Method and device for training ocean internal wave prediction model based on data physics double drive

Abstract

The application discloses a data-physical double-driven ocean internal wave prediction model training method and device, and relates to the technical field of ocean observation. The method is used to solve the problem of low prediction accuracy caused by the fact that the existing ocean internal wave prediction method cannot accurately capture the edge structure or local strength mutation of isolated internal waves and other detailed features. The method comprises the following steps: obtaining target ocean data; determining a symbolic partial differential equation representing the propagation of ocean internal waves of the target ocean data by using a symbolic regression method; constructing an initial ocean internal wave prediction model based on the symbolic partial differential equation; and training the initial ocean internal wave prediction model based on the target ocean data to obtain a trained ocean internal wave prediction model. The data-physical double-driven ocean internal wave prediction model training method provided by the application is used to construct an ocean internal wave prediction model with accuracy and physical consistency.

Description

Technical Field

[0001] This invention relates to the field of marine observation technology, and in particular to a training method and apparatus for a marine internal wave prediction model based on data-physics dual-drive. Background Technology

[0002] Internal ocean waves are wave phenomena occurring at density stratification interfaces within the ocean, with their wave surfaces typically located in regions of significant density gradients, such as thermoclines or haloclines. Unlike surface waves that occur at the sea surface, the wave energy of internal waves is primarily distributed within the ocean interior. Internal solitary waves are a special form of internal wave, characterized by large amplitude, concentrated energy, and a largely unchanged waveform during propagation—a nonlinear wave. They are usually excited by tidal currents passing through seabed slopes or strait topography, and may intensify during propagation from deep to shallow water, significantly impacting ocean mixing, nutrient transport, and the safety of offshore operations and engineering projects.

[0003] Existing methods for predicting internal ocean waves can be broadly categorized into two types: numerical simulation methods based on physical mechanisms and data-driven machine learning methods. Traditional numerical simulation methods rely on nonlinear partial differential equations, such as the nonlinear Schrödinger equation and three-dimensional ocean circulation models, to characterize the generation, propagation, and evolution of internal waves through analytical derivation and numerical calculation. They offer advantages such as clear physical mechanisms and strong interpretability, but are highly sensitive to initial and boundary conditions in practical applications and incur high computational costs. In recent years, deep learning methods have begun to be applied to image-based temporal prediction of internal wave propagation. For example, fully convolutional networks, convolutional neural networks, and convolutional long short-term memory networks can learn the spatiotemporal characteristics of remote sensing images and profile observation data to achieve rapid prediction and demonstrate strong capabilities in modeling complex nonlinear relationships. However, purely data-driven methods, lacking physical consistency constraints, are prone to overfitting the statistical correlation of data, making it difficult to accurately reflect the true dynamic process of internal waves. Furthermore, in situations involving multi-scale coupling and abrupt changes in edge structures, their characterization of key details such as the edge morphology and local intensity of isolated internal waves remains insufficient. Summary of the Invention

[0004] The purpose of this invention is to provide a training method and apparatus for ocean internal wave prediction models based on data and physics dual-drive, which solves the problem that existing ocean internal wave prediction models cannot accurately capture detailed features such as the edge structure and local intensity abrupt changes of isolated internal waves due to the lack of physical consistency constraints, resulting in low prediction accuracy.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] In a first aspect, the present invention provides a method for training an ocean internal wave prediction model based on a data-physical dual-drive approach, comprising:

[0007] Acquire target ocean data; the target ocean data is two-dimensional data of the target sea surface region in three-dimensional ocean data; the three-dimensional ocean data is obtained by numerical simulation of the ocean field of the target region within a preset time period.

[0008] The symbolic partial differential equation representing the propagation of internal ocean waves in the target ocean data was determined using the symbolic regression method.

[0009] An initial prediction model for ocean internal waves is constructed based on the symbolic partial differential equations. The initial prediction model for ocean internal waves includes a physically guided neural network and an encoder and decoder with a convolutional long short-term memory network as the core. The physical constraint of the initial prediction model for ocean internal waves is the symbolic partial differential equations.

[0010] The initial prediction model for ocean internal waves is trained based on the target ocean data to obtain a trained prediction model for ocean internal waves.

[0011] Optionally, after training the initial prediction model of ocean internal waves based on the target ocean data to obtain the trained prediction model of ocean internal waves, the method further includes:

[0012] The first frame of data to be predicted is input into the trained ocean internal wave prediction model to predict the result of the second frame.

[0013] The prediction result of the second frame is input into the trained ocean internal wave prediction model to obtain the prediction result of the next frame.

[0014] Recursive prediction yields prediction results for multiple frames.

[0015] Optionally, the step of using the symbolic regression method to determine the symbolic partial differential equation representing the propagation of internal ocean waves in the target ocean data includes:

[0016] The amplitude field data of internal ocean waves is extracted from the target ocean data and normalized to obtain normalized amplitude field data.

[0017] The normalized amplitude field data is divided into regions to obtain multiple spatial blocks;

[0018] The sparse regression method is used to determine the target spatial derivative term corresponding to each spatial block from the candidate function library, and a symbolic partial differential equation is generated based on the target spatial derivative term.

[0019] Optionally, the step of determining the target spatial derivative term corresponding to each spatial block from the candidate function library using the sparse regression method, and generating a symbolic partial differential equation based on the target spatial derivative term, includes:

[0020] The sequential threshold optimization algorithm is used to filter out the target spatial derivative term and the coefficient of the target spatial derivative term from the candidate function library;

[0021] Formula used:

[0022]

[0023] Determine the sign of the partial differential equation for each space block;

[0024] in, For the symbolic partial differential equation expression of a block of space, ξ k Let θ be the coefficient of the derivative term in the target space. k (u) represents the target space derivative term, u represents the normalized amplitude field data, x represents the abscissa of the normalized amplitude field data, y represents the ordinate of the normalized amplitude field data, t represents time, P represents the total number of target space derivative terms, and k>0.

[0025] Optionally, training the initial prediction model of ocean internal waves based on the target ocean data to obtain a trained prediction model of ocean internal waves includes:

[0026] The encoder and decoder of the initial prediction model of ocean internal waves are trained based on the normalized amplitude field data to obtain the trained encoder and decoder.

[0027] The normalized amplitude field data of the target time period is input into the trained encoder and decoder to obtain the first prediction result.

[0028] The first prediction result is divided into regions according to the coordinates of the spatial blocks to obtain the first prediction result corresponding to each spatial block;

[0029] The physical guided neural network is trained based on the first prediction results corresponding to each spatial block and the symbolic partial differential equation to obtain a trained ocean internal wave prediction model.

