Marine sound velocity field prediction method and system

Abstract

The invention discloses an ocean sound velocity field prediction method and system, and relates to the technical field of data processing, and the method comprises the steps: carrying out the quantitative diagnosis of key driving factors affecting the evolution of an ocean sound velocity field of a target sea area from the ocean environment data, and building a causal network diagram based on the information flow of the key driving factors and a structural equation model, obtaining a core feature set; the ocean sound velocity field sequence data in the core feature set are decomposed into data in a space-time coherent mode through dynamic mode decomposition, and then the data are mapped into low-dimensional space-time features; learning the evolution dynamic state of the ocean sound velocity field according to the low-dimensional spatial-temporal characteristics by using a KAN network, and outputting an ocean sound velocity field prediction result at a future moment; future guide learning is used in the training stage of the KAN network, and real observation data in future set time is used as an auxiliary supervision signal; and using a dynamic feedback mechanism to calibrate the ocean sound velocity field prediction result based on the real-time observation data in the online prediction stage. The accuracy of predicting the ocean sound velocity can be improved.

Description

Technical Field

[0001] This application relates to the field of data processing technology, and in particular to a method and system for predicting ocean sound velocity fields. Background Technology

[0002] The ocean sound velocity field is a key physical field describing the spatial distribution of sound wave propagation speed in the ocean, and its accurate prediction is the core foundation for underwater acoustic applications. In fields such as ocean development, military anti-submarine warfare, underwater navigation, resource exploration, and marine scientific research, sound waves are the only information carrier capable of effectively propagating over long distances in seawater. Even subtle changes in sound velocity can significantly alter the propagation path of sound waves, leading to a sharp decline in the performance of acoustic systems. Therefore, high-precision and timely sound velocity field prediction is of irreplaceable value for improving the detection accuracy of underwater targets, ensuring the reliability of underwater communications, and optimizing the performance of sonar equipment, and is an urgent need for modern underwater information technology. Summary of the Invention

[0003] In view of this, embodiments of this application provide a method and system for predicting ocean sound velocity fields to accurately obtain ocean sound velocity fields.

[0004] One aspect of this application provides a method for predicting ocean sound velocity fields, the method comprising the following steps:

[0005] From historical and real-time marine environmental data, the key driving factors affecting the evolution of the marine sound velocity field in the target sea area are quantitatively diagnosed, and a causal network diagram is constructed based on the information flow and structural equation model of the key driving factors to obtain the core feature set.

[0006] The ocean sound velocity field sequence data in the core feature set is decomposed into spatiotemporally coherent mode data through dynamic mode decomposition, and then mapped to a low-dimensional feature space to obtain low-dimensional spatiotemporal features.

[0007] The low-dimensional spatiotemporal features are input into the KAN network, and the KAN network is used to learn the evolution dynamics of the ocean sound velocity field, outputting the prediction results of the ocean sound velocity field at future times.

[0008] In the training phase of the KAN network, future-guided learning is used, with real observation data at a future set time as auxiliary supervision signals; in the online prediction phase, a dynamic feedback mechanism is used to calibrate the ocean sound velocity field prediction results based on real-time observation data.

[0009] In some embodiments, the process of quantitatively diagnosing key driving factors affecting the evolution of the ocean sound velocity field in a target sea area from historical and real-time marine environmental data, and constructing a causal network graph based on the information flow and structural equation model of the key driving factors to obtain a core feature set, includes the following steps:

[0010] The transfer entropy method is used to calculate the transfer entropy from candidate environmental factors to the ocean sound velocity field to quantify the key driving factors that include causality, and bidirectional information flow calculation is performed between environmental factors to draw a causal network diagram.

[0011] The core feature set is determined based on the causal network diagram and the structural equation model.

[0012] In some embodiments, determining the core feature set based on the causal network graph and the structural equation model includes the following steps:

[0013] The causal network graph is validated and quantified using the structural equation model. The coefficients of the causal paths are estimated by fitting observational data and the goodness of fit of the model is evaluated, thereby constructing a core feature set. The core feature set includes core causal variables and causal interaction features of ocean sound velocity field sequence data.

[0014] In some embodiments, the process of decomposing the ocean sound velocity field sequence data in the core feature set into spatiotemporally coherent mode data through dynamic mode decomposition, and then mapping it to a low-dimensional feature space to obtain low-dimensional spatiotemporal features, includes the following steps:

[0015] Constructing the spatiotemporal matrix of ocean sound velocity field sequence data;

[0016] Perform singular value decomposition on the aforementioned spacetime matrix;

[0017] Calculate the modes and eigenvalues ​​of the dynamic mode decomposition;

[0018] Low-dimensional spatiotemporal features are constructed based on the dominant mode.

[0019] In some embodiments, the step of inputting the low-dimensional spatiotemporal features into a KAN network, using the KAN network to learn the evolution dynamics of the ocean sound velocity field, and outputting the prediction result of the ocean sound velocity field at future times includes the following steps:

[0020] Construct the KAN network; wherein the edges of the KAN network are learnable spline functions;

[0021] The low-dimensional spatiotemporal features are input into the KAN network, and the KAN network outputs the ocean sound velocity field prediction results for one or more future times.

[0022] The KAN network is trained using historical time-series data, and the parameters of the spline function are optimized using the backpropagation algorithm to minimize the error between the predicted output of the KAN network and the actual future state.

[0023] In the prediction phase, an iterative approach is used for multi-step prediction: the prediction output at the current moment is used as the input at the next moment, and the process is repeated to generate the predicted results of the ocean sound velocity field in the future.

[0024] In some embodiments, the use of future-guided learning during the training phase of the KAN network to set future real-world observation data as auxiliary supervision signals includes the following steps:

[0025] When training the KAN network, historical data is provided to predict the next state, while real observation data at a future set time is introduced as an auxiliary supervision signal.

[0026] Construct a loss function that includes information about the future state, the loss function taking into account both the prediction error of the next step and the prediction error of the state at a certain future moment;

[0027] By minimizing the loss function, the KAN network is guided to learn and internally represent the dynamic evolution law.

