Target drift trajectory visualization prediction method based on multi-source power field and probability lstm

Abstract

The application provides a target drift trajectory visualization prediction method based on a multi-source power field and a probability LSTM, and relates to the technical field of maritime search and rescue prediction. In view of the problems of poor physical interpretability of a model, difficulty in quantifying prediction uncertainty, lack of ability of real-time assimilation of observation data and non-intuitive prediction results in the prior art, the application constructs a parameterized Lagrange drift equation into a trainable differentiable layer to form a physical model branch, and adopts a Bayesian long short-term memory network fusing Monte Carlo Dropout to construct a data model branch, so that deep fusion and complementary advantages of physical mechanism and data driving are realized. The application improves the precision, reliability and physical consistency of drift trajectory prediction, realizes quantitative evaluation of prediction uncertainty, and provides efficient, intuitive and dynamically optimized intelligent decision support for maritime search and rescue.

Description

Technical Field

[0001] This invention relates to the field of maritime search and rescue prediction technology, and in particular to a method for visualizing and predicting target drift trajectories based on multi-source dynamic fields and probabilistic LSTM. Background Technology

[0002] Rapid location and trajectory prediction of people or drifting objects in the ocean are key technologies for maritime safety and emergency response systems. The drifting motion of targets is primarily driven by the combined dynamic fields of the complex marine environment, including ocean currents, wind, and waves. With the rapid development of marine observation technology, multi-source, high-frequency, and large-scale marine hydrological and meteorological data are becoming increasingly abundant. Simultaneously, artificial intelligence technologies, represented by deep learning, especially sequence models such as Long Short-Term Memory (LSTM) networks, have demonstrated powerful capabilities in uncovering nonlinear relationships in spatiotemporal data, providing an important data-driven supplement to traditional prediction models based on physical equations, thus constituting an important development direction in this field.

[0003] However, existing technologies still have significant shortcomings. First, the models suffer from poor interpretability and physical consistency. Purely data-driven models are like black boxes, lacking physical support for their predictions. They exhibit weak generalization ability and high misjudgment rates when data is scarce or in unfamiliar environments. Second, the ability to quantify prediction uncertainty is insufficient. Traditional deterministic prediction methods only output a single trajectory, failing to reflect the inherent uncertainties of environmental input errors, model limitations, and individual target differences. Third, there is a lack of lightweight, automated update mechanisms to dynamically correct predicted trajectories by incorporating the latest observational data, such as survivor reports and aerial visual information, during search and rescue operations. Fourth, the visualization of forecast results is not intuitive.

[0004] Therefore, it is of great significance to develop a target drift trajectory visualization prediction method based on multi-source dynamic field and probabilistic LSTM with higher prediction accuracy and higher environmental generalization ability. Summary of the Invention

[0005] To address these issues, this invention provides a target drift trajectory visualization prediction method based on multi-source dynamic fields and probabilistic LSTM, which overcomes the problems of poor model interpretability and physical consistency, insufficient quantification of prediction uncertainty, lack of an automated update mechanism to integrate the latest observation data in real time during search and rescue, and unintuitive visualization of prediction results in existing technologies.

[0006] To achieve the above objectives, this invention provides a method for visualizing and predicting target drift trajectories based on multi-source dynamic fields and probabilistic LSTM, comprising:

[0007] S1, acquire multi-source spatiotemporal hydrological and meteorological data covering the target sea area, and preprocess the hydrological and meteorological data;

[0008] S2, a two-dimensional hydrodynamic model is constructed based on the preprocessed hydrological data;

[0009] S3 uses the parameterized Lagrange drift equation as a branch of the physical model to construct differentiable hierarchical structure.

[0010] S4 uses a Bayesian long short-term memory network and Monte Carlo Dropout to construct the data model branch;

[0011] S5 integrates a two-dimensional hydrodynamic model, preprocessed meteorological data, physical model branches, and data model branches to generate a dual-branch hybrid prediction model.

[0012] S6. Based on the preprocessed hydrological and meteorological data, the physical model branch is trained by combining the corresponding historical measured drift trajectory data. The physical parameter constraint mechanism is integrated to ensure that the physical parameters conform to the laws of fluid mechanics, and the physical interpretability is verified.

[0013] S7: Based on the prediction residuals of the physical model branches, an adaptive weight function is constructed to dynamically adjust the contribution weights of the physical branch and the data branch, and a dual-branch hybrid prediction model is jointly trained.

[0014] S8 inputs the initial state information of the target to be searched and rescued along with the real-time or predicted environmental dynamic field into the trained dual-branch hybrid prediction model. Through multiple forward propagation sampling, it outputs a probabilistic drift trajectory cluster representing uncertainty.

[0015] S9, perform visualization processing on the probabilistic drift trajectory cluster to generate a visualized forecast including a probability heatmap, confidence corridor and average path;

[0016] S10, during the search and rescue process, receive real-time observation data, correct the probabilistic drift trajectory cluster based on the Bayesian update method, and refresh the visualization forecast in real time.

[0017] Furthermore, the multi-source spatiotemporal hydrological and meteorological data includes:

[0018] Measured data, including on-site ocean current, water temperature, salinity, wind speed and wind direction data obtained from buoys, drift devices, vessels, shore-based or mobile platforms;

[0019] Remote sensing inversion data includes data on sea surface currents, significant wave height, sea surface temperature, sea surface wind field, and sea ice concentration acquired by satellite remote sensing or shipborne radar;

[0020] Numerical simulation and forecast data, including three-dimensional ocean current field, wave field, temperature and salinity field, wind field and pressure field data output from operational marine environmental information forecasts or atmospheric forecasts.

[0021] Furthermore, the hydrological and meteorological data are preprocessed, including:

[0022] S11 performs spatiotemporal matching of measured data, remote sensing inversion data, and numerical forecast data from different sources, aligns them with time using coordinate system one, and integrates them into a unified geographic grid and time series.

[0023] S12, identify and remove significant outliers and invalid data from each data source, and reconstruct the missing data using spatial interpolation or time series imputation methods to form a continuous and complete data sequence set;

[0024] S13, normalize each physical quantity in the data sequence set to eliminate the influence of dimensions, and according to the grid resolution of the two-dimensional hydrodynamic model and the time step of the prediction task, perform spatial resampling and temporal resampling on the data sequence set to generate standardized dynamic field data that can be directly input into the model.

[0025] Furthermore, the method of using the parameterized Lagrange drift equation as a branch of the physical model to construct differentiable hierarchical structures includes:

[0026] S31, based on the kinematics of a particle, the core computational unit of the physical model branch is defined as the parameterized Lagrange drift equation. The parameterized Lagrange drift equation expresses that the position of the target at the next moment is determined by the position at the current moment, the environmental dynamic field at the current moment, and the parameterized coefficients to be learned, in order to describe the combined contribution of wind flow, Stokes drift, and other unresolved physical effects.

