Two-dimensional wave spectrum intelligent forecasting method based on physical information neural network

Abstract

The invention discloses a two-dimensional wave spectrum intelligent forecasting method based on a physical information neural network, and belongs to the technical field of ocean information prediction.The two-dimensional wave spectrum intelligent forecasting method comprises the steps that basic data are collected, and the basic data comprise high-temporal-spatial-resolution sea surface wind field data and sea wave height data within the research range; historical sea wave data are obtained, ocean and meteorological data closely related to sea wave changes are integrated and processed, and a sea wave forecasting database is constructed; physical constraints are determined according to the sea wave forecasting database; an ANN neural network model is adopted as a basic model, physical constraints are added, the neural network meets the control equation of the mode, and a PINN physical information neural network is constructed; and carrying out interpretability analysis on the model forecasting process and result. According to the method, the sea wave dynamic process and the deep learning method are fused, interpretability is added for deep learning, and the black box problem of the deep learning method is solved.

Description

Technical Field

[0001] The present invention relates to the technical field of ocean information prediction, and particularly relates to a two-dimensional wave spectrum intelligent prediction method based on a physics-informed neural network. Background Art

[0002] China is a major ocean country, spanning dozens of latitudes, which has created its long coastline. The coastal areas of China are relatively economically developed, with a dense population, numerous ports and offshore platforms, frequent maritime activities, and are harassed by many marine disasters. The timeliness and accuracy of wave forecasting are of great significance for disaster prevention and mitigation, coastal engineering construction, offshore operations, ship navigation safety, etc. However, due to the complex causes of wave formation, involving many physical processes, and the strong nonlinearity of waves themselves, it is very difficult to accurately forecast sea waves.

[0003] Although traditional wave forecasting methods have played a certain role in wave forecasting, there are still certain limitations in the universality and accuracy in the forecasting area and different wave processes. As the current mainstream wave forecasting model, the solution of the numerical model is mainly based on the spectral action balance equation, which has problems such as large computational amount and non-convergence, and is difficult to solve in a short time. Corresponding to the numerical model is the deep learning forecasting method. As a new forecasting method, deep learning can solve the problems of large computational amount, high computational resource consumption, and poor prediction timeliness of the numerical model in wave forecasting. However, as a machine learning method, the prediction process of deep learning still does not get rid of the black box effect of machine learning methods, cannot explain the principle of its forecasting, and ignores the relevant physical mechanisms in the wave generation process. The above reasons make the forecasting of deep learning models have high requirements for the quantity and quality of training data, there is a time lag in the forecasting results, insufficient learning ability for wave extreme values, and poor generalization ability, which limits its practical application. Summary of the Invention

[0004] The present invention provides a two-dimensional wave spectrum intelligent prediction method based on a physics-informed neural network, aiming to improve problems such as large computational resource consumption and long calculation time in numerical model forecasting, while reducing the dependence of the neural network model on the data volume, improving the time lag of intelligent forecasting and the poor prediction effect of extreme values; by integrating the control equation (spectral action equation) of the sea wave numerical model into the loss function of the neural network to construct a physics-informed neural network, improving the timeliness, accuracy and interpretability of intelligent forecasting. By integrating the sea wave dynamic process with the deep learning method, adding interpretability to the deep learning and overcoming the black box problem of the deep learning method. By introducing physical mechanisms, solving the problems of large demand for training data by deep learning and insufficient learning ability for extreme values.

[0005] A two-dimensional wave spectrum intelligent prediction method based on a physics-informed neural network provided by the present invention adopts the following technical solutions:

[0006] In a first aspect, the present invention provides a two-dimensional wave spectrum intelligent prediction method based on a physics-informed neural network, including the following steps:

[0007] Collect basic data, where the basic data includes sea surface wind field data and wave height data with high spatio-temporal resolution within the research scope;

[0008] Obtain historical wave data, integrate and process ocean and meteorological data closely related to wave changes, and construct a wave prediction database;

[0009] Determine physical constraints according to the wave prediction database;

[0010] Use an ANN neural network model as the basic model, add physical constraints to make the neural network satisfy the control equation of the pattern, and construct a PINN physics-informed neural network;

[0011] Conduct an interpretability analysis on the model prediction process and results.

