Deep learning tide prediction method based on physical method constraint

Abstract

The invention discloses a deep learning tide prediction method based on physical method constraint, which comprises the following steps: collecting tide level data, and preprocessing the tide level data; carrying out tide harmonic analysis based on the tide level data to determine the amplitude and phase angle of partial tide; constructing a prediction model, determining a loss function based on a tidal harmonic analysis result, synthesizing an error of model prediction and an error of physical constraint, and training the prediction model through tidal level data; and carrying out tide prediction through the trained prediction model. According to the deep learning tide prediction method based on the physical method constraint, model output is constrained through the harmonic analysis result, non-physical understanding of pure data driving is avoided, and the physical consistency and reliability of the model are improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of tide forecasting, and in particular relates to a deep learning tide prediction method based on physical method constraints. Background Art

[0002] Tidal phenomena are the periodic rise and fall of Earth's oceans caused by the tidal forces of various celestial bodies. This natural phenomenon not only has a profound impact on marine ecosystems but also plays a vital role in navigation, fisheries, port operations, and coastal flood control. The formation of tides is closely related to the gravitational interaction between the Earth, Moon, and Sun, with the Moon's gravity being the primary factor causing tides. Because the Earth is a near-sphere and its various parts vary in distance and direction from tidal bodies, the magnitude and direction of tidal forces at different locations on the Earth's surface vary. This, in turn, causes the ocean water to deform periodically under the influence of these tidal forces, resulting in the tidal rise and fall. The periodic variation of tides is based on profound mechanical and astronomical principles, and their complex patterns make tidal forecasting a crucial topic in marine science.

[0003] Existing tidal forecasting methods mainly include tidal harmonic analysis, numerical simulation methods and machine learning models.

[0004] The tidal harmonic analysis method is based on the linear superposition principle of astronomical tidal components and predicts future tidal changes by analyzing historical tidal data. This method has a certain degree of accuracy when dealing with simple tidal phenomena, but its forecast accuracy is significantly insufficient under complex meteorological conditions. This is because the tidal harmonic analysis method ignores the influence of meteorological factors (such as wind speed, air pressure, and temperature) on tides and does not consider the nonlinear effects of tides. In practical applications, the influence of meteorological factors on tides cannot be ignored, especially in extreme weather conditions, where these factors can cause significant tidal changes, thus affecting the accuracy of forecasts.

[0005] Numerical simulation is another commonly used tidal forecasting method that relies on high-precision terrain and boundary condition data. This method simulates the physical process of tides by establishing complex mathematical models, which can take into account more physical factors and thus improve the accuracy of the forecast. However, the numerical simulation method also has obvious limitations. First, it requires a large amount of computing resources, has a large amount of calculations and poor real-time performance, making it difficult to meet the needs of real-time forecasting. Second, the numerical simulation method has extremely high requirements for the accuracy of the input data, and any slight error may lead to significant deviations in the forecast results. In practical applications, it is often very difficult to obtain high-precision terrain and boundary condition data, which further limits the scope of application of the numerical simulation method.

[0006] In recent years, machine learning models have been widely used in the field of tidal forecasting. These models predict future tidal changes by learning patterns from historical data, demonstrating a certain degree of adaptability and flexibility. However, machine learning models also face numerous challenges. First, these models rely on large amounts of historical data for training, and the quality and quantity of this data directly impact model performance. Second, machine learning models lack interpretability and struggle to provide clear physical explanations. Furthermore, machine learning models lack the constraints of physical laws and are prone to non-physical interpretations, resulting in forecasts that lack practical significance in certain situations. In extreme weather or data-sparse scenarios, the forecast errors of machine learning models increase significantly, making it difficult to meet the requirements of high-precision forecasts. Therefore, a new approach is needed to overcome the shortcomings of existing technologies and improve the accuracy and reliability of tidal forecasts. Summary of the Invention

[0007] The present invention provides a deep learning tide prediction method based on physical method constraints to solve the above-mentioned technical problems, specifically adopting the following technical solutions:

[0008] A deep learning tide prediction method based on physical method constraints, characterized by comprising the following steps:

[0009] Collect tide data and pre-process the tide data;

[0010] Tidal harmonic analysis is performed based on tide level data to determine the amplitude and phase angle of the tidal component;

[0011] Construct a prediction model, determine the loss function based on the results of tidal harmonic analysis, integrate the errors of model prediction and the errors of physical constraints, and train the prediction model using tide level data;

[0012] Tidal prediction is performed using the trained prediction model.

