Internal wave characteristic field information rapid prediction method based on deep learning

Abstract

The invention discloses an internal wave characteristic field information rapid prediction method based on deep learning, and belongs to the technical field of ocean internal wave detection. According to the method, rapid prediction is carried out on the basis of traditional numerical simulation data by using deep learning, so that the efficiency of inner solitary wave prediction is remarkably improved; through multi-channel coupling learning and an iterative prediction strategy, the inner wave field prediction achieves the effect of high precision and high efficiency. Meanwhile, in combination with high-resolution numerical mode data, the consistency of a model prediction result and a physical process is ensured, and rapid extension period prediction of a solitary wave characteristic field in the ocean is realized while low error and high relevancy are kept. The method is suitable for application scenes of real-time ocean internal wave monitoring and early warning and the like, and can be widely applied to the technical fields of ocean environment monitoring and early warning, intelligent ocean observation, ocean engineering safety and the like.

Description

Technical Field

[0001] The present invention belongs to the technical field of ocean internal wave detection, and specifically relates to a fast prediction method for internal wave feature field information based on deep learning. Background Art

[0002] With the integration of advanced technologies such as the Internet of Things, big data, and artificial intelligence, ocean monitoring is gradually becoming automated and intelligent. The development of sensor technology has enabled ocean environmental monitoring to enter the era of real-time and three-dimensional monitoring, improving the accuracy and timeliness of monitoring. Internal solitary waves (ISWs) are common non-linear internal wave phenomena in the ocean, widely existing in the continental shelf edges and strait regions of the world's major oceans. These waves carry a large amount of energy during propagation, posing potential threats to the marine ecosystem, offshore operation safety, and ocean engineering structures (such as submarines, subsea pipelines, and oil platforms). Therefore, accurately predicting the generation, propagation path, and evolution characteristics of internal solitary waves is of great significance for ensuring ocean engineering safety, implementing ocean environmental monitoring and early warning. The propagation and evolution of internal solitary waves are jointly affected by factors such as seawater temperature, salinity gradient, and flow field. Traditionally, the prediction of ocean internal solitary waves mainly relies on high-precision numerical simulations, which can realistically simulate the propagation characteristics of internal waves at high resolutions. However, such numerical simulations are computationally intensive and time-consuming, and are not suitable for real-time and rapid forecasting.

[0003] In recent years, deep learning has made breakthrough progress in the fields of meteorological and ocean prediction. Among them, the FourCastNet model jointly developed by NVIDIA and others adopts a hybrid architecture of Fourier neural operator (FNO) and Transformer, which can quickly and efficiently predict the global weather at a resolution of 0.25 degrees, and only takes a few seconds of computing time for a one-week forecast; its efficiency is several orders of magnitude higher than traditional numerical methods. To process high-resolution spatio-temporal data, an adaptive Fourier neural operator (AFNO) module is introduced, which effectively captures long-range spatial dependencies while reducing computational complexity through frequency-domain sparsification and block processing strategies. Although FourCastNet and AFNO have shown high efficiency in meteorological field prediction, their application in the prediction of ocean internal wave feature fields has not been fully studied.

[0004] In summary, there is an urgent need for a new technical solution that combines deep learning with high-resolution numerical model data to achieve efficient and rapid prediction of internal solitary wave information. Summary of the Invention

[0005] Aiming at the problems of complex calculation and time-consuming prediction of traditional numerical models, the purpose of the present invention is to provide a fast prediction method for internal wave feature field information based on deep learning to make up for the deficiencies of the existing technology.

[0006] To achieve the above object, the present invention adopts the following technical solutions: A fast prediction method for internal wave characteristic field information based on deep learning, comprising the following steps: S1: Obtain high-resolution numerical model data and preprocess the data; S2: Construct a spatio-temporal prediction network model based on AFNO; the model includes a Patch module, multiple AFNO modules, a linear mapping layer, and an output layer; the AFNO module includes a spatial mixing layer, a channel mixing layer, multi-layer stacking, and non-linear mapping; S3: Adopt a two-stage training strategy to optimize the performance of the spatio-temporal prediction network model based on AFNO to better improve the model's ability to predict internal wave for a long time; S4: Predict the internal wave field data at the current moment based on the trained spatio-temporal prediction network model.