[0012] Further, the step of determining physical constraints according to the wave prediction database specifically includes:

[0013] Call the WAVEWATCH-III numerical model;

[0014] Convert the spectral action balance equation in the WAVEWATCH-III numerical model to spherical coordinates defined by longitude λ and latitude φ and retain the local variance:

[0015]

[0016] Among them, N represents the spectral action, t represents time, c g represents the wave speed, φ represents the latitude, λ represents the longitude, θ represents the direction, k represents the wave number, σ represents the frequency, represents the component of the wave speed in the latitude direction, represents the component of the wave speed in the longitude direction, represents the component of the wave speed in the wave number direction, represents the component of the wave speed in the direction, represents the correction term of the component of the wave speed in the direction propagating along the great circle, R represents the radius of the earth, k represents the wave number vector, d_avg represents the water depth, U represents the flow velocity, s represents the coordinate consistent with the θ direction, and m is the coordinate perpendicular to s, U φ and U λ respectively represent the tidal current directions in the φ and λ directions, S represents the source function term, and rewrite (1) as:

[0017]

[0018] Taking f as the physical constraint of the equation, and f tends to zero, which means that the spectral action balance equation in the numerical model is satisfied.

[0019] Furthermore, in the steps of constructing the physics-informed neural network, it specifically includes:

[0020] Randomly select single-point data as the training set. When selecting data, divide it into deep-water areas and shallow-water areas, and select the same number of points to ensure the universality of the model in deep water and shallow water;

[0021] From the relationship of equation (1), it can be obtained that the spectral action N is related to t, φ, λ, θ, k and the source term S, where t represents time, λ represents longitude, φ represents latitude, θ represents direction, and k represents wave number; the two-dimensional sea wave spectrum and the source term are output through the numerical model;

[0022] Split the prepared data, where 90% is used for model training, 5% is used as the validation set, and 5% is used as the test set;

[0023] Normalize the data to ensure that the contribution of each variable to the model result is consistent. The formula used for normalization is as follows:

[0024]

[0025] where, X is the original data, X min and X max are the minimum and maximum values in the dataset respectively, and X norm is the result of normalization;

[0026] Design the network architecture. The number of nodes in the input layer is equal to the number of input elements, and the number of nodes in the hidden layer and the hidden layer is determined according to the model test effect;

[0027] Design the model loss. The loss of a general neural network model includes the loss Loss _ξ between the model output and the true value. On this basis, add the loss Loss _pde of the physical equation, where Loss _pde is defined as:

[0028]

[0029]

[0030] Loss = Loss _ξ + Loss _pde (11)

[0031] Among them, Loss _pde represents the loss of the physical equation, and Loss _ξ represents the loss between the neural network output and the target value. Loss represents the total loss, and N t represents the total number of data. i represents the i-th data, ξ represents the target value, and ξ* represents the value of the neural network model;

[0032] Model training is carried out. During the model training process, a learning rate decay strategy and an early stopping mechanism are adopted. Among them, the learning rate decay strategy is adjusted according to the change of the training loss during the training process, and it is determined whether to stop early according to the change of the test loss during the test process.

[0033] Furthermore, the steps of performing interpretability analysis on the model prediction process and results specifically include:

[0034] Visualize the wave elements to verify whether the prediction results of PINN are reasonable;

[0035] Compare the prediction results of PINN with traditional physical models, analyze the differences between the two, and verify whether PINN can reasonably simulate the physical process;

[0036] Quantify the uncertainty of the model output through different training sets or model architectures to evaluate the credibility of the prediction results.

[0037] In summary, compared with the prior art, the beneficial effects of the above technical solutions are:

[0038] A two-dimensional wave spectrum intelligent prediction method based on a physics-informed neural network according to the present invention can introduce the control equation in the ocean wave numerical model as a loss into the neural network, use physical laws to constrain the neural network, and thus make the neural network model interpretable, overcoming the "black box" problem of the neural network model.

