A fast prediction method for internal wave characteristic field information based on deep learning

Abstract

The present invention discloses a method for rapid prediction of internal wave characteristic field information based on deep learning, which belongs to the technical field of ocean internal wave detection. The present invention uses deep learning to perform rapid predictions based on traditional numerical simulation data, significantly improving the efficiency of internal solitary wave predictions; through multi-channel coupled learning and iterative prediction strategies, the internal wave field prediction achieves both high precision and high efficiency. At the same time, combined with high-resolution numerical model data, the consistency of the model prediction results and the physical process is guaranteed, while maintaining low error and high correlation, achieving rapid extended-period prediction of the characteristic field of ocean internal solitary waves. The present invention is suitable for application scenarios such as real-time ocean internal wave monitoring and early warning, and can be widely used in technical fields such as marine environmental monitoring and early warning, intelligent ocean observation, and marine engineering safety.

Description

Technical Field

[0001] The present invention belongs to the technical field of ocean internal wave detection, and specifically is a method for quickly predicting internal wave characteristic 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. Advances in sensor technology have ushered in real-time and three-dimensional marine environmental monitoring, improving both accuracy and real-time performance. Internal solitary waves (ISWs) are common nonlinear internal wave phenomena in the ocean, widespread along the continental shelf margins and in straits across the world's oceans. These waves carry significant energy during propagation, posing a potential threat to marine ecosystems, offshore operational safety, and offshore engineering structures (such as submarines, submarine pipelines, and oil platforms). Therefore, accurately predicting the generation, propagation paths, and evolution characteristics of ISWs is crucial for ensuring marine engineering safety and implementing marine environmental monitoring and early warning. The propagation and evolution of ISWs are influenced by factors such as seawater temperature, salinity gradients, and current fields. Traditionally, prediction of ISWs in the ocean relies on high-precision numerical simulations that can realistically simulate the propagation characteristics of internal waves at high resolution. However, these numerical simulations are computationally intensive and time-consuming, making them unsuitable for real-time and rapid forecasting.

[0003] In recent years, deep learning has made breakthroughs in the fields of meteorological and oceanographic forecasting. Among them, the FourCastNet model jointly developed by NVIDIA and others uses a hybrid architecture of Fourier Neural Operator (FNO) and Transformer, which can quickly and efficiently predict global weather at a resolution of 0.25 degrees, and a one-week forecast only takes seconds to calculate; its efficiency is several orders of magnitude higher than traditional numerical methods. In order to process high-resolution spatiotemporal data, the Adaptive Fourier Neural Operator (AFNO) module was introduced. Through frequency domain sparsification and block processing strategies, it effectively captures long-range spatial dependencies while reducing computational complexity. Although FourCastNet and AFNO have shown high efficiency in meteorological field forecasting, research on their application to the prediction of internal ocean wave characteristic fields is still insufficient.

[0004] In summary, a new technical solution is urgently needed to combine deep learning with high-resolution numerical model data to achieve efficient and rapid prediction of internal solitary wave information. Summary of the Invention

[0005] In view of the problems of complex calculations and time-consuming predictions in traditional numerical models, the purpose of the present invention is to provide a method for rapid prediction of internal wave characteristic field information based on deep learning to make up for the shortcomings of the existing technology.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] A method for rapidly predicting internal wave characteristic field information based on deep learning, comprising the following steps:

[0008] S1: Acquire high-resolution numerical model data and preprocess the data;

[0009] S2: Construct a spatiotemporal 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 nonlinear mapping;

[0010] S3: A two-stage training strategy is used to optimize the performance of the AFNO-based spatiotemporal prediction network model to better enhance the model's ability to predict intra-wavelength time.

[0011] S4: Predict the wave field data at the current moment based on the trained spatiotemporal prediction network model.

[0012] Furthermore, the S1 includes:

[0013] S1-1: Use a high-resolution numerical model to obtain high-resolution multi-physical data of water temperature, salinity, and velocity fields of solitary waves in the target sea area, and construct a dataset containing samples at multiple time points;

[0014] 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 height and width of the grid.