[0027] S32, using an automatic differentiation framework, each computational step in the parameterized Lagrange drift equation is constructed as a differentiable computational operation, making the parameterized Lagrange drift equation as a whole a trainable differentiable layer;

[0028] S33, using the target's position and state vector from the previous moment as input, the predicted position for the next moment is calculated using the differentiable parameterized Lagrange drift equation, forming a physics-driven sequence state transition function;

[0029] S34, the sequence state transition function is used as the forward propagation core of the physical model branch, and the trainable differentiable layer is initialized according to fluid mechanics, thereby completing the construction of the physical model branch, enabling it to simulate the drift trajectory of the target from the environmental dynamic field and the initial state in a differentiable manner.

[0030] Furthermore, the method of constructing data model branches using Bayesian Long Short-Term Memory Networks and Monte Carlo Dropout includes:

[0031] S41, Construct a core architecture based on a long short-term memory network, wherein the long short-term memory network has at least one hidden layer for learning complex spatiotemporal dependencies and unmodeled dynamic patterns from the input historical trajectory sequence and environmental dynamic field sequence;

[0032] S42, Monte Carlo Dropout layers are embedded between each hidden layer of the Long Short-Term Memory network and before the fully connected output layer; during the model training phase, the Monte Carlo Dropout layers randomly drop some neuron connections during forward propagation; during the model prediction phase, the Monte Carlo Dropout layers are kept active, and multiple forward propagation samplings are performed to quantify the uncertainty of the model itself.

[0033] S43, with the goal of maximizing the likelihood function between the predicted trajectory and the historical measured trajectory, the parameters of the data model branch are trained using the negative log-likelihood loss function, so that the data model branch performs residual correction during the target drift process;

[0034] S44, at the end of the Bayesian Long Short-Term Memory network, a fully connected layer is connected so that the Long Short-Term Memory network predicts and outputs the mean and variance of the drift position in the longitude and latitude directions, thereby generating a probabilistic prediction result in the form of a Gaussian distribution;

[0035] S45, input the historical trajectory, environmental dynamic field and the prediction residual generated by the physical model branch into the data model branch; the network weight parameters of the data model branch are randomly initialized to construct a data model branch that focuses on learning complex, nonlinear drift patterns that the physical model fails to capture.

[0036] Furthermore, the physical interpretability verification includes:

[0037] Analyze the parameterized coefficients obtained after training the physical model branches to check whether their values ​​fall within a reasonable physical range defined based on fluid mechanics and empirical knowledge;

[0038] The environmental dynamic field is input and subjected to controllable perturbation. The trajectory change trend of the output branch of the physical model is analyzed and verified to conform to physical laws.

[0039] The physical model branch is placed in a typical ideal dynamic field with a known analytical solution for simulation. The output trajectory of the physical model branch is compared with the known analytical solution to verify whether the accuracy of the simulation meets the target requirements.

[0040] Furthermore, the visualization processing of the probabilistic drift trajectory cluster to generate a visualized forecast including a probability heatmap, confidence corridor, and average path includes:

[0041] S91, Spatial superposition of the probabilistic drift trajectory clusters output by multiple forward propagation sampling, statistical analysis of the frequency of the target appearing in each grid cell of geographic space in all sampling trajectories, and normalization of them into a spatial probability density distribution.

[0042] S92, the spatial probability density distribution is mapped into a color gradient map, wherein the color from dark to light represents the probability of the target appearing in each grid cell of the geographic space from high to low, and a probability heat map is generated.

[0043] S93, in the probabilistic drift trajectory cluster, for each future prediction time, calculate the distribution of the position coordinates of all sampled trajectories at that time, filter the position coordinates at that time based on a preset confidence threshold, connect all position coordinates corresponding to each time to form a strip-shaped region that changes with time, i.e., a confidence corridor, and draw it in the visualization layer.

[0044] S94, calculate the arithmetic mean of the position coordinates of all sampled trajectories in the probabilistic drift trajectory cluster at each prediction time, connect the arithmetic mean position points at each prediction time in chronological order to form an average path, and draw it in the visualization layer;

[0045] S95, integrate the probability heatmap, confidence corridor and average path into the same geographic base map coordinate system, and add timestamp, scale bar, direction indicator and legend to generate a comprehensive visual forecast for search and rescue decision support.

[0046] Furthermore, the modification of the probabilistic drift trajectory cluster based on the Bayesian update method includes:

[0047] During the search and rescue operation, real-time observation data about the search and rescue target is received, and the real-time observation data is spatiotemporally aligned with the predicted time.

[0048] The previous forecasting process was immediately interrupted, and the real-time observation data was used as the new, defined initial state.

[0049] The real-time observation data is input into the trained dual-branch hybrid prediction model;

[0050] Using the real-time observation data as input, the dual-branch hybrid prediction model is driven to perform a new round of multiple forward propagation sampling to generate an updated probabilistic drift trajectory cluster that represents the real-time conditions and current uncertainties.

[0051] Furthermore, the real-time observation data includes at least one of the following: location report of the search and rescue target, hydrological data, and meteorological data. Moreover, the real-time observation data is different from the initial state information or environmental dynamic field of the target to be searched and rescued input in S8.

[0052] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0053] Firstly, this invention constructs the parameterized Lagrange drift equation into a trainable differentiable layer, forming a branch of the physical model. This solves the technical problems of traditional physical drift models having fixed parameters, being unable to adapt to complex and changing sea conditions, and being difficult to deeply integrate and coordinate with data-driven models for optimization. It expresses physical effects such as wind-driven currents and wave drift as equations with learnable coefficients, and transforms them into part of a neural network using an automatic differentiation framework. This transforms the physical model from a static formula into a calibrable physical computation layer, which retains clear physical interpretability and allows for parameter optimization through data-driven training. This significantly improves the adaptability and accuracy of basic physical simulations to real environments.

[0054] Secondly, this invention addresses the technical problems of insufficient uncertainty quantification capability and low learning efficiency caused by unclear division of labor between pure data-driven models and the physical model by constructing data model branches using a Bayesian long short-term memory network incorporating Monte Carlo Dropout and designing an architecture with the prediction residuals of the physical model as the core input. This invention maintains Dropout activation and performs multiple samplings during the prediction phase, achieving the quantification of model cognitive uncertainty; by using the prediction residuals of the physical branch as the key input of the data branch, it guides the data branch to focus on learning complex residual patterns not described by physical equations, enabling the model to output probabilistic trajectory clusters to quantify risk. Furthermore, through clear functional division of labor, it significantly improves the overall learning efficiency and prediction reliability of the hybrid model.

[0055] Thirdly, this invention addresses the systemic technical problems of existing search and rescue prediction methods, such as fragmented processes, unintuitive decision support information, and the inability to utilize real-time observation for closed-loop optimization, by constructing a complete technical system encompassing multi-source data fusion preprocessing, dual-branch hybrid model training, probabilistic prediction, and dynamic visualization updates. It provides an integrated solution. This solution ensures input quality through standardized data processing, guarantees model reliability through physical constraint training and interpretability verification, achieves intelligent fusion through adaptive weighting functions, and ultimately forms a data-model-forecast-observation-update decision-making closed loop through probabilistic trajectory clusters, confidence corridor visualization, and real-time re-prediction based on new observations. This successfully transforms advanced mechanisms and data fusion models into visualized reports that directly support search and rescue command and dynamically respond to on-site situations, significantly improving the scientific rigor, timeliness, and success rate of maritime search and rescue operations. Attached Figure Description

[0056] Figure 1 The flowchart illustrates the method for visualizing and predicting target drift trajectories based on multi-source dynamic fields and probabilistic LSTM, as provided in this embodiment of the invention. Detailed Implementation

[0057] To make the objectives and advantages of the present invention clearer, the present invention will be further described below with reference to embodiments; it should be understood that the specific embodiments described herein are merely for explaining the present invention and are not intended to limit the present invention.