[0039] By introducing physical information, the dependence of the neural network on a large amount of data is solved, and at the same time, the problem of accurate prediction of unknown data by the neural network is solved. Integrating physical laws makes the intelligent prediction model interpretable. Analyzing the model prediction process and results analyzes the interpretability and uncertainty of the model, improving the reliability, accuracy, and interpretability of machine learning algorithms. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 is a schematic flow chart of a two-dimensional wave spectrum intelligent prediction method based on a physics-informed neural network according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0041] The present invention will be further described in detail below with reference to all the drawings.

[0042] An embodiment of the present invention discloses a two-dimensional wave spectrum intelligent prediction method based on a physics-informed neural network. Refer to Figure 1 , a two-dimensional wave spectrum intelligent prediction method based on a physics-informed neural network includes:

[0043] S101. Collect basic data.

[0044] Specifically, collect basic data, where the basic data includes sea surface wind field data and sea wave height data with high spatio-temporal resolution within the research scope; use devices such as remote sensing satellites and meteorological observation stations to collect data of ocean satellites, buoys, and meteorological forecasting systems within the research area, and then obtain sea surface wind field data with high spatio-temporal resolution within the research area. These data include key information such as wind speed and wind direction to reflect the spatio-temporal variation characteristics of the sea surface wind field. Through means such as wave observation buoys and radar monitoring, obtain sea wave height data. These data should have high spatio-temporal resolution to accurately reflect the wave conditions of the sea waves. The collected basic data provides important input information for sea wave prediction and helps to construct an accurate sea wave prediction model. Data with high spatio-temporal resolution can more precisely reflect the spatio-temporal variation characteristics of sea waves and improve the prediction accuracy.

[0045] S102. Obtain historical sea wave data.

[0046] Specifically, obtain historical sea wave data, integrate and process ocean and meteorological data closely related to sea wave changes, and construct a sea wave prediction database; obtain sea wave data from channels such as historical observation records and numerical simulation results, integrate and process ocean and meteorological data (such as wind speed, wind direction, air temperature, air pressure, temperature, humidity, wave height, wave direction, wave period, etc.) closely related to sea wave changes to form a unified data format and standard, and store the collected historical sea wave data and the integrated and processed ocean and meteorological data into the database to form a sea wave prediction database. Use numerical models such as SWAN, WAM, or WAVEWATCH-III for simulation to build a neural network training database.

[0047] S103. Determine physical constraints.

[0048] Specifically, according to the sea wave prediction database, determine physical constraints; according to the parameter settings of the numerical model used to establish the training database, analyze the physical mechanism of sea wave changes, including processes such as sea wave generation, propagation, and attenuation. According to the physical mechanism of sea wave changes, determine the main physical factors affecting sea wave changes, and accordingly establish corresponding physical constraint conditions. The constraint condition is the spectral action control equation. The introduction of physical constraint conditions enables the neural network prediction model to conform to the control equation to accurately reflect the physical process of sea wave changes. Through the limitation of physical constraint conditions, the demand for data volume by the neural network can be reduced, and the prediction accuracy of the neural network prediction model for unknown data can be improved.

[0049] S104. Construct a PINN (Physics-Informed Neural Network).

[0050] Specifically, an ANN (Artificial Neural Network) model is used as the basic model, and physical constraints are added to make the neural network satisfy the governing equations of the pattern, thereby constructing a Physics-Informed Neural Network (PINN for short); the ANN (Artificial Neural Network) is selected as the basic model, which has the advantages of high flexibility and fast efficiency. The network includes fully connected layers, regularization layers (optional), activation functions, etc. By adjusting the number of hidden layers, it can meet tasks of different complexities and has strong learning ability and non-linear mapping ability.