[0030] Optionally, the step of training the physical-guided neural network based on the first prediction results corresponding to each spatial block and the symbolic partial differential equation to obtain a trained ocean internal wave prediction model includes:

[0031] The first prediction result and the symbolic partial differential equation corresponding to the spatial block are input into the physical guidance neural network to predict the second prediction result.

[0032] Formula used:

[0033]

[0034] Determine the residuals for each spatial block;

[0035] in, For residuals, This is the second prediction result corresponding to the spatial block;

[0036] Formula used:

[0037]

[0038] Determine the initial boundary loss;

[0039] in, Let be the initial boundary loss, t0 be the initial time step, and u′(x, y, t0) be the first prediction result corresponding to the spatial block at the initial time step. The second prediction result corresponding to the spatial block at the initial time;

[0040] Formula used:

[0041]

[0042] Determine the total loss function;

[0043] in, For the total loss function, Minimization of collocations within a spatial block λ0 and λ1 are weighting coefficients;

[0044] The parameters of the physical guided neural network are optimized based on the total loss function of each spatial block to obtain a trained ocean internal wave prediction model.

[0045] Optionally, the initial prediction model for ocean internal waves is optimized based on the total loss function to obtain a trained prediction model for ocean internal waves, including:

[0046] Based on the total loss function, the Adam optimizer is used to perform the first optimization of the parameters of the physically guided neural network;

[0047] The parameters of the physical guided neural network are optimized a second time using the L-BFGS algorithm to obtain a trained ocean internal wave prediction model.

[0048] Optionally, the encoder includes multiple stacked layers, including convolutional layers and convolutional long short-term memory network layers; the decoder includes convolutional long short-term memory network layers and inverse convolutional layers arranged symmetrically with the encoder.

[0049] Optionally, the amplitude field data is normalized to obtain normalized amplitude field data, including:

[0050] The amplitude values ​​of the amplitude field data are scaled to the range of [-1, 1] to obtain scaled data;

[0051] The coordinate values ​​of the scaled data are mapped to the target reference space to obtain normalized amplitude field data.

[0052] Compared with existing technologies, the present invention provides a data-physical dual-driven method for training ocean internal wave prediction models, comprising: acquiring target ocean data; determining the symbolic partial differential equations representing ocean internal wave propagation using symbolic regression; constructing an initial prediction model for ocean internal waves based on the symbolic partial differential equations; the initial prediction model for ocean internal waves includes a physically guided neural network and an encoder and decoder with a convolutional long short-term memory network as its core; the physical constraint of the initial prediction model for ocean internal waves is the symbolic partial differential equations; and training the initial prediction model for ocean internal waves based on the target ocean data to obtain a trained ocean internal wave prediction model. The ocean internal wave prediction model trained in this application can achieve effective prediction of isolated ocean internal waves over a longer timescale. By using the symbolic partial differential equations as physical constraints, the non-physical divergence behavior of the model can be effectively constrained without increasing the prediction time overhead. In particular, it exhibits good structure preservation ability and energy propagation consistency in seabed slope break zones and strong stratification zones, thereby improving the prediction accuracy of the model. Furthermore, this application uses numerical simulation data as training samples, requiring only one numerical simulation to obtain training samples. Compared to the traditional method of using remote sensing data as training samples, which is limited by the acquisition frequency, this significantly reduces the time required to acquire training samples. Additionally, this application provides a model for predicting ocean internal waves applicable to different sea states and ocean regions.

[0053] Secondly, the present invention also provides a training device for an ocean internal wave prediction model based on data-physical dual-drive, comprising:

[0054] The target ocean data acquisition module is used to acquire target ocean data; the target ocean data is two-dimensional data of the target sea surface area in three-dimensional ocean data; the three-dimensional ocean data is obtained by numerical simulation of the ocean field of the target area within a preset time period.

[0055] The symbolic partial differential equation confirmation module is used to determine the symbolic partial differential equation representing the propagation of internal ocean waves in the target ocean data using a symbolic regression method.

[0056] An initial prediction model construction module for ocean internal waves is used to construct an initial prediction model for ocean internal waves based on the symbolic partial differential equations; the initial prediction model for ocean internal waves includes a physically guided neural network and an encoder and decoder with a convolutional long short-term memory network as the core; the physical constraint of the initial prediction model for ocean internal waves is the symbolic partial differential equations.

[0057] The model training module is used to train the initial prediction model of ocean internal waves based on the target ocean data, so as to obtain a trained prediction model of ocean internal waves.

[0058] Compared with the prior art, the beneficial effects of the ocean internal wave prediction model training device based on data physics dual drive provided by the present invention are the same as the beneficial effects of the ocean internal wave prediction model training method based on data physics dual drive described in the above technical solution, and will not be repeated here. Attached Figure Description

[0059] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this invention, illustrate exemplary embodiments of the invention and are used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings:

[0060] Figure 1 A flowchart of the ocean internal wave prediction model training method based on data physics dual-drive provided by the present invention;

[0061] Figure 2 A schematic diagram of the encoder and decoder of the ocean internal wave initial prediction model provided by the present invention;

[0062] Figure 3 A schematic diagram of the structure of the convolutional long short-term memory network layer of the ocean internal wave initial prediction model provided by the present invention;

[0063] Figure 4 A diagram illustrating the construction process of the symbolic partial differential equations provided by this invention;

[0064] Figure 5 A diagram illustrating the physical constraint process of the physical guidance neural network provided by this invention;

[0065] Figure 6 This is a schematic diagram of the structure of the ocean internal wave prediction model training device based on data physics dual-drive provided by the present invention. Detailed Implementation

[0066] To facilitate a clear description of the technical solutions in the embodiments of the present invention, the terms "first" and "second" are used to distinguish identical or similar items with essentially the same function and effect. For example, the first threshold and the second threshold are merely used to distinguish different thresholds and do not limit their order. Those skilled in the art will understand that the terms "first" and "second" do not limit the quantity or execution order, and that the terms "first" and "second" are not necessarily different.

[0067] It should be noted that in this invention, the terms "exemplary" or "for example" are used to indicate examples, illustrations, or descriptions. Any embodiment or design described as "exemplary" or "for example" in this invention should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of terms such as "exemplary" or "for example" is intended to present the relevant concepts in a concrete manner.

[0068] In this invention, "at least one" refers to one or more, and "more than one" refers to two or more. "And / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A alone, A and B simultaneously, or B alone, where A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one of the following" or similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one of a, b, or c can represent: a, b, c, a combination of a and b, a combination of a and c, a combination of b and c, or a, b, and c, where a, b, and c can be single or multiple.