[0058] Preferred embodiments of the present invention will now be described with reference to the accompanying drawings. Those skilled in the art should understand that these embodiments are merely illustrative of the technical principles of the present invention and are not intended to limit the scope of protection of the present invention.

[0059] It should be noted that in the description of this invention, the terms "upper", "lower", "left", "right", "inner", "outer", etc., which indicate directions or positional relationships, are based on the directions or positional relationships shown in the accompanying drawings. This is only for the convenience of description and is not intended to indicate or imply that the device or element must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, it should not be construed as a limitation of this invention.

[0060] Furthermore, it should be noted that, in the description of this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0061] Example 1

[0062] like Figure 1 As shown, this invention provides a method for visualizing and predicting target drift trajectories based on multi-source dynamic fields and probabilistic LSTM, comprising:

[0063] S1, acquire multi-source spatiotemporal hydrological and meteorological data covering the target sea area, and preprocess the hydrological and meteorological data;

[0064] The multi-source spatiotemporal hydrological and meteorological data include:

[0065] Measured data, including on-site ocean current, water temperature, salinity, wind speed and wind direction data obtained from buoys, drift devices, vessels, shore-based or mobile platforms;

[0066] Remote sensing inversion data includes data on sea surface currents, significant wave height, sea surface temperature, sea surface wind field, and sea ice concentration acquired by satellite remote sensing or shipborne radar;

[0067] Numerical simulation and forecast data, including three-dimensional ocean current field, wave field, temperature and salinity field, wind field and pressure field data output from operational marine environmental information forecasts or atmospheric forecasts.

[0068] The hydrological and meteorological data are preprocessed, including:

[0069] S11 performs spatiotemporal matching of measured data, remote sensing inversion data, and numerical forecast data from different sources, aligns them with time using coordinate system one, and integrates them into a unified geographic grid and time series.

[0070] S12, identify and remove significant outliers and invalid data from each data source, and reconstruct the missing data using spatial interpolation or time series imputation methods to form a continuous and complete data sequence set;

[0071] S13, normalize each physical quantity in the data sequence set to eliminate the influence of dimensions, and according to the grid resolution of the two-dimensional hydrodynamic model and the time step of the prediction task, perform spatial resampling and temporal resampling on the data sequence set to generate standardized dynamic field data that can be directly input into the model.

[0072] In one possible implementation, real-time observation data from fixed ocean buoys within and around the target search and rescue area are obtained from an ocean monitoring network, including hourly surface current velocity and direction, seawater temperature, salinity, wind speed and direction; profile drifting buoy data from the international Argo program that traverses the target search and rescue area are obtained to provide temperature and salinity profile information; and volunteer ship observation data from passing merchant ships and research vessels are collected to supplement point-based sea surface temperature, salinity and meteorological information.

[0073] The 10-meter sea surface wind field was obtained using scatterometer wind field data from the HY-2C / D satellite; high-resolution sea surface current field was retrieved using Sentinel-1 SAR imagery via Doppler centroid analysis; sea surface temperature was retrieved using MODIS satellite data; significant wave height was obtained using radar altimeter data from CFOSAT or Sentinel-3; and real-time sea surface current field grid data monitored by the coastal high-frequency ground wave radar system was acquired.

[0074] We obtained 6-hour interval forecast products from the operational marine forecasting system from the Marine Environmental Forecasting Center, including three-dimensional ocean current field, three-dimensional temperature and salinity field, ocean wave field, including wave height, period, and direction, as well as sea surface wind field; and we obtained sea level pressure field and 10-meter wind field forecast data from the regional atmospheric numerical forecast output from the meteorological department.

[0075] After acquiring the raw data, the spatial coordinates of all data are uniformly converted to the WGS-84 geographic coordinate system. Various grid and point data are resampled to a predefined unified spatial grid, such as a regular 0.05° × 0.05° latitude and longitude grid, covering the target sea area, using a unified time reference, such as UTC time. For discontinuous observation data, their observation timestamps are used to assign them to unified time series nodes through time interpolation, such as nearest neighbor or linear interpolation, for example, four times each day: 0:00, 6:00, 12:00, and 18:00. Finally, a data cube is formed, with each time point corresponding to a complete set of gridded environmental parameters.

[0076] For each data source, set a physically reasonable threshold range; for example, ocean current speed should be greater than 0 m / s and less than 2 m / s, and water temperature should be greater than -2℃ and less than 40℃. Significant outliers are detected and removed using the Laida criterion. Simultaneously, invalid data is identified and marked, such as landmasses and cloud-covered areas in satellite data.

[0077] For large-scale grid data gaps caused by quality control or original missing data, objective analysis methods, such as optimal interpolation or Kriging interpolation, are used to fill the gaps in space using information from surrounding valid grid points. For time series data, such as buoy data, gaps caused by quality control or original missing data are filled by linear interpolation or methods based on autoregressive models to fill short-term gaps, forming a continuous and complete set of data sequences in time and space.

[0078] For each physical variable in the data sequence set, such as U / V flow velocity, wind speed, and temperature, normalization is performed to eliminate dimensional differences and accelerate model training. Z-score normalization is used; for example, for the U component of ocean currents, the mean and standard deviation of all grid point data over the entire training period are calculated. Based on the grid resolution of the subsequently constructed 2D hydrodynamic model (e.g., 0.01° × 0.01°) and the time step required for trajectory prediction (e.g., 1 hour), the normalized continuous data field undergoes final spatial resampling, such as bilinear interpolation to a 0.01° grid, and temporal resampling, such as linear interpolation to a 1-hour interval. The final output is a series of spatiotemporally aligned, scale-uniform, and numerically standardized dynamic field data files, which can be directly used as input for subsequent physical and data model branches.

[0079] This invention addresses the technical problems of incomplete coverage and limited accuracy of single data sources by using spatiotemporal fusion and matching technology for multi-source heterogeneous data, significantly improving the spatiotemporal continuity and integrity of environmental dynamic fields. Through automated quality control and intelligent reconstruction technology, it solves the technical problem of outliers and numerous missing values ​​in the original data interfering with model training and prediction, effectively improving the quality and reliability of input data. Furthermore, through standardized normalization processing and task-oriented resampling technology, it addresses the technical problems of inconsistent physical dimensions and mismatch between data scale and model input requirements, significantly improving the convergence speed of model training and the timeliness of prediction.

