A sea ice movement prediction method and system fusing physical information and historical track

Abstract

The application discloses a sea ice movement prediction method based on fusion of physical information and historical track, comprising the following steps: obtaining and arranging historical observation data of floating ice, pre-processing the historical observation data to form floating ice track segments sorted by time; constructing floating ice state variables including historical window position sequence, speed sequence, scale, shape, time characteristics and deep neural network coding representation thereof; establishing a shared forced dissipative floating ice dynamics model which is a fusion of a historical data driven deep neural network and a physical knowledge driven Lagrangian dynamics; learning, by the deep neural network, driving terms shared among multiple floating ice track segments, historical movement characteristics and non-negative dissipative terms adaptively generated from the current state from the historical track data; converting the track segments into supervised training samples to train the model; inputting the current floating ice state into the trained model to predict the floating ice track result at one or more future time points in a multi-step rolling recursive manner.

Description

Technical Field

[0001] This invention relates to the fields of sea ice motion analysis, deep learning trajectory prediction, and physical knowledge-driven dynamics modeling, and in particular to a sea ice motion prediction method and system that fuses physical information with historical trajectories. Background Technology

[0002] Blitz ice motion analysis is a crucial component of polar sea ice monitoring, marine environmental research, and navigational safety assurance. Current sea ice motion studies typically employ Lagrange and Eulerian methods: the former analyzes sea ice movement over time through buoy or target tracking, while the latter retrieves the sea ice displacement field from remote sensing imagery on a fixed grid. Existing research has enabled the automatic identification and tracking of blitz ice using visible light remote sensing imagery such as MODIS, obtaining the blitz ice's Lagrange trajectory, velocity, and geometric parameters, thus providing an effective data foundation for blitz ice motion analysis.

[0003] However, existing technologies mainly focus on ice floe detection, matching, and trajectory extraction, and still have shortcomings in predicting future ice floe trajectories, especially in stable modeling and recursive prediction under conditions of a large number of short trajectory segments. On the one hand, a single ice floe trajectory usually has few observation points, making it difficult to stably identify dynamic parameters for each trajectory individually. On the other hand, while purely empirical methods or deep learning methods that rely solely on historical data have strong nonlinear fitting capabilities, they often lack explicit constraints on the physical knowledge of ice floes driven by the environment, damping dissipation, and inertial motion, resulting in weak physical interpretability and a tendency for error accumulation and trajectory drift during multi-step rolling prediction. Therefore, there is an urgent need to propose an ice floe trajectory prediction method that can adapt to short trajectory sample conditions and take into account both dynamic mechanism expression and prediction capabilities. Summary of the Invention

[0004] The purpose of this invention is to propose a sea ice motion prediction method and system that integrates physical information and historical trajectories to solve the problems existing in the prior art. This invention constructs a shared dynamic backbone of floating ice based on historical observation data composed of a large number of short trajectory fragments, and introduces state-related dissipation terms to characterize the damping differences of different floating ices under different states, thereby realizing the recursive prediction of the trajectory of floating ice at one or more future moments.

[0005] To achieve the above objectives, the present invention provides the following solution: A method for predicting sea ice movement by fusing physical information with historical trajectories includes: S1. Acquire and organize historical observation data of floating ice, preprocess the historical observation data of floating ice to form floating ice trajectory segments sorted by time; S2. Construct ice floe state variables and historical window state sequences based on the ice floe trajectory segments; S3. Establish a shared forced dissipative floating ice dynamics model that integrates historical data-driven deep neural networks and physical knowledge-driven Lagrange dynamics. Utilize deep neural networks to construct shared driving terms, historical window encoding terms, and state-related dissipative terms, and establish a floating ice state update model based on the Lagrange dynamics state update mechanism. S4. Convert the ice floe trajectory fragment into supervised training samples, and train the ice floe dynamics model based on the supervised training samples to jointly optimize the parameters of the deep neural network driven by historical data, the parameters of the shared driving term, the parameters of the historical window encoding, and the parameters of the state-related dissipation term. S5. Input the current state of the floating ice and its historical window state sequence into the trained floating ice dynamics model, use historical data to drive the deep neural network to extract historical motion features, and under the physical knowledge-driven Lagrange dynamics state update mechanism, use the current predicted state as the next step input to perform multi-step rolling recursion, predict the floating ice state at one or more future moments, and output the future trajectory result of the floating ice.

[0006] Optionally, the historical observation data of the floating ice includes: the coordinates of the centroid position of the floating ice at multiple times, the corresponding observation time, and characteristic quantities of the ice's geometric properties; The characteristic quantities of the ice geometric properties include one or more of the following: velocity components, equivalent scale, ellipticity, and time properties; The preprocessing includes one or more of the following: outlier removal, missing value processing, time sorting, coordinate system unification, unit normalization, velocity difference estimation, noise smoothing, and trajectory segment selection.