[0013] Furthermore, the specific method for preprocessing the tide level data is as follows:

[0014] The tide data are processed using sliding windows and normalized.

[0015] Furthermore, the size of the sliding window is 24 and the step size is 1.

[0016] Furthermore, the prediction model is a CNN-LSTM model that includes a convolutional neural network and a long short-term memory network. The convolutional neural network is used to extract local features in the data, and the long short-term memory network is used to capture long-term dependencies in the time series.

[0017] Furthermore, a weighted combination loss function is defined to perform a weighted summation of the model prediction error and the physical constraint error, and the weight coefficient is controlled by a parameter.

[0018] Furthermore, the loss function of the tidal water level prediction model is as follows:

[0019] Loss=λmodelloss+(1-λ)phyloss

[0020] Where modelloss is the loss function of the deep learning model, phyloss is the physical loss function, and λ is the weight coefficient:

[0021]

[0022] in, is the model prediction value, y i is the actual observed value, y phy is the harmonic analysis forecast value,

[0023]

[0024] Among them, A i represents the amplitude of the i-th tidal component, f i is the frequency of the i-th tidal component, g i is the initial phase, t is the time variable, and R(t) is the residual term, which represents the part of the observed data that is not explained by the tidal component.

[0025] Furthermore, when training the model, the range of the weight coefficient λ is [0.9, 1], the step size is 0.05, and the weight coefficient is controlled by the parameter.

[0026] Furthermore, the optimization algorithm used in model training is the Adam optimization algorithm.

[0027] Furthermore, the prediction results of tide prediction using the trained prediction model are converted back to the original data range through denormalization.

[0028] Furthermore, the prediction model performance was evaluated by root mean square error, mean absolute error, mean absolute percentage error, and coefficient of determination.

[0029] The benefit of the present invention lies in the deep learning tide prediction method based on physical method constraints, which constrains the model output by harmonizing the analysis results, avoids purely data-driven non-physical solutions, and improves the physical consistency and reliability of the model.

[0030] The deep learning tide prediction method based on physical method constraints provided by the present invention avoids the non-physical solution that may occur in pure data-driven models by introducing tidal harmonic analysis results as physical constraints, and significantly improves the forecast accuracy of the model under complex meteorological conditions. Especially in extreme weather scenarios, the forecast error of the model is significantly reduced, and tidal changes can be predicted more accurately. The introduction of physical constraints makes the forecast results of the model more consistent with the physical laws of tides and enhances the physical interpretability of the model. This not only helps scientists better understand tidal phenomena, but also provides a more reliable basis for practical applications.

[0031] The deep learning tidal prediction method based on physical constraints provided by this paper can adapt to different application scenarios by adjusting the weight coefficients, including data-rich and data-sparse scenarios, as well as tidal forecasting under extreme weather conditions. This flexibility enables the model to maintain high forecast accuracy under various conditions.

[0032] The deep learning tidal prediction method proposed in this paper, based on physical constraints, uses LSTM to jointly process tidal time series signals, improving feature characterization capabilities and enhancing the model's adaptability to complex data. This multi-source data fusion method can better capture the dynamic characteristics of tidal changes and improve forecast accuracy.

[0033] The model has demonstrated excellent performance in practical applications, providing highly accurate tidal forecasts for marine science research, port operations, fisheries, and coastal flood control. Comparing the forecast results with actual observational data allows for further optimization of model parameters, improving the accuracy and reliability of the forecast. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0035] Figure 1 is a schematic diagram of the deep learning tide prediction method based on physical method constraints of the present application;

[0036] Figure 2 It is a schematic diagram of the prediction situation of the prediction model of this application. DETAILED DESCRIPTION

[0037] The following describes embodiments of the present invention in detail. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to explain the present invention, but are not to be construed as limiting the present invention.

[0038] like Figure 1 The present invention shows a deep learning tide prediction method based on physical method constraints, which includes the following steps:

[0039] S1: Collect tide data and preprocess the tide data.