[0028] In some embodiments, the step of using a dynamic feedback mechanism to calibrate the ocean sound velocity field prediction results based on real-time observation data during the online prediction phase includes the following steps:

[0029] Continuously acquire current real-time ocean sound velocity field observation data;

[0030] The real-time ocean sound velocity field observation data is compared with the prediction sequence at the corresponding time to calculate the prediction error;

[0031] The prediction error is analyzed by applying the kernel density estimation method, and the probability distribution of the prediction error is estimated in a non-parametric manner, thereby quantifying the uncertainty of the current prediction.

[0032] The quantified uncertainty information is dynamically fed back to the KAN network to correct the deviation of subsequent prediction results in real time, or to fine-tune the parameters of the KAN network.

[0033] Another aspect of this application provides a marine sound velocity field prediction system, the system comprising:

[0034] The causal analysis and feature construction module is used to quantitatively diagnose the key driving factors affecting the evolution of the ocean sound velocity field in the target sea area from historical and real-time marine environmental data, and construct a causal network graph based on the information flow and structural equation model of the key driving factors, thereby obtaining the core feature set.

[0035] The spatiotemporal feature extraction and dimensionality reduction module is used to decompose the ocean sound velocity field sequence data in the core feature set into spatiotemporal coherent mode data through dynamic mode decomposition, and then map it to a low-dimensional feature space to obtain low-dimensional spatiotemporal features.

[0036] The dynamic prediction module is used to input the low-dimensional spatiotemporal features into the KAN network, use the KAN network to learn the evolution dynamics of the ocean sound velocity field, and output the prediction results of the ocean sound velocity field at future times.

[0037] The future guidance and adaptive feedback module is used to use future guidance learning during the training phase of the KAN network, with real observation data at a future set time as auxiliary supervision signals; and to use a dynamic feedback mechanism to calibrate the ocean sound velocity field prediction results based on real-time observation data during the online prediction phase.

[0038] Another aspect of this application embodiment provides an electronic device, including a processor and a memory;

[0039] The memory is used to store programs;

[0040] The processor executes the program to implement any of the methods described above.

[0041] Another aspect of this application provides a computer-readable storage medium storing a program that is executed by a processor to implement the method described in any of the above embodiments.

[0042] This application includes at least the following beneficial effects:

[0043] This application can quantitatively diagnose the key driving factors influencing the evolution of the ocean sound velocity field in a target sea area from historical and real-time marine environmental data. Based on the information flow and structural equation model of these key driving factors, a causal network graph is constructed to obtain a core feature set. Dynamic mode decomposition is used to decompose the ocean sound velocity field sequence data in the core feature set into spatiotemporally coherent mode data, which is then mapped to a low-dimensional feature space to obtain low-dimensional spatiotemporal features. These low-dimensional spatiotemporal features are input into a KAN network, which learns the dynamic evolution of the ocean sound velocity field and outputs predictions of the ocean sound velocity field at future times. Future-guided learning is used during the training phase of the KAN network, with real-time observation data at a future time as auxiliary supervision signals. During the online prediction phase, a dynamic feedback mechanism is used to calibrate the ocean sound velocity field prediction results based on real-time observation data. This application obtains a causal network graph through causal analysis, thus obtaining a core feature set. Based on this core feature set, features containing causal relationships can be extracted, providing evidence-based features for predicting ocean sound velocity and improving the accuracy of ocean sound velocity prediction. Attached Figure Description

[0044] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0045] Figure 1 A flowchart illustrating a method for predicting ocean sound velocity fields provided in an embodiment of this application;

[0046] Figure 2 This is a structural block diagram of an ocean sound velocity field prediction system provided in an embodiment of this application. Detailed Implementation

[0047] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0048] Before providing a detailed description of the embodiments of this application, some related technologies involved in the embodiments of this application will be described first, as follows:

[0049] Currently, the mainstream methods for acquiring and predicting sound velocity fields mainly fall into the following three categories:

[0050] Firstly, there is the direct calculation method based on empirical formulas. This method uses field-measured hydrological data such as temperature, salinity, and depth to directly calculate the speed of sound using empirical formulas. While simple and direct, this method heavily relies on expensive shipboard field measurements, has limited spatial coverage, and a long update cycle, making it difficult to achieve large-scale, real-time prediction of the speed of sound field.

[0051] Secondly, there is the static modeling method based on traditional interpolation. This method collects historical hydrological databases and limited real-time observation data, and uses algorithms such as Kriging interpolation and optimal interpolation to construct static or quasi-static sound velocity fields. This method expands the spatial coverage to some extent, but it is essentially a reproduction or simple extrapolation of historical states, failing to effectively integrate ocean dynamic processes. It is also slow to respond to rapid spatiotemporal changes in the sound velocity field caused by mesoscale eddies and internal waves, resulting in insufficient prediction accuracy and timeliness.

[0052] Third, numerical forecasting based on data assimilation. This method combines in-situ observation data with ocean numerical models, corrects the model state through data assimilation techniques, and thus predicts the future evolution of the sound velocity field. This method is currently widely used, but its computational complexity is extremely high, heavily reliant on large computing resources and accurate initial field and boundary conditions. Furthermore, the efficiency and accuracy of the assimilation process remain technical challenges, creating bottlenecks when addressing the needs of rapid and mobile applications.

[0053] In summary, existing technologies are limited by data acquisition constraints, static and lagging models, or face significant computational resource challenges, making it difficult to achieve a good balance between accuracy and efficiency. Therefore, there is an urgent need for a novel method for predicting ocean sound velocity fields that can achieve both high accuracy and high efficiency.

[0054] Reference Figure 1 This application provides a method for predicting ocean sound velocity fields, specifically including the following steps S100~S130:

[0055] S100: Quantitatively diagnose the key driving factors affecting the evolution of the ocean sound velocity field in the target sea area from historical and real-time marine environmental data, and construct a causal network diagram based on the information flow and structural equation model of the key driving factors to obtain the core feature set.

[0056] S110: The ocean sound velocity field sequence data in the core feature set is decomposed into spatiotemporally coherent mode data through dynamic mode decomposition, and then mapped to a low-dimensional feature space to obtain low-dimensional spatiotemporal features.

