A method, system and device for predicting a concentration field of a marine diffusive substance

Abstract

The present application relates to a kind of marine diffusible matter concentration field prediction method, system and equipment, belong to marine environment monitoring technical field.It includes: respectively deploying acoustic sensor node cluster to each sub-region of diffusible matter distribution, and constructs multiple NG-RC module;The acoustic sensor node in each acoustic sensor node cluster is divided into prediction and observation sensor node, and corresponding original observation sequence is obtained;Input vector is obtained according to original observation sequence, the vector is input into NG-RC module, and the local concentration prediction result of each sub-region is obtained;Cross-regional association information fusion is carried out to each NG-RC module, and according to local concentration prediction result, the global prediction result of each sub-region is obtained;According to the spatial position of each sub-region, the global prediction result of each sub-region is spliced, and the prediction concentration value of corresponding time whole region is obtained.The present application improves timing prediction ability and improves prediction precision, and enhances the adaptability to complex environment.

Description

Technical Field

[0001] This invention relates to the field of marine environmental monitoring technology, and in particular to a method, system and equipment for predicting the concentration field of marine diffusible substances. Background Technology

[0002] In the field of marine transport, the spatiotemporal evolution of the concentration fields of diffusing substances such as hydrothermal plumes, pollutants, nutrients, and suspended particles has always been a core research focus. The concentration distribution of these substances is not static but exhibits significant dynamic changes. These changes are influenced by multiple factors: complex seafloor topography alters the diffusion paths, hydrodynamic disturbances accelerate or slow the diffusion process, temperature gradients indirectly affect diffusion behavior by influencing fluid properties, and biogeochemical processes further reshape the concentration field through substance transformation and consumption. Therefore, the evolution of diffusing substances in the ocean exhibits significant nonlinearity, non-steady-state characteristics, and multi-scale coupling features, making the dynamic laws governing their concentration fields extremely complex.

[0003] Accurate prediction of the concentration distribution of diffusing substances has significant theoretical and practical value. From an ecological perspective, it directly relates to the structural stability and functional maintenance of local marine ecosystems. For example, the distribution of nutrients affects the growth of plankton, thus impacting the entire food chain. From an engineering application perspective, it can help detect pollution diffusion trends in environmental monitoring, provide crucial evidence for locating pollution sources in pollution tracing, and help locate deep-sea resources through characteristic signals such as hydrothermal plumes in resource exploration. It is a core support for the efficient advancement of many marine engineering projects.

[0004] However, current traditional methods for concentration field prediction have significant limitations. While traditional neural networks can handle certain nonlinear problems, they rely on specific activation functions and connection structures to ensure nonlinear expressive power. Faced with highly complex, multi-factor coupled scenarios in the marine environment, their adaptability and accuracy are often insufficient. Traditional dynamic graph models generally rely on global synchronization mechanisms when updating node states, but in the seabed environment, underwater acoustic communication is limited by bandwidth and latency fluctuations, making such synchronization mechanisms difficult to implement practically. More importantly, traditional methods fail to fully consider the inherent characteristics of underwater diffusive material concentration fields: spatially, due to differences in topography and currents, material diffusion exhibits significant heterogeneity; temporally, its evolution is often a mixed dynamic process intertwined with sudden and persistent events, which greatly reduces the predictive performance of traditional models. Summary of the Invention

[0005] Therefore, the technical problem to be solved by the present invention is to overcome the problems of poor adaptability and low prediction accuracy in the prior art, which are difficult to adapt to the strong nonlinearity and multi-scale coupling characteristics of concentration field evolution.

[0006] In a first aspect, to solve the above-mentioned technical problems, the present invention provides a method for predicting the concentration field of marine diffusible substances, comprising: A cluster of underwater acoustic sensor nodes is deployed for each sub-region of the diffusing material distribution; and multiple NG-RC modules are constructed based on each of the underwater acoustic sensor node clusters. The underwater acoustic sensor nodes in each of the underwater acoustic sensor node clusters are divided into prediction sensor nodes and observation sensor nodes; a first original observation sequence of the prediction sensor nodes is obtained; a second original observation sequence of the observation sensor nodes is obtained; and an input vector is obtained based on the first original observation sequence and the second original observation sequence. The input vector is input into the corresponding NG-RC module to obtain the local concentration prediction result for each sub-region; Cross-regional correlation information is fused for each of the NG-RC modules, and a global prediction result for each sub-region is obtained based on the local concentration prediction result; Based on the spatial location of each sub-region, the global prediction results of each sub-region are spliced ​​together to obtain the predicted concentration value of the entire region at the corresponding time.

[0007] In one embodiment of the present invention, the step of obtaining the input vector based on the first original observation sequence and the second original observation sequence is as follows: The second original observation sequence is transmitted to the prediction sensor node through an underwater acoustic channel to obtain the third original observation sequence; The first original observation sequence and the third original observation sequence are concatenated to obtain the input vector.

[0008] In one embodiment of the present invention, the step of transmitting the second original observation sequence to the prediction sensor node via an underwater acoustic channel to obtain the third original observation sequence is as follows: Based on the propagation characteristics of the underwater acoustic channel, a signal propagation equation is constructed; wherein, the signal propagation equation is: ; in, Indicates the receiving sensor node The final received signal, Represents a nonlinear operator. Represents the delay operator, Represents sensor nodes To sensor node The propagation delay Indicates to sensor nodes The set of sensor nodes that transmit signals. Indicates the receiving sensor node Additive noise, Represents the set of sensor nodes sent. Each sending sensor node The signal sent; According to the propagation formula, the second original observation sequence is transformed to obtain multiple transformed signals; the prediction sensor node receives the multiple transformed signals and performs superposition processing to obtain the third original observation sequence.

[0009] In one embodiment of the present invention, the input vector is input to the corresponding NG-RC module to obtain the local concentration prediction result for each sub-region, wherein the processing steps of the NG-RC module for the input vector are as follows: The input vector is subjected to a Voltra series mapping to obtain a nonlinear feature vector; the input vector and the nonlinear feature vector are concatenated to obtain a local concentration prediction feature vector; wherein, the expression of the local concentration prediction feature vector is: ; in, Represents the input vector. Represents a nonlinear eigenvector. Symbols indicating splicing; The local concentration prediction feature vector is linearly mapped to obtain the local concentration prediction result.

[0010] In one embodiment of the present invention, the steps of fusing cross-regional correlation information for each NG-RC module and obtaining the global prediction result for each sub-region based on the local concentration prediction result are as follows: Each NG-RC module is defined as a graph node, resulting in a graph node set; the underwater acoustic channels between each NG-RC module are defined as graph edges, resulting in an edge set; the graph node set and the edge set are constructed into a continuous-time dynamic graph; Based on the continuous-time dynamic graph, each graph node maintains and updates a spatiotemporal embedding vector representing its current synthesis state; wherein the expression for the spatiotemporal embedding vector is: ; in, This represents the feature vector for local concentration prediction. Indicates spatial characteristics, Symbols indicating splicing; The spatiotemporal embedding vector is mapped using a spatial correction weight matrix to generate a correction amount for cross-regional coupling effects; Based on the correction amount and the local concentration prediction results, the global prediction results for each sub-region are obtained.