[0051] Physical constraints are added to the ANN model to enable the model to satisfy the physical laws of ocean wave changes. Specifically, an additional loss function can be added to the model, and the data in the ocean wave prediction database is used to train the model, and the parameters and structure of the model are adjusted to enable it to accurately predict the two-dimensional wave spectrum of ocean waves. The Physics-Informed Neural Network adds physical constraints on the basis of the neural network model, making the neural network conform to objective physical laws. Through the trained model, intelligent prediction of the two-dimensional wave spectrum of ocean waves can be realized, improving the accuracy and reliability of the prediction.

[0052] S105. Conduct interpretability analysis on the model prediction process and results.

[0053] Specifically, conduct interpretability analysis on the model prediction process and results. Analyze the input features of the model to understand which features have important impacts on the ocean wave spectrum prediction results, and use visualization tools to display the prediction results of the model, including parameters of ocean waves, two-dimensional wave spectra, etc. Explain the decision-making process of the model, including how the model makes predictions based on input features and the interpretability of the neural network model after adding physical information constraints. Interpretability analysis helps users better understand and trust the prediction results of the model. Through visualization display and explanation, users can more intuitively understand the fluctuation situation of ocean waves and the prediction results, providing support for decision-making.

[0054] In another embodiment, S103 specifically includes the following sub-steps:

[0055] Call the WAVEWATCH-III numerical model;

[0056] Convert the spectral action balance equation in the WAVEWATCH-III numerical model to spherical coordinates defined by longitude λ and latitude φ while retaining the local variance:

[0057]

[0058]

[0059] Among them, N represents the spectral action, t represents time, c g represents the wave speed, φ represents latitude, λ represents longitude, θ represents direction, k represents the wave number, σ represents the frequency, represents the component of the wave speed in the latitude direction, represents the component of the wave speed in the longitude direction, represents the component of the wave speed in the wave number direction, represents the component of the wave speed in the direction, represents the correction term for the component of the wave speed in the direction propagating along the great circle. R represents the radius of the Earth, k represents the wave number vector, d_avg represents the water depth, U represents the flow velocity, s represents the coordinate in the same direction as θ, and m is the coordinate perpendicular to s. U φ and U λ respectively represent the tidal current directions in the φ and λ directions. S represents the source function term. Rewrite (1) as:

[0060]

[0061] Taking f as the physical constraint of the equation, f tends to zero, that is, the spectral action balance equation in the numerical model is satisfied.

[0062] Specifically, in this embodiment, the WAVEWATCH-III numerical model is selected. WAVEWATCH-III is a third-generation ocean wave numerical model in the full spectral space developed by NOAA / NCEP of the United States. It has been recognized in the industry for its advantages of good stability, high calculation accuracy, and fast parallel speed. Selecting WAVEWATCH-III as the numerical model can ensure the accuracy and reliability of ocean wave forecasting. According to the data in the ocean wave forecasting database, the WAVEWATCH-III numerical model is run to simulate the generation, propagation, and dissipation processes of ocean waves. By adjusting the parameters and initial conditions in the model, ocean wave simulation results matching the observed data can be obtained. The WAVEWATCH-III numerical model can simulate the complex change process of ocean waves, determine the physical constraints, and provide a data basis for the training of the neural network. The results of the WAVEWATCH-III numerical model are compared with the observed data to verify the accuracy and reliability of the model.

[0063] In practical applications, the numerical simulation of the ocean wave model is generally applied to regions above the mesoscale. Therefore, the spherical coordinate spectral action balance equation defined by longitude and latitude coordinates is used to simulate ocean waves. The specific equation is shown in (1). Move all terms in equation (1) to the left side and set it as f, and the rewritten result is equation (7). Equation (7) is used as a physical constraint to make it tend to zero. The purpose of this step is to ensure that the physics-informed neural network can satisfy the physical laws of the spectral action balance equation during the training process. By rewriting the equation and determining the physical constraint, it can be ensured that the physics-informed neural network follows the physical laws of ocean wave changes during the training process. The introduction of the physical constraint helps to improve the stability and reliability of the ocean wave prediction model.