[0057] S120: Input the low-dimensional spatiotemporal features into the KAN network, use the KAN network to learn the evolution dynamics of the ocean sound velocity field, and output the prediction results of the ocean sound velocity field at future times;

[0058] S130: During the training phase of the KAN network, future-guided learning is used, with real observation data at a future set time as auxiliary supervision signals; during the online prediction phase, a dynamic feedback mechanism is used to calibrate the ocean sound velocity field prediction results based on real-time observation data.

[0059] Optionally, the step of quantitatively diagnosing key driving factors affecting the evolution of the ocean sound velocity field in the target sea area from historical and real-time marine environmental data, and constructing a causal network graph based on the information flow and structural equation model of the key driving factors to obtain a core feature set, includes the following steps:

[0060] The transfer entropy method is used to calculate the transfer entropy from candidate environmental factors to the ocean sound velocity field to quantify the key driving factors that include causality, and bidirectional information flow calculation is performed between environmental factors to draw a causal network diagram.

[0061] The core feature set is determined based on the causal network diagram and the structural equation model.

[0062] Optionally, determining the core feature set based on the causal network graph and the structural equation model includes the following steps:

[0063] The causal network graph is validated and quantified using the structural equation model. The coefficients of the causal paths are estimated by fitting observational data and the goodness of fit of the model is evaluated, thereby constructing a core feature set. The core feature set includes core causal variables and causal interaction features of ocean sound velocity field sequence data.

[0064] Optionally, the step of decomposing the ocean sound velocity field sequence data in the core feature set into spatiotemporally coherent mode data through dynamic mode decomposition, and then mapping it to a low-dimensional feature space to obtain low-dimensional spatiotemporal features, includes the following steps:

[0065] Constructing the spatiotemporal matrix of ocean sound velocity field sequence data;

[0066] Perform singular value decomposition on the aforementioned spacetime matrix;

[0067] Calculate the modes and eigenvalues ​​of the dynamic mode decomposition;

[0068] Low-dimensional spatiotemporal features are constructed based on the dominant mode.

[0069] Optionally, the step of inputting the low-dimensional spatiotemporal features into a KAN network, using the KAN network to learn the evolution dynamics of the ocean sound velocity field, and outputting the prediction result of the ocean sound velocity field at future times includes the following steps:

[0070] Construct the KAN network; wherein the edges of the KAN network are learnable spline functions;

[0071] The low-dimensional spatiotemporal features are input into the KAN network, and the KAN network outputs the ocean sound velocity field prediction results for one or more future times.

[0072] The KAN network is trained using historical time-series data, and the parameters of the spline function are optimized using the backpropagation algorithm to minimize the error between the predicted output of the KAN network and the actual future state.

[0073] In the prediction phase, an iterative approach is used for multi-step prediction: the prediction output at the current moment is used as the input at the next moment, and the process is repeated to generate the predicted results of the ocean sound velocity field in the future.

[0074] Optionally, the step of using future-guided learning during the training phase of the KAN network, using real-world observation data from the future at a set time as auxiliary supervision signals, includes the following steps:

[0075] When training the KAN network, historical data is provided to predict the next state, while real observation data at a future set time is introduced as an auxiliary supervision signal.

[0076] Construct a loss function that includes information about the future state, the loss function taking into account both the prediction error of the next step and the prediction error of the state at a certain future moment;

[0077] By minimizing the loss function, the KAN network is guided to learn and internally represent the dynamic evolution law.

[0078] Optionally, the step of using a dynamic feedback mechanism to calibrate the ocean sound velocity field prediction results based on real-time observation data during the online prediction phase includes the following steps:

[0079] Continuously acquire current real-time ocean sound velocity field observation data;

[0080] The real-time ocean sound velocity field observation data is compared with the prediction sequence at the corresponding time to calculate the prediction error;

[0081] The prediction error is analyzed by applying the kernel density estimation method, and the probability distribution of the prediction error is estimated in a non-parametric manner, thereby quantifying the uncertainty of the current prediction.

[0082] The quantified uncertainty information is dynamically fed back to the KAN network to correct the deviation of subsequent prediction results in real time, or to fine-tune the parameters of the KAN network.

[0083] The following section will provide a detailed introduction and explanation of the solutions in the embodiments of this application, using specific application examples.

[0084] This embodiment proposes a spatiotemporal prediction scheme for ocean sound velocity, involving the following four core modules:

[0085] Module 1: Causal Analysis and Feature Construction Module.

[0086] This module forms the foundation of the entire model, aiming to ensure the interpretability of input features from a physical mechanism perspective. It first employs an information flow approach to quantitatively diagnose the key driving factors and their causal directions influencing the evolution of the sound velocity field in the target sea area from massive amounts of historical and real-time marine environmental data (such as temperature, salinity, depth, current velocity, and satellite remote sensing data). Based on this, structural equation modeling is used to formally represent and verify these causal relationships, constructing a clear causal network. The output of this module is a core feature set that has been stripped of redundant information and contains physical causal relationships, laying a solid physical foundation for subsequent accurate predictions.

[0087] This module forms the cornerstone of the entire prediction framework. Its core idea is to move from "data-driven" to "causal-driven" approaches, aiming to overcome the limitations of traditional methods that rely solely on statistical correlations while ignoring physical causal relationships. Traditional model inputs often contain a large number of redundant or even spuriously correlated variables, making the models difficult to generalize and resulting in poor physical interpretability. This module, through a rigorous causal inference process, systematically identifies and quantifies the causal chains between key environmental variables affecting the sound velocity field (such as temperature, salinity, pressure, current velocity, geographical location, and time), thereby constructing a high-quality feature set that is both informative and consistent with ocean physical mechanisms, laying a solid foundation for subsequent high-precision predictions.

[0088] Its implementation process can be divided into three core steps:

[0089] Step 1: Initial causal discovery based on information flow.

[0090] The goal of this step is to initially clarify the causal network structure among variables from the observational data. This embodiment uses information flow methods (such as transfer entropy and convergent cross-mapping) as the core tool. Specifically, the transfer entropy from each candidate environmental factor (such as the temperature of a certain water layer) to the sound velocity field is calculated to quantify the extent to which the factor can reduce the uncertainty of the future state of the sound velocity field, thereby confirming its causal driving force. Simultaneously, this embodiment also performs bidirectional information flow calculations between environmental factors; for example, it distinguishes whether temperature changes cause salinity changes or vice versa, thereby initially drawing a directed causal network diagram. This process can effectively screen out the core variables that truly have a causal relationship with the evolution of the sound velocity field and preliminarily determine their direction of influence.