[0080] S2, a two-dimensional hydrodynamic model is constructed based on the preprocessed hydrological data;

[0081] In one possible implementation, to balance computational efficiency with the simulation accuracy of the dominant dynamics of surface drift (i.e., horizontal flow field), this embodiment chooses to construct a numerical model based on a two-dimensional depth-averaged shallow water equation set. This model can simulate the horizontal circulation and transport processes generated by forcing effects such as wind stress, tides, and water level gradients. Its output two-dimensional depth-averaged flow field is the core driving force source for the Lagrange drift calculation in the subsequent physical model branch.

[0082] The computational domain of the model is determined based on the scope of the target sea area. A structured curved grid or regular rectangular grid matching the final preprocessing output is used, for example, with a horizontal resolution set to 0.01° × 0.01°, to ensure data consistency. Water depth data is obtained by fusing preprocessed standardized seafloor topography data with tidal forecast data.

[0083] The initial-moment ocean current field from the preprocessed, inverse-normalized, standardized dynamic field data is used as the initial condition for the model. At the open boundaries of the computational domain, such as the junction with the Pacific Ocean, the driving data directly adopts preprocessed, time-series standardized water level boundary data or current velocity boundary data. These data typically originate from the outputs of larger-scale global or regional operational ocean forecasting models, such as HYCOM and FIOCOM, and have been aligned and standardized with the target grid through the S1 step. Sea surface wind stress is calculated from preprocessed standardized 10-meter sea surface wind field data using the standard block formula. This is the key external force driving changes in the model's flow field. Seabed stress is parameterized using the second-order friction law, with its drag coefficient determined based on the seabed type and water depth. The horizontal eddy viscosity coefficient uses the Smagorinsky subgrid-scale parameterization scheme to adapt to the flow state.

[0084] After configuration, the governing equations are discretized and numerically solved using the finite volume method or the finite difference method. Driven by the aforementioned initial conditions, boundary conditions, and surface forcing, the model performs integral operations to simulate the two-dimensional flow field evolving over time in the target sea area. During model execution, a two-dimensional depth-averaged velocity field is output across the entire computational domain at a preset prediction task time step, for example, every hour. This output flow field is temporally synchronized with the input forcing field and spatially consistent with the model mesh.

[0085] S3 uses the parameterized Lagrange drift equations as a branch of the physical model to construct differentiable hierarchical structures, including:

[0086] S31, based on the kinematics of a particle, the core computational unit of the physical model branch is defined as the parameterized Lagrange drift equation. The parameterized Lagrange drift equation expresses that the position of the target at the next moment is determined by the position at the current moment, the environmental dynamic field at the current moment, and the parameterized coefficients to be learned, in order to describe the combined contribution of wind flow, Stokes drift, and other unresolved physical effects.

[0087] S32, using an automatic differentiation framework, each computational step in the parameterized Lagrange drift equation is constructed as a differentiable computational operation, making the parameterized Lagrange drift equation as a whole a trainable differentiable layer;

[0088] S33, using the target's position and state vector from the previous moment as input, the predicted position for the next moment is calculated using the differentiable parameterized Lagrange drift equation, forming a physics-driven sequence state transition function;

[0089] S34, the sequence state transition function is used as the forward propagation core of the physical model branch, and the trainable differentiable layer is initialized according to fluid mechanics, thereby completing the construction of the physical model branch, enabling it to simulate the drift trajectory of the target from the environmental dynamic field and the initial state in a differentiable manner.

[0090] In one possible implementation, the core of the physical model branch is a parameterized equation of motion that treats the target as the displacement of a point mass at a discrete time step, expressed as a function of the environmental dynamic field and a set of learnable parameters. The physical meaning of this equation is that the next position of the target is determined by the contributions of the current advection, wind-induced current, and wave drift. The current advection component includes an advection coefficient close to 1, used to correct the deviation of the model flow field from the actual advection effect. The wind-induced current component includes an wind-induced current coefficient, representing the drag effect of wind on surface water, with a theoretical value typically between 0.01 and 0.05, approximately 1%-5% of the wind speed. The wave drift component includes a wave drift coefficient, used to characterize the mass transport generated by the nonlinear effects of waves.

[0091] Using the automatic differentiation capabilities of deep learning frameworks such as PyTorch or TensorFlow, the above equations are implemented as a differentiable module. Specifically, the location is converted from geographic coordinates to model grid indices, and a differentiable bilinear interpolation function is used to extract the vector value of the point from the discrete current advection, wind-driven current, and wave drift fields. The calculated displacement is then added to the target's position at the previous time step.

[0092] The aforementioned differentiable computation layer is packaged into a loop computation unit. At each time step, the current state is input, which includes at least the target's position, windward area, and underwater volume as part of the learnable parameters, thus outputting the state for the next time step.

[0093] The initial values ​​of the parameters are set based on prior knowledge of fluid mechanics. For example, the advection coefficient is initialized to 1.0, the wind-driven flow coefficient is initialized to 0.03, and the wave drift coefficient is initialized to 0.01. During prediction, given the initial position and the temporal environmental dynamic field, the complete physical-driven drift trajectory can be simulated by repeatedly calling the loop calculation unit.

[0094] This invention addresses the technical problem of fixed parameters in traditional Lagrange drift models being unable to adapt to complex and ever-changing real-world sea conditions by introducing learnable parameterized physical coefficients, significantly improving the accuracy and environmental adaptability of physical simulations. Furthermore, by constructing the physical equations as differentiable hierarchical layers and integrating them into an automatic differentiation framework, it solves the technical problem of end-to-end collaborative optimization between physical models and data-driven models, achieving deep coupling and complementary advantages between mechanisms and data. Finally, by maintaining the interpretability of the core architecture and parameters of the physical equations, it solves the technical problems of black-box decision-making in pure data-driven models and the lack of physical guarantees and credibility support for prediction results, greatly enhancing the credibility and decision support value of prediction results.

[0095] S4 uses a Bayesian Long Short-Term Memory network and Monte Carlo Dropout to construct the data model branch, including:

[0096] S41, Construct a core architecture based on a long short-term memory network, wherein the long short-term memory network has at least one hidden layer for learning complex spatiotemporal dependencies and unmodeled dynamic patterns from the input historical trajectory sequence and environmental dynamic field sequence;

[0097] S42, Monte Carlo Dropout layers are embedded between each hidden layer of the Long Short-Term Memory network and before the fully connected output layer; during the model training phase, the Monte Carlo Dropout layers randomly drop some neuron connections during forward propagation; during the model prediction phase, the Monte Carlo Dropout layers are kept active, and multiple forward propagation samplings are performed to quantify the uncertainty of the model itself.

[0098] S43, with the goal of maximizing the likelihood function between the predicted trajectory and the historical measured trajectory, the parameters of the data model branch are trained using the negative log-likelihood loss function, so that the data model branch performs residual correction during the target drift process;

[0099] S44, at the end of the Bayesian Long Short-Term Memory network, a fully connected layer is connected so that the Long Short-Term Memory network predicts and outputs the mean and variance of the drift position in the longitude and latitude directions, thereby generating a probabilistic prediction result in the form of a Gaussian distribution;

[0100] S45, input the historical trajectory, environmental dynamic field and the prediction residual generated by the physical model branch into the data model branch; the network weight parameters of the data model branch are randomly initialized to construct a data model branch that focuses on learning complex, nonlinear drift patterns that the physical model fails to capture.