[0011] In one embodiment of the present invention, the step of obtaining the spatial features is as follows: A buffer is set for each graph node; the buffer stores the spatiotemporal features of neighboring graph nodes in the form of ordered pairs, resulting in an ordered pair set; wherein the expression for the ordered pair set is: ; in, Indicates ordered pairs, Represents an embedding vector. Indicates time, Indicates the serial number. Represents graph nodes. Represents the set of nodes in the neighbor graph. Indicates the quantity of ordered pairs. A constant representing the fixed size of the buffer; The buffer aggregates the spatiotemporal features of neighborhood graph nodes through weighted averaging and max pooling, and obtains spatial features based on the ordered set of pairs; wherein the expression for the spatial features is: ; in, Represents aggregate functions, Indicates hyperparameters, Represents graph nodes and At any moment The weight.

[0012] In one embodiment of the present invention, the underwater acoustic channel between each of the NG-RC modules is defined as a graph edge. The process of obtaining the edge set includes: determining whether there is a valid communication link between the prediction sensor nodes of each of the NG-RC modules, specifically: During the transmission period, the underwater acoustic sensors of the predictive sensor nodes periodically transmit broadcast signals; during the non-transmission period, the predictive sensor nodes continuously and passively listen to the underwater acoustic channel. During non-transmission periods, the predictive sensor nodes calculate the link quality index pointing to the sender based on the received broadcast signal. If the link quality index is greater than a preset threshold, it is determined that there is a valid one-way communication link between the prediction sensor node that sends the broadcast signal and the prediction sensor node that receives the broadcast signal at the current moment; otherwise, there is no valid one-way communication link.

[0013] In one embodiment of the present invention, the process of obtaining the global prediction result for each sub-region based on the correction amount and the local concentration prediction result includes optimizing the spatial correlation correction amount weight matrix of the correction amount and the output weight matrix of the local concentration prediction result, wherein the optimization objective is expressed as: ; in, This represents the output weight matrix. This represents the weight matrix for spatial correlation correction. Describe the objective function. This represents the predicted output. Represents the true value. and Represents the regularization parameter. This represents the L2 norm symbol.

[0014] Secondly, to solve the above-mentioned technical problems, the present invention provides a marine diffusive substance concentration field prediction system, comprising: A construction module is used to deploy underwater acoustic sensor node clusters for each sub-region of the diffusing material distribution; and to construct multiple NG-RC modules based on each underwater acoustic sensor node cluster. The input vector acquisition module is used to divide the underwater acoustic sensor nodes in each of the underwater acoustic sensor node clusters into prediction sensor nodes and observation sensor nodes; acquire a first original observation sequence of the prediction sensor nodes; acquire a second original observation sequence of the observation sensor nodes; and obtain an input vector based on the first original observation sequence and the second original observation sequence. The first prediction result output module is used to input the input vector into the corresponding NG-RC module to obtain the local concentration prediction result for each sub-region; The second prediction result output module is used to perform cross-regional correlation information fusion on each of the NG-RC modules, and obtain the global prediction result for each sub-region based on the local concentration prediction result; The third prediction result output module is used to stitch together the global prediction results of each sub-region according to the spatial location of each sub-region to obtain the predicted concentration value of the whole region at the corresponding time.

[0015] Thirdly, in order to solve the above-mentioned technical problems, the present invention provides a marine diffuse substance concentration field prediction device, including the above-mentioned marine diffuse substance concentration field prediction system.

[0016] Compared with the prior art, the above-described technical solution of the present invention has the following advantages: (1) The method, system, and device for predicting the concentration field of marine diffusing substances described in this invention organizes a cluster of underwater acoustic sensor nodes into multiple lightweight NG-RC modules, forming a small-scale time-series prediction unit to process the concentration prediction of local areas in parallel, which enhances the transformation capability of the preset nonlinear basis function. By dividing the underwater acoustic sensor nodes into prediction sensor nodes and observation sensor nodes, the functional roles of different nodes are clearly defined. At the same time, by acquiring the first original observation sequence of the prediction sensor node and the second original observation sequence of the observation sensor node, and fusing these sequences into an input vector, the data advantages of different nodes are fully utilized, improving the accuracy and reliability of the prediction. On this basis, cross-regional correlation information fusion is performed on each NG-RC module, and the global prediction results of each sub-region are generated by combining the local concentration prediction results. This fusion mechanism can effectively capture the dynamic influence relationship between different sub-regions, correct local prediction deviations through inter-regional information complementarity, and further improve the prediction accuracy. According to the spatial location of each sub-region, the global prediction results of each sub-region are spliced ​​to obtain the predicted concentration value of the entire region at the corresponding time. This process not only enables prediction of the entire region, but also ensures the spatiotemporal continuity of the prediction results, providing comprehensive and accurate concentration distribution information for applications such as marine environmental monitoring, pollution source tracing, and resource exploration.

[0017] (2) Based on the NG-RC module, this invention constructs an event-driven dynamic graph network. The network uses each NG-RC module as a graph node and the communication link as a graph edge. The node state change is used as an event triggering mechanism to drive the real-time evolution and dynamic reconstruction of the graph structure, thereby continuously learning the dynamic correlation between the concentration states of different regions and realizing accurate modeling of multi-scale dependencies in the dynamic field.

[0018] (3) This invention proposes an asynchronous information transmission mechanism based on a message buffer. Each module independently maintains a local message queue and manages asynchronously arriving neighbor information through a joint tagging of timestamps and sequence numbers. A weighted aggregation and replacement strategy is used to construct a spatial context representation. This mechanism allows nodes to adaptively update feature representations without synchronizing the entire graph state, significantly reducing computational latency while ensuring full utilization of information.