[0091] Step 2: Causal verification and quantification based on structural equation modeling (SEM).

[0092] After obtaining the initial causal network, this embodiment uses structural equation modeling (SEM) to validate and refine this hypothetical causal structure. SEM decomposes a complex causal system into a series of linear or nonlinear regression equations, each describing how a variable is influenced by its causal parent node. This embodiment embeds the key variables and relationships identified in the first step into the SEM framework, estimates the coefficients of each causal path (i.e., the strength of the causal effect) by fitting observed data, and evaluates the goodness of fit of the entire model to the data. If some hypothetical paths are not significant or conflict with the data, the network structure is modified. Finally, SEM outputs a validated, quantified causal network that clearly reveals quantitative causal mechanisms such as "an increase in the heat content of the upper ocean, through the intensity of X, leads to an increase in the sound speed at depth Y by Z m / s".

[0093] Step 3: Construction of feature sets guided by physical mechanisms.

[0094] Finally, based on the refined causal knowledge described above, this embodiment constructs the input feature set ultimately used for the core prediction model. It doesn't simply pile up all causal variables, but rather constructs them intelligently:

[0095] Core causal variable selection: Environmental variables that have been proven to have a direct and significant causal effect on the sound speed field are directly selected as basic features.

[0096] Creating causal interaction features: Based on the interactions revealed in the causal network, new features are artificially constructed. For example, if SEM shows that the joint effect of temperature and salinity on sound speed is not independent, then a "temperature-salinity coupling term" is introduced as a new feature.

[0097] Embedded physical constraints: Combining basic physical constraints (such as the relationship implied by the empirical formula for the speed of sound) with causal discovery results to ensure that the constructed features are also physically reasonable.

[0098] Module 2: Spatiotemporal Feature Extraction and Dimensionality Reduction Module.

[0099] This module handles the complex spatiotemporal dynamics of the sound velocity field. It introduces a dynamic mode decomposition method to decompose high-dimensional, nonlinear sound velocity field sequence data into a set of optimal spatiotemporally coherent modes that capture its intrinsic evolutionary patterns. Each mode is characterized by a specific frequency and attenuation rate, thus mapping the complex spatiotemporal dynamics to a low-dimensional feature subspace. This process achieves data dimensionality reduction, significantly reducing the learning difficulty of the core prediction model. Simultaneously, the extracted dominant modes can effectively characterize the evolutionary dynamics of key ocean phenomena such as mesoscale eddies, greatly enhancing the model's generalization ability.

[0100] The core idea of ​​this module is to reduce the dimensionality of complex spatiotemporal dynamic systems to their essential low-dimensional space for representation. While the spatiotemporal variations of the ocean sound velocity field are complex, its energy is often concentrated in a few dominant spatiotemporal modes with specific frequencies and growth / decay rates. Traditional methods directly process high-dimensional gridded data, which is not only computationally burdensome but also susceptible to noise interference. This module introduces Dynamic Mode Decomposition (DMD), whose core advantage lies in its ability to automatically extract these dominant, physically meaningful spatiotemporal coherent structures purely from a data-driven perspective, without pre-setting any physical equations. This transforms a high-dimensional, nonlinear spatiotemporal prediction problem into a simpler linear or weakly nonlinear problem of tracking the amplitude evolution of a few modes in a low-dimensional space.

[0101] The process and implementation steps are as follows:

[0102] Step 1: Data preparation and spatiotemporal matrix construction.

[0103] First, the processed spatiotemporal sound velocity field data (typically a three-dimensional data volume: time × latitude × longitude, possibly including a depth layer) obtained from the causal analysis module is standardized. Then, it is organized into a mathematical form suitable for DMD processing. In this embodiment, the entire spatial field at each time step (e.g., all grid points) is flattened into a high-dimensional column vector s. n Next, these column vectors are arranged in chronological order to construct two large spatiotemporal data matrices:

[0104] Matrix X: Contains data from time t1 to t {m-1} All snapshot vectors [s1, s2, ..., s {m-1} ].

[0105] Matrix X': Contains data from time t2 to t m All snapshot vectors [s2, s3, ..., s {m} ].

[0106] This establishes a fundamental assumption: there exists a linear operator A such that X' ≈ AX. The goal of DMD is to approximate this operator A and analyze its characteristics.

[0107] Step 2: Perform Dynamic Mode Decomposition (DMD) and low-dimensional spatial projection.

[0108] These are the core calculation steps of this module, as detailed below:

[0109] Singular Value Decomposition (SVD): Dimensionality reduction of matrix X is achieved using SVD, i.e., X ≈ U Σ V*. Here, U contains the dominant spatial pattern (left singular vector), Σ is the singular value matrix, and V contains the temporal variation. By truncating small singular values, this embodiment can approximate X with a low-rank matrix, achieving the first step of dimensionality reduction and noise reduction.

[0110] Approximate Operator and Eigenvalue Analysis: In the dimensionality-reduced subspace, this embodiment constructs an approximation of operator A, ...

[0111] Constructing DMD modes: Projecting the modes W in the low-dimensional space back into the original high-dimensional space to obtain the final DMD spatiotemporal modes Φ. Each column of the matrix Φ is a DMD mode, which is a spatial distribution map that describes a certain coherent spatiotemporal structure (such as a moving mesoscale vortex).

[0112] Step 3: Feature reconstruction and verification.

[0113] Finally, this embodiment uses the extracted DMD modes to reconstruct the sound velocity field and verify its effectiveness.

[0114] Low-dimensional feature construction: The sound velocity field at any given time can be approximated as a linear combination of these DMD modes: s(t) ≈ Φ * b(t). Here, b(t) is a low-dimensional time coefficient vector describing the amplitude of each mode at time t. This vector b(t) is the low-dimensional spatiotemporal feature output by this module and fed into the core prediction module. Its dimension is much lower than the original grid data, and each component has a clear physical dynamic meaning.