[0069] Before introducing the embodiments of the present invention, the relevant terms involved in the embodiments of the present invention are first defined as follows:

[0070] The Finite Difference Method (FDM) is an approximate method for solving numerical solutions to differential equations. Its main principle is to directly approximate the differential terms in the differential equation by difference, thereby transforming the differential equation into a system of algebraic equations for solution.

[0071] Sparse regression is a special type of regression analysis method. Its core idea is to introduce a regularization term, such as L1 regularization, during the construction of the regression model to make the model's parameter vector sparse, meaning that most parameter values ​​tend to zero, with only a few parameters being non-zero. This sparsity not only simplifies the model but also makes it easier to interpret, because the features corresponding to non-zero parameters are often factors that have a significant impact on the response variable.

[0072] CROCO (Coastal and Regional Ocean COmmunity model) is an open-source numerical model used to simulate physical processes in the ocean and coastal areas.

[0073] The L-BFGS algorithm is a machine learning algorithm used for function optimization problems. It's a variant of the BFGS algorithm, designed to address the excessive memory usage of BFGS when handling large-scale problems. Its core idea is to use historical information to approximate the inverse of the Hessian matrix, thus avoiding the large amount of memory required to directly compute the Hessian matrix and its inverse. In each iteration, the L-BFGS algorithm only retains information from the most recent iterations, rather than retaining the complete Hessian matrix inverse.

[0074] Physics-Informed Neural Networks (PINN) are machine learning models that combine knowledge of physics with deep learning. Unlike traditional data-driven neural networks, PINN incorporates physical laws into its loss function, ensuring that the model's predictions conform to physical principles. This approach performs particularly well in situations where data is scarce or highly noisy.

[0075] Currently, methods for predicting internal ocean waves can be broadly categorized into four types: physical models, statistical learning, deep learning, and remote sensing inversion fusion. Each method has its own emphasis, implementation approach, and application effectiveness, as well as its own limitations.

[0076] Physical modeling methods, based on nonlinear shallow water theory, simulate the generation and propagation of internal waves by solving ocean dynamic models such as the Korteweg–de Vries equations, the Internal Solitary Wave (NLIW) model, or ROMS. These methods have clear physical mechanisms and are suitable for studying internal wave formation mechanisms and conducting numerical verification. However, they are highly dependent on initial fields and boundary conditions, and are prone to significant biases when the accuracy of observational data is insufficient. Furthermore, solving complex nonlinear equations requires high computational resources, making it difficult to meet the needs of real-time prediction, and they are also prone to dynamic distortion in multi-scale coupled scenarios.

[0077] Statistical learning methods rely heavily on historical observation data to extract empirical patterns in the evolution of internal waves, such as ARIMA time series models, wavelet neural network combination models, and Kalman filtering. These methods can make relatively accurate short-term predictions of internal wave amplitude, period, and other characteristics, with relatively simple model structures and fast computation speeds. However, due to the lack of direct modeling of nonlinear dynamic mechanisms, these methods are less adaptable to anomalous internal waves caused by sudden sea states such as typhoons, and their prediction performance is easily affected by changes in data distribution.

[0078] Deep learning methods have seen rapid development in internal wave prediction in recent years. Architectures such as fully convolutional networks, convolutional neural networks, and convolutional long short-term memory networks can directly extract spatiotemporal features from remote sensing images or profile observation data, possessing strong nonlinear modeling capabilities and a certain degree of generalization performance. However, these methods often rely on large-scale, high-quality labeled datasets for training. Lacking physical constraints, they tend to learn statistical correlations rather than the dynamic laws of internal waves. Therefore, in complex situations such as multi-scale coupling and abrupt changes in edge structures, they struggle to accurately reproduce the edge morphology and local intensity of isolated internal waves, limiting prediction accuracy.

[0079] To address the aforementioned issues, this invention provides a method and apparatus for training an ocean internal wave prediction model based on a data-physical dual-drive approach, which will be described below with reference to the accompanying drawings.

[0080] See Figure 1 The ocean internal wave prediction model training method based on data and physics dual-drive provided by this invention includes the following steps:

[0081] Step 100: Acquire target ocean data;

[0082] The target ocean data refers to the target sea surface region within the 3D ocean data, which is 2D data. This target sea surface region exhibits continuous and active internal wave activity and is minimally affected by land boundary interference. Selecting this region significantly reduces the computational burden of model training and avoids interference from coastal topography on internal wave evolution. The 3D ocean data is obtained by numerically simulating the ocean field of the target region within a preset time period and extracting the amplitude field of significant internal wave regions and its time-varying characteristics; the target ocean data includes the amplitude field data of internal waves and their time-varying characteristics.

[0083] For example, the target area spatially covers 116° to 124° E and 16° to 23° N. The numerical simulation is based on the CROCO experimental setup, with a horizontal resolution of approximately 1 / 240° × 1 / 120°. A full-depth internal wave field is generated on a 3D grid with a spatial resolution of 1920 × 892 × 45. CROCO runs for 30 days, and data from 7 days with significant internal wave activity is selected, comprising 1009 time steps with 10-minute intervals. Data from a region with a sea surface area of ​​1248 × 568 is selected as the target ocean data.

[0084] Step 200: Use the symbolic regression method to determine the symbolic partial differential equation representing the propagation of internal ocean waves in the target ocean data;

[0085] The constructed symbolic partial differential equations are the main control terms for ocean internal wave propagation. The dominant dynamic mechanism is identified primarily using sparse regression methods, thereby generating region-adaptive partial differential control equations. These symbolic partial differential equations not only possess data-dependent flexibility but also have explicit physical interpretations, providing a foundation for incorporating physical priors into the model.

[0086] Step 300: Construct an initial prediction model for ocean internal waves based on the symbolic partial differential equation;

[0087] The initial prediction model for ocean internal waves includes an encoder and decoder with a convolutional long short-term memory network as its core. The encoder and decoder integrate convolutional operations with the temporal modeling capabilities of LSTM, which can preserve the spatial structure of the input image and capture its dynamic changes across time frames, thus achieving a preliminary prediction of the future internal wave field. The model is trained with a large amount of simulated data and has mastered the ability to infer future wave trends from historical image sequences.