[0040] In this application, tide data from a station in Hangzhou Bay are used. The entire data processing process starts with reading the raw data, which is stored in an Excel file. First, multiple columns of data are converted into a single column to facilitate subsequent time series analysis. Then, the data is processed using sliding window technology, with the window size set to 24 and the step size set to 1, so that the data can be divided into multiple windows, each containing 24 consecutive data points. These window data will be used for model training and forecasting. In order to improve the stability of model training and the accuracy of forecasting, the data is normalized and the data values ​​are scaled to a range of 0 to 1. The processed data is divided into training set, validation set, and test set, and encapsulated by the data loader (DataLoader) so that the data can be efficiently loaded and iterated during the model training process.

[0041] In practical applications, data preprocessing is a key step in ensuring model performance. Sliding window techniques can effectively capture both short-term fluctuations and long-term trends in time series. Normalization helps accelerate model convergence and avoid training instabilities caused by differences in data dimensions. Furthermore, properly partitioning the dataset ensures that the model learns sufficient patterns during training and accurately assesses its generalization capabilities during validation and testing.

[0042] S2: Perform tidal harmonic analysis based on tide level data to determine the amplitude and phase angle of the tidal component.

[0043] Tidal phenomena are the periodic rise and fall of Earth's oceans caused by the gravitational forces of various celestial bodies. The complex patterns of these changes are rooted in profound mechanical and astronomical principles. Tidal harmonic analysis is an effective method for deconstructing and analyzing tides based on these principles. Tidal forces originate from the relative motion of the Earth, Moon, and Sun, and the resulting gravitational interactions. The Moon has the most significant influence on Earth's tides, although the Sun's gravitational influence is also significant. From a mechanical perspective, the tidal force experienced by any point on Earth's surface is the combined force of the gravitational forces of celestial bodies and the inertial centrifugal force generated by Earth's circular motion around the center of mass of the Earth-Moon (or Earth-Sun) system. Because Earth is a near-sphere and its various parts vary in distance and direction from the tidal bodies, the magnitude and direction of these tidal forces vary at different locations on the Earth's surface. This, in turn, causes the ocean waters to deform periodically under the influence of these tidal forces, resulting in the tidal rise and fall. These tidal forces are not simple force fields with a single frequency; they are composed of multiple components with varying periods, corresponding to different partial tides. Based on the laws of relative motion between celestial bodies and the mechanism of gravitational interaction, we can theoretically deduce the existence of numerous partial tides. For example, the Moon's average orbital period around Earth is approximately 27.32 days (a sidereal month). However, due to factors such as Earth's simultaneous rotation and the angle between the Moon's orbital plane and Earth's equatorial plane, the tidal effects of the Moon's gravitational force on Earth exhibit a variety of different periodicities. Semidiurnal partial tides, such as the M2 partial tide, are the most typical. Their generation is closely related to the periodic variations of the Moon's gravitational force on Earth's surface, with a period of approximately 12 hours and 25 minutes (this is the period of this partial tide observed at a fixed location on Earth, after accounting for factors such as Earth's rotation and the Moon's revolution). From a tidal perspective, the Moon's gravitational force on Earth's oceans reaches two peaks, causing the sea water to rise and fall, approximately every 12 hours and 25 minutes, resulting in this semidiurnal tidal period. Similarly, the solar tidal force also generates corresponding tidal components. The combined influence of the solar and lunar tidal forces creates complex tidal phenomena. For example, the K1 component of the diurnal tidal component, with a period of approximately 23 hours and 56 minutes, is primarily caused by the combined effects of Earth's rotation, the relative positions of the Moon and the Sun, and their combined tidal forces. In addition to the common semidiurnal and diurnal tidal components mentioned above, there are numerous other tidal components, such as the S2 component (also a semidiurnal tidal component, with a period of approximately 12 hours, primarily caused by solar tidal forces) and the O1 component (a diurnal tidal component, with a period of approximately 25 hours and 49 minutes, influenced by factors such as the specific angle of the lunar tidal force on the Earth's surface). Each component has its own unique tidal force generation mechanism and corresponding periodic characteristics. The combined effects of these tidal components contribute to the immense complexity and diversity of observed tidal phenomena.

[0044] Based on the above-mentioned formation principle of the tide and the periodic characteristics of tidal phenomena, tidal harmonic analysis uses the superposition principle of trigonometric functions to express the tidal water level changes as a linear combination of a series of harmonic functions, and constructs a corresponding mathematical model to describe tidal phenomena. The mathematical model of tidal harmonic analysis can be expressed as:

[0045]

[0046] Among them, H represents the water level, A i represents the amplitude of the i-th tidal component, f i is the frequency of the i-th tidal component, g i is the initial phase, t is the time variable, and R(t) is the residual term, which represents the part of the observed data that is not explained by the tidal component. The least squares method is used to determine the various parameters of the tidal component.