[0019] (4) In this invention, the feature updates of each graph node and the message transmission between nodes are all performed independently based on the local clock, and do not interfere with each other in the time dimension, thus completely getting rid of the dependence on the global synchronization mechanism. Attached Figure Description

[0020] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings, wherein: Figure 1This is a flowchart of a method for predicting the concentration field of marine diffusing substances in a preferred embodiment of the present invention; Figure 2 This is a schematic diagram of the NG-RC module construction in a preferred embodiment of the present invention; Figure 3 This is a schematic diagram of the construction of an event-driven continuous-time dynamic graph in a preferred embodiment of the present invention; Figure 4 This is a schematic diagram of the message buffer in a preferred embodiment of the present invention; Figure 5 This is a schematic diagram of prediction optimization for cross-regional spatiotemporal correlation correction in a preferred embodiment of the present invention. Detailed Implementation

[0021] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0022] Example 1: Reference Figure 1 As shown, this embodiment of the invention provides a method for predicting the concentration field of marine diffusing substances, including but not limited to the following steps: S1. Deploy underwater acoustic sensor node clusters for each sub-region of the diffusing material distribution; construct multiple NG-RC modules based on each underwater acoustic sensor node cluster; S2. Divide the underwater acoustic sensor nodes in each underwater acoustic sensor node cluster into prediction sensor nodes and observation sensor nodes; obtain the first original observation sequence of the prediction sensor nodes; obtain the second original observation sequence of the observation sensor nodes; obtain the input vector based on the first and second original observation sequences. S3. Input the input vector into the corresponding NG-RC module to obtain the local concentration prediction results for each sub-region; S4. Perform cross-regional correlation information fusion for each NG-RC module, and obtain the global prediction result for each sub-region based on the local concentration prediction results; S5. Based on the spatial location of each sub-region, the global prediction results of each sub-region are spliced ​​together to obtain the predicted concentration value of the entire region at the corresponding time.

[0023] This invention provides a method for predicting the concentration field of diffusing substances in the ocean. It organizes a cluster of underwater acoustic sensor nodes into multiple lightweight NG-RC modules, forming a small-scale time-series prediction unit to process concentration predictions for local areas in parallel. The sensor nodes receive underwater acoustic signals and generate responses, possessing the ability to update their states and evolve independently. Underwater acoustic signals are subjected to complex disturbances such as multipath propagation, frequency dispersion, and time delay attenuation during transmission, naturally enhancing the transformation capability of the preset nonlinear basis function. By dividing the underwater acoustic sensor nodes into prediction sensor nodes and observation sensor nodes, the functional roles of different nodes are clearly defined. By acquiring the first original observation sequence from the prediction sensor nodes and the second original observation sequence from the observation sensor nodes, and fusing these sequences into an input vector, the data advantages of different nodes are fully utilized, improving the accuracy and reliability of the prediction. Based on this, cross-regional correlation information fusion is performed on each NG-RC module, and the global prediction results for each sub-region are generated by combining the local concentration prediction results. This fusion mechanism effectively captures the dynamic influence relationships between different sub-regions, corrects local prediction deviations through inter-regional information complementarity, further improves prediction accuracy, and makes the results more consistent with the actual changing patterns of the marine environment. Based on the spatial location of each sub-region, the global prediction results for each sub-region are stitched together to obtain the predicted concentration value for the entire region at the corresponding time. This process not only achieves prediction for the entire region but also ensures the spatiotemporal continuity of the prediction results, providing comprehensive and accurate concentration distribution information for applications such as marine environmental monitoring, pollution source tracing, and resource exploration.

[0024] To effectively predict the concentration evolution of underwater diffusing substances, this invention proposes a distributed prediction method. Multiple underwater acoustic sensor node clusters are deployed in the diffusing substance distribution area, with each cluster forming a physical NG-RC (Next Generation Reservoir Computing) module. Each NG-RC module outputs a local prediction of the future concentration in its sub-region based on historical observations from its constituent nodes, and integrates cross-regional correlation information to form a global prediction for that sub-region. The overall framework of the marine diffusing substance concentration field prediction method described in this invention is as follows: First, assume that there are a total of [number] diffusive substances within the distribution area. A cluster of underwater acoustic sensor nodes has been formed, corresponding to... The NG-RC module, the first Each NG-RC module contains There are one underwater acoustic sensor node. Then, at time [time missing], this module... The observation vector is represented as: ; in, Representation module Inner Each underwater acoustic sensor node Concentration value at time, This represents the matrix transpose symbol.

[0025] Secondly, the NG-RC module Based on its past Local observation sequence at each time step To conduct future work in this sub-region The local concentration prediction step is expressed as follows: ; in, It is a prediction model jointly constructed by underwater acoustic sensor nodes and propagation channels, used to capture the temporal characteristics of the evolution of diffusing substance concentration in a local area.

[0026] Then, based on the local concentration prediction results, each NG-RC module further integrates cross-regional correlation information to ultimately form the future concentration prediction results for that sub-region. Global prediction of step concentration, where the expression for global prediction is: ; in It is an NG-RC module At any moment Cross-regional spatiotemporal correlation features constructed by network connections, Based on local prediction model A global prediction model constructed through collaborative network connections is used to integrate cross-regional spatiotemporal correlation features on the basis of local prediction.

[0027] Finally, each NG-RC module independently generates concentration predictions for its responsible sub-region, and the prediction of the entire diffusive substance concentration field is obtained by combining all... The local prediction results of each NG-RC module are stitched together according to the spatial location of its corresponding sub-region. Therefore, the expression for the predicted concentration value of the entire region at the corresponding time is: ; in, Represents the predicted future Concentration values ​​for all regions at any given time.

[0028] Based on the above framework, this invention fully utilizes the physical characteristics of underwater acoustic channels and cleverly integrates lightweight neural computing and dynamic graph mechanisms to accurately achieve distributed intelligent prediction of underwater diffusive substance concentration fields. The following sections will elaborate on each key aspect.

[0029] Specifically, in step S1, refer to Figure 2As shown, in this embodiment, adjacent underwater acoustic sensor nodes self-organize into multiple NG-RC units that are physically represented (see reference). Figure 2 (As shown in the "Sensor Node Cluster" area), each NG-RC unit is responsible for predicting the concentration of diffusing substances in the local area where its sensor node is located. Each NG-RC unit integrates the diffusing substance concentration data observed by multiple sensor nodes within its coverage area and uses it as input. The data is processed through a nonlinear transformation of the underwater acoustic channel (…). Figure 2 The red wavy lines connecting the nodes symbolize the underwater acoustic channel and its nonlinear effects. Then, nonlinear feature vectors are generated through nonlinear mapping, and finally, local prediction of concentration diffusion is completed through the output layer. Figure 2 This diagram illustrates the physical construction of the NG-RC module based on an underwater acoustic sensor network proposed in this embodiment. The diagram visually depicts how spatially adjacent sensor nodes self-organize into a physical NG-RC prediction unit and its operational process.

[0030] This invention organizes the underwater acoustic sensor node cluster into multiple lightweight NG-RC modules, avoiding the need for traditional neural networks to rely on activation functions and connection structures to ensure the model's nonlinear expressive power. The NG-RC module is a lightweight architecture based on mathematically constructed pre-defined nonlinear basis functions. By fixing the feature generation mechanism and training only the output layer, it reduces training complexity while maintaining high performance.