[0088] See Figure 2 The encoder comprises multiple stacked layers, including convolutional layers (Conv) and convolutional long short-term memory (cLSTM) networks. The outputs of the convolutional layers are connected to the inputs of the cLSTM networks. The decoder comprises stacked cLSTM networks and deflected convolutional layers (dconv). The outputs of the deflected convolutional layers are connected to the inputs of the cLSTM networks. Figure 2 As shown, from left to right, the encoder's structure is named as follows: First Convolutional Layer, First Convolutional Long Short-Term Memory (LSM) Network Layer, Second Convolutional Layer, Second Convolutional Long Short-Term Memory (LSM) Network Layer, Third Convolutional Layer, Third Convolutional Long Short-Term Memory (LSM) Network Layer. The decoder's structure is named as follows: Fourth Inverse Convolutional Layer, Fourth Convolutional Long Short-Term Memory (LSM) Network Layer, Fifth Inverse Convolutional Layer, Fifth Convolutional Long Short-Term Memory (LSM) Network Layer, Sixth Convolutional Layer, Sixth Convolutional Long Short-Term Memory (LSM) Network Layer. The output of the First Convolutional Long Short-Term Memory (LSM) Network Layer is connected to the input of the Fourth Inverse Convolutional Layer, the output of the Second Convolutional Long Short-Term Memory (LSM) Network Layer is connected to the input of the Fifth Inverse Convolutional Layer, and the output of the Third Convolutional Long Short-Term Memory (LSM) Network Layer is connected to the input of the Sixth Inverse Convolutional Layer. The encoder's First Convolutional Layer has 16 kernels and 64 cell units. The Second and Third Convolutional Layers have 96 kernels, corresponding to 96 cell units in their respective LSM Network Layers. The decoder's Fourth Convolutional Long Short-Term Memory (LSM) Network Layer has 64 cell units. The encoder progressively extracts hierarchical spatial features from the input image with a single input channel by stacking convolutional and convolutional long short-term memory network layers, while compressing information to obtain a latent representation, which includes hidden states and cell states. This latent representation is then propagated forward through a symmetric decoder consisting of convolutional long short-term memory network layers and deconvolution operations to finally obtain the prediction result.

[0089] See Figure 3 The convolutional long short-term memory (cLSTM) network layer includes forget gates, input gates, and output gates to regulate memory flow and temporal state transitions. X(t) represents the input data at the current time step, h(t-1) is the hidden state at the previous time step, carrying information from that time step, and c(t-1) is the cell state at the previous time step, used for long-term memory storage. The forget gate determines how much information to retain from the cell state at the previous time step. The input gate determines how much of the current input information needs to be stored in the cell state. The cell state is updated through the forget gate and the input gate. The output gate determines how much information from the current cell state needs to be output to the hidden state. The final output h(t) is the hidden state at the current time step, which will be used as one of the inputs for the next time step and for subsequent prediction tasks. c(t) is the cell state at the current time step, which will be passed to the next time step for long-term memory storage.

[0090] The initial prediction model for ocean internal waves also includes a physically guided neural network. The physical constraints of the initial prediction model for ocean internal waves are symbolic partial differential equations. The physically guided neural network is constructed by embedding the symbolic partial differential equations into the loss function.

[0091] In the initial prediction model of ocean internal waves, the prediction results are not only affected by data supervision, but also need to meet the requirement of minimizing the residuals derived from the symbolic partial differential equations. By embedding the symbolic partial differential equations as differentiable physical constraints into a physics-guided neural network for modeling, unlike explicitly solving these partial differential equations, the physics-guided neural network acts as a post-processing regularizer on the encoder and decoder outputs, ensuring consistency with the identified physical laws.

[0092] Step 400: Train the initial prediction model of ocean internal waves based on the target ocean data to obtain a trained prediction model of ocean internal waves.

[0093] The encoder and decoder structures, along with the physically guided neural network, are trained separately. First, the encoder and decoder are trained using target ocean data, resulting in well-trained models. Then, the prediction results output by the encoder and decoder are used to divide the ocean into regions. Based on these region-divided prediction results, the physically guided neural network is trained to obtain a trained ocean internal wave prediction model. When training the encoder and decoder, target ocean data from all time periods are used as training samples. However, when training the physically guided neural network, only target ocean data corresponding to the target time period can be used as training samples.

[0094] The ocean internal wave prediction model obtained through this data-physical dual-driven training method balances efficiency, reliability, and physical consistency. It can effectively predict isolated ocean internal waves over longer timescales. By using symbolic partial differential equations as physical constraints, it effectively constrains the model's non-physical divergence behavior without increasing prediction time overhead. It exhibits excellent structure preservation and energy propagation consistency, particularly in seafloor break zones and strongly stratified areas, thus improving prediction accuracy. Furthermore, this application uses numerical simulation data as training samples, requiring only one numerical simulation to obtain training samples. Compared to traditional methods using remote sensing data, which are limited by acquisition frequency, this significantly reduces training sample acquisition time. Additionally, this application is applicable to the construction of ocean internal wave prediction models for different sea states and ocean regions.

[0095] As an alternative approach, step 200 above can be implemented based on the following steps:

[0096] Step 210: Extract the amplitude field data of internal ocean waves from the target ocean data and normalize the amplitude field data to obtain normalized amplitude field data;

[0097] Specifically, the normalization process includes: scaling the amplitude values ​​of the amplitude field data to the interval [-1, 1] to obtain scaled data; and mapping the coordinate values ​​of the scaled data to a target reference space to obtain normalized amplitude field data. For example, the target reference space can be [-4, 4]. 2 This setting removes the latitude and longitude coordinates while satisfying the internal wave evolution within the amplitude range of [-1, 1]. The coordinates of the amplitude field data include both horizontal and vertical axes. The amplitude field data is processed using the finite difference method.

[0098] Step 220: Divide the normalized amplitude field data into regions to obtain multiple spatial blocks;

[0099] The space blocks are the same size.

[0100] Step 230: Use the sparse regression method to determine the target spatial derivative term corresponding to each spatial block from the candidate function library, and generate a symbolic partial differential equation based on the target spatial derivative term.

[0101] The candidate function library contains linear terms, spatial derivative terms characterizing advection and dispersion, and nonlinear interaction terms reflecting amplitude-related deformation. The library is constructed based on a priori knowledge of ocean physical mechanisms. The linear and nonlinear terms, as well as derivative terms of various orders, reflecting key physical mechanisms such as advection, dispersion, and the interaction between gradient and amplitude, serve as possible terms describing the system dynamics. The term design in the candidate function library fully considers the physical characteristics of internal wave propagation. First, it includes a constant term 1 and the variable itself u, used to represent the contributions of the background field or bias term and the variable itself. Second, it includes first-order spatial derivatives. and second derivative This is used to describe linear mechanisms related to propagation direction, diffusion process, and dispersion effects, such as spatial gradient and curvature. Building upon this, the candidate function library further introduces nonlinear coupling terms: These terms characterize nonlinear convection processes and are typical of structures found in equations such as the Burgers equation and the KdV equation. Additionally, the product of u and its second derivative is included: This combination of terms, used to model the interaction between nonlinearity and dispersion, helps to characterize more complex wave behavior. Since ocean internal waves typically exhibit a coupling between nonlinear propagation and multidimensional dispersion in actual propagation, this combination has strong physical interpretability.