[0015] S1-3: In order to improve the training effect of the model, the original data is standardized. For each variable, the mean and standard deviation of its training set are calculated, and the standardized processing method is applied.

[0016] The standardization process is as follows: for each variable, the mean (μ) and standard deviation (σ) of its training set are calculated and applied to the standardization transformation:

[0017] ;

[0018] in: is the original value of the i-th sample; is the sample mean; is the sample standard deviation;

[0019] At the same time, the time mean is introduced as an additional input feature to enhance the model's ability to model time trends:

[0020] ;

[0021] Compared to using the raw time series data directly, temporal averaging can reduce the impact of noise on the model and improve generalization. Similarly, to avoid data leakage, temporal averaging is only applied to the training set.

[0022] Furthermore, in S2, each AFNO module consists of a spatial mixing layer and a channel mixing layer. The spatial mixing component uses a fast Fourier transform (FFT) to convert the input patch features to the frequency domain, performs a linear transformation on the frequency domain features, and applies a sparsification function to remove unimportant high-frequency components. The filtered spectrum is then converted back to the spatiotemporal domain using an inverse FFT (IFFT), thereby capturing the global spatial dependencies between patches. The channel mixing component performs interactive fusion across channels, regardless of spatial dimensionality. A shared multi-layer perceptron (MLP) is applied to the patch's channel vectors to enable information exchange between physical fields such as temperature, salinity, and flow velocity. AFNO uses a block-diagonal MLP plus soft thresholding for block-level channel mixing. Output reconstruction: After processing by multiple layers of AFNO modules, a high-dimensional feature representation is obtained for each patch. In the final step, the features of all patches are reassembled into the original h×w grid. The concatenated high-dimensional features are converted back to physical quantity dimensions (temperature, salinity, velocity, etc.) through the output linear mapping layer to generate a complete three-channel internal wave field prediction result at the corresponding time (e.g., t+Δt). This output tensor is the predicted distribution of each physical quantity at the next time, describing the evolution of internal solitary waves in the temperature, salinity, and velocity fields. Multiple AFNO modules are stacked layer by layer to form a deep network. Each layer includes the above-mentioned spatial mixing and channel mixing operations, and a nonlinear activation function is subsequently added to enhance the expressive power. By stacking multiple layers, the model can gradually extract the rich spatiotemporal characteristics of the internal solitary wave field and learn the complex internal wave dynamics.

[0023] Furthermore, the process of predicting internal waves by the model constructed in S2 is as follows:

[0024] S2-1: Patch division and embedding: Divide the multi-channel spatiotemporal tensor into several h-sized p ×w p Patch area, flatten and high-dimensional linear mapping are performed on each patch to obtain Patch Embedding; at the same time, position encoding is superimposed to enable the model to perceive the relative position information of each patch in the overall grid; here, the input image is .

[0025] Image segmentation:

[0026] ;

[0027] Where p is the block size (here 8×8), .

[0028] Linear projection:

[0029] ;

[0030] Output Token tensor . Where p is the block size and d is the model embedding dimension.

[0031] S2-2: Spatial mixing processing: Use Fast Fourier Transform (FFT) to extract long-range spatial dependencies. Map the spatiotemporal features of each patch to the frequency domain:

[0032] ;

[0033] The advantage of this approach is that in the frequency domain, many long-range spatial correlations become clearer. In particular, low-frequency components can well reflect global features, while high-frequency components can provide local details. However, directly using all frequency components will result in excessive computational overhead, and many high-frequency components are not actually useful information. Therefore, a linear transformation R is used to filter the frequency domain features and remove useless high-frequency components:

[0034] ;

[0035] Sparsification function The part of the eigenvalue that is less than the threshold λ is set to zero, thereby improving the computational efficiency.

[0036] The final output is returned to the time-space domain through an inverse Fourier transform (IFFT):

[0037] ;

[0038] After this series of transformations, the model can better understand the global spatial characteristics of internal waves and retain important long-distance dependency information.