[0007] Optionally, the ice floe state variables include: position features, velocity features, scale features, shape features, and time features; wherein, the position features are used to characterize the spatial position of the ice floe's center of mass in the plane, the velocity features are used to characterize the ice floe's motion state, the scale features are used to characterize the ice floe's geometric size, the shape features are used to characterize the ice floe's external shape, and the time features are used to characterize the time information corresponding to the observation time. The historical window state sequence is used to extract historical motion features by a deep neural network.

[0008] Optionally, in S3, the floating ice is regarded as a forced dissipative motion body on a two-dimensional plane. The equivalent environmental driving effect in the floating ice motion process is described by the driving term shared among all floating ice trajectory segments, and the damping, friction and velocity decay effects are described by the non-negative state-related dissipation term adaptively generated by the current state. The shared driving term and the state-related dissipation term work together in the ice floe state update process to predict the future state of the ice floe.

[0009] Optionally, the shared driving term is implemented by a deep neural network driven by historical data. The deep neural network includes a multilayer perceptron, a recurrent neural network, a temporal convolutional network, a Transformer network, a graph neural network, or a combination thereof. Its input is the current ice floe state variable and / or the historical window state sequence, and its output is two-dimensional equivalent acceleration information used to update the velocity state of the ice floe at the next moment. The shared driving term is shared among all ice floe trajectory samples, rather than setting independent parameters for each ice floe trajectory; The state-related dissipation term is a non-negative scalar function or a non-negative vector function with respect to the current ice floe state variable. Its output is used to characterize the dissipation intensity of the ice floe under different scale, shape, velocity and time conditions, and participates in the calculation of the ice floe velocity decay term. The state-related dissipation term is adaptively adjusted as the state of the ice floes changes, so that different individual ice floes or the same ice floe at different time stages have different dissipation characteristics. The state-related dissipation term is associated with at least one or more of the following: equivalent scale characteristics, ellipticity characteristics, velocity magnitude characteristics, and time characteristics of the ice floes. By using a shared function to generate different dissipation values ​​under different state conditions, the method of identifying dissipation parameters individually for each ice floe trajectory can be replaced.

[0010] Optionally, in S4, ice floe trajectory segments with a length of not less than 2 are constructed as one-step state transition samples, and ice floe trajectory segments with a length of not less than 3 are constructed as two-step state transition samples. The model takes the current state as input, predicts the state at the next moment, and uses the actual state at the next moment for supervised training. For a two-step state transition sample, after obtaining the predicted state at the next time step, we continue to recursively predict the state at subsequent time steps.

[0011] Optionally, the training objectives used in S4 include position error terms, velocity error terms, and multi-step rolling prediction error terms; S4 also applies nonnegativity constraints, smoothness constraints, or parameter norm constraints to state-related dissipation terms to improve the stability and generalization ability of model training. The ice floe dynamics model is jointly trained by sharing driving term parameters and state-related dissipation term parameters through iterative optimization.

[0012] Optionally, in S5, the currently predicted state of the floating ice is used as the input for the next prediction, and the state update process is repeated until the preset number of prediction steps is reached. The output should include at least a sequence of ice floe centroid coordinates for one or more future time points; the output should also include future velocity sequences, dissipation term change sequences, intermediate state variables, or trajectory visualizations.

[0013] A sea ice motion prediction system that integrates physical information and historical trajectories includes: The data acquisition and preprocessing module is used to acquire historical observation data of floating ice and form floating ice trajectory fragments sorted by time. The state variable construction module is used to construct ice floe state variables based on the ice floe trajectory fragment, including historical window position sequence, velocity sequence, scale, shape, time features and their deep neural network encoding representation; The integrated dynamics modeling module is used to construct a deep neural network driven by historical data, a shared driving term, a historical window encoding term, and a non-negative state-related dissipation term, and to establish a floating ice state update mechanism based on physical knowledge-driven Lagrange dynamics. The model training module is used to convert ice floe trajectory fragments into supervised training samples and train a shared forced dissipative ice floe dynamics model that integrates historical data-driven deep neural networks and physical knowledge-driven Lagrange dynamics. The trajectory prediction module is used to input the current state of the ice floes into the trained model and output the future trajectory results of the ice floes using a multi-step rolling recursion method.

[0014] An electronic device includes a processor and a memory, wherein the memory stores a computer program, and when the computer program is executed by the processor, it implements the sea ice motion prediction method that fuses physical information with historical trajectories.

[0015] The beneficial effects of this invention are as follows: This invention addresses the common characteristics of ice floe trajectory data, namely "a large number of short trajectory segments and a limited number of observation points per trajectory". It adopts a unified modeling method that shares driving terms among all trajectory segments, eliminating the need to identify independent dynamic parameters for each ice floe trajectory. This reduces the problems of unstable parameter estimation, model overfitting, and difficulty in generalizing to new ice floe trajectories under short trajectory conditions.

[0016] This invention introduces a state-dependent non-negative dissipation term in the process of modeling ice floes dynamics, so that the dissipation intensity can be adaptively generated according to the ice floe velocity, scale characteristics, shape characteristics and time characteristics, thereby characterizing the damping differences of different ice floes and the same ice floe at different stages, avoiding the insufficient expressive power caused by using fixed damping parameters.