[0031] Specifically, in step S2, each NG-RC module input vector It is not simply a patchwork of raw observations from all sensor nodes within its coverage area, but rather fully utilizes the physical characteristics of the underwater acoustic communication channel. Therefore, the underwater acoustic sensor nodes in each cluster are divided into prediction sensor nodes and observation sensor nodes. The sensor node responsible for prediction within the module (i.e., the prediction sensor node) provides its own historical first raw concentration observation sequence, while the observations from other sensor nodes within the module (i.e., the observation sensor node) (i.e., the second raw observation sequence) must undergo a nonlinear transformation of the underwater acoustic channel before being used as part of the input.

[0032] Furthermore, the steps to obtain the input vector based on the first and second original observation sequences are as follows: S210. The second original observation sequence is transmitted to the prediction sensor node through the underwater acoustic channel to obtain the third original observation sequence.

[0033] S220. The first and third original observation sequences are concatenated to obtain the input vector.

[0034] For example, such as Figure 2 As shown in the sensor node cluster area, the NG-RC module It contains multiple underwater acoustic sensor nodes, numbered as follows: The red sensor node is used to perform prediction tasks and belongs to the prediction sensor node category. Its past... The first original observation sequence at time 1 Directly used as input vector Part of it, each blue sensor node within the module This belongs to the observation sensor node, and its second raw observation sequence go through Figure 2 The underwater acoustic channel, indicated by the red wavy arrow, transmits data to the sensor node. Because the underwater acoustic channel provides a natural nonlinear perturbation, the perturbation reaching the sensor node... The sequence data is no longer the original observation sequence. Instead, it is a sequence after nonlinear transformation by the underwater acoustic channel. Ultimately, the NG-RC module At any moment input vector From sensor nodes The original concentration observation sequence and other sensor nodes within the module Received sequence after channel transformation It is constructed by concatenation. Therefore, the input vector... The expression is: ; (1) in Representation module Other sensor nodes Observational data propagated through the underwater acoustic channel Representation module Internal sensor node The set of neighbors.

[0035] Furthermore, when underwater acoustic sensor nodes perform underwater acoustic communication, the transmitted data is affected by the nonlinear characteristics of underwater acoustic propagation (such as multipath propagation, frequency dispersion, and signal attenuation) and time-varying characteristics, resulting in natural nonlinear distortion and dynamic transformation of the signal. Therefore, the physical dynamic characteristics of the underwater acoustic channel can serve as a natural nonlinear transformation mechanism. For step S210, the specific steps are as follows: S211. Based on the propagation characteristics of the underwater acoustic channel, construct the signal propagation equation. For the signal propagation process, it is the signal... The propagation process from the sending sensor node to the receiving sensor node. The constructed signal propagation equation is: ; (2) in, It represents a nonlinear operator used to characterize the nonlinear transformation of the channel on the input signal, comprehensively covering the influence of various nonlinear effects; This represents a delay operator used to characterize the time delay during signal propagation. This reflects path length and medium characteristics, etc. Represents sensor nodes To sensor node The propagation delay Indicates to sensor nodes The set of sensor nodes that transmit signals; Indicates the receiving sensor node Additive noise refers to random interference introduced at the receiver, such as environmental background noise (e.g., marine life sounds, wind and waves, ship noise, etc.) or electronic noise of the sensor itself. Indicates the receiving sensor node The final received signal; Represents the set of sensor nodes sent. Each sending sensor node The signal sent.

[0036] Furthermore, Each sending sensor node in The signal emitted After propagating through the underwater acoustic channel (including time delay and nonlinear transformation), it reaches the sensor node. These signals are superimposed at the receiving end, plus additive noise. Together they form the received signal .

[0037] S212. According to the propagation relationship, the second original observation sequence is transformed to obtain multiple transformed signals; the prediction sensor node receives the multiple transformed signals and performs superposition processing to obtain the third original observation sequence.

[0038] Specifically, in step S3, this embodiment utilizes the natural nonlinear perturbation provided by the aforementioned underwater acoustic channel, superimposed with an active, structured feature map based on a second-order Volterra series, and simultaneously combines it with the NG-RC module to obtain the local concentration prediction results for each sub-region. The specific steps are as follows: S310. Perform a Voltra series mapping on the input vector to obtain a nonlinear feature vector; concatenate the input vector and the nonlinear feature vector to obtain the local concentration prediction feature vector. Specifically, at time... , No. One NG-RC module is used for local prediction of feature vectors. The input vector after transformation through the underwater acoustic channel and Nonlinear eigenvectors obtained through the Voltra series mapping The feature vector for local concentration prediction is obtained by concatenation. ; (3) in, This indicates a direct concatenation operation symbol.

[0039] S320. Perform a linear mapping on the local concentration prediction feature vector to obtain the local concentration prediction result. Specifically, in the... In the readout layer of each NG-RC module, a linear mapping operation is performed to convert the module's feature vector into a local concentration prediction result. The expression for the local concentration prediction result is: ; (4) in, Representation module exist The local prediction output at time step; The output weight matrix represents the linear mapping of the prediction model.

[0040] Furthermore, output the weight matrix. The training will incorporate cross-regional spatiotemporal correlations within a unified joint optimization framework. This joint training mechanism aims to synergistically optimize local physical evolution modeling and global spatial correlation modeling, thereby significantly improving the overall prediction accuracy of diffusing substance concentration fields. The specific joint optimization mechanism will be detailed in step S4. Through this linear regression process, the NG-RC module can transform the nonlinear local concentration prediction feature vector... Mapping to the output space generates prediction results for the concentration of diffusive substances in local regions.

[0041] The NG-RC unit, constructed primarily from underwater acoustic sensor nodes, relies solely on local observation data and cannot perceive concentration changes and physical influences in other regions (such as plume drift, turbulent diffusion, and other cross-regional coupling effects), leading to inherent prediction biases. To capture the temporal and spatial evolution dependencies between concentration sequences across multiple regions and achieve dynamic modeling of the spatiotemporal correlation of diffusing substance concentrations, this embodiment organizes multiple NG-RC modules in a local water area into an event-driven continuous-time dynamic graph (CTDG). Therefore, for step S4, the specific steps are as follows: S410. Define each NG-RC module as a graph node to obtain a graph node set; define the underwater acoustic channel between each NG-RC module as a graph edge to obtain an edge set; construct the graph node set and edge set into a continuous-time dynamic graph.

[0042] Specifically, CTDG uses NG-RC modules as graph nodes and underwater acoustic communication links between modules as graph edges. As events occur and spread over time, CTDG supports changes in graph node characteristics and edge connections, adapting to the real-time evolution of data and relationships. (Refer to...) Figure 3 As shown, Figure 3 This demonstrates the construction mechanism of an event-driven continuous-time dynamic graph (CTDG). The dynamic graph uses NG-RC modules as graph nodes. Figure 3 (Middle circular node), the effective underwater acoustic communication link between modules is the graph edge ( Figure 3 (Arrow connecting the nodes in the middle circle).