[0102] Specifically, the candidate function libraries are as follows:

[0103]

[0104] Where Θ is the candidate function library, u is the normalized amplitude field data, x is the abscissa of the normalized amplitude field data, and y is the ordinate of the normalized amplitude field data.

[0105] Specifically, step 230 may include:

[0106] Step 231: Use the sequential threshold optimization algorithm to filter out the target spatial derivative term and the coefficient of the target spatial derivative term corresponding to the spatial block from the candidate function library;

[0107] To select a minority of effective terms for the target quantity from a large number of candidate features, this application employs the Sequential Thresholding Optimization (STO) algorithm, an efficient method for solving least squares problems. The core idea of ​​this algorithm is as follows: First, perform full regression on all derivative terms in the candidate function library to solve for the coefficient of each derivative term. Term terms with coefficients whose absolute values ​​are less than a preset threshold are eliminated. Perform full regression on the remaining derivative terms, iterating in this way until the number of remaining derivative terms remains unchanged after further elimination. The final remaining derivative terms are then determined as the derivative terms of the target space.

[0108] Step 232: For the amplitude field at a certain moment, the target sea surface area is divided into multiple spatial blocks, each spatial block is initialized with its corresponding local value, using formula (1):

[0109]

[0110] Determine the sign of the partial differential equation for each space block;

[0111] in, The symbolic partial differential equation for the space block, expressed by the objective derivative term θ k (u)∈Θ(u) is a weighted combination, ξ k Let be the coefficients of the derivative terms in the target space, representing the relative importance of each term, and denoted as Ξ=[ξ1,ξ2,...,ξ] . P ], θ k (u) represents the derivative term of the target space, u represents the normalized amplitude field data, x represents the abscissa of the normalized amplitude field data, y represents the ordinate of the normalized amplitude field data, t represents time, P represents the total number of derivative terms of the target space, i.e. the number of active terms with non-zero coefficients in the candidate function library, and k>0.

[0112] For example, such as Figure 4 As shown, starting with the normalized amplitude field data of the three spatial blocks on the left side of the figure, the calculated temporal derivatives are... As a regression target, This is the matrix data corresponding to the first spatial block. This is the matrix data corresponding to the second spatial block. Let X be the matrix data corresponding to the third spatial block. The candidate spatial matrix Θ(X) consists of multiple linear and nonlinear terms. Therefore, the sparse regression solution equation is: The coefficient vector Ξ is used to determine the effective terms that best explain the local dynamic characteristics. The target derivative terms and their corresponding coefficients selected for the three spatial blocks are shown in Table 1, where ξ1, ξ2, and ξ3 are the coefficients of the three spatial blocks, respectively.

[0113] Table 1. Target spatial derivative terms and corresponding coefficients for the three spatial blocks

[0114]

[0115] Based on Table 1, the symbolic partial differential equations for the three space blocks are shown in equations (2) to (4):

[0116]

[0117] The symbolic partial differential equations constructed above are used to characterize the local dynamics of spatial blocks. These equations are not traditional analytical physical laws, but physical expressions that can adapt to the heterogeneity of different regions and are constructed based on observation data. They can transform remote sensing sequence data into interpretable physical laws.

[0118] Combination Figure 2 and Figure 5 Step 400, the training of the initial prediction model for ocean internal waves, includes two parts: training the encoder and decoder, and training the physically guided neural network. Specifically, step 400 can be implemented based on the following steps:

[0119] Step 410: Train the encoder and decoder of the initial prediction model of ocean internal waves based on the normalized amplitude field data to obtain the trained encoder and decoder.

[0120] Specifically, t n The normalized amplitude field data at time t is input into the encoder and decoder structure to predict t. n+1 The first prediction result at time t. n+1 The first prediction result at time t and t n+1 The normalized amplitude field data at each time step is used to adjust the parameters of the encoder and decoder; and so on, the normalized amplitude field data at all time steps are input into the encoder and decoder structure to complete the training.

[0121] Step 420: Input the normalized amplitude field data of the target time period into the trained encoder and decoder to predict the first prediction result;

[0122] The target time period falls within the preset time period range and is less than or equal to that range. It should be noted that the data input into the model each time is data at a specific moment or time step.

[0123] Step 430: Divide the first prediction result into regions according to the spatial blocks to obtain the first prediction result corresponding to each spatial block;

[0124] The spatial blocks obtained by dividing the first prediction result into regions have the same size and spatial location as the spatial blocks obtained in step 220.

[0125] Step 440: Train the physical guided neural network based on the first prediction results corresponding to each spatial block and the symbolic partial differential equation to obtain a trained ocean internal wave prediction model.

[0126] Physically guided neural networks include fully connected neural networks. The training process of a physically constrained network is as follows: When predicting the t-th... n+1 At frame t, n+1The first prediction result of the frame contains all spatial blocks and their corresponding spatial symbolic partial differential equations, which are then fed into a fully connected neural network for joint processing. After all spatial blocks have been processed, the physical constraint neural network will output the t-th... n+1 The final prediction result of the frame, i.e. the second prediction result.

[0127] By introducing a differentiable residual function during the training of a physics-guided neural network, local physical constraints are incorporated into the prediction process. The governing equations for each spatial block are derived from time-series observation data and expressed in explicit symbolic form through sparse regression. Partial differential equations serve as physical priors, guiding the network output to not only conform to the data but also follow the dynamic laws of spatial heterogeneity. Furthermore, to integrate local spatiotemporal dynamics, a function approximator with smooth, high-dimensional expressive capabilities is needed. Therefore, a fully connected neural network is constructed to model the amplitude evolution process within each spatial block. This network takes normalized spatiotemporal coordinates as input, sequentially feeding them into ten hidden layers, each containing 64 neurons, and employs a smooth tanh activation function to ensure differentiability. This structure supports automatic differentiation, such as... Figure 5 As shown, the physical prior is introduced in the form of a residual term embedded in the loss function, which measures the deviation between the network's predicted time derivative and the identified physical laws. Therefore, step 440 includes the following steps:

[0128] Step 441: Input the first prediction result and the symbolic partial differential equation corresponding to the spatial block into the physical guidance neural network to predict the second prediction result;

[0129] Step 442: Use formula (5):

[0130]

[0131] Determine the residuals for each spatial block;

[0132] in, For residuals, This is the second prediction result corresponding to the spatial block; This represents a symbolic partial differential equation obtained through sparse regression. The residual serves as a soft constraint, guiding the network to generate solutions that conform to both the observed data and local physical laws.