[0039] S2-3: Channel Mixing Processing: This section focuses not on spatial dimensions but on the information interaction between different channels. Temperature (T), salinity (S), and flow velocity (U) have complex intrinsic relationships, and the model automatically learns these dependencies.

[0040] The mixing process is implemented by a shared MLP, and the formula is:

[0041] ;

[0042] The MLP here acts as an inter-channel attention mechanism, enabling better interaction of information between different physical variables.

[0043] S2-4: Multi-layer stacking and nonlinear mapping: The entire model is not a single layer, but rather a stack of multiple AFNO modules. Each layer includes a spatial blending and a channel blending operation. To increase the model's expressive power, a nonlinear activation function is added after each layer to enhance the model's ability to fit complex patterns.

[0044] The calculation form of each layer is as follows:

[0045] ;

[0046] in represents a local linear transformation. Represents the global characteristics of the internal wave obtained through the Fourier operation. By stacking layers, the model gradually extracts the spatiotemporal characteristics of the data and eventually learns the complex dynamics of the internal wave. Nonlinear activation function:

[0047] ;

[0048] S2-5: Output Reconstruction: The final step involves mapping the processed features back to the original spatial grid to generate the prediction X(t+Δt) for the next time step t+Δt. Specifically, the model reassembles the features of all patches back into a complete h×w grid. Then, a linear mapping layer transforms the high-dimensional features back to the physical dimensions of the input variables (i.e., temperature, salinity, and flow velocity). The resulting output is a new spatiotemporal distribution matrix that predicts the state of all internal wave characteristic variables at the next time step.

[0049] Splicing formula:

[0050] ;

[0051] in , spatial grid Since the tokens after AFNO processing are arranged according to their original spatial positions (row and column indices (i, j) correspond to grid positions), splicing only needs to keep the tensor structure unchanged and no explicit operations are required.

[0052] Mapping formula:

[0053] ;

[0054] in is the learnable weight matrix, is the bias vector.

[0055] Furthermore, the S3 includes:

[0056] S3-1: In the pre-training phase, the goal is single-step prediction (predict k+1 at input time k), and the L2 loss function is used to update the model parameters to achieve initial learning of the network;

[0057] S3-2: In the fine-tuning stage, to improve the accuracy of multi-step predictions, the model's predictions at time k+1 are used again as input to predict time k+2 (i.e., two-step iterative prediction). The model is trained using a mixed L1 and L2 loss function to enhance the model's robustness to outliers. The L1 and L2 loss functions are defined as follows:

[0058] ;

[0059] ;

[0060] in represents the true value, Represents the predicted value.

[0061] Furthermore, in S4: given the temperature, salinity, flow rate and other data at time k, the internal wave field at time k+1 is obtained through model prediction, and then the prediction result at time k+1 is iteratively used as input to continue predicting future times such as k+2, k+3..., thereby realizing the spatiotemporal prediction of multi-step internal wave characteristic fields.

[0062] Compared with the prior art, the advantages and beneficial effects of the present invention are:

[0063] This method leverages deep learning to rapidly predict internal solitary waves based on traditional numerical simulation data, significantly improving the efficiency of internal solitary wave prediction. Through multi-channel coupled learning and an iterative prediction strategy, internal wave field prediction achieves both high precision and high efficiency. Furthermore, by integrating high-resolution numerical model data, the consistency of model predictions with physical processes is ensured. This method achieves rapid, extended-range predictions of the characteristic fields of internal solitary waves in the ocean while maintaining low error and high correlation.

[0064] This method combines numerical model data with a high-resolution deep learning model, leveraging the collaborative nature of multiple physical quantities to improve prediction accuracy and significantly enhance computational efficiency. It can rapidly and extensively predict future multi-physical field information for internal waves. This method is suitable for applications such as real-time ocean internal wave monitoring and early warning, and can be widely used in technical fields such as marine environmental monitoring and early warning, intelligent ocean observation, and marine engineering safety. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 This is a flow chart for predicting the characteristic field information of the internal solitary wave in the present invention.

[0066] Figure 2 This is the visualization example data of the temperature field, salinity field, and east-west current velocity field in the model data.