[0101] In one possible implementation, an LSTM network with an encoder-decoder structure is designed as the core of the data branch. Specifically, the encoder consists of two stacked LSTM layers, each containing 128 hidden units. The encoder's input is a fragment of historical trajectory sequence, such as the target's latitude and longitude sequence from the previous 6 hours, along with the corresponding multi-dimensional environmental dynamic field sequence, such as U / V ocean current velocity, U / V wind speed, and significant wave height at the same time step. The decoder consists of one LSTM layer with 128 hidden units. The initial hidden state is initialized by the encoder's final state, and the decoder gradually generates predictions for future moments. This architecture aims to encode the spatiotemporal evolution pattern from the input historical sequence and decode future motion trends. It is particularly adept at capturing nonlinear, long-range dependencies and dynamic factors not explicitly included in the physical equations, such as subgrid-scale vortex effects and target-specific characteristics.

[0102] To transform the LSTM network into a Bayesian neural network with quantifiable cognitive uncertainty, Monte Carlo Dropout layers are inserted between the recurrent connections of each LSTM layer and before the final fully connected output layer. The Dropout rate is set to 0.2. During forward propagation in the training phase, these Dropout layers randomly zero out a portion of the neurons' outputs according to a set probability, serving as a regularization method to prevent overfitting. The Dropout layers remain active during the prediction phase. When a prediction is needed, instead of a single forward propagation, 100 forward propagation samples are performed on the same input. Due to the randomness of Dropout, each sample is equivalent to drawing a sub-network from the approximate posterior distribution of parameters learned from the training data for prediction. The distribution of the 100 prediction results reflects the cognitive uncertainty of the model itself due to limited training data and structural uncertainty.

[0103] In each prediction step, the network outputs the probability distribution of the target location. This embodiment assumes that this distribution is a two-dimensional Gaussian distribution, meaning that the mean and variance in the latitude and longitude directions need to be output. A negative log-likelihood loss function is used to simultaneously optimize the accuracy of the prediction and the reasonableness of the uncertainty estimation; specifically, the variance increases when the error is large and decreases when the error is small.

[0104] At the end of the LSTM decoder, a fully connected layer is connected as the output layer. Specifically, this fully connected layer has four neurons, corresponding to the mean and logarithm of the variance in the latitude and longitude directions at the next time step. The logarithm of the variance is output to ensure that the variance remains positive and stable during training. After obtaining the network output, the variance is obtained by performing an exponential operation on the last two neurons. At this point, the network directly generates a complete two-dimensional Gaussian distribution.

[0105] One of the key inputs to the data branch is the prediction residual from the physical model branch. Specifically, during training, the current-state physical model branch is used to perform a forward simulation of the same historical sequence to obtain the predicted physical trajectory. Then, the difference between the actual trajectory and the predicted physical trajectory, i.e., the residual, is used as an additional feature sequence, concatenated with the environmental dynamic field and the true historical trajectory values, and input into the encoder. This explicitly guides the data branch to learn residual signals that the physical model cannot explain. Through this design, the data model branch is shaped into a residual corrector and uncertainty quantizer, not attempting to relearn basic advection motion, but focusing on capturing complex, nonlinear, and random deviations, and providing a crucial uncertainty range estimate for the final prediction through multiple dropout samplings. For example, the directional swimming of people being searched may cause drift trajectories that do not conform to physical drift laws.

[0106] This invention addresses the technical problem of traditional deterministic neural networks' inability to quantify their own cognitive uncertainty by introducing Monte Carlo Dropout technology to perform Bayesian approximation on standard LSTM. For the first time, it achieves the assessment of the model's own credibility in trajectory prediction, significantly improving the risk knowability and decision support value of the prediction results. By designing a network architecture with the prediction residuals of the physical model as one of the core inputs, it solves the technical problem of data-driven models and physical models simply existing in parallel or competing, failing to form efficient collaboration. It guides the data branches to focus on learning residual signals beyond the physical mechanism, greatly improving the overall prediction accuracy and efficiency of the hybrid model. Furthermore, by employing a negative log-likelihood loss function and a probabilistic output layer, it solves the technical problem that traditional mean squared error loss can only optimize the predicted point location and cannot simultaneously optimize the quality of uncertainty estimation, achieving direct optimization of the prediction probability distribution, thereby simultaneously improving the accuracy of prediction and the reliability of uncertainty estimation.

[0107] S5 integrates a two-dimensional hydrodynamic model, preprocessed meteorological data, physical model branches, and data model branches to generate a dual-branch hybrid prediction model.

[0108] S6. Based on the preprocessed hydrological and meteorological data, the physical model branch is trained by combining the corresponding historical measured drift trajectory data. The physical parameter constraint mechanism is integrated to ensure that the physical parameters conform to the laws of fluid mechanics, and the physical interpretability is verified.

[0109] S7: Based on the prediction residuals of the physical model branches, an adaptive weight function is constructed to dynamically adjust the contribution weights of the physical branch and the data branch, and a dual-branch hybrid prediction model is jointly trained.

[0110] The physical interpretability verification includes:

[0111] Analyze the parameterized coefficients obtained after training the physical model branches to check whether their values ​​fall within a reasonable physical range defined based on fluid mechanics and empirical knowledge;

[0112] The environmental dynamic field is input and subjected to controllable perturbation. The trajectory change trend of the output branch of the physical model is analyzed and verified to conform to physical laws.

[0113] The physical model branch is placed in a typical ideal dynamic field with a known analytical solution for simulation. The output trajectory of the physical model branch is compared with the known analytical solution to verify whether the accuracy of the simulation meets the target requirements.

[0114] In one possible implementation, a unified input interface is first defined to receive:

[0115] The temporal environmental dynamic field includes the flow field of the two-dimensional hydrodynamic model from S2, and meteorological data such as wind speed, wind direction, and significant wave height from S1 preprocessed data. All data are standardized temporal grid data.

[0116] The initial state of the target includes the initial position of the target to be predicted, and optional attribute vectors, such as type labels;

[0117] Historical sequence, including fragments of the target's historical trajectory.

[0118] The initial state and environmental dynamic field are input into the physical model branch, which calculates a deterministic physical trajectory step by step based on its differentiable Lagrange equation. Simultaneously, the historical trajectory, environmental dynamic field, and real-time prediction residuals from the physical branch are input into the data model branch. This branch, through its Bayesian LSTM network, outputs a probabilistic prediction distribution—the Gaussian distribution parameters for each future time step. At each time step of training and prediction, an adaptive weight function calculates the weights of the current time step's output for both the physical and data branches. Finally, the model outputs a data-corrected trajectory and its uncertainty estimate. This design generates an end-to-end dual-branch hybrid prediction model. This model has a unified interface and internally implements the dynamic fusion of physical mechanisms and data-driven signals.