[0047] Tidal harmonic analysis not only helps us understand the physical nature of tidal phenomena but also provides an important theoretical foundation for tidal forecasting. By analyzing historical tidal data, the amplitude and phase angle of each component tide can be accurately determined, thereby constructing a physical model that reflects the laws of tidal water level changes. This method performs well when processing tidal data with obvious periodic characteristics and can effectively capture the main characteristics of tides. However, tidal harmonic analysis also has its limitations, especially when dealing with tidal changes under complex meteorological conditions, which may affect its accuracy. Therefore, combining tidal harmonic analysis with modern machine learning techniques can fully leverage the advantages of both and improve the accuracy and reliability of tidal forecasts.

[0048] S3: Construct a prediction model, determine the loss function based on the results of tidal harmonic analysis, integrate the errors of model prediction and physical constraints, and train the prediction model through tide level data.

[0049] The prediction model is a CNN-LSTM model that incorporates a convolutional neural network (CNN) and a long short-term memory (LSTM) network. The CNN is used to extract local features from the data. The LSTM is designed to capture long-term dependencies in time series. Through its internal gating mechanism (input gate, forget gate, and output gate), it selectively memorizes and forgets sequence information, effectively capturing dynamic patterns in time series. The CNN-LSTM model combines the advantages of both convolutional neural networks (CNN) and LSTM. First, a CNN is used to extract features from the data. The convolutional layer automatically learns the local features and spatial hierarchical structure in the data. The extracted feature sequence is then fed into the LSTM layer to further capture dependencies along the temporal dimension. Finally, a fully connected layer outputs the final forecast result.

[0050] The loss function is a mathematical expression used to quantify the difference between the model's prediction results and the true label, and it is at the core. It sets a clear optimization goal for model training. Based on this goal, the optimization algorithm minimizes the loss value by adjusting the model parameters, thereby improving the generalization ability of the model so that it can perform well on both training data and test data. During the model training phase, the model is first initialized, and the loss function and optimizer are defined. The loss function is the mean square error (MSE), which is used to measure the difference between the model's predicted value and the true value. In order to balance the model's predictive ability and the compliance with physical constraints, a weighted combination loss function is adopted to weight the sum of the model's predicted error and the physical constraint error, and the weight coefficient is controlled by the parameter number. The loss function of the tidal water level forecast model is as follows:

[0051] Loss=λmodelloss+(1-λ)phyloss

[0052] Where modelloss is the loss function of the deep learning model, phyloss is the physical loss function, and λ is the weight coefficient:

[0053]

[0054] in, is the model prediction value, y i is the actual observed value, y phy is the harmonic analysis forecast value,

[0055]

[0056] Among them, A i represents the amplitude of the i-th tidal component, f i is the frequency of the i-th tidal component, g i is the initial phase, t is the time variable, and R(t) is the residual term, which represents the part of the observed data that is not explained by the tidal component.

[0057] In the present invention, balancing the model prediction error and the physical constraint error is achieved by designing a weighted combination loss function. This loss function combines the model prediction error and the physical constraint error, and adjusts the relative importance of the two through a weight coefficient. Modelloss is the mean square error (MSE) between the model prediction value and the actual observation value, which is used to measure the prediction accuracy of the model. Physicalloss is the physical constraint error based on tidal harmonic analysis, which is used to ensure that the model's prediction results conform to the physical laws of the tide. The weight coefficient λ is used to balance the relative importance of the model prediction error and the physical constraint error.

[0058] Through this approach, the present invention achieves a good balance between model prediction accuracy and physical consistency. By introducing physical constraints, the non-physical interpretation that may occur in purely data-driven models is avoided, and the model's prediction accuracy under complex meteorological conditions is improved. The introduction of physical constraints makes the model's prediction results more consistent with the physical laws of tides, enhancing the model's physical interpretability. By adjusting the weight coefficients, the model can adapt to different application scenarios, including data-rich and data-sparse situations, as well as tidal forecasting under extreme weather conditions.

[0059] In summary, through the weighted combination of loss functions and experimental verification, the present invention can effectively balance the model prediction error and physical constraint error, thereby improving the accuracy and reliability of tidal forecasting.