[0115] Modal selection and verification: Not all modes are important. This embodiment selects dominant modes based on their amplitude (determined by initial conditions) and growth rate (modulus of eigenvalues), discarding secondary modes with small amplitudes or rapid decay, thus achieving further dimensionality reduction. Simultaneously, the field reconstructed by the DMD is compared with partially retained verification data to ensure that no key dynamic information is lost during the dimensionality reduction process.

[0116] Module 3: Core Dynamic Prediction Module.

[0117] This module is the intelligent hub of the entire framework, responsible for executing the final sound velocity field prediction. It takes features, after causal filtering and spatiotemporal dimensionality reduction, as input and employs the Kolmogorov-Arnold Network (KAN) as its core architecture to learn the complex nonlinear mapping from the current state to the future state. Compared to traditional neural networks, KAN, with its unique spline function-based design, possesses higher accuracy and parameter efficiency in representing complex functions, enabling more precise simulation of the evolution dynamics of the sound velocity field in a low-dimensional feature space and outputting high-precision future sound velocity field predictions.

[0118] This module serves as the intelligent hub and computational engine of the entire prediction framework, bearing the core responsibility of inferring future states from historical states. Its basic idea is to construct a highly efficient and powerful nonlinear mapping network specifically designed to learn and predict the dynamic evolution patterns of low-dimensional spatiotemporal features extracted from preceding modules. Traditional neural networks, when dealing with such complex sequence problems, often struggle to balance accuracy and efficiency due to fixed activation functions and redundant parameter structures. Therefore, this module innovatively adopts a network architecture based on the Kolmogorov-Arnold representation theorem. The fundamental innovation of this architecture lies in transforming the learning task from finding the optimal linear weights to directly learning the optimal nonlinear function itself. Specifically, in this network, each "edge" connecting nodes is no longer a simple numerical weight, but a complex function that can be flexibly adjusted and learned using techniques such as spline functions. This design theoretically gives the network higher representational power and parameter efficiency than traditional networks when approximating complex dynamic systems, thus enabling it to more accurately capture the subtle evolutionary patterns contained in the low-dimensional feature space.

[0119] The specific implementation process follows a clear sequence. First, the input and output are defined. The module's input is the low-dimensional feature vector output by the spatiotemporal feature extraction module, which encodes the core spatiotemporal state of the sound velocity field at the current moment. The module's output is the predicted value of the low-dimensional feature vector at one or more specific future moments, representing the expected state of the future sound velocity field. Next, the network's structure is designed and configured. This embodiment requires determining the number of network layers and the number of nodes in each layer; its input and output dimensions are determined by the length of the low-dimensional feature vector. The most crucial step is parameterizing and initializing all learnable "side functions" in the network. Typically, smooth spline curves are used as the starting point, and appropriate regularization constraints are set to ensure these functions maintain good behavior during the learning process, avoiding excessively violent or absurd oscillations, thereby ensuring the model's stability and generalization ability.

[0120] Then, the network enters the training and dynamic learning phase. This process involves preparing a large amount of historical time-series data as training samples, with each sample containing an input state and its corresponding future target state. The core of training is to continuously compare the network's predicted output with the true target value, calculate the error, and use the backpropagation algorithm to propagate this error signal back to the entire network. It's worth noting that the parameters optimized here are no longer simple weight matrices, but rather numerous coefficients defining learnable functions on all edges. The optimizer iteratively adjusts these coefficients, enabling the entire network to map from the input state to the target state more and more accurately. Future-guided learning strategies can also be incorporated into the training process; that is, instead of learning the next state, the network is encouraged to simultaneously perceive state information from further into the future as auxiliary supervision, thereby cultivating its long-term predictive ability.

[0121] Finally, during model deployment and actual prediction, iterative prediction and state deduction are performed. The trained network acts as a fixed dynamic operator. The prediction process begins by inputting the latest current low-dimensional state vector into the network to obtain the predicted state for the next time step. For multi-step predictions, a rolling prediction approach is used: the previously obtained prediction output is treated as the new "current state" and input into the network again to obtain the prediction for the next time step. This process is repeated to generate a complete state trajectory leading to the future. Ultimately, these predicted low-dimensional vectors are fed into the reconstruction part and combined with the previously extracted spatiotemporal modes to reconstruct a complete, high-dimensional, spatiotemporally continuous future ocean sound velocity field. In summary, this core dynamic prediction module, through its unique and powerful function learning capabilities, efficiently grasps the evolutionary dynamics of the system in low-dimensional space, which is key to achieving high-precision sound velocity field prediction.

[0122] Module 4: Future Guidance and Adaptive Feedback Module.

[0123] This module represents a key innovation in enhancing the model's forward-looking capabilities and robustness. Through a future-guided learning paradigm, it uses real-world observational data from the near future (even if unavailable in the prediction time domain) as supplementary supervision signals during the training phase, guiding the KAN model to learn more forward-looking dynamic representations. In the online prediction phase, a dynamic feedback mechanism is activated: the system continuously compares the latest real-time observational data with the prediction sequence and uses kernel density estimation to evaluate the distribution of prediction errors online, thereby quantifying uncertainty. This uncertainty information is dynamically fed back to the core prediction module for real-time calibration of prediction results or fine-tuning of model parameters, forming a closed-loop system with continuous self-correction capabilities, ensuring the model's long-term predictive stability under changing environments.

[0124] This module is the heart of the entire prediction framework. Its core idea is to break away from the limitations of traditional models that rely solely on historical data for "open-loop" predictions, and instead build a "closed-loop" intelligent system capable of sensing future trends and self-correcting online. Traditional models have fixed parameters after training, making them unable to cope with sudden dynamic changes in the marine environment that are not fully reflected in historical data, causing prediction errors to accumulate over time. This module introduces two innovative mechanisms—future-guided learning and dynamic feedback—aiming to endow the model with forward-thinking capabilities and dynamic adaptability to the real world, thereby significantly improving its long-term prediction accuracy and robustness.