[0067] Figure 3 This is the overall framework diagram of the Fourier neural operator FNO.

[0068] Figure 4 This is a schematic diagram of the framework of the FourCastNet model for predicting internal wave characteristic field information.

[0069] Figure 5 This is a schematic diagram of the model training, fine-tuning and prediction principles.

[0070] Figure 6 This is a demonstration diagram of the prediction results, which is a predicted example diagram of the internal wave east-west flow velocity characteristic field at 0:00 on April 9, 2024. From top to bottom are the true value, predicted value and error diagram.

[0071] Figure 7 This is the MAE, RMSE and ACC evaluation index result diagram in Example 2. DETAILED DESCRIPTION

[0072] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments, but the present invention is not limited to the following description of the specific embodiments.

[0073] Example 1:

[0074] A fast prediction method for internal wave characteristic field information based on deep learning, such as Figure 1 As shown, the following steps are included:

[0075] Step 1: Data Preparation and Preprocessing: Based on the target area to be predicted, a three-dimensional ocean model is constructed using high-resolution simulation to generate high-resolution characteristic data of internal solitary waves in the ocean. The input X(t) is a spatiotemporal matrix containing multiple internal wave characteristic variables, specifically temperature (T), salinity (S), and east-west current 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, i.e., the grid size of the divided ocean area; c represents the number of channels, a key variable for internal waves.

[0076] In this embodiment, the characteristic variables selected according to the model data include the temperature field, salinity field and east-west flow velocity field at a given water depth plane (e.g. Figure 2 (as shown). Spatially, the study area is divided into a grid of h × w, and temporally, data are recorded at a fixed time step (e.g., 1 hour). Data at each moment are first organized into a three-dimensional tensor of shape h × w × 3, where the three channels correspond to temperature, salinity, and east-west current velocity. This yields multiple continuous time samples of three-channel internal wave spatiotemporal data.

[0077] Before entering 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 standardized transformation:

[0078] ;

[0079] in: is the original value of the i-th sample; is the sample mean; is the sample standard deviation. Meanwhile, the time mean is introduced as an additional input feature to enhance the model's ability to model temporal trends. Normalization and time mean processing are calculated only on the training set to avoid information leakage.

[0080] Step 2: Model architecture design: Figure 3 The figure shows the structure of the deep learning prediction model based on AFNO. The model adopts the Vision Transformer concept to perform patch division and embedding on the input tensor. Specifically, the entire h×w grid is divided into several h p ×w p Each patch is flattened and mapped to a high-dimensional feature vector, and then the corresponding position encoding is added. The patch sequence processed in this way is used as the input of the Transformer model, effectively preserving the spatial position information.

[0081] The AFNO model is an improvement on the FNO (Fourier Neural Operator), a deep learning model specifically designed for solving partial differential equations (PDEs). FNO aims to efficiently approximate the solution of a PDE system by learning a mapping between input parameters and the solution space. The core concept of 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, global convolution in the spatial domain can be converted into a simple matrix multiplication in the frequency domain, significantly improving computational efficiency. 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.

[0082] like Figure 3Figure 1 shows the overall framework of this neural network architecture. After the input a(x) undergoes high-dimensional mapping through the neural network P, it passes through T Fourier layers, is processed by Q, and is ultimately restored to the output u(x). Figure 1(b) further reveals the internal structure of a single Fourier layer. When the input v(x) enters, it is first converted to the frequency domain via a Fourier transform. In the frequency domain, the model uses a linear transformation R to filter high-frequency modal information to enhance generalization. The data is then returned to the original space via an inverse Fourier transform (iFFT), and the residual is added to the bypassed features. The data is then nonlinearly mapped using an activation function to enhance the model's expressive power. This bypass structure, similar to the "skip" connections in ResNet, facilitates efficient information flow.

[0083] Fourier Operator solves the problem of kernel integration, and K is used to represent the kernel integration operator:

[0084] ;

[0085] Where K is the kernel integral operator that describes the global relationship between input and output. κ is the kernel function that depends on the input and the domain D.