[0060] In an embodiment of the present application, the optimizer adopts the Adam optimization algorithm to automatically adjust the model parameters to minimize the loss function. The training process includes multiple rounds. In each round, the model performs forward propagation on the training set to calculate the predicted value and calculate the loss, and then performs back propagation to calculate the gradient and update the model parameters. The model performance is evaluated on the validation set, and the validation loss is monitored. When the validation loss is lower than the historical minimum, the current model parameters are saved as the optimal model. During the training process, the training loss and validation loss of each round are recorded for subsequent analysis of the training process and performance of the model. And during the training process, the weight range is set to [0.9, 1], and the step size is 0.05 for experiments, and the weight with the best effect is selected. Then the optimal weight is used for retraining to obtain the tide forecast model to predict the tide level.

[0061] By introducing a loss function with physical constraints, the model of this invention not only learns patterns in the data but also ensures that the forecast results conform to the physical laws of tides. This approach, combining physical methods with deep learning, performs well when processing complex tidal data, significantly improving the accuracy and stability of forecasts, especially under extreme weather conditions. Furthermore, through fine-tuning of the optimization algorithm and multiple experimental verifications, the robustness and reliability of the model under different conditions are ensured.

[0062] In order to comprehensively and accurately evaluate the prediction performance of the model, the prediction model performance is evaluated by the root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE) and coefficient of determination (R 2 ) for evaluation.

[0063] The root mean square error (RMSE) is a commonly used indicator to measure the difference between the predicted value and the actual value. Its calculation formula is:

[0064]

[0065] Among them, y i represents the true value, represents the predicted value, and n represents the size of the time series. RMSE measures the magnitude of the overall error. It penalizes forecasts with larger deviations more severely and is therefore very sensitive to outliers. A smaller RMSE value indicates a smaller forecast error and better model performance.

[0066] The mean absolute error (MAE) measures the average of the absolute errors between the forecast value and the actual value. The calculation formula is:

[0067]

[0068] The symmetric mean absolute percentage error (SMAPE) measures the relative error between the forecast value and the true value and is expressed as a percentage. The calculation formula is:

[0069]

[0070] MAPE can intuitively display the relative size of the forecast error as a percentage, making it easier to compare forecast errors of data of different magnitudes. The smaller the MAPE value, the higher the forecast accuracy of the model.

[0071] Coefficient of determination (R 2 ) is the goodness-of-fit index of the regression model, which is used to measure the model's ability to explain changes in independent variables. Its calculation formula is:

[0072]

[0073] in, Represents the mean of the true values. R 2 It reflects the strength of the relationship between the forecast value and the actual value, and its value range is between 0 and 1. 2 The closer the value is to 1, the better the model fits the data and the higher the prediction accuracy; on the contrary, R 2 The closer the value is to 0, the worse the prediction performance of the model.

[0074] In summary, the smaller the values ​​of RMSE, MAE and MAPE, and the 2 The closer the value of is to 1, the smaller the model's forecast error and the higher the forecast accuracy. In this article, we will use these four indicators to comprehensively analyze the forecast results of this model and the comparison model to objectively evaluate the performance of each model.

[0075] After completing the model training, the test set is used to conduct the final performance evaluation of the model. The model is predicted on the test set to obtain the predicted value and the true value, such as Figure 2 By calculating the mean square error (MSE), root mean square error (RMSE), mean absolute error (MAE) and coefficient of determination (R 2 ) and other indicators to quantify the model's predictive performance, as shown in the following table. It can be seen that the best prediction effect is achieved when Number is 0.98.