[0064] In another embodiment, S104 specifically includes the following sub-steps:

[0065] Randomly select single-point data as the training set. When selecting data, use the deep-water area and shallow-water area division, and select the same number of points to ensure the generality of the model in deep water and shallow water;

[0066] From the relationship in equation (1), the spectral action N can be obtained to be related to t, φ, λ, θ, k, and the source term S; where t represents time, λ represents longitude, φ represents latitude, θ represents direction, and k represents wave number; the two-dimensional ocean wave spectrum and the source term are output through a numerical model;

[0067] Split the prepared data, where 90% is used for model training, 5% is used as the validation set, and 5% is used as the test set;

[0068] Normalize the data to ensure that the contribution of each variable to the model result is consistent. The formula used for normalization is as follows:

[0069]

[0070] where X is the original data, X min and X max are the minimum and maximum values in the dataset respectively, and X norm is the result of normalization;

[0071] Conduct network architecture design. The number of nodes in the input layer is equal to the number of input elements, and the number of nodes in the hidden layer and the hidden layer is determined according to the model test effect;

[0072] Conduct model loss design. The loss of a general neural network model includes the loss Loss _ξ between the model output and the true value. On this basis, add the loss Loss _pde of the physical equation, where Loss _pde is defined as:

[0073]

[0074] Loss = Loss _ξ + Loss _pde (11)

[0075] Among them, Loss _pde represents the loss of the physical equation, Loss _ξ represents the loss between the neural network output and the target value, Loss represents the total loss, N t represents the total number of data, i represents the i-th data, ξ represents the target value, and ξ* represents the value of the neural network model;

[0076] Model training is carried out. During the model training process, a learning rate decay strategy and an early stopping mechanism are adopted. Among them, the learning rate decay strategy is adjusted according to the change of the training loss during the training process, and whether to stop early is determined according to the change of the test loss during the test process.

[0077] Specifically, single-point data is randomly selected from the wave forecasting database as the training set. When selecting data, deep water area and shallow water area are divided to ensure that the same number of points are selected in each area. This can ensure the universality of the model in deep water and shallow water environments. By randomly selecting and partitioning the data, the generalization ability of the model can be increased, enabling it to accurately predict waves under different water depth conditions.

[0078] According to the governing equations in the numerical model: clarify the relationship between the spectral action N and t (time), λ (longitude), φ (latitude), θ (direction), k (wave number), and the source term S. These relationships are used to obtain the two-dimensional wave spectrum and the source term through the output of a numerical model (such as WAVEWATCH-III). By clarifying the governing equations, it can be ensured that the physical information neural network follows the physical laws of wave changes during the training process.

[0079] The prepared data is split according to the ratio of 90% for training, 5% for validation, and 5% for testing. This can ensure that there is enough data for the model to learn during the training process, and at the same time, the performance of the model can be accurately evaluated during the validation and testing processes. Formula (8) is used to normalize the data to ensure that the contribution of each variable to the model result is consistent. Normalization can accelerate the training process of the model and help improve the accuracy of the model. Data splitting and normalization help ensure the stability and accuracy of the model during the training, validation, and testing processes.

[0080] The number of nodes in the input layer is equal to the number of input features, i.e., the number of variables such as t, φ, λ, θ, k, and the source term S. The number of hidden layers and the number of nodes in each layer are determined according to the model test results. By adjusting the number of hidden layers and the number of nodes, the performance of the model can be optimized. A reasonable network architecture design can ensure that the model has sufficient capacity to capture the complex characteristics of wave changes. Based on the loss of the general neural network model (i.e., the loss between the model output and the true value), the loss of the physical equation is added. The losses of the neural network are represented by formulas (9), (10), and (11), where formula (9) represents the loss of the physical equation, formula (10) represents the loss between the output of the neural network and the true value, and formula (11) represents the total loss of the neural network. By adding the loss of the physical equation, it can be ensured that the physics-informed neural network not only pursues the accuracy of data fitting during training but also follows the physical laws of wave changes.