[0007] Further, the S1 includes: S1-1: Use a high-resolution numerical model to obtain multi-physical quantity data of high-resolution water temperature, salinity, and flow velocity fields of internal solitary waves in the target sea area, and construct a data set containing multiple moment samples; S1-2: Organize the data at each moment, and merge channels such as temperature T, salinity S, and east-west flow velocity U into a three-dimensional tensor with a shape of h×w×3, where h and w are the grid height and width.

[0008] S1-3: To improve the training effect of the model, perform standardization processing on the original data. For each variable, calculate the mean and standard deviation of its training set, and apply the standardization processing method.

[0009] The standardization processing is: for each variable, calculate the mean (μ) and standard deviation (σ) of its training set, and apply the standardization transformation: ; where: is the original value of the i-th sample; is the sample mean; is the sample standard deviation; At the same time, introduce the time mean as an additional input feature to enhance the model's ability to model time trends: ; Compared with directly using the original time series data, the time mean can reduce the interference of noise on the model and improve the generalization ability. Similarly, to avoid data leakage, the time mean is also only applied to the training set.

[0010] Furthermore, in S2: Each AFNO module consists of a spatial mixing layer and a channel mixing layer. In the spatial mixing part, the input Patch features are transformed to the frequency domain using the Fast Fourier Transform (FFT), linear transformation is applied to the frequency domain features, and a sparsification function is used to remove unimportant high-frequency components. The filtered spectrum is transformed back to the spatio-temporal domain through the Inverse FFT (IFFT) to capture the global spatial dependence features between Patches. In the channel mixing part, without considering the spatial dimension, interaction and fusion are performed among channels. A shared multi-layer perceptron (MLP) acts on the channel vectors of the Patch to achieve information interaction between physical fields such as temperature, salinity, and flow velocity; AFNO uses block diagonal MLP plus soft threshold processing for block-level channel mixing; Output reconstruction: After being processed by multiple AFNO modules, a high-dimensional feature representation of each Patch is obtained. In the last step, the features of all Patches are re-stitched into a grid of the original h×w size. The stitched high-dimensional features are transformed back to the physical quantity dimension (temperature, salinity, flow velocity, etc.) through the output linear mapping layer to generate the complete three-channel internal wave field prediction result at the corresponding moment (such as t+Δt). This output tensor is the predicted distribution of each physical quantity at the next moment, describing the evolution of internal solitary waves in the temperature, salinity, and flow velocity fields. Multiple AFNO modules are stacked layer by layer to form a deep network. Each layer contains the above-mentioned one-time spatial mixing and one-time channel mixing operations, and a non-linear activation function is added subsequently to enhance the expressive ability. Through multi-layer stacking, the model can gradually extract rich spatio-temporal features of the internal wave field and learn complex internal wave dynamics laws.

[0011] Furthermore, the process of the model constructed in S2 for predicting internal waves is as follows: S2-1: Patch division and embedding: The multi-channel spatio-temporal tensor is divided into several Patch regions of size h p ×w p according to the spatial grid. Each Patch is flattened and subjected to high-dimensional linear mapping to obtain Patch Embedding; at the same time, positional encoding is superimposed to enable the model to perceive the relative position information of each Patch in the overall grid; here, the input image .

[0012] Image tiling: ; where p is the block size (here it is 8×8), .

[0013] Linear projection: ; Output Token tensor . Where p is the block size and d is the model embedding dimension.

[0014] S2-2: Spatial Mixing Processing: Use the Fast Fourier Transform (FFT) to extract long-range dependencies in space. Map the spatio-temporal features of each patch to the frequency domain: ; The advantage of this is that in the frequency domain, many long-range spatial correlations become clearer. In particular, the low-frequency components can well reflect the global features, while the high-frequency components can provide local detailed information. However, directly using all frequency components will lead to excessive computational complexity, and many high-frequency components are actually not useful information. Therefore, use the linear transformation R to filter the frequency domain features and remove the useless high-frequency components: ; Sparsification function Set to zero the parts where the eigenvalues are less than the threshold λ, thereby improving the computational efficiency.

[0015] Finally, output back to the spatio-temporal domain through the inverse Fourier transform (IFFT): ; After this series of transformations, the model can better understand the global features of internal waves in space and retain important long-range dependency information.

[0016] S2-3: Channel Mixing Processing: In this part, no longer focus on the spatial dimension, but focus on the information interaction between different channels. There is a certain complex internal correlation between temperature (T), salinity (S), and flow velocity (U), and the model can automatically learn these dependencies.

