A storm surge artificial intelligence prediction method based on physical equation constraints

Abstract

The application discloses a storm surge artificial intelligence prediction method based on physical equation constraints and relates to the technical field of artificial intelligence storm surge prediction, and comprises the following steps: step 1, collecting multi-source data; step 2, data assimilation and preprocessing; step 3, realizing a machine learning calculation method of physical loss; step 4, constructing an artificial intelligence model jointly constrained by physics and data; step 5, using a random search algorithm to adjust hyperparameters, and further optimizing the model; and step 6, performing explainability analysis on a prediction process and results. The three control equations used for storm surge calculation are introduced into the machine learning model, the dependence on the training data volume is greatly reduced compared with a traditional data-driven intelligent prediction model, the trend of the change of the physical variables in the prediction process is analyzed, visual display and uncertainty analysis are performed, and the unexplainability problem of the artificial intelligence prediction model is solved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of artificial intelligence storm surge prediction, and particularly relates to a storm surge artificial intelligence prediction method based on physical equation constraint. BACKGROUND

[0002] The importance of storm surge prediction lies in early warning and prevention of disasters caused by storm surges, supporting emergency response and rescue work, protecting marine traffic and port safety, promoting scientific research and guiding tourism and coastal development planning; accurate storm surge prediction can help people make wise decisions and reduce the risk and loss caused by storm surges; however, storm surge prediction usually relies on complex numerical models to simulate ocean and atmospheric processes; these models need to consider sea water dynamics, ocean topography, wind field, pressure field and other factors, while also need to handle the interaction on different scales, which increases the complexity and uncertainty of the model.

[0003] Analysis of defects in prior art:

[0004] A. One of the traditional storm surge prediction methods is based on linear data mathematical statistical analysis and empirical prediction, which usually assumes that the change of storm surge is according to linear trend, however, the change of storm surge is usually nonlinear, affected by multiple complex factors such as wind speed, wind direction, tide, etc.; therefore, the linear method may not accurately capture the nonlinear change rule of storm surge, and can only fit and predict simple linear trend, but cannot adapt to the nonlinear and complex changes in storm surge; at the same time, the empirical method mainly relies on historical data for prediction; however, storm surges may be affected by climate change, sea level rise and other factors, and past data may not accurately reflect future conditions; therefore, the prediction results of the empirical method may have large uncertainty;

[0005] B. Numerical simulation method based on physical mechanism is the most commonly used traditional storm surge prediction method, which usually involves solving partial differential equations (PDEs) or large linear / nonlinear equation systems, the solution of these problems needs to be subdivided and iterated in space and time; with the increase of simulation scale (such as higher resolution, larger physical range or longer time step), the amount of calculation increases exponentially; for complex earth system models such as storm surge and wave, millions or even hundreds of millions of computing units may be needed to accurately simulate; different numerical methods or parameter selection will also lead to different simulation results, increasing the uncertainty of the results, and greatly increasing the workload of numerical prediction;

[0006] C. Machine learning methods based on big data are emerging prediction methods that have developed rapidly in recent years. Common methods include recurrent neural networks (RNN), convolutional neural networks (CNN), and ConvLSTM. Although a large number of studies and engineering practices have shown that this method performs well in the prediction task, there are still many problems. First, these models usually require a large amount of high-quality data for training. For marine forecasting, it is already difficult to obtain enough reliable historical data, and for storm surges that occur less frequently, the problem of insufficient training data is exacerbated. At the same time, since RNN, CNN and ConvLSTM models are all deep learning algorithms, the model network they construct is much more complex than the multi-layer perceptron (MLP). Their training requires higher performance computing resources, especially when dealing with two-dimensional marine elements in a larger field. This requires higher computing devices (such as GPUs, TPUs) and computing time, which limits the real-time application of the model. It is often a "black box" model, and it is difficult to explain its internal working principle and prediction results. This is an important disadvantage for fields that require explanation and analysis of the decision-making process (such as scientific research or safety-critical systems). At the same time, since this machine learning method is driven by big data and does not involve physical processes, its accuracy is lower than numerical models based on physical equation calculations, and the effective duration of the forecast is shorter. SUMMARY

[0007] To solve the problems in the prior art, the present application provides a storm surge artificial intelligence prediction method based on physical equation constraints, which aims to embed physical mechanisms into the multi-layer perceptron (MLP) of the machine learning algorithm to form a variant PINN (Physics-Informed Neural Networks). MLP has certain advantages over CNN, ConvLSTM, etc. in terms of task versatility, architecture flexibility, feature learning ability, task adaptability, and model interpretability. This model no longer relies solely on big data, but rather considers physical mechanisms more, greatly reducing training time and dependence on data. At the same time, compared to traditional empirical prediction methods, it can better predict the nonlinear and complex changes in storm surges, while also improving the explainability, accuracy, and effective duration of neural network predictions, reducing the uncertainty of the predictions. The prediction effect can meet the physical equation of the storm surge, making the model have certain transferability, and can be applied to non-training sea areas with slight training, reducing the calculation time of storm surge prediction.

[0008] To solve the problems in the prior art, the technical solution of the present application is as follows:

[0009] The storm surge artificial intelligence prediction method based on physical equation constraints comprises the following steps:

[0010] Step 1. Collection of multi-source data: Collect multi-source data from ocean satellites, ocean buoys, weather stations and global weather forecasting systems;

[0011] Step 2. Data assimilation and preprocessing: Use optimal interpolation data assimilation technology to fuse data from different sources, ensure the spatio-temporal consistency and accuracy of the data; clean the collected data, remove noise and outliers, and fill in missing data to ensure the integrity and quality of the data;

[0012] Step 3. Machine learning calculation method for physical loss: Implement and verify the calculation of 3 control equations for storm surge through Python, and prepare for the subsequent construction of neural network model (PINN) embedded with physical mechanism;

[0013] Step 4. Construction of artificial intelligence model jointly constrained by physics and data;

[0014] Step 5. Hyperparameter adjustment using random search algorithm for further optimization of the model;

[0015] Step 6. Explainability analysis of the prediction process and results.

[0016] Preferably, in step 1, the ocean satellite data includes sea surface height, sea surface wind field, sea wave height and air pressure; the ocean buoy data includes real-time storm surge water level data; the weather station and global weather forecasting system data includes wind speed, wind direction and air pressure.

[0017] Preferably, in step 2, the solution steps of optimal interpolation are as follows:

[0018] The initial estimate of the point to be fused is , is the observation value of the surrounding area, is the initial estimate corresponding to the observation point, then the fusion value of the point is written as:

[0019] ;

[0020] When the following conditions are met, the error variance of the analysis value is minimized:

[0021] ;

[0022] Take as , then write as:

[0023] ;

[0024] that is ;

[0025] ;

[0026] ;

[0027] in, For background error cocorrelation, For observation error cocorrelation, for The ratio of the standard deviation of the point observation error to the standard deviation of the initial estimate error. To analyze the error cocorrelation between the analysis point and the initial estimated field.

[0028] Preferably, in step 3, the three governing equations are as follows:

[0029] (1);

[0030] (2);

[0031] (3);

[0032] Formulas (1), (2), and (3) are the continuity equations used in the physical method of storm surge calculation, respectively. For the directional momentum equation, Here is the equation for directional momentum; where, Indicates water depth; Coulomb coefficient, It is the acceleration due to gravity; , They are respectively and Sea surface wind stress in the direction of the wind; and They are respectively , Wave radiation stress gradient; It is the Xie Cai coefficient.

[0033] Preferably, in step 4, MLP is selected as the main body of the intelligent forecasting model, and the specific steps are as follows:

[0034] (a) Data splitting: The collected and processed data is split, with 80% used for model training, 10% as a validation set, and 10% as a test set;

[0035] (b) Normalize the inputs of different orders of magnitude. The normalization formula is as follows:

[0036] ;

[0037] in, It is the raw data. and These are the minimum and maximum values ​​in the dataset, respectively. It is normalized data;

[0038] (c) Design the network architecture: Set the number of nodes in the input layer to be equal to the number of features, select the number of hidden layers and the number of nodes in each layer, set the activation function between hidden layers, and set the number of nodes in the output layer; use the L-BFGS (Limited-memory Broyden-Fletcher-Goldfarb-Shanno) optimizer, which is suitable for handling large-scale unconstrained optimization problems.

[0039] (d) Multi-loss fusion processing: Using loss weight optimization methods to process the data loss generated during model training. Loss corresponding to the three governing equations , , The total loss from the fusion The losses are calculated using MSE, and the formula for calculating the losses is as follows:

[0040] ;

[0041] ;

[0042] ;

[0043] ;

[0044] ;

[0045] ;

[0046] in, , These represent the increase or decrease of water at time 𝑖. The actual and predicted values; Indicates the forecast duration; Indicates water depth; Coulomb coefficient, It is the acceleration due to gravity; , They are respectively and Sea surface wind stress in the direction of the wind; and They are respectively , Wave radiation stress gradient; It is the Xie Cai coefficient. , These represent the magnitude of each loss and its weight in the overall trend;

[0047] (e) Network training: Set an early stopping mechanism during model training to improve training efficiency, that is, stop training when the loss of three consecutive validation sets does not decrease.

[0048] Preferably, in step 5, a random search algorithm is used to adjust hyperparameters to optimize model parameters, and the search strategy is as follows:

[0049] (a) Determine the search space for network parameters;

[0050] (b) Random sampling based on the given hyperparameter interval probability;

[0051] (c) Substitute the hyperparameter sampling results obtained in (b) into the prediction model; repeat the operation n times without resampling, and record the model's effect each time;

[0052] (d) Compare the effects of each model, discard the combination with large error, and keep the combination with small error. Finally, we get the hyperparameter scheme with better model performance in the search space.

[0053] Preferably, step 6 includes: visualizing storm surge elements to intuitively observe whether the prediction results of PINN are reasonable; comparing the prediction results of PINN with traditional physical models, analyzing the differences between the two, and verifying whether PINN can reasonably simulate physical processes; and quantifying the uncertainty of the model output through different training sets or model architectures to evaluate the credibility of the prediction results.

[0054] The storm surge artificial intelligence forecasting method based on physical equation constraints of the present invention has the following beneficial effects:

[0055] 1. Lightweight intelligent forecasting was achieved by using machine learning algorithms, and randomized algorithms were used to optimize network parameters, enabling the forecasting model to simulate the nonlinear and complex changes of storm surge processes;

[0056] 2. By incorporating existing multi-source datasets into the forecast model of this invention, and employing a dual-driven approach of physics and data for training and forecasting, the computation time is significantly reduced, the computational resource requirements are lowered, and the reliability of the forecast results is improved compared with traditional numerical simulation methods.

[0057] 3. By incorporating the three governing equations used in storm surge calculations into the machine learning model, the dependence on the amount of training data is greatly reduced compared to traditional data-driven intelligent forecasting models; the changing trends of physical variables in the forecasting process are analyzed, visualized, and uncertainty is analyzed, thus solving the problem of the uninterpretability of artificial intelligence forecasting models. Attached Figure Description

[0058] Figure 1 This is a technical roadmap of the present invention. Detailed Implementation

[0059] The following description provides a detailed explanation of the embodiments of the present invention in a step-by-step manner. This description is only a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0060] In the description of this invention, it should be noted that the terms "upper," "lower," "left," "right," "top," "bottom," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or a specific orientational structure and operation. Therefore, they should not be construed as limiting this invention.

[0061] In the initial embodiment, the present invention provides an artificial intelligence forecasting method for storm surge based on physical equation constraints, such as... Figure 1 As shown, it includes the following steps:

[0062] Step 1. Collection of multi-source data: Collect multi-source data from ocean satellites, ocean buoys, weather stations, and global weather forecasting systems;

[0063] