A multiscale physically enhanced irregular sea wave prediction method

Abstract

The present application relates to the technical field of sea wave height prediction, and discloses a multiscale physical enhancement type irregular sea wave prediction method, comprising the following steps: (1) collecting marine wave historical data, preprocessing the data, and dividing the data into a training set, a verification set and a test set; (2) decomposing the wave data into three components of high, medium and low frequencies through wavelet decomposition; (3) constructing a WaveFormer model; (4) training the WaveFormer model; and (5) inputting the test set into the trained WaveFormer model to obtain a wave height prediction value. The present application decomposes the original wave sequence into three components of high, medium and low frequencies through two-layer stationary wavelet transformation, explicitly allows the model to capture the multiscale characteristics of irregular waves, ensures the rationality of wave prediction, realizes sequence-level prediction on the premise of ensuring prediction accuracy, improves the prediction efficiency, and constructs a data-driven item based on the wave prediction result, so that the model prediction accuracy is further improved.

Description

Technical Field

[0001] This invention relates to the field of ocean wave height prediction technology, and in particular to a multi-scale physical enhancement method for predicting irregular ocean waves. Background Technology

[0002] As a key external environmental factor affecting ship navigation safety, marine engineering structure stability, and nearshore infrastructure durability, changes in ocean waves have a wide and far-reaching impact on the design, operation, and maintenance of offshore engineering systems.

[0003] In actual sea conditions, wind waves and swells often overlap, and energy continuously transfers between different frequency bands. Wave elements such as wave height, wavelength, and period fluctuate constantly, often exhibiting highly irregular, nonlinear, and multi-scale evolutionary characteristics, significantly increasing the difficulty of prediction and assessment. Therefore, correctly understanding and mastering the long-term distribution patterns of wave elements and effectively predicting irregular waves is of great significance for the safety of offshore structures and cost savings.

[0004] Traditional sequence models include Long Short-Term Memory (LSTM) networks, gated recurrent units (GNUs), convolutional neural networks (CNNs), and deep neural networks. These data-driven methods utilize the approximation capabilities of neural networks to predict wave height. Numerical wave models include spectral models and Boussinesq models.

[0005] Because the above methods are insufficient in perceiving the multi-scale characteristics of waves, as well as the irregularity and strong nonlinearity of waves, they cannot achieve high-precision prediction. Summary of the Invention

[0006] This invention addresses the shortcomings of existing wave height prediction technologies by providing a multi-scale, physically enhanced irregular wave prediction method capable of high-precision prediction of irregular wave heights. This method is based on a physical information Transformer architecture—WaveFormer—for irregular wave prediction, solving the problems of lack of physical interpretation and insufficient perception of multi-scale features in current irregular wave prediction methods, as well as addressing the problem of high-precision wave prediction under low data requirements.

[0007] The multi-scale physically enhanced irregular ocean wave prediction method of this invention specifically includes the following steps:

[0008] (1) Collect historical ocean wave data, preprocess the data, and divide it into training set, validation set and test set;

[0009] (2) Wave data is decomposed into three components: high, medium and low frequency by wavelet decomposition;

[0010] (3) Construct the WaveFormer model, which includes the encoder containing the physical augmentation attention mechanism, the decoder containing the multi-layer fully connected feedforward network, and the loss layer containing the physical information-based neural network.

[0011] (4) Train the WaveFormer model by inputting the training set constructed in step (1) into the WaveFormer model for iterative training and optimizing the validation set constructed in step (1) to obtain the trained WaveFormer model.

[0012] (5) Feed the test set into the training WaveFormer model to obtain the wave height prediction value.

[0013] The above steps are further defined as follows.

[0014] In step (1), the ratio of the training set, validation set, and test set is 8:1:1.

[0015] The wavelet decomposition in step (2) consists of two levels of stationary wavelet transform. The first level decomposes the sequence into short-period perturbations. D The first layer consists of medium- and long-term disturbances, while the second layer decomposes these disturbances into mesoscale wind and wave characteristics. D 2 and long-term surge trends D 3.

[0016] The process of constructing the WaveFormer model in step (3) includes the following steps:

[0017] (a) Using the linear module in the encoder to process the short-period perturbation obtained in step (2) D 1. Mesoscale wind and wave characteristics D 2 and long-term surge trends D The three components are projected into a high-dimensional model space, and combined with position encoding and input embedding, spatial and temporal information is preserved.

[0018] (b) Pass the position-encoded and input-embedded data into the encoder;

[0019] (c) The encoded data is decoded by a decoder;

[0020] (d) The decoded data is processed through a loss layer to optimize the model (learnable parameters, weights, etc.);

[0021] The encoder containing the physical enhancement attention mechanism in step (3) includes a physical enhancement attention mechanism, a normalization module, a linear module, and a feedforward network module;

[0022] The physically enhanced attention mechanism includes a basic Transformer attention mechanism and a physical feature information matching mechanism. The basic Transformer attention mechanism is used to obtain the basic correlation between wave data, ensuring basic prediction performance (black box). The physical feature information matching mechanism is used to obtain the magnitude of the correlation between wave data at different times at the physical level (white box). The formula is as follows:

[0023] ;

[0024] ;

[0025] ;

[0026] Among them, head i Indicates the first i The attention of each head Q i Indicates the first i A query vector for each head. K i Indicates the first i A key vector for each head, where T denotes the transpose. V i Indicates the first i A vector of head values, where Softmax(·) represents the normalization function and mask(·) represents the masking function, used to mask future information during prediction to prevent data leakage and to mask data beyond 300 seconds from the current time. d k This represents the dimension of the corresponding key vector. P Wave and P Stokes This represents the physical feature information matching matrix, and Concat(·) represents the connection function. nheads This indicates the total number of heads; Multi-Head signifies multi-head attention. W o The weight matrix represents the mapping;

[0027] The normalization module is used to obtain the results of the physical augmented attention mechanism, normalize the feature distribution, reduce internal covariate bias, and improve the stability and generalization ability of model training.

[0028] The linear module is used to process the short-period perturbation obtained in step (2). D 1. Mesoscale wind and wave characteristics D 2 and long-term surge trends D The three components are projected onto a higher-dimensional model space;

[0029] The feedforward network module is used to independently perform nonlinear transformations at each location to enhance feature representation. This includes the ReLU function between three linear transformations and two linear transformations, as shown in the following formula:

[0030] ;

[0031] in, FFN (·) represents the feedforward network function. W 1. W 2 and W 3 represents the learnable weight matrix. b 1. b 2 and b 3 represents the learnable model parameters; the results of the feedforward network module are then normalized again to obtain the encoder output.

[0032] The physical feature information matching mechanism obtains the correlation between data by the physical properties of wave data at different times, including an acceleration similarity module obtained through the wave equation and a curvature nonlinear phase similarity module obtained through the third-order Stokes expansion.

[0033] The formula for the acceleration similarity module is as follows:

[0034] ;

[0035] ;

[0036] in, Indicates the first i At the [time]th moment j The acceleration characteristics of each component D i,j Indicates the first i At the [time]th moment j Each data component D i+1,j Indicates the first i+ 1st moment j Each data component D i-1,j Indicates the first i- 1st moment j One data component, Δ t Indicates the time interval of wave data. d a The dimension of the acceleration vector;

[0037] The formula for the curvature nonlinear phase similarity module is as follows:

[0038] ;

[0039] ;

[0040] in, P Indicated by curvature k and nonlinear phase The combined characteristic obtained by adding them together, where ζ represents the weights of the two balancing terms. d p The dimension of the eigenvector; curvature in the formula k and nonlinear phase The formula is as follows:

[0041] ;

[0042] ;

[0043] ;

[0044] in, or Indicates the Stokes wavefront. a j Indicates the first j The amplitude of each component, k j Indicates the first j The wavenumber of each component, oh j Indicates the first j The angular frequency of each component, x and t Representing spatial and temporal coordinates respectively. k i,j Indicates the first i At the [time]th moment j The curvature corresponding to each data component or i,j Indicates the first i At the [time]th moment j Wave height of each data component i,j Indicates the first i At the [time]th moment j The nonlinear phase corresponding to each data component.

[0045] The decoder containing the multilayer fully connected feedforward network in step (3) includes a multilayer fully connected feedforward network module and a wavelet inverse transform module;

[0046] The multi-layer fully connected feedforward network module is used to obtain the wave prediction results in wavelet decomposition form, and the inverse wavelet transform module is used to obtain the future wave sequence with the final predicted length, as shown in the following formula:

[0047] ;

[0048] ;

[0049] Among them, outputs FFN This represents the output of the multilayer fully connected feedforward network module, while encoder outputs represent the output of the model encoder. W 4. W 5 and W 6 represents the learnable weight matrix. b 4. b 5 and b 6 represents the learnable model parameters;

[0050] The inverse wavelet transform module consists of two levels of inverse wavelet transform, as shown in the following expression:

[0051] .

[0052] The loss layer in step (3) based on the physical information neural network includes the physical constraint term of the Korteweg-de Vries (KdV) equation considering the physical information neural network and the data-driven term based on the model prediction results;

[0053] The physical constraint terms of the Korteweg-de Vries (KdV) equations considering a physical information neural network are used to constrain the learning process, obtaining a solution that conforms to the nonlinear propagation law. It is assumed that the wave prediction result of the model is... u The formula for the physical constraint term is as follows:

[0054] ;

[0055] The part of the formula concerning the x-dimensional dimension is obtained through the traveling wave solution assumption:

[0056] ;

[0057] in, R KdV This represents the physical constraints of the loss layer. c Indicates wave speed. t Indicates time;

[0058] The data-driven term based on the model prediction results is used to obtain the direct difference between the prediction results and the corresponding true values, as shown in the following formula:

[0059] ;

[0060] in, R data This represents the data-driven term of the loss layer. D i Indicates the first i Real-time wave height data u i Indicates the firsti Time-based model predicts wave height data. L out Indicates the predicted length.

[0061] The loss function in the WaveFormer model training process mentioned in (4) is:

[0062] ;

[0063] in, R total This represents the total loss during one training iteration of the model. l 1 indicates the weight of the physical loss term. l 2 indicates the weight of the data-driven item.

[0064] Compared with the prior art, the present invention has the following beneficial effects:

[0065] This invention constructs a multi-scale physically-enhanced irregular wave prediction method. It employs a two-layer stationary wavelet transform to decompose the original wave sequence into three components: high-frequency, mid-frequency, and low-frequency, explicitly allowing the model to capture the multi-scale features of irregular waves. Unlike traditional attention mechanisms, the physically-enhanced attention mechanism guides the attention process towards physically consistent dependencies, ensuring the rationality of wave prediction. In the prediction stage, a fully connected feedforward network is designed as a decoder, achieving sequence-level prediction while maintaining prediction accuracy, thus improving prediction efficiency. During model training, a physical information neural network is used to add physical constraint terms to the loss layer, and data-driven terms are constructed based on wave prediction results, further improving the model's prediction accuracy. Attached Figure Description

[0066] Figure 1 This is a system schematic diagram of the present invention.

[0067] Figure 2 This is a structural diagram of the wavelet decomposition and information embedding layer in this invention.

[0068] Figure 3 This is a structural diagram of the encoder in which the physical enhancement attention mechanism is located in this invention.

[0069] Figure 4 This is a structural diagram of the decoder in this invention.

[0070] Figure 5 This is a structural diagram of the loss layer in this invention. Detailed Implementation

[0071] like Figure 1 As shown, the multi-scale physically enhanced irregular ocean wave prediction method of the present invention includes the following steps:

[0072] (1) Collect historical ocean wave data, preprocess the data, and divide the training, validation, and test sets.

[0073] The prediction dataset is divided into training, validation, and test sets in a ratio of 8:1:1.

[0074] (2) Wave data is decomposed into three components: high, medium and low frequency by wavelet decomposition.

[0075] like Figure 2 As shown, the wavelet decomposition used consists of two levels of stationary wavelet transform. The first level decomposes the sequence into short-period perturbations. D The first layer consists of medium- and long-term disturbances, while the second layer decomposes these disturbances into mesoscale wind and wave characteristics. D 2 and long-term surge trends D 3.

[0076] (3) Construct the WaveFormer model.

[0077] The WaveFormer model includes an encoder containing a physically enhanced attention mechanism, a decoder containing a multi-layer fully connected feedforward network, and a loss layer containing a physically based neural network.

[0078] like Figure 3 As shown, the encoder of the WaveFormer model includes a physically enhanced attention mechanism, a normalization module, a linear module, and a feedforward network module. Figure 4 As shown, the decoder includes a multi-layer fully connected feedforward network module and a wavelet inverse transform module. Figure 5 As shown, the loss layer includes physical constraint terms of the Korteweg-de Vries (KdV) equations that consider the physical information neural network and data-driven terms based on the model prediction results.

[0079] The process of building a WaveFormer model includes the following steps.