[0076] Table 1 Prediction performance of the CNN-LSTM model in this application

[0077] Number MSE RMSE MAE <![CDATA[R 2 ]]> 0.9 0.001277 0.035742 0.032282 0.974821 0.905 0.001108 0.03329 0.030863 0.978157 0.91 0.00088 0.029669 0.026841 0.98265 0.915 0.001097 0.033116 0.03077 0.978385 0.92 0.000857 0.02928 0.026448 0.983103 0.925 0.001599 0.039988 0.037648 0.968483 0.93 0.001526 0.039068 0.037034 0.969917 0.935 0.00081 0.028464 0.025938 0.984031 0.94 0.001097 0.033115 0.030841 0.978386 0.945 0.000336 0.018328 0.015349 0.993379 0.95 0.000686 0.026196 0.023346 0.986474 0.955 0.000267 0.016329 0.013288 0.994744 0.96 0.00104 0.032242 0.029666 0.979511 0.965 0.000173 0.013145 0.010108 0.996594 0.97 0.000504 0.022457 0.019465 0.99006 0.975 0.000324 0.018014 0.014708 0.993604 0.98 0.00013 0.011384 0.008742 0.997446 0.985 0.000157 0.012513 0.009817 0.996914 0.99 0.000142 0.011908 0.009081 0.997205 0.995 0.000132 0.011484 0.008555 0.997401 1 0.000177 0.01332 0.01061 0.996503

[0078] S4: Tidal prediction using the trained prediction model.

[0079] To forecast future data, the data being forecasted undergoes the same preprocessing steps as the training data, including data format conversion and normalization. The trained model is then used to forecast the processed data, generating a forecast result. Finally, the forecast result is denormalized to convert it back to the original data range. The forecast result and the ground truth are then saved in an Excel file for subsequent analysis and visualization.

[0080] The model presented in this paper has demonstrated excellent performance in practical applications, providing highly accurate tidal forecasts for applications such as marine scientific research, port operations, fisheries, and coastal flood control. By comparing and analyzing the forecast results with actual observational data, model parameters can be further optimized, improving the accuracy and reliability of the forecast. Furthermore, saving the forecast results to an Excel file facilitates subsequent data analysis and visualization, providing strong support for relevant decision-making.

[0081] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the above embodiments do not limit the present invention in any form, and any technical solutions obtained by equivalent replacement or equivalent transformation fall within the scope of protection of the present invention.

Claims

1. A deep learning tide prediction method based on physical method constraints, characterized by: The following steps are involved: Collect tide data and pre-process the tide data; Tidal harmonic analysis is performed based on tide level data to determine the amplitude and phase angle of the tidal component; Construct a prediction model, determine the loss function based on the results of tidal harmonic analysis, integrate the errors of model prediction and the errors of physical constraints, and train the prediction model using tide level data; Tidal prediction is performed using the trained prediction model.

2. The deep learning tide prediction method based on physical method constraints according to claim 1 is characterized in that: The specific method for preprocessing tide data is as follows: The tide data are processed using sliding windows and normalized.

3. The deep learning tide prediction method based on physical method constraints according to claim 2 is characterized in that: The sliding window size is 24 and the step size is 1.

4. The deep learning tide prediction method based on physical method constraints according to claim 1 is characterized in that: The prediction model is a CNN-LSTM model that includes a convolutional neural network and a long short-term memory network. The convolutional neural network is used to extract local features in the data, and the long short-term memory network is used to capture long-term dependencies in time series.

5. The deep learning tide prediction method based on physical method constraints according to claim 1 is characterized in that: Define a weighted combination loss function, perform weighted summation of the model prediction error and the physical constraint error, and the weight coefficient is controlled by a parameter.

6. The deep learning tide prediction method based on physical method constraints according to claim 5 is characterized in that: The loss function of the tidal water level prediction model is as follows: Loss=λmodelloss+(1-λ)phyloss Where modelloss is the loss function of the deep learning model, phyloss is the physical loss function, and λ is the weight coefficient: in, is the model prediction value, y i is the actual observed value, y phy is the harmonic analysis forecast value, Among them, A i represents the amplitude of the i-th tidal component, f i is the frequency of the i-th tidal component, g i is the initial phase, t is the time variable, and R(t) is the residual term, which represents the part of the observed data that is not explained by the tidal component.

7. The deep learning tide prediction method based on physical method constraints according to claim 6 is characterized in that: When training the model, the weight coefficient λ ranges from [0.9, 1], with a step size of 0.05, and the weight coefficient is controlled by the parameter.

8. The deep learning tide prediction method based on physical method constraints according to claim 1 is characterized in that: The optimization algorithm used in model training is the Adam optimization algorithm.

9. The deep learning tide prediction method based on physical method constraints according to claim 1 is characterized in that: The prediction results of tide prediction using the trained prediction model are converted back to the original data range through denormalization.

10. The deep learning tide prediction method based on physical method constraints according to claim 1 is characterized in that: Prediction model performance was evaluated by root mean square error, mean absolute error, mean absolute percentage error, and coefficient of determination.

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