[0086] The expression of Fourier transform is as follows:

[0087] ;

[0088] Then we can deduce:

[0089] ;

[0090] Thus, the Fourier integral operator can be written as

[0091] ;

[0092] Therefore, the Fourier neural operator is proposed to solve the integral term in operator learning. Combined with the following iterative relationship, the original input is added to the result of the frequency domain operation through the short-circuit connection of ResNet, and nonlinear mapping is performed through the activation function. The mathematical principle of the model can be expressed:

[0093] ;

[0094] in is a local linear transformation, σ is an activation function, and the output is restored to the target space through the dimensionality reduction operation u(x)=Q(vT(x)).

[0095] The improvements of the AFNO model over the FNO model are mainly reflected in the following aspects:

[0096] (1) Sparse operation

[0097] During the learning process, the neural network may capture a lot of irrelevant high-frequency noise. AFNO directly removes irrelevant frequency components through hard thresholding.

[0098] The sparsification is calculated as follows:

[0099] ;

[0100] in is the sparsification function, and λ is the sparsification threshold.

[0101] (2) Long position operation

[0102] AFNO uses a block diagonal weight matrix to mix frequency domain features, dividing the entire frequency domain features into multiple small blocks, and then processing each block separately. This can not only reduce the computational complexity, but also capture more detailed information in the local range.

[0103] The specific calculation is as follows:

[0104] ;

[0105] in is the number of blocks, is the weight of each block.

[0106] (3) Residual Connection

[0107] Finally, it is also necessary to ensure that the gradient can be propagated stably to ensure that the model is easier to train. AFNO uses a residual connection, which means that after performing frequency domain operations, the converted result is added to the original input to ensure that information is not lost during the transformation process.

[0108] The calculation is as follows:

[0109] ;

[0110] The figure below shows the FourCastNet model for predicting internal waves, which uses the AFNO model architecture.

[0111] exist Figure 4In the AFNO module, each module consists of a spatial mixing layer and a channel mixing layer. The spatial mixing layer uses a fast Fourier transform (FFT) to convert the input patch features into the frequency domain, performs a linear transformation on the frequency domain features, and applies a sparsification function to remove unimportant high-frequency components. The filtered spectrum is then converted back to the spatiotemporal domain using an inverse FFT (IFFT), thereby capturing the global spatial dependencies between patches. The channel mixing layer does not consider spatial dimensions but instead performs interactive fusion between channels. A shared multi-layer perceptron (MLP) is applied to the patch's channel vectors to enable information exchange between physical fields such as temperature, salinity, and flow velocity. Figure 3 The right side illustrates the operation of different models during the channel mixing stage: GFN multiplies each channel by a weight, FNO performs full matrix multiplication on all channels, and AFNO uses block-diagonal MLP plus soft thresholding for block-level channel mixing (shown in the figure as k blocks × MLP). Output reconstruction: After processing by multiple layers of AFNO modules, a high-dimensional feature representation is obtained for each patch. In the final step, the features of all patches are reassembled into the original h × w grid. The assembled high-dimensional features are converted back to physical quantity dimensions (temperature, salinity, current velocity, etc.) through the output linear mapping layer to generate the complete three-channel internal wave field prediction at the corresponding time (e.g., t + Δt). This output tensor is the predicted distribution of each physical quantity at the next time, describing the evolution of the internal solitary wave in the temperature, salinity, and current fields.

[0112] In this example, multiple AFNO modules are stacked layer by layer to form a deep network. Each layer incorporates the aforementioned spatial mixing and channel mixing operations, followed by a nonlinear activation function to enhance expressive power. By stacking these layers, the model can gradually extract the rich spatiotemporal characteristics of the internal solitary wave field and learn the complex dynamics of internal waves.

[0113] Step 3: Model training: According to the method of the present invention, Figure 5 As shown, the model training adopts a two-stage progressive strategy. In the pre-training stage, the goal is a single-step prediction: the input data set X(k) at time k is used, and the output is the predicted internal wavefield X̂(k+1) at time k+1. The mean squared error (L2 loss) is used as the optimization objective function. During the training process, historical data generated by a large amount of high-resolution numerical models is used for iteration to optimize the network parameters, so that the model can better fit the one-step evolution of the internal wavefield.