[0080] (a) Using a linear module to obtain the result from step (2) D 1. D 2. D The three components are projected into a high-dimensional model space, and combined with position encoding and input embedding, spatial and temporal information is preserved.

[0081] (b) The position-encoded and input-embedded data is fed into the encoder. The encoder's physically enhanced attention mechanism includes a basic Transformer attention mechanism and a physical feature information matching mechanism, such as... Figure 3As shown. The basic Transformer attention mechanism is used to obtain the correlation between basic wave data, ensuring basic prediction performance (black box); the physical feature information matching mechanism is used to obtain the correlation magnitude between wave data at different times at the physical level (white box). The formula is as follows:

[0082] ;

[0083] ;

[0084] ;

[0085] Among them, head i Indicates the first i The attention of each head Q i Indicates the first i A query vector for each head. K i Indicates the first i A key vector for each head, where T denotes the transpose. V i Indicates the first i A vector of head values, where Softmax(·) represents the normalization function and mask(·) represents the masking function, used to mask future information during prediction to prevent data leakage and to mask data beyond 300 seconds from the current time. d k This represents the dimension of the corresponding key vector. P Wave and P Stokes This represents the physical feature information matching matrix, and Concat(·) represents the connection function. nheads This indicates the total number of heads; Multi-Head signifies multi-head attention. W o This represents the weight matrix of the mapping.

[0086] The physical feature information matching mechanism obtains the correlation between wave data by examining the physical properties of wave data at different times. This includes an acceleration similarity module derived from the wave equation and a curvature and nonlinear phase similarity module derived from a third-order Stokes expansion. The formula for the acceleration similarity module is as follows:

[0087] ;

[0088] ;

[0089] in, Indicates the first i At the [time]th moment jThe acceleration characteristics of each component D i,j Indicates the first i At the [time]th moment j One data component, Δ t Indicates the time interval of wave data. d a This represents the dimension of the acceleration vector.

[0090] The formulas for curvature and nonlinear phase similarity modules are as follows:

[0091] ;

[0092] ;

[0093] in, P Indicated by curvature k and nonlinear phase The combined characteristic obtained by adding them together, where ζ represents the weights of the two balancing terms. d p This represents the dimension of the eigenvector. The formulas for curvature and nonlinear phase are as follows:

[0094] ;

[0095] ;

[0096] ;

[0097] in, or Indicates the Stokes wavefront. a j Indicates the first j The amplitude of each component, k j Indicates the first j The wavenumber of each component, oh j Indicates the first j The angular frequency of each component, x and t These represent spatial and temporal coordinates, respectively.

[0098] The normalization module, which yields the results of the physically enhanced attention mechanism, is used to normalize the feature distribution, reduce internal covariate bias, and improve the stability and generalization ability of the model training. The feedforward network module performs independent nonlinear transformations at each location to enhance feature representation, including the ReLU function between three linear transformations and two linear transformations, as shown in the following formula:

[0099] ;

[0100] in, FFN(·) represents the feedforward network function. W 1. W 2. W 3 represents the learnable weight matrix. b 1. b 2. b 3 represents the learnable model parameters. The results from the feedforward network module are then normalized to obtain the encoder output.

[0101] (c) The encoded data is decoded by a decoder.

[0102] like Figure 4 As shown, the multilayer fully connected feedforward network module is used to obtain the wave prediction results in wavelet decomposition form, and the inverse wavelet transform module is used to obtain the future wave sequence with the final predicted length, as shown in the following formula:

[0103] ;

[0104] ;

[0105] Among them, outputs FFN This represents the output of the multilayer fully connected feedforward network module, while encoder outputs represent the output of the model encoder. W 4. W 5. W 6 represents the learnable weight matrix. b 4. b 5. b 6 represents the learnable model parameters.

[0106] The inverse wavelet transform module also consists of two levels of inverse wavelet transform, as shown in the following expression:

[0107] .

[0108] (d) After decoding, the data is processed through a loss layer to optimize the model's learnable parameters, weights, etc., such as... Figure 5 As shown: The physical constraint term of the Korteweg-de Vries (KdV) equation in the physical information neural network is used to constrain the learning process, obtaining a solution that conforms to the nonlinear propagation law. The wave prediction result of the model is assumed to be... u The formula for the physical constraint term is as follows:

[0109] ;

[0110] The part of the formula concerning the x-dimensional dimension is obtained through the traveling wave solution assumption:

[0111] ;

[0112] in, R KdV This represents the physical constraints of the loss layer. c Indicates wave speed. t Indicates time.