[0125] The specific implementation process can be divided into two main stages. The first stage is future-guided learning, a mechanism activated during model training. In this stage, this embodiment not only provides the model with historical data to predict the next state, but also provides a short-term future sequence of real data as a "mentor signal" or "reference target." This does not require the model to directly output this future sequence, but rather guides its internal representation learning to contain an "expectation" or "preparation" for future dynamics. For example, the model will be trained to simultaneously minimize the prediction error of the next step and a loss due to the difference from the state at some future moment. This process forces the model's internal parameters to adjust to a state that enables it not only to fit historical patterns but also to generate dynamics that conform to short-term future evolution trends, thereby learning more forward-looking and physically consistent evolutionary patterns and preparing it internally to cope with uncertainties in the prediction time domain.

[0126] The second phase is online dynamic feedback and adaptation, a mechanism initiated during model deployment and real-time prediction. As the model begins rolling predictions, the system continuously monitors newly acquired observational data in the real ocean environment. Once new observational data arrives, the system immediately performs a detailed comparison with the model's predictions at the corresponding time point, calculating the prediction error. Next, the system analyzes this error sequence using kernel density estimation. This method non-parametrically estimates the probability distribution of the prediction error, thus accurately quantifying the current model's uncertainty level—for example, whether the error follows a normal distribution with a mean of zero, or whether significant bias and distribution broadening have occurred. This uncertainty assessment is crucial to the entire feedback loop. Subsequently, the system initiates a dynamic feedback mechanism, transforming this quantified uncertainty information into concrete corrective actions. Correction methods can be direct, such as using the error distribution to correct future predictions in real-time; or more sophisticated, such as using the uncertainty information as an additional input signal to slightly adjust certain key parameters or gates in the core prediction model, achieving fine-tuning of the model. This forms a continuous online closed loop of "prediction-observation-comparison-evaluation-correction", which makes the whole system no longer a rigid prediction machine, but an intelligent agent that can learn from the constantly changing environment and adjust its behavior in real time, thus maintaining high-precision prediction performance when facing complex and ever-changing marine environments.

[0127] In summary, this embodiment includes the following key technical solutions:

[0128] (1) Introducing "Time-Delayed Causal Discovery" to Construct Dynamic Prospective Features. Traditional causal analysis often focuses on instantaneous causal relationships between variables, which is essentially a "static" description. This innovation proposes and systematically explores time-delayed causal effects between variables for the first time. Specifically, through improved information flow algorithms (such as time-varying transfer entropy), it not only identifies the cause and effect but also more precisely quantifies how long (e.g., 6 hours, 1 day) it takes for a change in one variable (such as the heat content of the upper ocean) to have the greatest impact on another variable (such as the speed of sound at a specific depth). Accordingly, this embodiment no longer simply uses the current causal variable value as a feature but actively constructs a set of "prospective" features, such as using the historical state of the key dependent variable (based on its identified time delay length) as the predictive input for the effect variable. This is equivalent to providing the model with "precursor signals" that conform to physical laws, enabling it to predict the future system state based on the causal driving force that has already occurred.

[0129] (2) Creating a "dynamic optimization of causal importance" process to achieve adaptive feature sets. Existing feature selection methods are usually fixed once completed, throughout the entire model lifecycle. This innovation breaks through this limitation by proposing a dynamic closed-loop process. During the online operation phase of the model, this process continuously monitors its predictive performance and links back to the causal analysis module. When the model exhibits systematic prediction bias under specific ocean conditions (such as strong vertical mixing periods), it automatically triggers a local "causal rediscovery" process for that condition. This process utilizes newly accumulated field data to quickly reassess the causal importance ranking of each environmental variable. Based on the new ranking, the system dynamically and adaptively adjusts the feature set input to the core prediction module, for example, increasing the causal weight of features with mixing layer depth under strong wind conditions, while suppressing features that are important only under calm weather conditions. This makes the model's input features no longer "unchanging," but rather, like an expert, it can intelligently switch the focus of causal factors according to different scenarios, thus possessing the ability to cope with complex and ever-changing ocean environments.

[0130] (3) Introducing the "Dynamic Mode Decomposition with Embedded Physical Constraints" method. Traditional dynamic mode decomposition is purely mathematically driven, and the extracted modes may be mathematically optimal but physically unrealizable (e.g., violating energy conservation). This innovation is the first to embed known physical conservation laws (e.g., mass and momentum conservation) or physical boundary conditions of sound speed propagation as hard constraints directly into the matrix decomposition optimization problem of DMD. Specifically, in the process of constructing the DMD approximation operator, this embodiment not only requires it to minimize data reconstruction errors, but also requires that all spatiotemporal modes it solves must satisfy the constraint equation set formed by discretizing the physical equations. This ensures that each extracted dominant mode is itself a physically feasible dynamic process, thereby upgrading the purely data-driven method to "data-driven under the guidance of physical mechanisms", fundamentally improving the physical consistency and generalization ability of the extracted features.

[0131] (4) Design a “multi-scale hierarchical DMD architecture” to separate coupled dynamics. Changes in the ocean sound velocity field involve coupling of processes at multiple scales, from large-scale climate modes to small- and medium-scale eddies and internal waves. Traditional single-scale DMDs are difficult to clearly separate these processes. This innovation proposes a novel hierarchical DMD architecture: First, the original spatiotemporal data is filtered at different scales to decompose it into subsets representing dynamics at different scales; then, DMD is performed independently on each scale subset to extract mode groups specific to that scale; finally, a lightweight coupling model is established to quantify the energy or information transfer between different scale modes. This method not only outputs cleaner, scale-separated spatiotemporal features, but more importantly, it provides key knowledge for prediction models on “how dynamics at different scales influence each other” by revealing cross-scale interactions. This is a deep information that no previous single DMD scheme could provide.

[0132] (5) Constructing a "differential equation-driven KAN dynamic learning" framework. Traditional KANs or neural networks learn direct mappings between states, while this innovation endows KANs with the ability to learn "differential equations." Specifically, this embodiment redesigns the output and objective of KAN: instead of directly predicting future low-dimensional states, KAN learns the derivative (i.e., rate of change) of low-dimensional feature vectors over time. The network takes the current state as input and outputs an estimate of its rate of change. Then, this embodiment uses a numerical integrator (such as the Runge-Kutta method) to deduce the future state from this derivative. This method uses KAN's powerful function approximation ability to learn the underlying dynamic equations of the system, making the prediction process strictly follow the continuous evolution law of the physical system, greatly enhancing the stability and physical consistency of long-term predictions. This is a fundamental change to all existing prediction paradigms based on direct mappings.