[0114] Step 4: Fine-tuning stage: In order to improve the accuracy of medium- and long-term predictions, iterative multi-step training is used. Specifically, the k+1 moment result predicted by the model in pre-training is used as input again to predict the k+2 moment; that is, training is performed in a way that inputs one step and continuously predicts 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 needs of longer sequences. Through two-stage training, the model has learned the co-evolution relationship between temperature, salinity and flow rate, so that it can maintain high accuracy in the subsequent prediction process. The definitions of L1 and L2 losses are as follows:

[0115] ;

[0116] ;

[0117] in represents the true value, Represents the predicted value.

[0118] Step 5: Prediction reasoning: Figure 4 As shown in the figure, after model training is complete, the prediction and inference phase begins. Given the observed or simulated data at the current time k, the model is fed with the predicted internal solitary wave characteristic field at time k+1. The predicted output at time k+1 is then fed back into the model, and through iterations, predictions are obtained for multiple future time periods, such as k+2, k+3, and so on. This iterative prediction mechanism enables the model to continuously output the internal wave field evolution at multiple future time periods in real-time applications.

[0119] Example 2:

[0120] This embodiment is actually verified using the method provided in Example 1. This implementation example uses one year of numerical simulation data for training, and selects data at a water depth of 50m. The internal solitary wave data from March 2023 to February 2024 is used as the training set, the internal solitary wave data from March 2024 is used as the validation set, and the internal solitary wave data from April 2024 is used as the test set. The time resolution is 1 hour, and the spatial resolution is 500m in the east-west direction and 1200m in the north-south direction. The longitude and latitude range covers 19°N-22.5°N and 115°E-121°E, the grid size is 336×1680, and the number of samples is approximately 8700. The data has good representativeness and adaptability.

[0121] The model evaluation formula in Example 1 is as follows:

[0122] ;

[0123] ;

[0124] ;

[0125] in is the true value, is the predicted value, is the total number of samples.

[0126] like Figure 6 As shown in the figure, the prediction element is the east-west velocity field, showing the results of the single-step iterative prediction of 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 of each step in this embodiment are as follows Figure 7 shown.

[0127] This method combines high-resolution internal wave numerical model data with the FourCastNet deep learning model, leveraging AFNO to efficiently capture long-range spatial dependencies and achieve rapid, high-precision prediction of internal solitary wave fields. Compared to traditional numerical simulations, the model's inference speed is significantly improved (FourCastNet has demonstrated a one-week forecast in just seconds), enabling rapid extended-range forecasts based on internal wave model data. In terms of prediction accuracy, the model's multi-channel collaborative learning and iterative strategy achieves excellent performance in metrics such as MAE, RMSE, and ACC, accurately reproducing the spatiotemporal distribution characteristics of internal solitary waves.

[0128] In summary, the present invention significantly improves the efficiency and accuracy of internal wave prediction, and provides a practical new tool for ocean internal wave research and application.

[0129] Although the above embodiment provides a detailed description of the present invention, it is only a part of the embodiments of the present invention, not all of the embodiments. Other embodiments can be obtained based on this embodiment without creativity, and these embodiments all fall within the scope of protection of the present invention.