[0081] During the model training process, the learning rate is dynamically adjusted according to the change of the training loss. When the training loss no longer decreases significantly, the learning rate is decreased to avoid overfitting of the model. During the testing process, if the test loss no longer decreases but increases for several consecutive times, the training is stopped to prevent overfitting of the model. The learning rate decay strategy and the early stopping mechanism help to ensure that the model does not overfit during the training process and improve the generalization ability of the model.

[0082] In another embodiment, S105 specifically includes the following sub-steps:

[0083] S105.1. Visualize the wave elements to verify whether the prediction results of the PINN are reasonable.

[0084] Specifically, visualize the wave elements to verify whether the prediction results of the PINN are reasonable; use professional visualization tools (such as TensorBoard, Graphviz, etc.) or programming libraries (such as matplotlib, seaborn, etc.) to draw graphs of wave elements (such as wave height, wavelength, wave speed, etc.). Compare the prediction results of the PINN with the visualization graphs and observe whether the prediction results are consistent with the actual change trends of the wave elements. By adjusting the visualization parameters (such as color, line thickness, legend, etc.), the graph can be made more clear and easy to understand, facilitating the verification of the rationality of the prediction results. The visualization graph can intuitively display the change trends of the wave elements, helping to quickly discover anomalies or unreasonableness in the prediction results. By comparing the prediction results with the visualization graph, it can be verified whether the prediction ability of the PINN is accurate, providing a basis for subsequent model optimization.

[0085] S105.2. Compare the prediction results of the PINN with traditional physical models.

[0086] Specifically, compare the prediction results of PINN with traditional physical models, analyze the differences between the two, and verify whether PINN can reasonably simulate physical processes; select appropriate traditional physical models (such as SWAN, WAM, and WAVEWATCH-III, etc.), compare the prediction results of numerical models and PINN, and analyze the accuracy of PINN forecasts. By comparing the prediction results of PINN and traditional physical models, the accuracy and reliability of PINN in simulating physical processes can be evaluated, and analyzing the differences between the two helps to discover potential problems in the simulation process of PINN, providing a direction for subsequent model improvement.

[0087] S105.3 Quantify the uncertainty of the model output to evaluate the credibility of the prediction results.

[0088] Specifically, quantify the uncertainty of the model output through different training sets or model architectures to evaluate the credibility of the prediction results. Use different training sets to train PINN, observe the prediction results and uncertainty changes of the model under different training sets, try different model architectures (such as multi-layer perceptron MLP, convolutional neural network CNN, etc.), compare the prediction performance and uncertainty of the model under different architectures, and introduce uncertainty quantification methods (such as Bayesian neural networks BNNs, model ensembles, etc.) to evaluate the uncertainty of the prediction results of PINN. By using different training sets and model architectures, the prediction performance and stability of PINN under different conditions can be evaluated. Introducing uncertainty quantification methods can more accurately evaluate the credibility of the prediction results and provide a more reliable basis for decision-making.

[0089] An embodiment of the present invention also discloses an intelligent terminal, which includes a memory and a processor. Among them, a computer program capable of being loaded and executed by the processor, such as a two-dimensional wave spectrum intelligent prediction method based on a physics-informed neural network as described above, is stored on the memory.

[0090] An embodiment of the present invention also discloses a computer-readable storage medium. A computer program capable of being loaded and executed by the processor, such as a two-dimensional wave spectrum intelligent prediction method based on a physics-informed neural network as described above, is stored in the computer-readable storage medium. The computer-readable storage medium includes, for example: various media that can store program codes such as USB flash drives, external hard drives, read-only memories (ROM), random access memories (RAM), magnetic disks, or optical discs.

[0091] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than limiting the protection scope of the invention. Obviously, the described embodiments are only partial embodiments of the present invention, rather than all embodiments. Based on these embodiments, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope to be protected by the present invention. Although the present invention has been described in detail with reference to the above embodiments, those of ordinary skill in the art can still, without conflict and without creative efforts, combine, add or delete the features in the embodiments of the present invention according to the circumstances or make other adjustments, so as to obtain different technical solutions that essentially do not deviate from the concept of the present invention, and these technical solutions also belong to the scope to be protected by the present invention.