[0119] The physics branch first undergoes independent pre-training to ensure its foundational rationality and interpretability. Specifically, it uses pre-processed environmental dynamic fields and corresponding historical measured drift trajectory data, employing mean square error loss at trajectory points to optimize the physics branch's parameters. A penalty term is added to the loss function to penalize situations where the wind-induced current coefficient exceeds the empirical upper limit of 0.05. Similarly, the wave drift coefficient is constrained to remain within a reasonable range.

[0120] The parameter values ​​after training convergence were checked. For example, the wind-induced flow coefficient was 0.032, falling within the typical wind drift coefficient range of 0.01-0.05; the wave drift coefficient was 0.012, consistent with the theoretical order of magnitude of wave drift; and the advection coefficient was 0.98, indicating that the model flow field was slightly weaker than the actual advection effect. All parameters conformed to physical laws, and the verification was successful.

[0121] Construct a test scenario. Suddenly increase the input wind field by a factor of 2 and observe the output trajectory. The predicted trajectory of the physical branch should show a significant increase in offset, and the increase should roughly correspond to the wind-generated flow coefficient. If the flow field is reversed, the predicted trajectory should flow almost in the opposite direction. This response trend, consistent with physical intuition, proves the physical consistency of the branch.

[0122] The physical branch is run in an ideal flow field with a known analytical solution. Its output trajectory should almost coincide with the theoretical solution, i.e., a straight line, and its root mean square error should be below a preset threshold. This test verifies the accuracy of the numerical results.

[0123] After pre-training the physics branch, the entire hybrid model undergoes end-to-end joint training. Specifically, an adaptive weight function is first constructed, which takes the statistical characteristics of the prediction residuals of the physics branch within the most recent time window as its main input. A lightweight neural network, such as a two-layer fully connected network or a sigmoid-based function, is designed. The goal is to assign higher weights to the physics branch when the physics residuals are small and stable, indicating that the physics model is reliable in the current environment; and to increase the weights of the data branch when the physics residuals are large or highly volatile, indicating that the current situation is complex or exceeds the physics model's representational capacity. The function outputs a dynamic weight between 0 and 1, which serves as the fusion weight for the physics model branches.

[0124] Subsequently, the dual-branch hybrid prediction model is jointly trained. Specifically, the historical sequence is input, the physical branch is run to obtain the prediction, the residual is calculated, the residual is input into the adaptive weight function to obtain the dynamic weight, the data branch is run, and the output of the data branch is fused with the output of the physical branch according to the dynamic weight. The negative log-likelihood loss between the final prediction and the future true value is calculated. Through backpropagation, the LSTM weights of the data branch, the parameters of the adaptive weight function, and the learnable parameters of the physical branch are updated simultaneously. The entire training process enables the dual-branch hybrid prediction model to find the optimal balance between physical laws and data patterns.

[0125] This invention addresses the technical challenges of inconsistent input / output formats, fragmented information flow, and lack of end-to-end optimization in traditional multi-model systems by constructing a unified forward propagation process and a deeply coupled architecture. It achieves, for the first time, seamless integration of the physical kernel and data-driven modules at the computational graph level, significantly improving the system's engineering efficiency and collaborative potential. Through pre-training with strong physical constraints and systematic interpretability verification, it overcomes the technical risks of violating physical laws and unreliable model behavior in data-driven methods, laying a solid and auditable physical foundation for the entire hybrid model and ensuring the baseline reliability of prediction results and the trustworthiness of decision-makers. Furthermore, by introducing an adaptive weight function based on physical residuals and conducting end-to-end joint training, it overcomes the technical bottlenecks of statically or manually set fusion weights failing to adapt to complex and ever-changing environments and fully unleashing the potential of hybrid models. This enables the model to intelligently perceive and autonomously decide on different prediction scenarios, achieving a fusion gain greater than the sum of its parts (1+1>2).

[0126] S8 inputs the initial state information of the target to be searched and rescued along with the real-time or predicted environmental dynamic field into the trained dual-branch hybrid prediction model. Through multiple forward propagation sampling, it outputs a probabilistic drift trajectory cluster representing uncertainty.

[0127] S9, perform visualization processing on the probabilistic drift trajectory cluster to generate a visualized forecast including a probability heatmap, confidence corridor and average path;

[0128] S10, during the search and rescue process, receive real-time observation data, correct the probabilistic drift trajectory cluster based on the Bayesian update method, and refresh the visualization forecast in real time.

[0129] The visualization processing of the probabilistic drift trajectory cluster to generate a visualized forecast including a probability heatmap, confidence corridors, and average paths includes:

[0130] S91, Spatial superposition of the probabilistic drift trajectory clusters output by multiple forward propagation sampling, statistical analysis of the frequency of the target appearing in each grid cell of geographic space in all sampling trajectories, and normalization of them into a spatial probability density distribution.

[0131] S92, the spatial probability density distribution is mapped into a color gradient map, wherein the color from dark to light represents the probability of the target appearing in each grid cell of the geographic space from high to low, and a probability heat map is generated.

[0132] S93, in the probabilistic drift trajectory cluster, for each future prediction time, calculate the distribution of the position coordinates of all sampled trajectories at that time, filter the position coordinates at that time based on a preset confidence threshold, connect all position coordinates corresponding to each time to form a strip-shaped region that changes with time, i.e., a confidence corridor, and draw it in the visualization layer.

[0133] S94, calculate the arithmetic mean of the position coordinates of all sampled trajectories in the probabilistic drift trajectory cluster at each prediction time, connect the arithmetic mean position points at each prediction time in chronological order to form an average path, and draw it in the visualization layer;

[0134] S95, integrate the probability heatmap, confidence corridor and average path into the same geographic base map coordinate system, and add timestamp, scale bar, direction indicator and legend to generate a comprehensive visual forecast for search and rescue decision support.

[0135] The method for correcting the probabilistic drift trajectory cluster based on the Bayesian update method includes:

[0136] During the search and rescue operation, real-time observation data about the search and rescue target is received, and the real-time observation data is spatiotemporally aligned with the predicted time.

[0137] The previous forecasting process was immediately interrupted, and the real-time observation data was used as the new, defined initial state.

[0138] The real-time observation data is input into the trained dual-branch hybrid prediction model;

[0139] Using the real-time observation data as input, the dual-branch hybrid prediction model is driven to perform a new round of multiple forward propagation sampling to generate an updated probabilistic drift trajectory cluster that represents the real-time conditions and current uncertainties.

[0140] The real-time observation data includes at least one of the following: location report of the search and rescue target, hydrological data, and meteorological data. Furthermore, the real-time observation data is different from the initial state information or environmental dynamic field of the target to be searched and rescued input in S8.

[0141] In one possible implementation, when a maritime search and rescue center receives an alarm that "a vessel was lost in a certain sea area at 06:00 Beijing time, for example, 123.5°E, 28.2°N, with personnel falling overboard," this prediction system is immediately activated. Using the coordinates of the accident and the time of the alarm as the initial state of the target to be searched, the system automatically retrieves high-resolution meteorological and marine environmental forecast data for the next 72 hours from the time of the alarm. This data has undergone real-time preprocessing, including flow fields, wind fields, and wave fields from numerical weather prediction models, constituting the forecast environmental dynamic field.