[0043] Furthermore, respectively using and Indicates that CTDG is at time... The graph node set and edge set, where The number in the diagram is The graph nodes, corresponding to the number are The NG-RC module uses graph node feature vectors (i.e., spatiotemporal embedding vectors) to... express. Represents graph nodes and The state of existence of the edges between them. The expression is: (5)

[0044] Furthermore, this embodiment, based on the actual communication behavior of the underwater acoustic sensor nodes undertaking the prediction task in each NG-RC module, adopts a passive listening method to plan the presence or absence of connections by receiving signals. For example... Figure 3 As shown, the decision graph nodes and At any moment To determine whether edge connections exist, it is only necessary to identify the sensor nodes in the corresponding NG-RC modules that perform the prediction task. Figure 3 Does a valid communication link exist between the red sensor nodes?

[0045] Specifically, the method for determining whether a valid communication link exists between the predictive sensor nodes of each NG-RC module is as follows: S411. During the transmission period, the underwater acoustic sensor of the predictive sensor node periodically transmits broadcast signals; during the non-transmission period, the predictive sensor node continuously and passively listens to the underwater acoustic channel.

[0046] S412. During non-transmission periods, the predictive sensor node calculates the link quality index pointing to the sender based on the received broadcast signal.

[0047] Specifically, the steps for calculating the link quality index pointing to the sender are as follows: S4121. Calculate the normalized signal-to-noise ratio pointing towards the sender. Its expression is: ; (6) in, This indicates the measured signal-to-noise ratio. For example, the WHOI Micro-Modem 2 micro-modem can directly obtain the measured signal-to-noise ratio of the received signal after completing signal reception through its built-in function. Set the demodulation threshold for the device. Ideal signal-to-noise ratio. Normalized signal-to-noise ratio. It reflects the instantaneous signal quality of the communication link.

[0048] S4122. Calculate the sequence number continuity pointing to the sender. Its expression is: ; (7) in, This represents the expected number of missing sequence numbers since the previous calculation. The expected total number of sequence numbers to be received is calculated based on the difference between the maximum received sequence number and the previous maximum sequence number. It is assumed that a certain underwater acoustic sensor node has already received sequence numbers belonging to graph nodes. The set of broadcast signal sequence numbers, after being sorted in ascending order, is , The largest sequence number in the set during the last calculation of sequence number continuity (during the first calculation). = ), Given the maximum sequence number in the set when calculating sequence number continuity, the expected number of sequence numbers is... The set of missing sequence numbers is: The number of missing sequence numbers is Serial number continuity Used to reflect the timing integrity and reliability of data transmission based on the proportion of missing sequence numbers.

[0049] S4123. Weight the normalized signal-to-noise ratio and sequence number continuity to obtain the link quality index. Among them, the link quality index The expression is: ; (8) in, and These are weighting coefficients, reflecting the degree of emphasis placed on instantaneous signal quality and transmission reliability, respectively.

[0050] S413. If the link quality index is greater than the preset threshold, it is determined that there is a valid one-way communication link between the prediction sensor node that sends the broadcast signal and the prediction sensor node that receives the broadcast signal at the current time; otherwise, there is no valid one-way communication link.

[0051] For example, refer to Figure 3 Graph nodes The corresponding NG-RC module The underwater acoustic sensor responsible for prediction periodically transmits broadcast signals. , containing graph nodes Identity identifier and monotonically increasing sequence numbers During non-transmitting periods, the underwater acoustic sensor nodes continuously and passively monitor the channel. Based on the received broadcast signals, they calculate the Link Quality Indicator (LQI) pointing to the transmitter. The LQI comprehensively considers the normalized signal-to-noise ratio (SNR) and sequence number continuity. ( When the preset threshold is used, it is determined that at time [time value missing]. From graph nodes To graph nodes Effective one-way communication link exist( ).

[0052] The evolution of S420 and CTDG is based on a sequence of events ordered by timestamps. Driver, in which , , indicating at time Graph nodes The feature vector is updated to The updating of graph node features triggers the evolution of CTDG. For example... Figure 3 As shown, graph nodes exist Its features are updated at any given time. (i.e., the event) ), driving the graph structure from time to time At the time The evolution of.

[0053] To address the inefficiency of traditional dynamic graph update mechanisms that rely on global synchronization in underwater acoustic communication scenarios characterized by high latency, strong uncertainty, and limited bandwidth, this embodiment designs an asynchronous spatiotemporal information transmission mechanism. The core of this mechanism is to utilize message buffers (MessageBoxes) to decouple, aggregate, and asynchronously update spatiotemporal information between graph nodes, thus eliminating the reliance on global synchronization.

[0054] Furthermore, referring to Figure 4 As shown, this embodiment designs a fixed-capacity buffer (MessageBox) for each graph node to store and aggregate spatiotemporal features from neighboring graph nodes through weighted averaging and max pooling. Each graph node, as shown in the MessageBox structure, is a fixed-capacity buffer (…). )( Figure 4 The yellow shaded area in the middle stores the spatiotemporal features of neighborhood graph nodes in the form of ordered pairs, thus obtaining an ordered pair set; the expression for the ordered pair set is: ; (9) Among them, ordered pairs From graph nodes At any moment Send to Embedded vector Its local timestamp and serial number composition, express Graph nodes The first one sent A set of embedding vectors is used to represent the order in which the embedding vectors are sent. Initial value is 0, graph node Each time the embedding vector is sent, The value increases by 1. Represents graph nodes The buffer at time Stored ordered sets of pairs express The set of neighboring graph nodes, express The buffer at time The number of ordered pairs stored. Represents graph nodes A constant with a fixed buffer size. For example... Figure 4 middle The corresponding buffer at time Stored ordered pairs and ,but , .

[0055] Furthermore, the buffer aggregates the spatiotemporal features of neighborhood graph nodes through weighted averaging and max pooling, and based on the ordered set... spatial features Spatial features The expression is: ; (10) in, Represents graph nodes The MessageBox at any time The aggregation results This represents the aggregation function, which uses a combination of weighted average and max pooling aggregation. This represents the hyperparameters used to control the degree of influence of weighted averaging and max pooling on the aggregation results. Represents graph nodes and At any moment The weight.

[0056] Furthermore, regarding weights The exponential decay function is used to calculate and assign higher weights to newer information. Its expression is: ; (11) in, It is the attenuation factor. Graph nodes At this moment, Graph nodes Send to The moment corresponding to the self-embedding vector.