[0113] The data-driven term based on the model prediction results is used to obtain the direct difference between the predicted results and the corresponding true values. The formula is as follows:

[0114] ;

[0115] in, R data This represents the data-driven term of the loss layer. D i Indicates the first i Real-time wave height data u i Indicates the first i Time-based model predicts wave height data. L out Indicates the predicted length.

[0116] (4) Train the WaveFormer model by inputting the training set constructed in step (1) into the WaveFormer model for iterative training and optimizing the validation set constructed in step (1) to obtain the trained WaveFormer model.

[0117] The loss function during the training of the WaveFormer model is:

[0118] ;

[0119] R total This represents the total loss during one training iteration of the model. l 1 indicates the weight of the physical loss term. l 2 indicates the weight of the data-driven item.

[0120] (5) Feed the test set into the trained WaveFormer model to obtain the wave height prediction value.

[0121] This invention selects four deep learning models to compare with its own model and calculates the Pearson correlation coefficient (R), root mean square error (RMSE), and standard deviation (SMR) of each model at 600 wave height acquisition test points. s As shown in Tables 1, 2, and 3, for ease of presentation, the results are displayed using average sampling at test points 120, 240, 360, 480, and 600. The results indicate that the predicted values ​​obtained by the model of this invention at all locations are closer to the observed values ​​than those of other models, demonstrating the best prediction performance.

[0122] Table 1. Results of R-index testing on the predictive performance of different models.

[0123]

[0124] Table 2. Results of testing the predictive performance of different models using the RMSE metric.

[0125]

[0126] Table 3 Different Models Used s Results of testing predictive performance using metrics

[0127] .

Claims

1. A multiscale physically enhanced irregular sea prediction method, characterized in that, The method comprises the following steps: (1) Collecting historical ocean wave data, preprocessing the data, and dividing the data into training set, validation set and test set; (2) Wavelet decomposition is used to decompose the wave data into three components of high, medium and low frequency; (3) A WaveFormer model is constructed, which comprises an encoder with a physical enhanced attention mechanism, a decoder with a multi-layer fully connected feedforward network, and a loss layer based on a physical information neural network; (4) The WaveFormer model is trained, the training set constructed in step (1) is input into the WaveFormer model for iterative training, the validation set constructed in step (1) is optimized, and a trained WaveFormer model is obtained; (5) The test set is input into the trained WaveFormer model to obtain the wave height prediction value; The wavelet decomposition in step (2) is two-layer stationary wavelet transform, the first layer decomposes the sequence into short-period disturbance D1 and medium-long-term disturbance, and the second layer decomposes the medium-long-term disturbance into medium-scale wind wave feature D2 and long-period swell trend D3; The process of constructing the WaveFormer model in step (3) comprises the following steps: (a) Projecting the short-period disturbance D1, medium-scale wind wave feature D2 and long-period swell trend D3 components obtained in step (2) into a high-dimensional model space, combining position encoding and input embedding to retain spatial and temporal information; (b) Passing the data with position encoding and input embedding into the encoder; (c) Decoding the encoded data through the decoder; (d) Optimizing the model through the loss layer after decoding the data; The encoder with a physical enhanced attention mechanism in step (3) comprises a physical enhanced attention mechanism, a normalization module, a linear module and a feedforward network module; The physical enhanced attention mechanism comprises a basic Transformer attention mechanism and a physical feature information matching mechanism; wherein the basic Transformer attention mechanism is used to obtain the correlation relationship between the basic wave data and ensure the basic prediction performance; the physical feature information matching mechanism is used to obtain the correlation size between the wave data at different times at the physical level; the formula is as follows: ； ； ； wherein head i denotes the attention of the i-th head, Q i denotes the query vector of the i-th head, K i denotes the key vector of the i-th head, T denotes the transpose, V i denotes the value vector of the i-th head, Softmax(·) denotes a normalization function, mask(·) denotes a mask function for masking future information to prevent data leakage and data outside 300 seconds from the current time, d k denotes the dimension of the corresponding key vector, Ψ Wave and Ψ Stokes denote the physical feature information matching matrix, Concat(·) denotes a connection function, nheads denotes the total number of heads, Multi-Head denotes multi-head attention, W o denotes the weight matrix of the mapping; The normalization module is used to obtain the physical enhanced attention mechanism result, standardize the feature distribution, reduce the internal covariate shift, and improve the stability and generalization ability of the model training; The linear module is used to project the short-period disturbance D1, medium-scale wind wave feature D2 and long-period swell trend D3 components obtained in step (2) into a high-dimensional model space; The feedforward network module is used for independent nonlinear transformation of each position to enhance feature expression, which comprises three layers of linear transformation and ReLU function between two layers of linear transformation, and the formula is as follows: ； Wherein, FFN(·) represents the feedforward network function, W1, W2 and W3 represent the learnable weight matrix, b1, b2 and b3 represent the learnable model parameters; the feedforward network module result is further normalized by the normalization module, and finally the encoder output is obtained.