[0017] The mixing process is implemented through a shared MLP, and the formula is: ; Here, the MLP acts as an attention mechanism between channels, enabling better information interaction between different physical variables.

[0018] S2-4: Multi-layer Stacking and Nonlinear Mapping: The entire model is not a single layer, but is stacked by multiple AFNO modules. Each layer contains one spatial mixing and one channel mixing operation. To increase the expressive power of the model, a non-linear activation function is added after each layer to enhance the model's fitting ability for complex patterns.

[0019] The specific calculation form of each layer is as follows: ; Among them represents the local linear transformation. Represents the global characteristics of internal waves obtained through Fourier operations. Through layer-by-layer stacking, the model gradually extracts spatio-temporal features from the data and finally learns the complex laws of internal wave dynamics. Non-linear activation function: ; S2-5: Output reconstruction: The last step is to map the processed features back to the original spatial grid in order to generate the prediction result X(t + Δt) at the next time step t + Δt. Specifically, the model will reassemble the features of all patches back into a complete h×w grid, and then pass through a linear mapping layer to transform the high-dimensional features back to the physical quantity dimensions of the input variables (i.e., temperature, salinity, flow velocity). Finally, the resulting output is a new spatio-temporal distribution matrix that can predict the states of all internal wave characteristic variables at the next time step.

[0020] Concatenation formula: ; where , the spatial grid . Since the Tokens processed by AFNO are already arranged in the original spatial positions (the row-column indices (i,j) correspond to the grid positions), the concatenation only needs to keep the tensor structure unchanged without explicit operations.

[0021] Mapping formula: ; where is the learnable weight matrix, is the bias vector.

[0022] Furthermore, the said S3 includes: S3-1: In the pre-training stage, aiming at single-step prediction (predicting k + 1 at input time k), use the L2 loss function to update the model parameters to achieve the initial learning of the network; S3-2: In the fine-tuning stage, to improve the multi-step prediction accuracy, use the result at the k + 1 time step predicted by the model as the input again to predict the k + 2 time step (i.e., two-step iterative prediction), and use a mixed L1 and L2 loss function for training to enhance the robustness of the model to outliers; The L1 and L2 loss functions are defined as follows: ; ; where represents the true value, represents the predicted value.

[0023] ​​Further, in S4: Given data such as temperature, salinity, and flow velocity at a given moment k, the internal wave field at moment k+1 is predicted through the model. Then, the prediction result at moment k+1 is iteratively used as the input to continue predicting future moments such as k+2, k+3... to achieve the spatio-temporal prediction of the multi-step internal wave characteristic field.

[0024] Compared with the prior art, the advantages and beneficial effects of the present invention are as follows: The present invention utilizes deep learning to perform rapid prediction based on traditional numerical simulation data, significantly improving the efficiency of internal solitary wave prediction; through multi-channel coupled learning and iterative prediction strategies, the internal wave field prediction achieves the effect of both high precision and high efficiency. At the same time, combined with high-resolution numerical model data, it ensures the consistency between the model prediction result and the physical process, and realizes the rapid extended-term prediction of the internal solitary wave characteristic field while maintaining low error and high correlation.

[0025] The present invention combines numerical model data and a high-resolution deep learning model, uses the collaborative characteristics of multiple physical quantities to improve the prediction accuracy, and at the same time significantly improves the calculation efficiency, and can rapidly extend the prediction of information on multiple future physical fields of internal waves. The present invention is applicable to application scenarios such as real-time ocean internal wave monitoring and early warning, and can be widely applied to technical fields such as ocean environmental monitoring and early warning, intelligent ocean observation, and ocean engineering safety. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 It is a flowchart for predicting the information of the internal solitary wave characteristic field in the present invention.

[0027] Figure 2 It is a visualization example data of the temperature field, salinity field, and east-west flow velocity field in the model data.

[0028] Figure 3 It is an overall framework diagram of the Fourier neural operator FNO.

[0029] Figure 4 It is a schematic framework diagram of the FourCastNet model for predicting the information of the internal wave characteristic field.

[0030] Figure 5 It is a schematic diagram of the model training, fine-tuning, and prediction principle.

[0031] Figure 6 It is a prediction result demonstration diagram, which is an example diagram of the prediction of the east-west flow velocity characteristic field of internal waves at 0:00 on April 9, 2024. From top to bottom, they are the true value, the predicted value, and the error diagram.

[0032] Figure 7 It is a diagram of the results of the MAE, RMSE, and ACC evaluation indicators in Example 2. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0033] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments, but the present invention is not limited to the following specific embodiments.

[0034] Embodiment 1: A fast prediction method for internal wave characteristic field information based on deep learning, as Figure 1 shown, includes the following steps: Step 1: Data preparation and preprocessing: According to the target area to be predicted, a three-dimensional ocean model is established using high-resolution simulation to simulate and generate high-resolution characteristic data of internal solitary waves in the sea area. The input X(t) is a spatio-temporal distribution matrix containing multiple internal wave characteristic variables, specifically including three variables: temperature (T), salinity (S), and east-west velocity (U). The data is generally organized as a three-dimensional tensor with a shape of h×w×c, where h and w represent the height and width of the spatial grid, that is, the grid size of the divided ocean area; c represents the number of channels, that is, the key variables of internal waves.

[0035] In this embodiment, the selected characteristic variables according to the model data include the temperature field, salinity field, and east-west velocity field at a given water depth plane (as Figure 2 shown). Spatially, the research area is divided into grids of size h×w and recorded at fixed time steps (such as 1 hour) in time. The data at each moment is first organized into a three-dimensional tensor with a shape of h×w×3, where the 3 channels correspond to temperature, salinity, and east-west velocity respectively. In this way, multiple three-channel internal wave spatio-temporal data samples at consecutive times are obtained.

[0036] Before inputting into the model, the original data is standardized. For each variable, the mean (μ) and standard deviation (σ) of its training set are calculated and applied to the standardization transformation: ; where: is the original value of the i-th sample; is the sample mean; is the sample standard deviation. At the same time, the time mean is introduced as an additional input feature to enhance the model's ability to model time trends. The standardization and time mean processing are calculated only based on the training set to avoid information leakage.

[0037] Step 2: Model architecture design: Figure 3 shown is a schematic diagram of the deep learning prediction model structure based on AFNO of the present invention. The model adopts the Vision Transformer idea to perform Patch division and embedding on the input tensor. Specifically, the entire h×w grid is divided into several grids of size h p ×w pThe small patches are flattened and mapped to high-dimensional feature vectors, and corresponding position encodings are added. The sequence of patches processed in this way serves as the input to the Transformer model, effectively retaining the spatial position information.

[0038] The AFNO model is improved based on the FNO (Fourier Neural Operator). The FNO is a deep learning model specifically designed to solve partial differential equations (PDEs), aiming to efficiently approximate the solutions of PDE systems by learning the mapping between input parameters and the solution space. The core idea of the FNO is to use the fast Fourier transform (FFT) to map the convolution operation from the spatial domain to the frequency domain. According to the convolution theorem, the global convolution in the spatial domain can be transformed into simple matrix multiplication in the frequency domain, thus significantly improving the computational efficiency. The FNO constructs a series of Fourier Layers to gradually extract the frequency-domain features of the data and perform nonlinear mapping, enabling the model to accurately capture the complex dynamic characteristics of the PDE system.

[0039] As Figure 3 shown, where (a) represents the overall framework diagram of this neural network structure. After the high-dimensional mapping of the input a(x) by the neural network P, it passes through T Fourier Layers in sequence, and then through Q processing, and finally is restored to the output u(x). Figure (b) further reveals the internal structure of a single Fourier Layer. When the input v(x) enters, it is first transformed to the frequency domain through the Fourier transform; in the frequency domain, the model uses the linear transformation R to perform high-frequency mode filtering to enhance the generalization ability of the model. Subsequently, the data passes through the inverse Fourier transform (iFFT) and returns to the original space, and is added to the features transmitted through the bypass in a residual manner, and then undergoes nonlinear mapping through the activation function to enhance the expression ability of the model. This bypass structure is similar to the "shortcut" connection (skip connection) of ResNet, which helps the efficient flow of information.

[0040] The Fourier Operator solves the problem of kernel integration, and uses K to represent the kernel integral operator: ; where K is the kernel integral operator, describing the global relationship between the input and output. κ is the kernel function, which depends on the input and the domain D.