[0133] (6) Design of a "Probabilistic KAN and Uncertainty Quantification" Structure. Existing KANs and most neural networks are deterministic models, unable to provide reliable predictions. This innovation fundamentally transforms the basic structure of KAN, changing its output from a deterministic value to a probability distribution. Specifically, this is achieved by introducing a probability distribution assumption into the final spline function coefficients of the KAN, or by superimposing a learnable conditional probability model at its output. This allows the model to not only provide a predicted value for any input, but also simultaneously output the confidence interval or complete probability density function of that predicted value. This inherent uncertainty measure can be linked with the feedback module in real time. When the model "knows" that the uncertainty is high, it will automatically increase the weight of its dependence on real-time observation data, achieving intelligent and risk-controllable prediction decisions. This is a key step towards reliable artificial intelligence with self-awareness.

[0134] (7) Constructing a forward-looking optimization mechanism of "internal simulator and strategy evaluation". Traditional future-guided learning only uses future data as a supervision signal, while this innovation gives the model an "internal simulator". During the training phase, the model not only makes single-step predictions, but also autonomously "infers" multiple possible future trajectories based on the current state and internal dynamic knowledge. At the same time, a built-in "evaluator" scores the quality of these inferred trajectories, and the evaluation criteria include their consistency with the real future trajectory and physical rationality. The training objective is no longer simply to fit the next step, but to optimize the core dynamic prediction module (KAN) so that the inferred trajectories it generates can obtain higher evaluation scores. This is equivalent to teaching the model how to "think forward" and optimize its own long-term inference strategy, thereby making current decisions that are more conducive to long-term accuracy.

[0135] (8) Creating a "Dynamic Feedback Arbitration System Based on Digital Twins". Traditional feedback correction usually involves directly applying error compensation. This innovation introduces a lightweight "digital twin" as an arbitrator. When discrepancies arise between online prediction and observation, the system does not immediately correct the main model. Instead, it first tests multiple correction strategies in parallel in the digital twin (a fast, simplified copy of the main model), such as adjusting input feature weights, fine-tuning specific spline functions of KAN, or changing the initial phase of the dynamic mode. The digital twin quickly simulates the short-term consequences of these strategies and selects the strategy that brings the system state back to the observation trajectory in the smoothest and most stable way. Ultimately, only this optimal strategy is applied to the main model. This upgrades the feedback process from a simple "error-driven" to a "strategy optimization-driven" approach, significantly improving the intelligence of the feedback and the long-term stability of the system.

[0136] Reference Figure 2 This application provides an ocean sound velocity field prediction system, comprising:

[0137] The causal analysis and feature construction module is used to quantitatively diagnose the key driving factors affecting the evolution of the ocean sound velocity field in the target sea area from historical and real-time marine environmental data, and construct a causal network graph based on the information flow and structural equation model of the key driving factors, thereby obtaining the core feature set.

[0138] The spatiotemporal feature extraction and dimensionality reduction module is used to decompose the ocean sound velocity field sequence data in the core feature set into spatiotemporal coherent mode data through dynamic mode decomposition, and then map it to a low-dimensional feature space to obtain low-dimensional spatiotemporal features.

[0139] The dynamic prediction module is used to input the low-dimensional spatiotemporal features into the KAN network, use the KAN network to learn the evolution dynamics of the ocean sound velocity field, and output the prediction results of the ocean sound velocity field at future times.

[0140] The future guidance and adaptive feedback module is used to use future guidance learning during the training phase of the KAN network, with real observation data at a future set time as auxiliary supervision signals; and to use a dynamic feedback mechanism to calibrate the ocean sound velocity field prediction results based on real-time observation data during the online prediction phase.

[0141] It is understood that the content of the above method embodiments is applicable to this system embodiment. The specific functions implemented in this system embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments.

[0142] In some alternative embodiments, the functions / operations mentioned in the block diagrams may not occur in the order shown in the operation diagrams. For example, depending on the functions / operations involved, two consecutively shown blocks may actually be executed substantially simultaneously, or the blocks may sometimes be executed in reverse order. Furthermore, the embodiments presented and described in the flowcharts of this application are provided by way of example to provide a more comprehensive understanding of the technology. The disclosed methods are not limited to the operations and logic flows presented herein. Alternative embodiments are contemplated in which the order of various operations is changed and sub-operations described as part of a larger operation are executed independently.

[0143] Furthermore, although this application is described in the context of functional modules, it should be understood that, unless otherwise stated to the contrary, one or more of the described functions and / or features may be integrated into a single physical system and / or software module, or one or more functions and / or features may be implemented in a separate physical system or software module. It is also understood that a detailed discussion of the actual implementation of each module is unnecessary for understanding this application. Rather, given the properties, functions, and internal relationships of the various functional modules in the system disclosed herein, the actual implementation of the module will be understood within the scope of conventional technology for an engineer. Therefore, those skilled in the art can implement the application set forth in the claims using ordinary techniques without excessive experimentation. It is also understood that the specific concepts disclosed are merely illustrative and not intended to limit the scope of this application, which is determined by the full scope of the appended claims and their equivalents.

[0144] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0145] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a ordered list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, system, or device (such as a computer-based system, a processor-including system, or other system that can fetch and execute instructions from, an instruction execution system, system, or device). For the purposes of this specification, "computer-readable medium" can mean any system that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, system, or device.

[0146] More specific examples of computer-readable media (a non-exhaustive list) include: electrical connections (electronic systems) with one or more wires, portable computer disk drives (magnetic systems), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic systems, and portable optical disc read-only memory (CDROM). Furthermore, computer-readable media can even be paper or other suitable media on which the program can be printed, because the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in computer memory.

[0147] It should be understood that various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0148] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0149] Although embodiments of this application have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of this application, the scope of which is defined by the claims and their equivalents.