[0017] This invention establishes a forced dissipation state update mechanism under the description of Lagrange motion. It describes the equivalent motion trend of ice floes driven by the environment through shared driving terms and describes the velocity decay process through non-negative dissipation terms. This enables the prediction model to have both the nonlinear expression capability of a deep learning model driven by historical data and the state evolution constraints and physical interpretability of a Lagrange dynamics model driven by physical knowledge.

[0018] This invention employs a one-step supervised training method combined with an optional multi-step assisted training method. This method can not only meet the stable training requirements under short trajectory sample conditions, but also improve the stability and continuous recursion capability of the model in the multi-step rolling prediction process, thus making it more suitable for the scenario of predicting the future trajectory of floating ice.

[0019] The method of this invention has relatively simple requirements for the form of input data. It can directly use easily obtainable features such as position, speed, scale, shape and time from historical trajectory records for modeling, and has good engineering feasibility. At the same time, the method can be easily extended to more complex scenarios such as ice floe shape evolution prediction, rotation state modeling and multi-ice floe interaction prediction, and has good scalability. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 This is a schematic diagram of a sea ice motion prediction method that fuses physical information with historical trajectories according to an embodiment of the present invention. Figure 2 This is a visualization diagram of some ice floe trajectories in an embodiment of the present invention. Different trajectories represent the position change paths of different ice floe centroids at consecutive moments. Arrows indicate the direction of movement, and colored markers indicate the starting position or observation node of the corresponding ice floe trajectory. Figure 3 This is a schematic diagram illustrating the construction of ice floe state variables according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the shared forced dissipation floating ice dynamics model structure according to an embodiment of the present invention; Figure 5 This is a schematic diagram illustrating the conversion from trajectory segments to training samples in an embodiment of the present invention. Detailed Implementation

[0022] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0023] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0024] To address the issue that existing technologies primarily focus on ice floe detection, matching, tracking, and motion measurement, while lacking methods for predicting future trajectories, this embodiment proposes a sea ice motion prediction method and system that integrates physical information with historical trajectories.

[0025] Existing ice floe trajectory data typically consists of numerous short trajectory segments, with a limited number of observation points per trajectory. This makes it difficult to stably identify dynamic parameters for each trajectory individually, leading to overfitting and insufficient generalization ability. Furthermore, purely empirical or data-driven prediction methods fail to adequately characterize the motion mechanisms of ice floes driven by the environment and damping dissipation, hindering stable multi-step rolling prediction. Therefore, this invention aims to provide an ice floe trajectory prediction method suitable for short trajectory sample conditions, while also considering dynamic mechanism representation, parameter sharing modeling capabilities, and multi-step prediction stability.

[0026] This embodiment proposes a sea ice motion prediction method that fuses physical information with historical trajectories, including: S1. Acquire and organize historical observation data of floating ice, preprocess the historical observation data of floating ice to form floating ice trajectory segments sorted by time; S2. Construct ice floe state variables and historical window state sequences based on ice floe trajectory segments; S3. Establish a shared forced dissipative floating ice dynamics model that integrates historical data-driven deep neural networks and physical knowledge-driven Lagrange dynamics. Utilize deep neural networks to construct shared driving terms, historical window encoding terms, and state-related dissipative terms, and establish a floating ice state update model based on the Lagrange dynamics state update mechanism. S4. Convert the ice floe trajectory fragments into supervised training samples, and train the ice floe dynamics model based on the supervised training samples to jointly optimize the parameters of the deep neural network driven by historical data, the parameters of the shared driving term, the parameters of the historical window encoding, and the parameters of the state-related dissipation term. S5. Input the current state of the floating ice and its historical window state sequence into the trained floating ice dynamics model, use historical data to drive the deep neural network to extract historical motion features, and under the physical knowledge-driven Lagrange dynamics state update mechanism, use the current predicted state as the next step input to perform multi-step rolling recursion, predict the floating ice state at one or more future moments, and output the future trajectory result of the floating ice.

[0027] This invention addresses the problem of unstable identification of single trajectory parameters under conditions of a large number of short trajectory segments. It combines the representational capabilities of deep neural networks driven by historical data with the Lagrange dynamic constraints driven by physical knowledge. By using neural network driving terms, historical window feature encoding, and non-negative state correlation dissipation terms shared among all ice floe trajectory segments, it improves the training stability, generalization ability, and multi-step prediction ability of the model under short sample conditions, and enhances the physical interpretability of the deep learning prediction model.

[0028] Furthermore, the historical observation data of the floating ice includes: the coordinates of the centroid of the floating ice at multiple times, the corresponding observation time, and characteristic quantities of the ice's geometric properties; The characteristic quantities of ice geometry include one or more of the following: velocity components, equivalent scale, ellipticity, and time properties; Preprocessing includes one or more of the following: outlier removal, missing value handling, time sorting, coordinate system unification, unit normalization, velocity difference estimation, noise smoothing, and trajectory segment selection.

[0029] Specifically, in this embodiment, step S1: acquire and organize historical observation data of floating ice.