[0057] Furthermore, since the buffer's capacity is fixed, when the MessageBox reaches its maximum capacity, the buffer's contents need to be managed: ;(12) in, This represents the new buffer after management operations. This describes the methods for managing the buffer contents, including two strategies: removal and replacement. Specifically, the removal strategy prioritizes removing vectors that have already been aggregated, assuming a graph node... The MessageBox buffer at time The stored ordered set of pairs is If vector If a user has previously participated in the aggregation, remove them: The replacement strategy replaces the oldest vector based on a combination of local timestamps and sequence numbers. Replacement prioritizes sorting by local timestamps, and if sorting fails, sequence numbers are used to supplement the sorting mechanism. Assume that when the buffer is full, a new embedding vector is received. First, determine if there are graph nodes in the buffer. If the previously sent embedding vector exists, then pair them according to their timestamps. Sort the previously sent embedding vectors and the new embedding vectors, assuming the earliest timestamp after sorting is... and Then use replace corresponding embedding vector : If it does not exist, then sort the vectors in the buffer and the new embedding vector according to their sequence numbers. Assume the smallest sequence number after sorting is... and Then use replace corresponding embedding vector : This combined strategy combines the timeliness of timestamps with the orderliness of sequence numbers, ensuring that the buffer retains newer, more relevant information.

[0058] Based on CTDG, MessageBox provides the ability to aggregate neighborhood spatial features. To comprehensively characterize the local state of a graph node, it is necessary to fuse features representing the temporal evolution of the region itself with features representing its spatial relationships to construct a unified graph spatiotemporal embedding vector.

[0059] Specifically, in this embodiment, based on the continuous-time dynamic graph, each graph node maintains and updates a spatiotemporal embedding vector representing its current integrated state. Specifically, as... Figure 4 As shown, graph nodes Maintain and update a spatiotemporal embedding vector representing its current synthesis state. , Predicting feature vectors (also known as time-series features) based on local concentrations and spatial features Constructed by splicing. Among them, the local concentration prediction feature vector... Constructed according to formula (3), it is formed by graph nodes. The corresponding NG-RC module utilizes its local concentration data and extracts temporal features using underwater acoustic channel nonlinearity and Volterra mapping. Spatial features From graph nodes The MessageBox is obtained by aggregating the spatiotemporal embedding vectors of the neighborhood graph nodes, such as... Figure 4 As shown, at time , The MessageBox stores data from neighbor graph nodes. and Two messages , ,at this time Its spatial features need to be updated, which calls the aggregation function. By aggregating and calculating these two messages, we obtain... Current moment Spatial features .final, spatiotemporal embedding vector Depend on and Constructed by direct concatenation. Spatiotemporal embedding vector. The expression is: ; (13) in, Includes graph nodes The evolution trend of temporal characteristics within the sub-region under its responsibility. By aggregating contextual information from adjacent regions in space, it effectively captures spatial correlation information influenced by the state of surrounding regions. Therefore, the spatiotemporal embedding vector obtained by concatenating these two elements is highly valuable. Represents graph nodes The current overall status of the sub-region under its responsibility.

[0060] It should be noted that in formula (10) With formula (13) The meanings are the same, and formula (10) is described as follows: In order to be with ordered sets The timestamp indices of the ordered pairs correspond to each other.

[0061] S430. Prediction optimization based on cross-regional spatiotemporal correlation correction. The spatiotemporal embedding vector is mapped through a spatial correction weight matrix to generate the correction amount for cross-regional coupling effects.

[0062] Specifically, the spatiotemporal embedding vector constructed in the aforementioned steps For each graph node A complete feature representation integrating local dynamics and spatial correlation is provided. To fully utilize this spatiotemporal feature for accurate prediction, this embodiment introduces a residual learning architecture for collaborative prediction. Its core idea is to decompose graph node-level prediction into a local physical prediction baseline and a spatial correlation correction. The local prediction is generated by the NG-RC module based on local observation data of its underwater acoustic sensor node coverage area, representing the concentration evolution trend captured by the underwater acoustic channel physical processes and local Volterra mapping. The spatial correlation correction is generated based on the spatiotemporal embedding vector constructed from CTDG, essentially learning and quantifying the correction amount generated by cross-regional physical coupling (such as plume transport and turbulent diffusion) on the local concentration. Each NG-RC module uses the local prediction as a baseline, superimposing the spatial correction amount provided by the network topology calculation to generate the global concentration prediction value for its responsible sub-region.

[0063] S440. Based on the correction amount and the local concentration prediction results, obtain the global prediction results for each sub-region.

[0064] Specifically, refer to Figure 5 As shown, each NG-RC module The global prediction generation process includes local prediction ( Figure 5 The "local prediction" area and spatial correlation correction ( Figure 5 The "spatial correlation correction" region has two calculation paths, and the outputs of the two paths are finally superimposed to generate the module. The module is responsible for predicting the global concentration in the assigned region. Specifically, when the module... When performing a global prediction task, the computational path for local prediction is first based on the observation data of the sensor nodes within the module and then constructs the input vector using the nonlinear transformation of the underwater acoustic channel. ( Figure 5 (Step ①) Then, obtain the nonlinear eigenvectors through Volterra series mapping. ( Figure 5 (Step ②) Input vector and nonlinear eigenvectors Directly concatenating to form local time-series feature vectors ( Figure 5(Step ③). Due to the continuous co-evolutionary characteristics of the NG-RC unit and the Dynamic Graph Network (CTDG), when performing the global prediction task, the temporal feature extraction of the NG-RC module represented by steps ①-③ and the spatial feature generation based on CTDG represented by step ⑤ are decoupled in the time dimension (the two have no shared data conflicts; the former only needs locally collected data, and the latter only needs neighbor messages, both relying on local sensor clock updates), and their calculation processes do not have strict temporal dependencies. Therefore, the calculations of steps ①-③ and step ⑤ are continuous background processes, and their outputs are cached in the sensor node undertaking the prediction task. After step ③ is completed, the local prediction process directly enters step ④ to generate local concentration prediction values, and the spatial correlation correction calculation process transfers to step ⑥ to update the spatiotemporal embedding vector. Then proceed to step ⑦. By spatially correcting the weight matrix Mapping generates corrections for cross-regional coupling effects. After both the local prediction and spatial correlation correction paths have been calculated, the residual superposition module generates the result. Global concentration prediction ( Figure 5 Step ⑧), its specific expression is: ;(14) in, Indicates NG-RC module At any moment The generated global prediction output, i.e., the future of its responsible sub-region. Concentration prediction vector of step, For module The generated local predictions, This is a spatial correlation correction term, used to compensate for potential biases in local forecasts caused by neglecting cross-regional dynamic correlations. This is the weight matrix for spatial correlation correction.

