation parameter matrix, This indicates the order of graph convolution propagation. Indicates the activation function; The temporal evolution characteristics of turbidity velocity and sediment concentration are extracted using a time series encoding module. This module employs a gated cyclic unit to temporally encode the spatial propagation characteristics of each prediction node, and the state update process satisfies the following: in, Indicates time The spatial propagation characteristics, namely the node spatial propagation characteristic matrix output by the directed graph spatial encoding module, Indicates the current hidden state. This indicates the hidden state in the previous moment. This represents the candidate hidden state at the current moment. Indicates an update to the door. This indicates that the door is being reset. This represents element-wise multiplication; , and These represent the input feature weight matrices corresponding to the update gate, reset gate, and candidate hidden state, respectively. , and These represent the weight matrices of the cyclic hidden states corresponding to the update gate, reset gate, and candidate hidden states, respectively. , and These represent the bias vectors corresponding to the update gate, reset gate, and candidate hidden state, respectively. Represents the hyperbolic tangent activation function; The multi-task prediction and decoding module is used to output the triaxial flow velocity, sediment concentration and turbidity front state at each prediction node at multiple future time points.

7. The turbidity flow prediction and visualization method based on a physically constrained directed spatiotemporal graph neural network according to claim 1, characterized in that, The joint loss function includes: velocity prediction error loss, sediment concentration prediction error loss, sediment mass conservation constraint loss, concentration non-negativity constraint loss, flow field continuity constraint loss, and boundary condition constraint loss; the sediment mass conservation constraint loss... Concentration non-negative constraint loss Flow field continuity constraint loss and boundary condition constraint loss They respectively satisfy: in, Indicates time The predicted total mass of sediment, Indicates time Predicted inlet sediment flux, Indicates time Predicted export sediment flux, Indicates the prediction time step. Indicates the prediction node At any moment Predicted sediment concentration, Indicates the prediction node Corresponding to the volume of the mesh cell, Indicates the number of predicted nodes. Indicates the length of the future forecast time window. Indicates the first The set of boundary surfaces of each grid cell. Indicates time Lower mesh cell face The predicted velocity vector at that location, Represents the mesh cell surface The outer normal vector, Represents the mesh cell surface The area of. Among them, This represents the set of prediction nodes corresponding to the turbidity inlet region. This represents the set of predicted nodes corresponding to the seabed boundary and the marine side boundary. Indicates the prediction node At any moment The predicted velocity vector, Indicates time Set the velocity vector in the lower inlet region. This indicates the set sediment concentration in the inlet region at time t. Indicates the prediction node The outer normal vector of the boundary. This indicates the predicted number of nodes in the turbidity inlet region. This indicates the number of predicted nodes for the seabed boundary and the marine side boundary. The joint loss function is expressed as: in, Denotes the joint loss function. This indicates the loss due to speed prediction error. This represents the weighting coefficient for the speed prediction error loss. This indicates the loss in sediment concentration prediction error. This represents the weighting coefficient for the prediction error of sediment concentration. This represents the weighting coefficient for the loss due to the conservation constraint on sediment mass. This represents the concentration non-negative constraint loss weighting coefficient. This represents the weighting coefficient for the flow field continuity constraint loss. This represents the weighting coefficient of the boundary condition constraint loss.

8. The turbidity flow prediction and visualization method based on a physically constrained directed spatiotemporal graph neural network according to claim 1, characterized in that, The initial parameters of the turbidity flow to be simulated include: inlet location, inlet velocity, inlet sediment concentration, inflow direction, inflow duration, inflow flow rate, and median sediment particle size. These initial parameters are input into a trained physically constrained directed spatiotemporal graph neural network. The velocity and sediment concentration of the predicted nodes in the inlet region are initialized based on the inlet location and inflow direction. Based on the initialized state of the predicted nodes in the inlet region, the trained physically constrained directed spatiotemporal graph neural network outputs the triaxial velocity, sediment concentration, and turbidity front information of each predicted node at multiple future time points within a preset future prediction time window. The turbidity front information is determined by the sediment concentration and velocity modulus at the predicted nodes, satisfying the following conditions: in, Indicates time The turbidity front region, Indicates the prediction node Spatial position vector, Indicates the prediction node At any moment Predicted sediment concentration, Indicates the prediction node At any moment The predicted velocity vector, Indicates the threshold for sediment concentration. Indicates the flow rate threshold; When it is necessary to make predictions for a period of time that exceeds the future prediction time window, the prediction node state at the end of the current prediction time window is used as the initial state of the next prediction time window, and rolling predictions are performed.

9. The turbidity flow prediction and visualization method based on a physically constrained directed spatiotemporal graph neural network according to claim 8, characterized in that, The three-dimensional visualization scene for predicting turbidity currents in the target sea area, generated based on fundamental parameters, specifically includes: The sediment concentration and velocity information at each prediction node are resampled to a regular three-dimensional volumetric data grid; for the coordinates in the regular three-dimensional volumetric data grid are... The resampling results of the voxels, sediment concentration, and velocity vectors satisfy: in, Indicates the voxel at time The resampling sediment concentration, Indicates the voxel at time The resampling velocity vector, Indicates the prediction node voxels Spatial interpolation weights, This represents the voxel resampling scale parameter; Turbidity volume rendering parameters are generated based on the resampled sediment concentration; the transparency of the turbidity volume rendering is determined by the voxel sediment concentration, satisfying the following: in, Voxel representation At any moment transparency, Indicates minimum transparency. Indicates maximum transparency. Indicates the lower limit of concentration mapping. Indicates the upper limit of concentration mapping. This represents the truncation function; This represents a preset minimum constant to prevent the denominator from being zero; Particle motion parameters and streamline parameters are generated based on the resampled velocity vector; the particle velocity and the number of particles generated satisfy the following conditions: in, Voxel representation At any moment Corresponding to the particle's velocity, The particle velocity display shows the scaling factor. Voxel representation At any moment The number of particles generated, Indicates the maximum number of particles generated. Indicates reference sediment flux; Streamlines are generated by successive integration of voxel velocity vectors, satisfying: in, Indicates the first The first streamline Each sampling location Indicates the first The next sampling position of the streamline, Indicates the streamline integration step size. Indicates sampling position The resampled velocity vector at the location; when the streamline integration position exceeds the boundary of the target sea area, the corresponding velocity modulus is less than the preset velocity threshold, the corresponding sediment concentration is less than the preset concentration threshold, or the streamline integration step reaches the preset maximum integration step, the integration generation of the corresponding streamline stops; The turbidity volume rendering parameters, particle motion parameters, and streamline parameters are updated according to the prediction sequence of multiple future time points to generate a 3D visualization scene of turbidity prediction. The turbidity volume rendering parameters, particle motion parameters, and streamline parameters are loaded into the visualization system, and the turbidity volume cloud is generated through the 3D texture rendering module of the visualization system. The turbidity particle motion state is updated through the particle module, and the spatial propagation direction of the turbidity velocity field is displayed through the streamline rendering module.

Images