[0030] Historical observation data of ice floes at continuous or discrete moments are acquired. This historical data can originate from satellite remote sensing imagery, aerial observation imagery, ice floe tracking result databases, or trajectory record tables extracted by image processing algorithms. The historical observation data undergoes preprocessing, including at least one or more methods: outlier removal, missing value handling, time alignment, spatial coordinate unification, noise smoothing, and trajectory segment selection. Records of the same ice floe at different observation times are arranged chronologically to form a set of ice floe trajectory segments. Preferably, the historical observation data includes at least the ice floe's centroid position, observation time, and features reflecting its geometric properties; furthermore, it may include velocity information calculated from the position difference between adjacent moments. Existing technologies can automatically obtain ice floe trajectories, velocity vectors, and geometric parameters from medium-resolution visible light imagery such as MODIS, providing a directly usable data foundation for this invention.

[0031] Furthermore, the state variables of the floating ice include: position characteristics, velocity characteristics, scale characteristics, shape characteristics, and time characteristics; among which, position characteristics are used to characterize the spatial position of the floating ice's center of mass in the plane, velocity characteristics are used to characterize the floating ice's motion state, scale characteristics are used to characterize the floating ice's geometric size, shape characteristics are used to characterize the floating ice's external shape, and time characteristics are used to characterize the time information corresponding to the observation time. Historical window state sequences are used to extract historical motion features by deep neural networks.

[0032] Specifically, in this embodiment, step S2: construct the floating ice state variables.

[0033] Based on the observation data processed in step S1, a state vector representing the motion state of the ice floes is constructed. Preferably, at time t, the ice floe state vector is represented as: in, and This represents the coordinates of the center of mass of the ice floe in a two-dimensional plane. and Represents the velocity component. Additional state features are represented. These additional state features include at least one of the following: ice floe scale features, ice floe shape features, temporal features, and environmental context features. Further, the additional state features can be specifically taken as the ice floe equivalent scale SIZE, ellipticity ELLIP, and temporal feature DAY. If the velocity component is not directly given in the original observation data, it can be estimated through the position difference between adjacent time points; if the observation time interval is not constant, the corresponding velocity or displacement increment is calculated based on the actual time difference between adjacent time points.

[0034] Furthermore, in S3, the floating ice is regarded as a forced dissipative motion body on a two-dimensional plane. The equivalent environmental driving effect in the floating ice motion process is described by the driving term shared among all floating ice trajectory segments, and the damping, friction and velocity decay effects are described by the non-negative state-related dissipation term adaptively generated by the current state. Shared driving terms and state-related dissipative terms work together in the ice floe state update process to predict the future state of the ice floes.

[0035] Furthermore, the shared driving term is implemented by a deep neural network driven by historical data, including a multilayer perceptron, a recurrent neural network, a temporal convolutional network, a Transformer network, a graph neural network, or a combination thereof; its input is the current ice floe state variable and / or the historical window state sequence, and its output is two-dimensional equivalent acceleration information used to update the ice floe velocity state at the next moment; The shared driver is shared across all ice floe trajectory samples, rather than setting independent parameters for each ice floe trajectory. The state-related dissipation term is a non-negative scalar function or a non-negative vector function of the current ice floe state variable. Its output is used to characterize the dissipation intensity of the ice floe under different scale, shape, velocity and time conditions, and participates in the calculation of the ice floe velocity decay term. The state-dependent dissipation term adaptively adjusts with the change of ice floe state, thus giving different individual ice floes or the same ice floe at different time stages different dissipation characteristics. The state-dependent dissipation term is associated with at least one or more of the following characteristics of the ice floes: equivalent scale, ellipticity, velocity magnitude, and time. By using a shared function to generate different dissipation values ​​under different state conditions, the method of identifying dissipation parameters individually for each ice floe trajectory can be replaced.

[0036] Specifically, in this embodiment, step S3: establish a shared forced dissipative ice floe dynamics model that integrates historical data-driven deep neural networks and physical knowledge-driven Lagrange dynamics, such as... Figure 4 As shown.

[0037] Treating the ice floe as a forced dissipative motion body on a two-dimensional plane, and under the Lagrangian description of its body motion, the state evolution relationship under the combined effects of environmental driving forces and damped dissipation is described, with the position and velocity of the ice floe's center of mass as the main state variables. Preferably, the ice floe dynamics model includes position update relationships and velocity update relationships, where the position state... The speed state is represented as ,satisfy: in, This represents the state-driven term shared across all ice floe trajectory segments, used to characterize the equivalent acceleration caused by environmental impetus, background drift, and unobserved factors. The table represents the non-negative dissipative terms adaptively generated from the current state, used to characterize damping, friction, and velocity decay effects; This represents the parameter to be learned.

[0038] Furthermore, to facilitate engineering implementation and supervised training, the continuous-time dynamic equations are discretized as follows: in, This indicates the time interval between adjacent observation times.