[0065] Furthermore, to optimize the weight parameters for physical modeling and structural calculation, this embodiment employs a gradient descent training strategy. The training objective is to minimize the mean squared error between the predicted outputs of all modules and the actual concentration values, and an L2 regularization term is introduced to prevent overfitting and improve the model's generalization ability. For the... The optimization objective of the NG-RC module is: ; (15) in, It is a module The objective function is denoted by the sum of the prediction error and the regularization penalty term. It is the predicted output; It is the actual value; , It is a regularization parameter that controls the strength of regularization. Indicates the L2 norm symbol; , These are the L2 norms of the local prediction weight matrix and the spatial correction weight matrix, respectively, used to prevent model overfitting.

[0066] This invention fully considers the inherent dynamic characteristics of underwater diffusive substance concentration fields: spatially, the diffusion process exhibits significant heterogeneity; temporally, its evolution presents a mixed pattern of sudden and persistent events. To model the high-order spatiotemporal correlations between concentration sequences in multiple regions, this invention constructs an event-driven dynamic graph network based on the NG-RC module. This graph structure uses each NG-RC module as a node and communication links as edges, with node state changes serving as the event trigger mechanism to drive the evolution and reconstruction of the graph structure. It continuously learns the dynamic correlations between concentration states in different regions, achieving multi-scale dependency modeling in the dynamic field.

[0067] Specifically, after improving the prediction capability of local regions based on spatiotemporal embedding vectors, each graph node then enters the feature update stage. The graph node independently calculates and updates its own features based on locally available information, without waiting for full graph synchronization.

[0068] Furthermore, referring to Figure 5 As shown, the feature update process of graph nodes is divided into local temporal features. Spatial features and spatiotemporal embedding vectors Update. Local time series features are updated based on nonlinear features extracted by the NG-RC module. Figure 5 Steps ①-③ in the middle section do not require interaction with other NG-RC modules, therefore there are no communication dependencies. Spatial characteristics Based on MessageBox aggregation, spatiotemporal feature updates across regions ( Figure 5 (Step ⑤) Since MessageBox is built into a local module, its updates rely solely on the local clock. Spatiotemporal embedding vector It is composed of updated temporal and spatial features spliced ​​together. Figure 5 In step ⑥), these updates do not depend on the current update status or calculation results of other nodes, therefore they do not need to be synchronized with the updates of other graph nodes. For example... Figure 5 Chinese map nodes At any moment Update its spatiotemporal embedding vector ( Figure 5 In step ⑦), the following is used It aggregates the neighbor graph nodes already cached in its own MessageBox. , old state and Meanwhile, the neighbor graph nodes It may be processing its own steps ①-④, but this does not affect... Update.

[0069] Furthermore, graph nodes update their spatiotemporal embedding vectors ( Figure 5 After step ⑦), it can be immediately packaged as a new message. Send to neighbor graph nodes such as MessageBox ( Figure 5 (As shown in the "Asynchronous Transmission of Spatiotemporal Information" section), no waiting is required. Update complete. Receiving this message will not interrupt any ongoing computations; instead, the message will be cached in its own MessageBox. Similarly, messages sent by neighboring graph nodes will arrive at the graph node asynchronously. The MessageBox, and in They are aggregated the next time spatial features are updated.

[0070] Furthermore, graph node feature updates are driven by updates to temporal and spatial features, and message sending is typically triggered immediately after a graph node feature update. Message reception and buffering are determined by the physical characteristics of the communication link and the processing capabilities of the receiving end, and are passive and asynchronous. In the three processes of updating the features of all graph nodes, sending messages to neighbors, and receiving and buffering neighbor messages, no step requires all nodes to stop and wait for a unified "synchronization moment." Therefore, the feature updates of each graph node and the message passing between them are independent in time, driven by the local clock of each graph node, eliminating the dependence of graph node feature updates on global synchronization. This allows each NG-RC module to maximize the use of local computing resources and currently available information to continuously and autonomously advance the prediction task and state updates.

[0071] Traditional dynamic graph models often rely on global synchronization when updating node states. However, in the underwater environment, underwater acoustic communication faces severe bandwidth limitations and latency fluctuations, making synchronization mechanisms difficult to implement. To address this, this invention proposes an asynchronous information transmission mechanism based on a message buffer. Each module maintains a local message queue (MessageBox), managing asynchronously arriving neighbor information through timestamps and sequence numbers, and constructing a spatial context representation using a weighted aggregation and replacement strategy. This mechanism supports adaptive feature representation updates by nodes even when the entire graph is not synchronized, significantly reducing computational latency while ensuring full information utilization.

[0072] Specifically, in step S5, the local prediction results of all NG-RC modules are spliced ​​together according to the spatial location of their corresponding sub-regions to obtain the prediction of the entire diffusive substance concentration field.

[0073] This invention proposes a design concept where sensor nodes, propagation channels, and network connections themselves constitute the key physical computing units of the prediction mechanism in traditional underwater sensor networks. The concept posits that sensor nodes are physical neurons, underwater acoustic channels are nonlinear activation functions, and distributed underwater acoustic networks are dynamic graph neural structures. This transforms underwater acoustic sensor networks into edge-agent prediction methods with self-organizing, adaptive, and low-power characteristics. This method integrates neural computation and physical propagation mechanisms. The underwater acoustic sensor network system is no longer merely a hardware platform carrying the prediction model; rather, it is directly embedded into the prediction framework through its physical structure and propagation mechanism, forming the prediction model itself. This provides a paradigm for embedded intelligence by physics in dynamic marine environments.

[0074] Example 2: Based on the same inventive concept, this embodiment provides a marine diffuse substance concentration field prediction system. The principle of solving the problem is similar to that of the marine diffuse substance concentration field prediction method provided in Embodiment 1, and the repeated parts will not be described again.

[0075] This embodiment provides a marine diffuse substance concentration field prediction system, including: The module is used to deploy underwater acoustic sensor node clusters for each sub-region of the diffusing material distribution; and multiple NG-RC modules are built based on each underwater acoustic sensor node cluster. The input vector acquisition module is used to divide the underwater acoustic sensor nodes in each underwater acoustic sensor node cluster into prediction sensor nodes and observation sensor nodes; acquire the first original observation sequence of the prediction sensor nodes; acquire the second original observation sequence of the observation sensor nodes; and obtain the input vector based on the first and second original observation sequences. The first prediction result output module is used to input the input vector into the corresponding NG-RC module to obtain the local concentration prediction result for each sub-region; The second prediction result output module is used to perform cross-regional correlation information fusion for each NG-RC module and obtain the global prediction result for each sub-region based on the local concentration prediction result; The third prediction result output module is used to stitch together the global prediction results of each sub-region according to the spatial location of each sub-region to obtain the predicted concentration value of the whole region at the corresponding time.

[0076] Example 3: This embodiment provides a marine diffuse substance concentration field prediction device, including the marine diffuse substance concentration field prediction system provided in Embodiment 2.