[0041] The expression of the Fourier transform is as follows: ; Then it can be deduced that: ; In this way, the Fourier integral operator can be written as ; Therefore, the proposed Fourier neural operator solves the integral term in operator learning. Combining with the following iterative relationship, adding the original input and the result of the frequency-domain operation through the shortcut connection of ResNet, and performing non-linear mapping through the activation function, the mathematical principle of the model can be expressed: ; where is a local linear transformation, and σ is the activation function. The output is restored to the target space through the dimensionality reduction operation u(x)=Q(vT(x)).

[0042] The improvement of the AFNO model over the FNO model is mainly reflected in the following aspects: (1) Sparsification operation During the learning process, the neural network may capture a lot of irrelevant high-frequency noise. AFNO directly removes the irrelevant frequency components through hard-threshold sparsification.

[0043] The calculation method of sparsification is as follows: ; where is the sparsification function, and λ is the sparsity threshold.

[0044] (2) Multi-head operation AFNO uses a block-diagonal weight matrix to mix the frequency-domain features, divides the entire frequency-domain features into multiple small blocks, and then processes each block separately. This can not only reduce the computational complexity but also capture more detailed information within a local range.

[0045] The specific calculation is as follows: ; where is the number of blocks, is the weight of each block.

[0046] (3) Residual connection Finally, it is also necessary to ensure that the gradient can be propagated stably to ensure that the model can be trained more easily. AFNO adopts a residual connection, that is, after the frequency-domain operation, the converted result is added to the original input to ensure that information is not lost during the transformation process.

[0047] The calculation method is as follows: ; The following figure is the FourCastNet model diagram for predicting internal waves, and this model adopts the AFNO model architecture.

[0048] In Figure 4In it, each AFNO module consists of a spatial mixing layer and a channel mixing layer. In the spatial mixing part, the fast Fourier transform (FFT) is used to transform the input Patch features into the frequency domain. A linear transformation is performed on the frequency domain features, and a sparsification function is applied to remove unimportant high-frequency components. The filtered spectrum is transformed back to the spatio-temporal domain through the inverse FFT (IFFT), thereby capturing the global spatial dependence features between Patches. In the channel mixing part, without considering the spatial dimension, interaction and fusion are carried out among the channels. A shared multi-layer perceptron (MLP) acts on the channel vectors of the Patch to achieve information interaction between physical fields such as temperature, salinity, and flow velocity. Figure 3 The right side shows the operation methods of different models in the channel mixing stage: for example, GFN multiplies each channel by weights respectively, FNO performs full matrix multiplication on all channels, while AFNO uses block diagonal MLP plus soft threshold processing for block-level channel mixing (shown in the figure in the form of k blocks × MLP). Output reconstruction: After being processed by multiple layers of AFNO modules, a high-dimensional feature representation of each Patch is obtained. In the last step, the features of all Patches are re-stitched into the original h×w size grid. The stitched high-dimensional features are transformed back to the physical quantity dimension (such as temperature, salinity, flow velocity, etc.) through the output linear mapping layer to generate the complete three-channel internal wave field prediction result at the corresponding moment (such as t+Δt). This output tensor is the predicted distribution of each physical quantity at the next moment, describing the evolution of internal solitary waves in the temperature, salinity, and flow velocity fields.

[0049] In this embodiment, multiple AFNO modules are stacked layer by layer to form a deep network. Each layer contains the above-mentioned one-time spatial mixing and one-time channel mixing operations, and a non-linear activation function is added subsequently to enhance the expression ability. Through multi-layer stacking, the model can gradually extract the rich spatio-temporal features of the internal solitary wave field and learn the complex internal wave dynamics law.

[0050] Step 3: Model training: According to the method of the present invention, as Figure 5 shown, the model training adopts a two-stage progressive strategy. In the pre-training stage, the goal is single-step prediction: input the data set X(k) at time k, output the predicted internal wave field X̂(k + 1) at time k + 1, and use the mean square error (L2 loss) as the optimization objective function. During the training process, a large amount of historical data generated by high-resolution numerical models is used for iteration to optimize the network parameters, so that the model can better fit the one-step evolution law of the internal wave field.

[0051] Step 4: Fine-tuning stage: To improve the medium- and long-term prediction accuracy, iterative multi-step training is adopted. Specifically, the result at time k+1 predicted by the model in the pre-training is used as the input again to predict the result at time k+2; that is, the training is carried out in the way of inputting one step and continuously predicting two steps. In this stage, a composite function of L1 and L2 losses is used for optimization to enhance the robustness to data outliers. The time step can be set during training to adapt to the prediction requirements of longer sequences. Through two-stage training, the model has learned the co-evolution relationship of temperature, salinity, and flow velocity, so that it can maintain high accuracy in the subsequent prediction process. The definitions of L1 and L2 losses are as follows: ; ; where represents the true value, represents the predicted value.