[0039] Shared driver Cocoa can be implemented by a linear mapping, a shallow multilayer perceptron, or other function approximators, with the current state vector as its input. The output is a two-dimensional equivalent acceleration component; state-dependent dissipation term. For the state vector A nonnegative scalar function, or a function of state vectors. The nonnegative vector function, whose output is constrained by nonnegativity, participates in the velocity update to ensure that the dissipation term has a clear physical meaning. Furthermore, the nonnegativity constraint can be implemented using the softplus function, the absolute value function, or other monotone nonnegative mappings.

[0040] State-dependent dissipation terms can be expressed as: in, , , , , The parameters to be learned Indicates the speed of the ice floes. This is used to ensure that the dissipation term is non-negative. In this way, the dissipation differences between ice floes, and between the same ice floe at different times, are not achieved by setting parameters for each trajectory individually, but by adaptively generating a shared function under different state conditions.

[0041] Furthermore, in S4, ice floe trajectory segments with a length of not less than 2 are constructed as one-step state transition samples, and ice floe trajectory segments with a length of not less than 3 are constructed as two-step state transition samples. The model takes the current state as input, predicts the state at the next moment, and uses the actual state at the next moment for supervised training. For a two-step state transition sample, after obtaining the predicted state at the next time step, we continue to recursively predict the state at subsequent time steps.

[0042] Furthermore, the training objectives used in S4 include position error terms, velocity error terms, and multi-step rolling prediction error terms; S4 also applies nonnegativity constraints, smoothness constraints, or parameter norm constraints to state-related dissipation terms to improve the stability and generalization ability of model training. The ice floe dynamics model is jointly trained by sharing driving term parameters and state-related dissipation term parameters through iterative optimization.

[0043] Specifically, in this embodiment, step S4: Model training based on trajectory segments.

[0044] The ice floe trajectory fragments obtained in step S1 are converted into supervised training samples. Preferably, for trajectory fragments with a length of not less than 2, a one-step state transition sample is constructed. For trajectory segments with a length of at least 3, two-step state transition samples are further constructed. In the current state As input to the model, the dynamic model established in step S3 is used to predict the state at the next moment. and utilize the real state Supervised training is performed; for two-step samples, then after obtaining... Then continue recursively predicting This enhances the stability of multi-step prediction. In this embodiment, the conversion from trajectory segments to training samples is as follows: Figure 5 As shown.

[0045] The training objective function includes a position error term, a velocity error term, and a rolling prediction error term, and its expression can be written as: in, , , For loss weighting coefficients, and These represent the predicted position and velocity, respectively. This represents the multi-step recursive prediction error. Furthermore, non-negativity constraint regularization terms, smoothing regularization terms, or parameter norm constraint terms can be introduced into the dissipation term to improve training stability and model generalization ability.

[0046] Stochastic gradient descent, Adam optimization algorithm, or other iterative optimization methods are employed to jointly optimize the shared driving term parameters, historical window encoding parameters, and state-related dissipation term parameters in a historical data-driven deep neural network. This allows the deep neural network to learn the motion patterns of ice floes under the supervision of historical trajectory data, while simultaneously being physically constrained by the Lagrange dynamics state update mechanism. The training, validation, and test sets can be divided by trajectory segments or by individual ice floes, with longer trajectories preferred for validating the multi-step rolling prediction effect.

[0047] Furthermore, in S5, the currently predicted state of the floating ice is used as the input for the next prediction, and the state update process is repeated until the preset number of prediction steps is reached. The output should include at least a sequence of ice floe centroid coordinates for one or more future time points; the output should also include future velocity sequences, dissipation term change sequences, intermediate state variables, or trajectory visualizations.

[0048] Specifically, in this embodiment, step S5: perform multi-step rolling prediction and output trajectory results.

[0049] After model training is complete, the current state of the ice floes, or the current state estimated from a given historical window, is input, and the dynamic model established in step S3 is used to recursively predict the state at future moments. Specifically, the currently predicted state is used as the input for the next prediction, and the state update process is repeated until a preset number of prediction steps are reached, outputting a sequence of ice floe centroid coordinates for one or more future moments; optionally, a future velocity sequence and intermediate state variables are also output simultaneously. Preferably, the output results include at least one or more of the following: the centroid position at the next moment, a sequence of trajectories at multiple future moments, a velocity evolution sequence, and trajectory visualization results.

[0050] The shared driving term in this invention employs globally shared parameter modeling, rather than setting independent dynamic parameters for each ice floe trajectory. Since ice floe trajectory data typically consists of numerous short trajectory segments, the number of observation points per trajectory is limited. Identifying dynamic parameters independently for each trajectory easily leads to parameter instability, severe overfitting, and the inability to generalize to new trajectories. This invention, by combining a shared driving term across all ice floe trajectory segments with a state-conditional dissipative function, improves adaptability to short trajectory sample conditions while retaining a certain degree of physical interpretability. In existing ice floe tracking studies, many trajectories consist of only a small number of trajectory points; even for ice floes lasting more than 24 hours, the average number of trajectory points is only about 7. This demonstrates the necessity of shared modeling for short trajectory samples.

[0051] The method of this invention is applicable not only to ice floe trajectory data automatically extracted from visible light remote sensing images, but also to historical motion records of single ice floes obtained by other types of observation methods; it can be used not only for position prediction at the next moment, but also for recursive prediction of trajectories at multiple future moments, and can serve as a basic framework for further extension to ice floe shape evolution, rigid body rotation, and multi-ice floe interaction modeling.