2. The multiscale physically enhanced irregular sea prediction method of claim 1, wherein, The proportion of the training set, the validation set and the test set in the step (1) is 8:1:

1.

3. The multiscale physically enhanced irregular sea prediction method of claim 1, wherein, The physical feature information matching mechanism obtains the correlation between the data through the physical properties of the wave data at different times, including an acceleration similarity module obtained through a wave equation and a curvature nonlinear phase similarity module obtained through a third-order Stokes expansion formula; The acceleration similarity module formula is as follows: ； ； wherein, represents the acceleration feature of the jthcomponent at the ithmoment, D i,j represents the jthdata component at the ithmoment, D i+1,j represents the jthdata component at the ith+1moment, D i-1,j represents the jthdata component at the ith-1moment, Δt represents the wave data time interval, d a represents the dimension of the acceleration vector; The curvature nonlinear phase similarity module formula is as follows: ； ； where P represents a comprehensive feature obtained by adding the curvature K and the nonlinear phase f, ζ represents a weight for balancing the two terms, d p represents the dimension of the feature vector; the curvature K and the nonlinear phase f in the formula are as follows: ； ； ； where η denotes the Stokes wave front, a j denotes the wave amplitude of the jth component, k j denotes the wave number of the jth component, ω j denotes the angular frequency of the jth component, x and t denote the spatial and temporal coordinates, respectively, κ i,j denotes the curvature corresponding to the jth data component at the ith time, η i,j denotes the wave height of the jth data component at the ith time, ϕ i,j denotes the nonlinear phase corresponding to the jth data component at the ith time.

4. The multi-scale physically enhanced irregular sea prediction method of claim 1, wherein, The multilayer full-connection feedforward network in the step (3) is a decoder, including a multilayer full-connection feedforward network module and a wavelet inverse transform module; The multilayer full-connection feedforward network module is used to obtain the wave prediction result in the wavelet decomposition form, and the wavelet inverse transform module is used to obtain the future wave sequence of the final prediction length, and the formula is as follows: ； ； wherein the outputs FFN represent the outputs of the multi-layer fully connected feedforward network module, the encoder outputs represent the model encoder outputs, W4, W5, and W6 represent the learnable weight matrices, and b4, b5, and b6 represent the learnable model parameters; The wavelet inverse transform module is two-layer wavelet inverse transform, and the expression is as follows: 。 5. The multi-scale physically enhanced irregular sea prediction method of claim 1, wherein, The loss layer based on the physical information neural network in the step (3) includes a Korteweg-de Vries equation physical constraint term considering the physical information neural network and a data-driven term based on the model prediction result; The Korteweg-de Vries equation physical constraint term considering the physical information neural network is used to constrain the learning process to obtain a solution conforming to the nonlinear propagation law, and the wave prediction result of the model is u, and the physical constraint term formula is as follows: ； In the formula, the part about the x dimension is obtained through a traveling wave solution assumption: ； where R KdV represents the physical constraint term of the loss layer, c represents the wave speed, and t represents the time. The data-driven term based on the model prediction result is used to obtain the direct difference between the prediction result and the corresponding true value, and the formula is as follows: ； wherein R data represents the data-driven term of the loss layer, D i represents the real wave height data at the i-th moment, u i represents the model-predicted wave height data at the i-th moment, L out represents the prediction length.

6. The multi-scale physically enhanced irregular sea prediction method of claim 1, wherein, The loss function in the WaveFormer model training process in the step (4) is as follows: ； wherein R total represents the total loss of one model training, λ1 represents the physical loss term weight, and λ2 represents the data-driven term weight.

Images