[0052] Step 5: Prediction and inference: As Figure 4 shown, after the model training is completed, it enters the prediction and inference stage. Given the observed or simulated data at the current time k as the input to the model, the predicted result of the internal solitary wave feature field at time k+1 is obtained. Then, the predicted output at time k+1 is input into the model again, and through such iteration, the predicted values at multiple future times such as k+2, k+3... can be obtained. This iterative prediction mechanism enables the model to continuously output the evolution of the internal wave field at multiple future times in real-time applications.

[0053] Example 2: This example is actually verified by using the method provided in Example 1. This implementation example uses one-year numerical simulation data for training, selects the data at a water depth of 50 m. Among them, the internal solitary wave data from March 2023 to February 2024 are used as the training set, the internal solitary wave data in March 2024 are used as the validation set, and the internal solitary wave data in April 2024 are used as the test set. The time resolution is 1 hour, and the spatial resolution is 500 m in the east-west direction and 1200 m in the north-south direction. The longitude and latitude range covers 19°N - 22.5°N, 115°E - 121°E, the number of grids is 336×1680, and the number of samples is about 8700. The data has good representativeness and adaptability.

[0054] The model evaluation formula in Example 1 is as follows: ; ; ; where is the true value, is the predicted value, is the total number of samples.

[0055] As shown Figure 6 in the figure, the predicted element of this figure is the east-west velocity field, which shows the results of single-step iteration predicting the next 20 steps at this moment. The longitude and latitude range is 19°N - 22.5°N, 115°E - 121°E, the time resolution is 1 hour, and the spatial resolution is 500 meters in the east-west direction and 1200 meters in the north-south direction. From top to bottom are the true value, predicted value, and error distribution map. The MAE, RMSE, and ACC evaluation indicators for each step of this embodiment are as Figure 7 shown

[0056] The present invention combines the internal wave high-resolution numerical model data with the FourCastNet deep learning model, and uses AFNO to efficiently capture long-distance spatial dependencies, realizing fast and high-precision prediction of the internal solitary wave field. Compared with traditional numerical simulations, the model inference speed has been greatly improved (FourCastNet has been proven to only take a few seconds for a one-week forecast), and it can be used for rapid extended-range prediction based on internal wave model data. In terms of prediction accuracy, multi-channel collaborative learning and iterative strategies enable the model to perform excellently in indicators such as MAE, RMSE, and ACC, and can accurately reproduce the spatio-temporal distribution characteristics of internal solitary waves.

[0057] In summary, the present invention significantly improves the efficiency and accuracy of internal wave prediction, providing a practical new tool for ocean internal wave research and applications.

[0058] Although the above embodiments have described the present invention in detail, they are only a part of the embodiments of the present invention, not all embodiments. Other embodiments can be obtained based on this embodiment without creative efforts, and these embodiments all fall within the protection scope of the present invention.

Claims

1. A fast prediction method for internal wave characteristic field information based on deep learning, characterized in that, It includes the following steps: S1: Obtain high-resolution numerical model data and preprocess the data; S2: Construct a spatio-temporal prediction network model based on AFNO; this model includes a Patch module, multiple AFNO modules, a linear mapping layer, and an output layer; the AFNO module includes a spatial mixing layer, a channel mixing layer, multi-layer stacking, and non-linear mapping; S3: Adopt a two-stage training strategy to optimize the performance of the spatio-temporal prediction network model based on AFNO, so as to better improve the model's ability to predict internal waves over a long time; S4: Predict the internal wave field data at the current moment based on the trained spatio-temporal prediction network model.

2. The rapid prediction method of internal wave characteristic field information according to claim 1, wherein The S1 includes: S1-1: Use a high-resolution numerical model to obtain multi-physical quantity data of high-resolution water temperature, salinity, and flow velocity fields of internal solitary waves in the target sea area, and construct a data set containing multiple moment samples; S1-2: Organize the data at each moment, and merge the temperature T, salinity S, and east-west flow velocity U channels into a three-dimensional tensor with a shape of h×w×3, where h and w are the grid height and width; S1-3: Perform standardization processing on the original data. For each variable, calculate the mean and standard of its training set.