[0052] The following further explains the implementation process of the sea ice motion prediction method based on the fusion of physical information and historical trajectories proposed in this embodiment, such as... Figure 1 As shown, the method includes the following steps: acquiring and organizing historical observation data of floating ice; constructing floating ice state variables; establishing a shared forced dissipation floating ice dynamic model based on Lagrange motion description; training the model based on trajectory segments; performing multi-step rolling prediction and outputting trajectory results.

[0053] Specifically, in step S1, historical observation data of the ice floes is first acquired. This historical observation data can originate from satellite remote sensing images, aerial observation images, ice floe tracking result databases, or trajectory record tables automatically extracted by image processing and target matching algorithms. Preferably, the historical observation data includes at least the coordinates of the ice floes' centroid positions at multiple times and the corresponding observation times; furthermore, it may also include additional information such as velocity components, scale characteristics, shape characteristics, and time attributes.

[0054] In a preferred embodiment, the historical trajectory of the ice floes can be automatically identified and tracked from visible light remote sensing imagery. Existing research on ice floe tracking has shown that the Lagrange trajectory, velocity vector, and geometric parameters of ice floes can be automatically extracted from medium-resolution imagery such as MODIS, thus providing the input data basis for this invention. For ice floes lasting more than 24 hours, the average number of trajectory points is still relatively small, therefore a shared modeling approach for short trajectory segments is suitable.

[0055] In step S1, the historical observation data also needs to be preprocessed. Preprocessing includes, but is not limited to: outlier removal, missing value handling, time sorting, coordinate system unification, unit normalization, velocity difference estimation, noise smoothing, and trajectory segment selection. For records of the same ice floe at different observation times, they are arranged in chronological order to form a set of trajectory segments.

[0056] In step S2, the ice floe state variables are constructed based on the preprocessed observation data. Further, at time t, the ice floe state vector can be expressed as: in, and This represents the coordinates of the center of mass of the ice floe in a two-dimensional plane. and Represents the velocity component. Indicates the equivalent scale characteristics of floating ice. Indicates the ellipticity characteristic of ice floes. Indicates time characteristics.

[0057] If the original observation data does not directly provide velocity components, they can be estimated from the position difference between adjacent time points; if the observation time interval is not constant, the corresponding velocity or displacement increment can be calculated based on the actual time difference between adjacent time points. In this way, a state representation suitable for dynamic modeling can be constructed without increasing the cost of complex observations. Figure 3 This example demonstrates the construction of the ice floe state variables.

[0058] In step S3, a shared forced dissipative ice floe dynamics model is established, integrating historical data-driven deep neural networks and physical knowledge-driven Lagrange dynamics. The ice floe is considered as a forced dissipative moving body on a two-dimensional plane, and its position and velocity states are described over time from a Lagrange perspective. Preferably, the continuous-time form can be expressed as: in, Indicates the position status. Indicates speed status. Indicates a shared driver item. Represents state-dependent dissipation terms. This represents the parameter to be learned.

[0059] In this model, shared driving terms describe environmental propulsion, background drift, and effective driving forces not explicitly modeled; state-related dissipation terms describe damping, friction, and velocity decay effects. Unlike methods that set a separate set of dynamic parameters for each trajectory, this invention employs globally shared dynamic backbone modeling, enabling the model to learn state transition laws using a large number of short trajectory segments.

[0060] To facilitate engineering implementation and supervised training, the continuous dynamic equations can be discretized as follows: in, This represents the time interval between adjacent observations. The discrete update form described above is applicable to both one-step supervised training and multi-step rolling recursive prediction during the testing phase.

[0061] Shared driver This can be implemented using linear mapping, shallow multilayer perceptrons, or other function approximators. Its input is the current state vector, and its output is a two-dimensional driving force or two-dimensional acceleration component. The parameters of the shared driving term are shared across all trajectory samples, rather than being set independently for each ice floe trajectory.

[0062] State-related dissipation terms The function is a nonnegative function of the state vector, and its output participates in the velocity update to ensure that the dissipation effect has a clear physical meaning. Preferably, the dissipation term can be expressed as: in, , , , , These are the parameters to be learned. This shared function allows the dissipation intensity of different ice floes, and even the same ice floe at different time stages, to adaptively change according to its state, without needing to identify damping parameters individually for each trajectory.

[0063] In step S4, the trajectory segments are converted into supervised training samples. For trajectory segments with a length of at least 2, one-step state transition samples can be constructed. For trajectory segments with a length of at least 3, two-step state transition samples can be further constructed. The model takes the current state as input and outputs the predicted state for the next time step. and the actual state Compare them.

[0064] To enhance the model's stability in multi-step recursive scenarios, for trajectory segments with a length of at least 3, after obtaining... Then, it can be used as input for the next step, recursively predicting. Furthermore, an auxiliary rolling loss term is constructed to suppress the accumulation of errors in multi-step prediction.