[0077] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0078] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0079] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0080] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0081] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A method for predicting the concentration field of marine diffusible substances, characterized in that, include: Deploy underwater acoustic sensor node clusters for each sub-region of the diffusing material distribution; Based on each of the aforementioned underwater acoustic sensor node clusters, multiple NG-RC modules are constructed; The underwater acoustic sensor nodes in each of the underwater acoustic sensor node clusters are divided into prediction sensor nodes and observation sensor nodes; a first original observation sequence of the prediction sensor nodes is obtained; a second original observation sequence of the observation sensor nodes is obtained; and an input vector is obtained based on the first original observation sequence and the second original observation sequence, specifically: The second original observation sequence is transmitted to the prediction sensor node via an underwater acoustic channel to obtain the third original observation sequence, specifically: Based on the propagation characteristics of the underwater acoustic channel, a signal propagation equation is constructed; wherein, the signal propagation equation is: ； in, Indicates the receiving sensor node The final received signal, Represents a nonlinear operator. Represents the delay operator, Represents sensor nodes To sensor node The propagation delay Indicates to sensor nodes The set of sensor nodes that transmit signals. Indicates the receiving sensor node Additive noise, Represents the set of sensor nodes sent. Each sending sensor node The signal sent; According to the propagation formula, the second original observation sequence is transformed to obtain multiple transformed signals; the prediction sensor node receives the multiple transformed signals and performs superposition processing to obtain the third original observation sequence. The first original observation sequence and the third original observation sequence are concatenated to obtain the input vector; The input vector is input into the corresponding NG-RC module to obtain the local concentration prediction result for each sub-region; wherein, the processing steps of the NG-RC module for the input vector are as follows: The input vector is subjected to a Voltra series mapping to obtain a nonlinear feature vector; the input vector and the nonlinear feature vector are concatenated to obtain a local concentration prediction feature vector; wherein, the expression of the local concentration prediction feature vector is: ； in, Indicates NG-RC module The input vector, Represents a nonlinear eigenvector. Symbols indicating splicing; The local concentration prediction feature vector is linearly mapped to obtain the local concentration prediction result; Cross-regional correlation information is fused for each of the NG-RC modules, and a global prediction result for each sub-region is obtained based on the local concentration prediction result, specifically as follows: Each NG-RC module is defined as a graph node, resulting in a graph node set; the underwater acoustic channels between each NG-RC module are defined as graph edges, resulting in an edge set; the graph node set and the edge set are constructed into a continuous-time dynamic graph; Based on the continuous-time dynamic graph, each graph node maintains and updates a spatiotemporal embedding vector representing its current synthesis state; wherein the expression for the spatiotemporal embedding vector is: ； in, This represents the feature vector for local concentration prediction. Indicates spatial characteristics, The steps to obtain the spatial features are as follows: (This refers to the splicing symbols.) A buffer is set for each graph node; the buffer stores the spatiotemporal features of neighboring graph nodes in the form of ordered pairs, resulting in an ordered pair set; wherein the expression for the ordered pair set is: ； in, Indicates ordered pairs, Represents an embedding vector. Indicates time, Indicates the serial number. Represents graph nodes. Represents the set of nodes in the neighbor graph. Indicates the quantity of ordered pairs. A constant representing the fixed size of the buffer. Represents graph nodes The buffer at time An ordered set of stored pairs; The buffer aggregates the spatiotemporal features of neighborhood graph nodes through weighted averaging and max pooling, and obtains spatial features based on the ordered set of pairs; wherein the expression for the spatial features is: ； in, Represents aggregate functions, Indicates hyperparameters, Represents graph nodes and At any moment The weights; The spatiotemporal embedding vector is mapped using a spatial correction weight matrix to generate a correction amount for cross-regional coupling effects; Based on the correction amount and the local concentration prediction result, the global prediction result for each sub-region is obtained; wherein, the expression for the global prediction result for each sub-region is: ； in, Indicates NG-RC module At any moment The generated global prediction output, Indicates NG-RC module The output weight matrix, Indicates NG-RC module Spatial correlation correction weight matrix, Indicates NG-RC module The output spatiotemporal embedding vector; Based on the spatial location of each sub-region, the global prediction results of each sub-region are spliced ​​together to obtain the predicted concentration value of the entire region at the corresponding time.

2. The method for predicting the concentration field of marine diffusing substances according to claim 1, characterized in that, The underwater acoustic channel between each NG-RC module is defined as a graph edge. The process of obtaining the edge set includes: determining whether there is a valid communication link between the predictive sensor nodes of each NG-RC module, specifically: During the transmission period, the underwater acoustic sensors of the predictive sensor nodes periodically transmit broadcast signals; during the non-transmission period, the predictive sensor nodes continuously and passively listen to the underwater acoustic channel. During non-transmission periods, the predictive sensor nodes calculate the link quality index pointing to the sender based on the received broadcast signal. If the link quality index is greater than a preset threshold, it is determined that there is a valid one-way communication link between the prediction sensor node that sends the broadcast signal and the prediction sensor node that receives the broadcast signal at the current moment; otherwise, there is no valid one-way communication link.

3. The method for predicting the concentration field of marine diffusing substances according to claim 1, characterized in that, The process of obtaining the global prediction result for each sub-region based on the correction amount and the local concentration prediction result includes optimizing the spatial correlation correction amount weight matrix and the output weight matrix of the local concentration prediction result, wherein the optimization objective is expressed as: ； in, Describe the objective function. This represents the predicted output. Represents the true value. and Represents the regularization parameter. This represents the L2 norm symbol.

4. A marine diffusible substance concentration field prediction system, used to implement the marine diffusible substance concentration field prediction method according to any one of claims 1 to 3, characterized in that, include: A module is built to deploy underwater acoustic sensor node clusters for each sub-region of the diffusing material distribution; Based on each of the aforementioned underwater acoustic sensor node clusters, multiple NG-RC modules are constructed; The input vector acquisition module is used to divide the underwater acoustic sensor nodes in each of the underwater acoustic sensor node clusters into prediction sensor nodes and observation sensor nodes; acquire a first original observation sequence of the prediction sensor nodes; acquire a second original observation sequence of the observation sensor nodes; and obtain an input vector based on the first original observation sequence and the second original observation sequence. The first prediction result output module is used to input the input vector into the corresponding NG-RC module to obtain the local concentration prediction result for each sub-region; The second prediction result output module is used to perform cross-regional correlation information fusion on each of the NG-RC modules, and obtain the global prediction result for each sub-region based on the local concentration prediction result; The third prediction result output module is used to stitch together the global prediction results of each sub-region according to the spatial location of each sub-region to obtain the predicted concentration value of the whole region at the corresponding time.

5. A device for predicting the concentration field of marine diffusing substances, characterized in that, Including the marine diffusive substance concentration field prediction system as described in claim 4.

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