3. The rapid prediction method for internal wave characteristic field information according to claim 2, wherein, The standardization processing is as follows: For each variable, calculate the mean μ and standard deviation σ of its training set, and apply them to the standardization transformation: ； Wherein: is the original value of the i-th sample; is the sample mean; is the sample standard deviation; At the same time, introduce the time mean as an additional input feature: 。 4. The rapid prediction method for internal wave characteristic field information according to claim 1, characterized in that In the S2: The spatial mixing layer uses the fast Fourier transform FFT to transform the input Patch features into the frequency domain, performs a linear transformation on the frequency domain features, and applies a sparsification function to remove high-frequency components; the filtered spectrum is transformed back to the spatio-temporal domain through the inverse FFT, so as to capture the global spatial dependence features between Patches; the channel mixing layer performs interactive fusion between channels, and uses a shared multi-layer perceptron MLP to act on the channel vectors of Patches; the AFNO module uses block diagonal MLP plus soft threshold processing for block-level channel mixing; output reconstruction: After being processed by multiple AFNO modules, a high-dimensional feature representation of each Patch is obtained, and then the features of all Patches are re-spliced into a grid of the original h×w size; the spliced high-dimensional features are transformed back to the physical quantity dimension through the output linear mapping layer to generate the complete three-channel internal wave field prediction result corresponding to the moment, that is, the prediction distribution of each physical quantity at the next moment, and complete the description of the evolution of internal solitary waves in the temperature, salinity, and flow velocity fields.

5. The rapid prediction method for internal wave characteristic field information according to claim 4, wherein The process of the model constructed in the S2 for predicting internal waves is: S2-1: Patch Partitioning and Embedding: Divide the multi-channel spatio-temporal tensor into several Patch regions of size h p ×w p through the spatial grid, flatten and perform high-dimensional linear mapping on each Patch to obtain Patch Embedding; at the same time, superimpose the position encoding to enable the model to perceive the relative position information of each Patch in the overall grid; assume the input image ; Image block division: ； Among them is the block size, ; Linear projection: ； Output Token Tensor ; where is the model embedding dimension; S2-2: Spatial mixing processing: Use the fast Fourier transform FFT to extract long-range dependencies in space; map the spatio-temporal features of each patch to the frequency domain: ； Use a linear transformation R to screen the frequency domain features: ； Sparsification function Set to zero the part where the eigenvalue is less than the threshold λ; Finally, the output is transformed back to the spatio-temporal domain through the inverse Fourier transform: ； S2-3: Channel mixing processing: The mixing process is realized through a shared MLP, and the formula is: ； S2-4: Multi-layer stacking and non-linear mapping: The AFNO module adds a non-linear activation function, and the specific calculation form is as follows: ； Among them represents a local linear transformation represents the global characteristics of internal waves obtained by Fourier operation; the non-linear activation function: ； S2-5: Output Reconstruction: The model will reassemble the features of all patches back into a complete grid, and then pass through a linear mapping layer to transform the high-dimensional features back to the physical quantity dimension of the input variables. Finally, the resulting output is a new spatio-temporal distribution matrix that can predict the states of all internal wave feature variables at the next moment: Splicing formula: ； Among them , the spatial grid ); Mapping formula: ； wherein is a learnable weight matrix, is a bias vector.

6. The rapid prediction method for internal wave characteristic field information according to claim 1, wherein The S3 includes: S3-1: In the pre-training stage, aiming at single-step prediction, use the L2 loss function to update the model parameters and achieve the initial learning of the network; S3-2: In the fine-tuning stage, to improve the multi-step prediction accuracy, take the predicted result at the k+1 moment of the model as the input again to predict the k+2 moment, and adopt the mixed L1 and L2 loss functions for training to enhance the robustness of the model to outliers; The L1 and L2 loss functions are defined as follows: ； ； Among them represents the true value, represents the predicted value.

7. The rapid prediction method for internal wave characteristic field information according to claim 1, wherein In S4: Given the temperature, salinity, and flow velocity data at time k, the internal wave field at the k+1 moment is predicted through the model, and then the predicted result at the k+1 moment is iteratively used as the input to continue predicting the future moments such as k+2, k+3... Finally, the spatio-temporal prediction of the multi-step internal wave feature field is achieved.

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