Claims

1. A method for rapid prediction of internal wave characteristic field information based on deep learning, characterized in that: The following steps are involved: S1: Acquire high-resolution numerical model data and preprocess the data; S1 includes: S1-1: Use a high-resolution numerical model to obtain high-resolution multi-physical data of water temperature, salinity, and velocity fields of solitary waves in the target sea area, and construct a dataset containing samples at multiple time points; S1-2: Arrange the data at each moment and merge the temperature T, salinity S, and east-west flow velocity U channel into a three-dimensional tensor with the shape of h×w×3, where h is the height of the grid and w is the width of the grid; S1-3: Standardize the original data and calculate the mean and standard of the training set for each variable; S2: Construct a spatiotemporal 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, a multi-layer stacking and a nonlinear mapping; in S2: the spatial mixing layer uses fast Fourier transform (FFT) to convert the input patch features to 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 converted back to the spatiotemporal domain through inverse FFT to capture the global spatial dependency features between patches; the channel mixing layer performs interactive fusion between channels , a shared multi-layer perceptron (MLP) is applied to the channel vectors of the patch; the AFNO module uses block diagonal MLP plus soft thresholding for block-level channel mixing; output reconstruction: After processing by the multi-layer AFNO module, a high-dimensional feature representation of each patch is obtained, and then the features of all patches are reassembled into the original h×w grid; the spliced ​​high-dimensional features are converted back to physical quantity dimensions through the output linear mapping layer to generate the complete three-channel internal wave field prediction result at the corresponding moment, that is, the predicted distribution of each physical quantity at the next moment, completing the description of the evolution of internal solitary waves in the temperature, salinity and velocity fields; S3: A two-stage training strategy is used to optimize the performance of the AFNO-based spatiotemporal prediction network model to better enhance the model's ability to predict intra-wavelength time. S4: Predict the wave field data at the current moment based on the trained spatiotemporal prediction network model.

2. The method for rapid prediction of internal wave characteristic field information according to claim 1, characterized in that: The standardization process is as follows: for each variable, the mean μ and standard deviation σ of its training set are calculated and applied to the standardization transformation: ； in: 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: 。 3. The method for rapid prediction of internal wave characteristic field information according to claim 1, wherein: The process of predicting internal waves by the model constructed in S2 is: S2-1: Patch division and embedding: Divide the multi-channel spatiotemporal tensor into several h-sized p ×w p Patch area, flatten and high-dimensional linear mapping are performed on each patch to obtain Patch Embedding; at the same time, position encoding is superimposed to enable the model to perceive the relative position information of each patch in the overall grid; suppose the input image ; Image segmentation: ； in is the block size, ; Linear projection: ； Output Token tensor ;in Embedding dimensions for the model; S2-2: Spatial mixing processing: Use fast Fourier transform (FFT) to extract long-distance spatial dependencies; map the spatiotemporal features of each patch to the frequency domain: ； Use linear transformation R to filter frequency domain features: ； Sparsification function Indicates that the part with eigenvalue less than the threshold λ is set to zero; The final output is transformed back to the space-time domain through inverse Fourier transform: ； S2-3: Channel mixing processing: The mixing process is implemented by a shared MLP, and the formula is: ； S2-4: Multi-layer stacking and nonlinear mapping: The AFNO module adds a nonlinear activation function. The specific calculation form is as follows: ； in represents a local linear transformation, Represents the global characteristics of the internal wave obtained by Fourier operation; the nonlinear activation function: ； S2-5: Output reconstruction: The model will reassemble the features of all patches back into a complete The grid is then transformed through a linear mapping layer to transform the high-dimensional features back to the physical dimension of the input variable. Finally, the output is a new spatiotemporal distribution matrix that can predict the state of all internal wave characteristic variables at the next moment: Splicing formula: ； in , spatial grid ; Mapping formula: ； in is the learnable weight matrix, is the bias vector.

4. The method for rapid prediction of internal wave characteristic field information according to claim 1, wherein: The S3 includes: S3-1: In the pre-training phase, with single-step prediction as the goal, the L2 loss function is used to update the model parameters to achieve initial learning of the network; S3-2: In the fine-tuning stage, to improve the multi-step prediction accuracy, the model's prediction at time k+1 is used again as input to predict time k+2, and the L1 and L2 mixed loss functions are used for training to enhance the model's robustness to outliers. The L1 and L2 loss functions are defined as follows: ； ； in represents the true value, Represents the predicted value.

5. The method for rapid prediction of 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 time k+1 is obtained through model prediction, and then the prediction result at time k+1 is iteratively used as input to continue predicting future times k+2, k+3, and so on, ultimately achieving a multi-step spatiotemporal prediction of the internal wave characteristic field.

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