[0133] Step 443: Use formula (6):

[0134]

[0135] Determine the initial boundary loss;

[0136] in, Let be the initial boundary loss, t0 be the initial time step, and u′(x, y, t0) be the first prediction result corresponding to the spatial block at the initial time step. The second prediction result corresponding to the spatial block at the initial time;

[0137] Step 444: To achieve a balance between data fitting and physical consistency, a total loss function needs to be defined, specifically using formula (7):

[0138]

[0139] Determine the total loss function for each spatial block;

[0140] in, For the total loss function, The initial boundary loss is used to penalize the deviation between the prediction and the observed values ​​at the initial time step, thereby ensuring the data fit at the initial time step. The residuals are minimized at collocation points within the space block to achieve consistency constraints on the symbolic partial differential equations, where λ0 and λ1 are weighting coefficients.

[0141] Step 444: Optimize the parameters of the physical guided neural network based on the total loss function of each spatial block to obtain a trained ocean internal wave prediction model;

[0142] Parameter optimization employs a two-stage optimization strategy. First, based on the total loss function of each spatial block, the Adam optimizer is used to perform a first optimization of the parameters of the physical guided neural network, resulting in a first-optimized physical guided neural network. Then, the L-BFGS algorithm is used to perform a second optimization of the parameters of the first-optimized physical guided neural network, resulting in a trained ocean internal wave prediction model. Pre-training with the Adam optimizer provides good initial parameters, while the L-BFGS-B optimizer allows for fine-tuning of the weights. This two-stage parameter optimization ensures the numerical stability and prediction accuracy of the physical guided neural network.

[0143] In the training process of the ocean internal wave prediction model, training sample points are uniformly sampled within a normalized spatiotemporal domain to ensure generalization ability across different regions. By transforming local symbolic partial differential equations into differentiable residual terms, the network predictions are effectively constrained by physical priors. This method achieves fine-grained control of physical consistency while preserving the expressive power of deep neural networks, thereby improving the model's generalization performance and interpretability. Notably, although each spatial block is trained independently, the complexity of the learned symbolic partial differential equations is generally high in regions with strong internal solitary wave activity, often containing higher-order derivatives or nonlinear coupling terms. This spatial distribution of symbolic representation complexity effectively forms a physically constrained "attention mechanism," enabling physical sensitivity modeling of key regions without the need for explicit construction of an attention module.

[0144] The initial prediction model for ocean internal waves constructed in this application transforms symbolic partial differential equations into operable neural network constraints, enabling local physical supervision to guide fine-tuning of spatiotemporal prediction results. Unlike the "black box" prediction of traditional deep learning models, this application dynamically generates local governing equations during training, which can reflect the dominant physical mechanisms of wave propagation in different regions, improving the physical interpretability of the model and making it suitable for ocean internal wave prediction in different sea states and regions.

[0145] After obtaining the trained ocean internal wave prediction model, it can be used to predict ocean internal waves, specifically including:

[0146] The first frame of data to be predicted is input into the trained ocean internal wave prediction model to predict the result of the second frame.

[0147] The prediction result of the second frame is input into the trained ocean internal wave prediction model to obtain the prediction result of the next frame.

[0148] The predicted structure of the next frame is then input into the ocean internal wave prediction model, and the prediction results for the next frame are obtained. This process is repeated to obtain the prediction results for multiple frames within the required time.

[0149] The prediction process for each frame of data is as follows: First, the frame to be predicted is input into the trained ocean internal wave prediction model, and the preliminary prediction result is output through the encoder-decoder architecture; then, the prediction result is divided into spatial regions to generate multiple spatial block prediction subsets; then, the prediction images of each spatial block are sequentially input into the physical guidance neural network, and the corresponding symbolic partial differential equations are introduced as physical constraints. After block-by-block processing, the prediction result of the target frame is finally output.

[0150] The model trained in this application can recursively predict the internal wave amplitude field at multiple future time points using only a single-frame input image. Validation experiments show that this method maintains good structural consistency and prediction stability within ten recursive steps, possessing strong generalization ability and physical interpretability. It is applicable to internal wave propagation simulation and prediction under complex terrain and non-uniform stratification conditions, providing efficient and reliable technical support for marine forecasting, navigation safety, and ecological analysis. For example, in a 10-step recursive experiment conducted on solitary wave simulation data in the South China Sea, the model's average absolute error in the first step was 0.729 km, and the error in the tenth step was controlled within 4.768 km, with a slow overall error growth, enabling effective prediction over a longer time scale. The model's prediction based on a single-frame input is suitable for practical applications with low remote sensing frame rates and discontinuous time series, demonstrating good practicality and engineering promotion value.

[0151] The embodiments of the present invention can divide functional modules according to the above method examples. For example, each function can be divided into its own functional module, or two or more functions can be integrated into one processing module. The integrated module can be implemented in hardware or as a software functional module. It should be noted that the module division in the embodiments of the present invention is illustrative and only represents one logical functional division; other division methods may be used in actual implementation.

[0152] When dividing each function into modules according to its corresponding function. Figure 6 A schematic diagram of the structure of the ocean internal wave prediction model training device based on data-physics dual-drive provided by the present invention is shown. Figure 6 As shown, the device includes:

[0153] The target ocean data acquisition module 601 is used to acquire target ocean data; the target ocean data is two-dimensional data of the target sea surface area in three-dimensional ocean data; the three-dimensional ocean data is obtained by numerical simulation of the ocean field of the target area within a preset time period.

[0154] The symbolic partial differential equation confirmation module 602 is used to determine the symbolic partial differential equation representing the propagation of internal ocean waves in the target ocean data using a symbolic regression method.

[0155] The ocean internal wave initial prediction model construction module 603 is used to construct an ocean internal wave initial prediction model based on the symbolic partial differential equation; the ocean internal wave initial prediction model includes a physically guided neural network and an encoder and decoder with a convolutional long short-term memory network as the core; the physical constraint of the ocean internal wave initial prediction model is the symbolic partial differential equation.

[0156] The model training module 604 is used to train the initial prediction model of ocean internal waves based on the target ocean data to obtain a trained prediction model of ocean internal waves.

[0157] Optionally, the device may also include a prediction module, which may specifically include:

[0158] The first frame prediction unit is used to input the data to be predicted in the first frame into the trained ocean internal wave prediction model to predict the result of the second frame.