[0150] The above is a detailed description of the preferred embodiments of this application, but this application is not limited to the embodiments described. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of this application, and these equivalent modifications or substitutions are all included within the scope defined by the claims of this application.

Claims

1. A method for predicting ocean sound velocity fields, characterized in that, The method includes the following steps: From historical and real-time marine environmental data, the key driving factors affecting the evolution of the marine sound velocity field in the target sea area are quantitatively diagnosed, and a causal network diagram is constructed based on the information flow and structural equation model of the key driving factors to obtain the core feature set. The ocean sound velocity field sequence data in the core feature set is decomposed into spatiotemporally coherent mode data through dynamic mode decomposition, and then mapped to a low-dimensional feature space to obtain low-dimensional spatiotemporal features. The low-dimensional spatiotemporal features are input into the KAN network, and the KAN network is used to learn the evolution dynamics of the ocean sound velocity field, outputting the prediction results of the ocean sound velocity field at future times. In the training phase of the KAN network, future-guided learning is used, with real observation data at a future set time as auxiliary supervision signals; in the online prediction phase, a dynamic feedback mechanism is used to calibrate the ocean sound velocity field prediction results based on real-time observation data.

2. The ocean sound velocity field prediction method according to claim 1, characterized in that, The process involves quantitatively diagnosing key driving factors influencing the evolution of the ocean sound velocity field in a target sea area from historical and real-time marine environmental data, and constructing a causal network graph based on the information flow and structural equation model of these key driving factors to obtain a core feature set. This includes the following steps: The transfer entropy method is used to calculate the transfer entropy from candidate environmental factors to the ocean sound velocity field to quantify the key driving factors that include causality, and bidirectional information flow calculation is performed between environmental factors to draw a causal network diagram. The core feature set is determined based on the causal network diagram and the structural equation model.

3. The ocean sound velocity field prediction method according to claim 2, characterized in that, Determining the core feature set based on the causal network graph and the structural equation model includes the following steps: The causal network graph is validated and quantified using the structural equation model. The coefficients of the causal paths are estimated by fitting observational data and the goodness of fit of the model is evaluated, thereby constructing a core feature set. The core feature set includes core causal variables and causal interaction features of ocean sound velocity field sequence data.

4. The ocean sound velocity field prediction method according to claim 1, characterized in that, The process of decomposing the ocean sound velocity field sequence data in the core feature set into spatiotemporally coherent mode data through dynamic mode decomposition, and then mapping it to a low-dimensional feature space to obtain low-dimensional spatiotemporal features, includes the following steps: Constructing the spatiotemporal matrix of ocean sound velocity field sequence data; Perform singular value decomposition on the aforementioned spacetime matrix; Calculate the modes and eigenvalues ​​of the dynamic mode decomposition; Low-dimensional spatiotemporal features are constructed based on the dominant mode.

5. The ocean sound velocity field prediction method according to claim 1, characterized in that, The process of inputting the low-dimensional spatiotemporal features into a KAN network, using the KAN network to learn the evolution dynamics of the ocean sound velocity field, and outputting the prediction result of the ocean sound velocity field at future times includes the following steps: Construct the KAN network; wherein the edges of the KAN network are learnable spline functions; The low-dimensional spatiotemporal features are input into the KAN network, and the KAN network outputs the ocean sound velocity field prediction results for one or more future times. The KAN network is trained using historical time-series data, and the parameters of the spline function are optimized using the backpropagation algorithm to minimize the error between the predicted output of the KAN network and the actual future state. In the prediction phase, an iterative approach is used for multi-step prediction: the prediction output at the current moment is used as the input at the next moment, and the process is repeated to generate the predicted results of the ocean sound velocity field in the future.

6. The ocean sound velocity field prediction method according to claim 1, characterized in that, The use of future-guided learning during the training phase of the KAN network, using real-world observation data from a predetermined future time as auxiliary supervision signals, includes the following steps: When training the KAN network, historical data is provided to predict the next state, while real observation data at a future set time is introduced as an auxiliary supervision signal. Construct a loss function that includes information about the future state, the loss function taking into account both the prediction error of the next step and the prediction error of the state at a certain future moment; By minimizing the loss function, the KAN network is guided to learn and internally represent the dynamic evolution law.

7. The ocean sound velocity field prediction method according to claim 1, characterized in that, The process of using a dynamic feedback mechanism to calibrate the ocean sound velocity field prediction results based on real-time observation data during the online prediction phase includes the following steps: Continuously acquire current real-time ocean sound velocity field observation data; The real-time ocean sound velocity field observation data is compared with the prediction sequence at the corresponding time to calculate the prediction error; The prediction error is analyzed by applying the kernel density estimation method, and the probability distribution of the prediction error is estimated in a non-parametric manner, thereby quantifying the uncertainty of the current prediction. The quantified uncertainty information is dynamically fed back to the KAN network to correct the deviation of subsequent prediction results in real time, or to fine-tune the parameters of the KAN network.

8. A marine sound velocity field prediction system, characterized in that, The system includes: The causal analysis and feature construction module is used to quantitatively diagnose the key driving factors affecting the evolution of the ocean sound velocity field in the target sea area from historical and real-time marine environmental data, and construct a causal network graph based on the information flow and structural equation model of the key driving factors, thereby obtaining the core feature set. The spatiotemporal feature extraction and dimensionality reduction module is used to decompose the ocean sound velocity field sequence data in the core feature set into spatiotemporal coherent mode data through dynamic mode decomposition, and then map it to a low-dimensional feature space to obtain low-dimensional spatiotemporal features. The dynamic prediction module is used to input the low-dimensional spatiotemporal features into the KAN network, use the KAN network to learn the evolution dynamics of the ocean sound velocity field, and output the prediction results of the ocean sound velocity field at future times. The future guidance and adaptive feedback module is used to use future guidance learning during the training phase of the KAN network, with real observation data at a future set time as auxiliary supervision signals; and to use a dynamic feedback mechanism to calibrate the ocean sound velocity field prediction results based on real-time observation data during the online prediction phase.

9. An electronic device, characterized in that, The electronic device includes a processor and a memory; The memory is used to store programs; The processor executes the program to implement the method as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The storage medium stores a program that is executed by a processor to implement the method as described in any one of claims 1 to 7.

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