[0065] The training objective function includes a position error term, a velocity error term, and a rolling prediction error term, and its expression can be written as: in, , and For loss weighting coefficients, This represents the multi-step rolling prediction error. Furthermore, non-negativity constraint regularization terms, smoothing regularization terms, or parameter norm constraint terms can be added to the dissipation term to improve the model's training stability and generalization ability.

[0066] Stochastic gradient descent, Adam optimization algorithm, or other iterative optimization algorithms can be used to jointly optimize the shared driving term parameters, historical window encoding parameters, and state-related dissipation term parameters in the historical data-driven deep neural network. This allows the deep neural network to learn the motion patterns of ice floes under the supervision of historical trajectory data, while being physically constrained by the Lagrange dynamics state update mechanism. The training, validation, and test sets can be divided by trajectory segments or by individual ice floes; preferably, relatively long trajectory segments are used for model validation and multi-step prediction performance evaluation.

[0067] After the model training is completed, the current state of the ice floes or the state corresponding to a given historical window is input into the trained dynamic model to obtain the predicted state for the next moment. This predicted state is then used as the input for the next step to continue the recursion until the preset number of prediction steps is reached, thereby outputting the ice floe trajectory results for one or more future moments.

[0068] The output includes at least one or more of the following: the centroid position at the next moment, a sequence of centroid coordinates for multiple future moments, a velocity evolution sequence, and trajectory visualization results. Therefore, this invention can achieve recursive prediction of the future trajectory of a single ice floe. Visualization of some ice floe trajectories is shown below. Figure 2 As shown, different trajectories represent the path of position change of different ice floe centroids at consecutive moments, arrows indicate the direction of motion, and colored markers indicate the starting position or observation node of the corresponding ice floe trajectory.

[0069] Since ice floe trajectories are typically composed of numerous short trajectory segments, identifying independent dynamic parameters for each trajectory can easily lead to parameter instability, severe overfitting, and insufficient generalization ability for new trajectories. Therefore, this invention employs a "shared driving term + state-conditional dissipative term" approach, enabling the model to possess both a certain degree of physical interpretability and suitability for stable training and prediction under short trajectory sample conditions.

[0070] This embodiment also proposes a sea ice motion prediction system that fuses physical information with historical trajectories, including: The data acquisition and preprocessing module is used to acquire historical observation data of floating ice and form floating ice trajectory fragments sorted by time. The state variable construction module is used to construct ice floe state variables based on the ice floe trajectory fragment, including historical window position sequence, velocity sequence, scale, shape, time features and their deep neural network encoding representation; The integrated dynamics modeling module is used to construct a deep neural network driven by historical data, a shared driving term, a historical window encoding term, and a non-negative state-related dissipation term, and to establish a floating ice state update mechanism based on physical knowledge-driven Lagrange dynamics. The model training module is used to convert ice floe trajectory fragments into supervised training samples and train a shared forced dissipative ice floe dynamics model that integrates historical data-driven deep neural networks and physical knowledge-driven Lagrange dynamics; such as Figure 4 As shown; The trajectory prediction module is used to input the current state of the ice floes into the trained model and output the future trajectory results of the ice floes using a multi-step rolling recursion method.

[0071] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for predicting sea ice movement by fusing physical information with historical trajectories, characterized in that, include: S1. Acquire and organize historical observation data of floating ice, preprocess the historical observation data of floating ice to form floating ice trajectory segments sorted by time; S2. Construct ice floe state variables and historical window state sequences based on the ice floe trajectory segments; S3. Establish a shared forced dissipative floating ice dynamics model that integrates historical data-driven deep neural networks and physical knowledge-driven Lagrange dynamics. Utilize deep neural networks to construct shared driving terms, historical window encoding terms, and state-related dissipative terms, and establish a floating ice state update model based on the Lagrange dynamics state update mechanism. S4. Convert the ice floe trajectory fragment into supervised training samples, and train the ice floe dynamics model based on the supervised training samples to jointly optimize the parameters of the deep neural network driven by historical data, the parameters of the shared driving term, the parameters of the historical window encoding, and the parameters of the state-related dissipation term. S5. Input the current state of the floating ice and its historical window state sequence into the trained floating ice dynamics model, use historical data to drive the deep neural network to extract historical motion features, and under the physical knowledge-driven Lagrange dynamics state update mechanism, use the current predicted state as the next step input to perform multi-step rolling recursion, predict the floating ice state at one or more future moments, and output the future trajectory result of the floating ice.

2. The sea ice movement prediction method based on the fusion of physical information and historical trajectories according to claim 1, characterized in that, The historical observation data of the floating ice includes: the coordinates of the centroid of the floating ice at multiple times, the corresponding observation time, and the characteristic quantities of the ice's geometric properties; The characteristic quantities of the ice geometric properties include one or more of the following: velocity components, equivalent scale, ellipticity, and time properties; The preprocessing includes one or more of the following: outlier removal, missing value processing, time sorting, coordinate system unification, unit normalization, velocity difference estimation, noise smoothing, and trajectory segment selection.