[0159] The recursive prediction unit is used to input the prediction result of the second frame into the trained ocean internal wave prediction model to obtain the prediction result of the next frame; the recursive prediction yields prediction results for multiple frames.

[0160] Optionally, the symbolic partial differential equation verification module 602 may include:

[0161] The normalization processing unit is used to extract the amplitude field data of internal ocean waves from the target ocean data and normalize the amplitude field data to obtain normalized amplitude field data.

[0162] A region partitioning unit is used to divide the normalized amplitude field data into regions to obtain multiple spatial blocks;

[0163] The symbolic partial differential equation confirmation unit is used to determine the target spatial derivative term corresponding to each spatial block from the candidate function library using a sparse regression method, and to generate a symbolic partial differential equation based on the target spatial derivative term.

[0164] Optionally, the symbolic partial differential equation verification unit may specifically include:

[0165] The sequential threshold optimization algorithm is used to filter out the target spatial derivative term and the coefficient of the target spatial derivative term from the candidate function library;

[0166] Formula used:

[0167]

[0168] Determine the sign of the partial differential equation for each space block;

[0169] in, For the symbolic partial differential equation expression of a block of space, ξ k Let θ be the coefficient of the derivative term in the target space. k (u) represents the target space derivative term, u represents the normalized amplitude field data, x represents the abscissa of the normalized amplitude field data, y represents the ordinate of the normalized amplitude field data, t represents time, P represents the total number of target space derivative terms, and k>0.

[0170] Optionally, the model training module 604 may include:

[0171] The encoder and decoder training unit is used to train the encoder and decoder of the initial prediction model of the ocean internal wave based on the normalized amplitude field data, so as to obtain the trained encoder and decoder.

[0172] The first prediction result determination unit is used to input the normalized amplitude field data of the target time period into the trained encoder and decoder to predict the first prediction result.

[0173] The first prediction result division unit is used to divide the first prediction result into regions according to the coordinates of the spatial block to obtain the first prediction result corresponding to each spatial block.

[0174] The physical-guided neural network training unit is used to train the physical-guided neural network based on the first prediction results corresponding to each spatial block and the symbolic partial differential equation, thereby obtaining a trained ocean internal wave prediction model.

[0175] Optionally, the physically guided neural network training unit may specifically include:

[0176] The second prediction result determination subunit is used to input the first prediction result corresponding to the spatial block into the physical guidance neural network, and the fully connected neural network in the physical guidance neural network outputs the second prediction result;

[0177] The residual determines the sub-unit, used to apply the formula:

[0178]

[0179] Determine the residuals for each spatial block;

[0180] in, For residuals, This is the second prediction result corresponding to the spatial block;

[0181] The initial boundary loss determination element is used to apply the formula:

[0182]

[0183] Determine the initial boundary loss;

[0184] in, Let be the initial boundary loss, t0 be the initial time step, and u′(x, y, t0) be the first prediction result corresponding to the spatial block at the initial time step. The second prediction result corresponding to the spatial block at the initial time;

[0185] The total loss function determination unit is used to apply the formula:

[0186]

[0187] Determine the total loss function for each spatial block;

[0188] in, For the total loss function, Minimization of collocations within a spatial block λ0 and λ1 are weighting coefficients;

[0189] The parameter optimization subunit is used to optimize the parameters of the physical guided neural network based on the total loss function of each spatial block to obtain a trained ocean internal wave prediction model.

[0190] Optionally, the parameter optimization subunit can be specifically used for:

[0191] Based on the total loss function of each spatial block, the Adam optimizer is used to perform the first optimization of the parameters of the physical guided neural network;

[0192] The parameters of the physical guided neural network are optimized a second time using the L-BFGS algorithm to obtain a trained ocean internal wave prediction model.

[0193] Optionally, the encoder includes multiple stacked layers, including convolutional layers and convolutional long short-term memory network layers; the decoder includes convolutional long short-term memory network layers and inverse convolutional layers arranged symmetrically with the encoder.

[0194] Optionally, the normalization processing unit may specifically include:

[0195] The amplitude values ​​of the amplitude field data are scaled to the range of [-1, 1] to obtain scaled data;

[0196] The coordinate values ​​of the scaled data are mapped to the target reference space to obtain normalized amplitude field data.

[0197] The above mainly describes the solutions provided by the embodiments of the present invention from the perspective of the interaction between various modules. It is understood that, in order to achieve the above functions, it includes corresponding hardware structures and / or software modules for executing each function. Those skilled in the art should readily recognize that, in conjunction with the units and algorithm steps of the various examples described in the embodiments disclosed herein, the present invention can be implemented in hardware or a combination of hardware and computer software. Whether a function is executed in hardware or by computer software driving hardware depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of the present invention.

[0198] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially in the form of a computer program product. The computer program product includes one or more computer programs or instructions. When the computer program or instructions are loaded and executed on a computer, the processes or functions described in the embodiments of the present invention are performed entirely or partially. The computer can be a general-purpose computer, a special-purpose computer, a computer network, a terminal, a user equipment, or other programmable device. The computer program or instructions can be stored in a computer-readable storage medium or transferred from one computer-readable storage medium to another. For example, the computer program or instructions can be transferred from one website, computer, server, or data center to another website, computer, server, or data center via wired or wireless means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium, such as a floppy disk, hard disk, or magnetic tape; it can also be an optical medium, such as a digital video disc (DVD); or it can be a semiconductor medium, such as a solid-state drive (SSD).

[0199] Although the invention has been described herein in conjunction with various embodiments, those skilled in the art will understand and implement other variations of the disclosed embodiments by reviewing the accompanying drawings, the disclosure, and the appended claims in carrying out the claimed invention. In the claims, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude a plurality. A single processor or other unit can implement several functions listed in the claims. While different dependent claims may recite certain measures, this does not mean that these measures cannot be combined to produce good results.

[0200] Although the invention has been described in conjunction with specific features and embodiments, it is obvious that various modifications and combinations can be made therein without departing from the spirit and scope of the invention. Accordingly, this specification and drawings are merely exemplary descriptions of the invention as defined by the appended claims, and are considered to cover any and all modifications, variations, combinations, or equivalents within the scope of the invention. Clearly, those skilled in the art can make various alterations and modifications to the invention without departing from its spirit and scope. Thus, if such modifications and modifications of the invention fall within the scope of the claims and their equivalents, the invention is also intended to include such modifications and modifications.