[0142] The above input is loaded into the trained two-branch hybrid prediction model, and 200 independent forward propagation samplings are performed. Since Monte Carlo Dropout in the data branch remains active during prediction, each sampling is equivalent to drawing a possible network instance from the model's posterior distribution for prediction, resulting in 200 slightly different future drift trajectories. These 200 trajectories form a probabilistic drift trajectory cluster. Each trajectory is a possible estimate of the drift path over the next 72 hours, and the entire trajectory cluster comprehensively represents the probability distribution of the target location given initial conditions and environmental forecasts. This distribution simultaneously incorporates the uncertainties of the environmental field and the model itself.

[0143] The trajectory clusters generated by S8 are processed to produce an intuitive visualization. Specifically, all the geographical locations traversed by the 200 trajectories are overlaid onto a grid with a resolution of 0.01° × 0.01°. The number of times each grid cell is traversed by a trajectory is counted and divided by the total number of trajectories to obtain the probability value of the target's appearance within each grid cell. This probability distribution is mapped to colors using a red-yellow-blue gradient. Red represents a high-probability area (probability value greater than 60%), yellow represents a medium-probability area (probability value between 20% and 60%), and blue represents a low-probability area (probability value less than 20%), generating a probability heatmap overlaid on the electronic nautical chart.

[0144] A preset confidence threshold is set; in this embodiment, it is set to 90%, meaning the confidence corridor aims to cover 90% of the most probable trajectories. For each discrete prediction time in the future, the set of location coordinates of all 200 sampled trajectories at that time is obtained. Based on the two-dimensional spatial distribution of all location points at that time, its kernel density estimate is calculated to obtain the probability density value at each location point. Trajectories represented by location points with density values ​​higher than the preset confidence threshold are selected, and their cumulative probability reaches or slightly exceeds the preset confidence threshold. All location coordinates with probability density values ​​greater than the preset confidence threshold are retained. The entire process is achieved by iteratively adjusting the preset confidence threshold.

[0145] For each prediction time, the minimum convex hull of the selected high-density location coordinates is calculated. The minimum convex hull represents the spatial range in which the target has a high confidence of appearing at that time. Finally, the convex hull regions at each time are connected and smoothed in chronological order to form a strip-shaped confidence corridor that changes continuously in space and gradually widens in time, and is drawn with semi-transparent color blocks.

[0146] Calculate the arithmetic mean of the position coordinates of all 200 sampled trajectories in the probabilistic drift trajectory cluster at each prediction time to obtain a series of average center points. Connect these average center points in chronological order to form a bold black average prediction path, and draw it on the visualization layer.

[0147] On the electronic nautical chart base map, a probability heat map, confidence corridor and average path are superimposed in sequence, and the initial location of the accident is superimposed, such as a red high-profile marker, current time, forecast validity period, scale, compass and legend, to generate a comprehensive visual forecast called the 72-hour drift probability forecast map of the person who fell into the water.

[0148] Two hours into the search and rescue operation, a sighting report of the missing persons at 124.1°E, 28.5°N is received. The system then interrupts the old forecast, uses the sighting point as the new initial state, and inputs the latest short-term forecast and real-time analysis field from the time of sighting. The new state and new environmental field drive the hybrid model, and 200 new samples are taken to generate an updated probabilistic drift trajectory cluster. Based on the new trajectory cluster, the probability heatmap, confidence corridor, and average path are regenerated according to the process described in S9 above, and the visualization forecast interface of the command center is refreshed in real time to guide the dynamic adjustment of search and rescue forces.

[0149] This invention addresses the technical problems of high decision-making risk and inability to assess prediction reliability caused by the single trajectory output of traditional deterministic prediction methods by generating probabilistic trajectory clusters through multiple forward propagation sampling. It transforms search and rescue planning from relying on single judgments to probability-based risk management, significantly improving the scientific nature of search and rescue operations and the efficiency of resource allocation. Furthermore, by using a visualization method based on a unified confidence threshold to generate probability heatmaps and confidence corridors, it solves the technical problem of complex and abstract probabilistic prediction results that are difficult for on-site commanders to quickly understand and directly apply. It presents multidimensional spatiotemporal uncertainties intuitively and comprehensively as an operable search and rescue map, greatly improving the intuitiveness and responsiveness of decision-making. Finally, through a lightweight real-time update mechanism based on interrupted and re-initialized latest observation data, it solves the technical problem of rigid traditional forecast models that cannot incorporate constantly emerging new intelligence during the search and rescue process, leading to rapidly outdated predictions. This achieves closed-loop linkage between prediction and observation, enabling dynamic optimization of search and rescue deployment to closely follow the ever-changing on-site situation.

[0150] The technical solution of the present invention has been described above with reference to the preferred embodiments shown in the accompanying drawings. However, it will be readily understood by those skilled in the art that the scope of protection of the present invention is obviously not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will all fall within the scope of protection of the present invention.

Claims

1. A target drift trajectory visualization and prediction method based on multi-source dynamic field and probabilistic LSTM, characterized in that, include: S1, acquire multi-source spatiotemporal hydrological and meteorological data covering the target sea area, and preprocess the hydrological and meteorological data; S2, a two-dimensional hydrodynamic model is constructed based on the preprocessed hydrological data; S3 uses the parameterized Lagrange drift equation as a branch of the physical model to construct differentiable hierarchical structure. S4 uses a Bayesian long short-term memory network and Monte Carlo Dropout to construct the data model branch; S5 integrates a two-dimensional hydrodynamic model, preprocessed meteorological data, physical model branches, and data model branches to generate a dual-branch hybrid prediction model. S6. Based on the preprocessed hydrological and meteorological data, the physical model branch is trained by combining the corresponding historical measured drift trajectory data. The physical parameter constraint mechanism is integrated to ensure that the physical parameters conform to the laws of fluid mechanics, and the physical interpretability is verified. S7: Based on the prediction residuals of the physical model branches, an adaptive weight function is constructed to dynamically adjust the contribution weights of the physical branch and the data branch, and a dual-branch hybrid prediction model is jointly trained. S8 inputs the initial state information of the target to be searched and rescued along with the real-time or predicted environmental dynamic field into the trained dual-branch hybrid prediction model. Through multiple forward propagation sampling, it outputs a probabilistic drift trajectory cluster representing uncertainty. S9, perform visualization processing on the probabilistic drift trajectory cluster to generate a visualized forecast including a probability heatmap, confidence corridor and average path; S10, during the search and rescue process, receive real-time observation data, correct the probabilistic drift trajectory cluster based on the Bayesian update method, and refresh the visualization forecast in real time.

2. The target drift trajectory visualization and prediction method based on multi-source dynamic field and probabilistic LSTM according to claim 1, characterized in that, The multi-source spatiotemporal hydrological and meteorological data include: Measured data, including on-site ocean current, water temperature, salinity, wind speed and wind direction data obtained from buoys, drift devices, vessels, shore-based or mobile platforms; Remote sensing inversion data includes data on sea surface currents, significant wave height, sea surface temperature, sea surface wind field, and sea ice concentration acquired by satellite remote sensing or shipborne radar; Numerical simulation and forecast data, including three-dimensional ocean current field, wave field, temperature and salinity field, wind field and pressure field data output from operational marine environmental information forecasts or atmospheric forecasts.

3. The target drift trajectory visualization and prediction method based on multi-source dynamic field and probabilistic LSTM according to claim 1, characterized in that, The hydrological and meteorological data are preprocessed, including: S11 performs spatiotemporal matching of measured data, remote sensing inversion data, and numerical forecast data from different sources, aligns them with time using coordinate system one, and integrates them into a unified geographic grid and time series. S12, identify and remove significant outliers and invalid data from each data source, and reconstruct the missing data using spatial interpolation or time series imputation methods to form a continuous and complete data sequence set; S13, normalize each physical quantity in the data sequence set to eliminate the influence of dimensions, and according to the grid resolution of the two-dimensional hydrodynamic model and the time step of the prediction task, perform spatial resampling and temporal resampling on the data sequence set to generate standardized dynamic field data that can be directly input into the model.

4. The target drift trajectory visualization and prediction method based on multi-source dynamic field and probabilistic LSTM according to claim 1, characterized in that, The method of using parameterized Lagrange drift equations as differentiable hierarchical branches to construct physical model branches includes: S31, based on the kinematics of a particle, the core computational unit of the physical model branch is defined as the parameterized Lagrange drift equation. The parameterized Lagrange drift equation expresses that the position of the target at the next moment is determined by the position at the current moment, the environmental dynamic field at the current moment, and the parameterized coefficients to be learned, in order to describe the combined contribution of wind flow, Stokes drift, and other unresolved physical effects. S32, using an automatic differentiation framework, each computational step in the parameterized Lagrange drift equation is constructed as a differentiable computational operation, making the parameterized Lagrange drift equation as a whole a trainable differentiable layer; S33, using the target's position and state vector from the previous moment as input, the predicted position for the next moment is calculated using the differentiable parameterized Lagrange drift equation, forming a physics-driven sequence state transition function; S34, the sequence state transition function is used as the forward propagation core of the physical model branch, and the trainable differentiable layer is initialized according to fluid mechanics, thereby completing the construction of the physical model branch, enabling it to simulate the drift trajectory of the target from the environmental dynamic field and the initial state in a differentiable manner.

5. The target drift trajectory visualization and prediction method based on multi-source dynamic field and probabilistic LSTM according to claim 1, characterized in that, The data model branch constructed using Bayesian Long Short-Term Memory Network and Monte Carlo Dropout includes: S41, Construct a core architecture based on a long short-term memory network, wherein the long short-term memory network has at least one hidden layer for learning complex spatiotemporal dependencies and unmodeled dynamic patterns from the input historical trajectory sequence and environmental dynamic field sequence; S42, Monte Carlo Dropout layers are embedded between each hidden layer of the Long Short-Term Memory network and before the fully connected output layer; during the model training phase, the Monte Carlo Dropout layers randomly drop some neuron connections during forward propagation; during the model prediction phase, the Monte Carlo Dropout layers are kept active, and multiple forward propagation samplings are performed to quantify the uncertainty of the model itself. S43, with the goal of maximizing the likelihood function between the predicted trajectory and the historical measured trajectory, the parameters of the data model branch are trained using the negative log-likelihood loss function, so that the data model branch performs residual correction during the target drift process; S44, at the end of the Bayesian Long Short-Term Memory network, a fully connected layer is connected so that the Long Short-Term Memory network predicts and outputs the mean and variance of the drift position in the longitude and latitude directions, thereby generating a probabilistic prediction result in the form of a Gaussian distribution; S45, input the historical trajectory, environmental dynamic field and the prediction residual generated by the physical model branch into the data model branch; the network weight parameters of the data model branch are randomly initialized to construct a data model branch that focuses on learning complex, nonlinear drift patterns that the physical model fails to capture.

6. The target drift trajectory visualization and prediction method based on multi-source dynamic field and probabilistic LSTM according to claim 1, characterized in that, The physical interpretability verification includes: Analyze the parameterized coefficients obtained after training the physical model branches to check whether their values ​​fall within a reasonable physical range defined based on fluid mechanics and empirical knowledge; The environmental dynamic field is input and subjected to controllable perturbation. The trajectory change trend of the output branch of the physical model is analyzed and verified to conform to physical laws. The physical model branch is placed in a typical ideal dynamic field with a known analytical solution for simulation. The output trajectory of the physical model branch is compared with the known analytical solution to verify whether the accuracy of the simulation meets the target requirements.

7. The target drift trajectory visualization and prediction method based on multi-source dynamic field and probabilistic LSTM according to claim 1, characterized in that, The visualization processing of the probabilistic drift trajectory cluster to generate a visualized forecast including a probability heatmap, confidence corridors, and average paths includes: S91, Spatial superposition of the probabilistic drift trajectory clusters output by multiple forward propagation sampling, statistical analysis of the frequency of the target appearing in each grid cell of geographic space in all sampling trajectories, and normalization of them into a spatial probability density distribution. S92, the spatial probability density distribution is mapped into a color gradient map, wherein the color from dark to light represents the probability of the target appearing in each grid cell of the geographic space from high to low, and a probability heat map is generated. S93, in the probabilistic drift trajectory cluster, for each future prediction time, calculate the distribution of the position coordinates of all sampled trajectories at that time, filter the position coordinates at that time based on a preset confidence threshold, connect all position coordinates corresponding to each time to form a strip-shaped region that changes with time, i.e., a confidence corridor, and draw it in the visualization layer. S94, calculate the arithmetic mean of the position coordinates of all sampled trajectories in the probabilistic drift trajectory cluster at each prediction time, connect the arithmetic mean position points at each prediction time in chronological order to form an average path, and draw it in the visualization layer; S95, integrate the probability heatmap, confidence corridor and average path into the same geographic base map coordinate system, and add timestamp, scale bar, direction indicator and legend to generate a comprehensive visual forecast for search and rescue decision support.

8. The target drift trajectory visualization and prediction method based on multi-source dynamic field and probabilistic LSTM according to claim 1, characterized in that, The method for correcting the probabilistic drift trajectory cluster based on the Bayesian update method includes: During the search and rescue operation, real-time observation data about the search and rescue target is received, and the real-time observation data is spatiotemporally aligned with the predicted time. The previous forecasting process was immediately interrupted, and the real-time observation data was used as the new, defined initial state. The real-time observation data is input into the trained dual-branch hybrid prediction model; Using the real-time observation data as input, the dual-branch hybrid prediction model is driven to perform a new round of multiple forward propagation sampling to generate an updated probabilistic drift trajectory cluster that represents the real-time conditions and current uncertainties.

9. The target drift trajectory visualization and prediction method based on multi-source dynamic field and probabilistic LSTM according to claim 1, characterized in that, The real-time observation data includes at least one of the following: location report of the search and rescue target, hydrological data, and meteorological data. Furthermore, the real-time observation data is different from the initial state information or environmental dynamic field of the target to be searched and rescued input in S8.

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