Claims

1. A two-dimensional wave spectrum intelligent forecasting method based on physical information neural network, characterized in that: The following steps are involved: Collect basic data, including sea surface wind field data and wave height data with high temporal and spatial resolution within the research scope; Obtain historical wave data, integrate and process oceanographic and meteorological data closely related to wave changes, and build a wave forecast database; determining physical constraints according to the wave forecast database; The ANN neural network model is used as the basic model, physical constraints are added to make the neural network satisfy the control equation of the model, and the PINN physical information neural network is constructed; Conduct interpretable analysis on the model prediction process and results.

2. According to claim 1, a two-dimensional wave spectrum intelligent forecasting method based on physical information neural network is characterized in that: The step of determining the physical constraints according to the wave forecast database specifically comprises: Call WAVEWATCH-III numerical mode; The spectral action balance equation in the WAVEWATCH-III numerical model is converted to spherical coordinates defined using longitude λ and latitude φ while preserving the local variance: Where N is the spectral action, t is the time, c g represents wave speed, φ represents latitude, λ represents longitude, θ represents direction, k represents wave number, σ represents frequency, represents the component of wave velocity in latitude, represents the component of wave velocity in longitude, represents the component of wave velocity in wave number, represents the component of wave velocity in direction, represents the correction term for the component of wave velocity in the direction propagating along the great circle, R represents the radius of the earth, R represents the radius of the earth, k represents the wave number vector, d represents the average water depth, U represents the flow velocity, s represents the coordinate consistent with the direction of θ, m is the coordinate perpendicular to s, and U φ and U λ denote the tidal flow directions in the φ and λ directions respectively, S denotes the source function term, and (1) is rewritten as: Taking f as the physical constraint of the equation, f tends to zero, which satisfies the spectral action balance equation in the numerical model.

3. The two-dimensional wave spectrum intelligent forecasting method based on physical information neural network according to claim 1 is characterized in that: The steps of constructing the physical information neural network specifically include: Randomly select single-point data as the training set. When selecting data, use deep water partition and shallow water partition to select the same number of points to ensure the universality of the model in deep water and shallow water. From the relationship in equation (1), it can be obtained that the spectral action N is related to t, φ, λ, θ, k and the source term S, where t represents time, λ represents longitude, φ represents latitude, θ represents direction, and k represents wave number; the two-dimensional wave spectrum and source term are output through the numerical model; The prepared data is divided into 90% for model training, 5% as a validation set, and 5% as a test set; Normalize the data to ensure that the contribution of each variable to the model results is consistent. The formula used for normalization is as follows: Among them, X is the original data, X min and X max are the minimum and maximum values ​​in the data set, respectively, and X norm is the result of normalization; Design the network architecture, the number of nodes in the input layer is equal to the number of input elements, and the number of nodes in the hidden layer and hidden layer is determined according to the model test results; Design the model loss. The loss of a general neural network model includes the loss between the model output and the true value. ξ On this basis, add the loss of the physical equation Loss _pde , where Loss _pde Defined as: Loss=Loss _ξ +Loss _pde (11) Among them, Loss _pde Represents the loss of the physical equation, Loss _ξ Represents the loss of neural network output and target value, Loss represents the total loss, N t represents the total number of data, i represents the i-th data, ξ represents the target value, ξ * Represents the value of the neural network model; The model is trained. The learning rate reduction strategy and early stopping mechanism are adopted in the model training process. The learning rate reduction strategy is adjusted according to the changes in the training loss during the training process, and whether to stop early is determined according to the changes in the test loss during the test process.

4. The two-dimensional wave spectrum intelligent forecasting method based on physical information neural network according to claim 1 is characterized in that: The steps of performing interpretability analysis on the model prediction process and results specifically include: Visualize the wave elements to verify whether the prediction results of PINN are reasonable; Compare the prediction results of PINN with those of traditional physical models, analyze the differences between the two, and verify whether PINN can reasonably simulate the physical process; The uncertainty of the model output is quantified through different training sets or model architectures to assess the credibility of the prediction results.

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