3. The sea ice motion prediction method based on the fusion of physical information and historical trajectories according to claim 1, characterized in that, The floating ice state variables include: position characteristics, velocity characteristics, scale characteristics, shape characteristics, and time characteristics; wherein, the position characteristics are used to characterize the spatial position of the floating ice's center of mass in the plane, the velocity characteristics are used to characterize the floating ice's motion state, the scale characteristics are used to characterize the floating ice's geometric size, the shape characteristics are used to characterize the floating ice's external shape, and the time characteristics are used to characterize the time information corresponding to the observation time. The historical window state sequence is used to extract historical motion features by a deep neural network.

4. The sea ice motion prediction method based on the fusion of physical information and historical trajectories according to claim 1, characterized in that, In S3, the floating ice is regarded as a forced dissipative motion body on a two-dimensional plane. The equivalent environmental driving effect in the floating ice motion process is described by the driving term shared among all floating ice trajectory segments, and the damping, friction and velocity decay effects are described by the non-negative state-related dissipation term adaptively generated by the current state. The shared driving term and the state-related dissipation term work together in the ice floe state update process to predict the future state of the ice floe.

5. The sea ice motion prediction method based on the fusion of physical information and historical trajectories according to claim 4, characterized in that, The shared driving term is implemented by a deep neural network driven by historical data. The deep neural network includes a multilayer perceptron, a recurrent neural network, a temporal convolutional network, a Transformer network, a graph neural network, or a combination thereof. Its input is the current ice floe state variable and / or the historical window state sequence, and its output is two-dimensional equivalent acceleration information used to update the velocity state of the ice floe at the next moment. The shared driving term is shared among all ice floe trajectory samples, rather than setting independent parameters for each ice floe trajectory; The state-related dissipation term is a non-negative scalar function or a non-negative vector function with respect to the current ice floe state variable. Its output is used to characterize the dissipation intensity of the ice floe under different scale, shape, velocity and time conditions, and participates in the calculation of the ice floe velocity decay term. The state-related dissipation term is adaptively adjusted as the state of the ice floes changes, so that different individual ice floes or the same ice floe at different time stages have different dissipation characteristics. The state-related dissipation term is associated with at least one or more of the following: equivalent scale characteristics, ellipticity characteristics, velocity magnitude characteristics, and time characteristics of the ice floes. By using a shared function to generate different dissipation values ​​under different state conditions, the method of identifying dissipation parameters individually for each ice floe trajectory can be replaced.

6. The sea ice motion prediction method based on the fusion of physical information and historical trajectories according to claim 1, characterized in that, In S4, ice floe trajectory segments with a length of not less than 2 are constructed as one-step state transition samples, and ice floe trajectory segments with a length of not less than 3 are constructed as two-step state transition samples. The model takes the current state as input, predicts the state at the next moment, and uses the actual state at the next moment for supervised training. For a two-step state transition sample, after obtaining the predicted state at the next time step, we continue to recursively predict the state at subsequent time steps.

7. The sea ice motion prediction method based on the fusion of physical information and historical trajectories according to claim 1, characterized in that, The training objectives used in S4 include position error terms, velocity error terms, and multi-step rolling prediction error terms; S4 also applies nonnegativity constraints, smoothness constraints, or parameter norm constraints to state-related dissipation terms to improve the stability and generalization ability of model training. The ice floe dynamics model is jointly trained by sharing driving term parameters and state-related dissipation term parameters through iterative optimization.

8. The sea ice motion prediction method based on the fusion of physical information and historical trajectories according to claim 1, characterized in that, In S5, the current predicted state of the floating ice is used as the input for the next prediction, and the state update process is repeated until the preset number of prediction steps is reached. The output should include at least a sequence of ice floe centroid coordinates for one or more future time points; the output should also include future velocity sequences, dissipation term change sequences, intermediate state variables, or trajectory visualizations.

9. A sea ice movement prediction system that fuses physical information with historical trajectories, characterized in that, The system for implementing the method as described in any one of claims 1-8 includes: The data acquisition and preprocessing module is used to acquire historical observation data of floating ice and form floating ice trajectory fragments sorted by time. The state variable construction module is used to construct ice floe state variables based on the ice floe trajectory fragment, including historical window position sequence, velocity sequence, scale, shape, time features and their deep neural network encoding representation; The integrated dynamics modeling module is used to construct a deep neural network driven by historical data, a shared driving term, a historical window encoding term, and a non-negative state-related dissipation term, and to establish a floating ice state update mechanism based on physical knowledge-driven Lagrange dynamics. The model training module is used to convert ice floe trajectory fragments into supervised training samples and train a shared forced dissipative ice floe dynamics model that integrates historical data-driven deep neural networks and physical knowledge-driven Lagrange dynamics. The trajectory prediction module is used to input the current state of the ice floes into the trained model and output the future trajectory results of the ice floes using a multi-step rolling recursion method.

10. An electronic device, characterized in that, It includes a processor and a memory, wherein the memory stores a computer program, and when the computer program is executed by the processor, it implements the sea ice motion prediction method by fusing physical information and historical trajectories as described in any one of claims 1 to 8.

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