Claims

1. A training method for an ocean internal wave prediction model based on data and physics dual-drive, characterized in that, include: Acquire target ocean data; The target ocean data is two-dimensional data of the target sea surface area in three-dimensional ocean data; The three-dimensional ocean data is obtained by numerical simulation of the ocean field of the target area within a preset time period. The symbolic partial differential equation representing the propagation of internal ocean waves in the target ocean data was determined using the symbolic regression method. An initial prediction model for ocean internal waves is constructed based on the symbolic partial differential equations. The initial prediction model for ocean internal waves includes a physically guided neural network and an encoder and decoder with a convolutional long short-term memory network as the core. The physical constraint of the initial prediction model for ocean internal waves is the symbolic partial differential equations. The initial prediction model of ocean internal waves is trained based on the target ocean data to obtain a trained prediction model of ocean internal waves. The symbolic partial differential equation representing the propagation of internal ocean waves in the target ocean data, determined using the symbolic regression method, includes: The amplitude field data of internal ocean waves is extracted from the target ocean data and normalized to obtain normalized amplitude field data. The normalized amplitude field data is divided into regions to obtain multiple spatial blocks; The sparse regression method is used to determine the target spatial derivative term corresponding to each spatial block from the candidate function library, and a symbolic partial differential equation is generated based on the target spatial derivative term.

2. The training method for ocean internal wave prediction model based on data-physical dual-drive as described in claim 1, characterized in that, After training the initial prediction model of ocean internal waves based on the target ocean data to obtain the trained prediction model of ocean internal waves, the process further includes: The first frame of data to be predicted is input into the trained ocean internal wave prediction model to predict the result of the second frame. The prediction result of the second frame is input into the trained ocean internal wave prediction model to obtain the prediction result of the next frame. Recursive prediction yields prediction results for multiple frames.

3. The training method for ocean internal wave prediction model based on data-physical dual-drive according to claim 1, characterized in that, The step of using sparse regression to determine the target spatial derivative term for each spatial block from the candidate function library, and generating a symbolic partial differential equation based on the target spatial derivative term, includes: The sequential threshold optimization algorithm is used to filter out the target spatial derivative term and the coefficient of the target spatial derivative term from the candidate function library; Formula used: ； Determine the sign of the partial differential equation for each space block; in, The symbolic partial differential equation expression for the space block. The coefficients of the derivative term in the target space are denoted as . For the derivative term in the target space, For normalized amplitude field data, The x-axis represents the normalized amplitude field data. The vertical axis represents the normalized amplitude field data. For time, Let k be the total number of derivative terms in the target space, where k >

0.

4. The training method for ocean internal wave prediction model based on data-physical dual-drive according to claim 3, characterized in that, The step of training the initial prediction model for ocean internal waves based on the target ocean data to obtain a trained prediction model for ocean internal waves includes: The encoder and decoder of the initial prediction model of ocean internal waves are trained based on the normalized amplitude field data to obtain the trained encoder and decoder. The normalized amplitude field data of the target time period is input into the trained encoder and decoder to obtain the first prediction result. The first prediction result is divided into regions according to the spatial blocks to obtain the first prediction result corresponding to each spatial block; The physical guided neural network is trained based on the first prediction results corresponding to each spatial block and the symbolic partial differential equation to obtain a trained ocean internal wave prediction model.

5. The training method for an ocean internal wave prediction model based on data-physical dual-drive as described in claim 4, characterized in that, The training of the physical-guided neural network based on the first prediction results corresponding to each spatial block and the symbolic partial differential equation to obtain the trained ocean internal wave prediction model includes: The first prediction result and the symbolic partial differential equation corresponding to the spatial block are input into the physical guidance neural network to predict the second prediction result. Formula used: ； Determine the residuals for each spatial block; in, For residuals, This is the second prediction result corresponding to the spatial block; Formula used: ； Determine the data fidelity items; in, For the initial boundary loss, This is the initial time. This is the first prediction result corresponding to the spatial block at the initial time. The second prediction result corresponding to the spatial block at the initial time; Formula used: ； Determine the total loss function; in, For the total loss function, Minimization of collocations within a spatial block ; and These are the weighting coefficients; The parameters of the physical guided neural network are optimized based on the total loss function of each spatial block to obtain a trained ocean internal wave prediction model.

6. The training method for an ocean internal wave prediction model based on data-physical dual-drive as described in claim 5, characterized in that, Based on the total loss function of each spatial block, the physical-guided neural network of the initial prediction model of ocean internal waves is optimized to obtain a trained ocean internal wave prediction model, including: Based on the total loss function of each spatial block, the Adam optimizer is used to perform the first optimization of the parameters of the physical guided neural network; The parameters of the physical guided neural network are optimized a second time using the L-BFGS algorithm to obtain a trained ocean internal wave prediction model.

7. The training method for an ocean internal wave prediction model based on data-physical dual-drive as described in claim 1, characterized in that, The encoder includes multiple stacked layers, including convolutional layers and convolutional long short-term memory network layers; the decoder includes convolutional long short-term memory network layers and inverse convolutional layers arranged symmetrically with the encoder.

8. The training method for ocean internal wave prediction model based on data-physical dual-drive according to claim 1, characterized in that, The amplitude field data is normalized to obtain normalized amplitude field data, including: The amplitude values ​​of the amplitude field data are scaled to the range of [-1, 1] to obtain scaled data; The coordinate values ​​of the scaled data are mapped to the target reference space to obtain normalized amplitude field data.

9. A training device for an ocean internal wave prediction model based on data and physics dual-drive, characterized in that, include: The target ocean data acquisition module is used to acquire target ocean data. The target ocean data is two-dimensional data of the target sea surface area in three-dimensional ocean data; The three-dimensional ocean data is obtained by numerical simulation of the ocean field of the target area within a preset time period. The symbolic partial differential equation confirmation module is used to determine the symbolic partial differential equation representing the propagation of internal ocean waves in the target ocean data using a symbolic regression method. An initial prediction model construction module for ocean internal waves is used to construct an initial prediction model for ocean internal waves based on the symbolic partial differential equations; the initial prediction model for ocean internal waves includes a physically guided neural network and an encoder and decoder with a convolutional long short-term memory network as the core; the physical constraint of the initial prediction model for ocean internal waves is the symbolic partial differential equations. The model training module is used to train the initial prediction model of ocean internal waves based on the target ocean data to obtain a trained prediction model of ocean internal waves. The symbolic partial differential equation verification module includes: The normalization processing unit is used to extract the amplitude field data of internal ocean waves from the target ocean data and normalize the amplitude field data to obtain normalized amplitude field data. A region partitioning unit is used to divide the normalized amplitude field data into regions to obtain multiple spatial blocks; The symbolic partial differential equation confirmation unit is used to determine the target spatial derivative term corresponding to each spatial block from the candidate function library using a sparse regression method, and to generate a symbolic partial differential equation based on the target spatial derivative term.

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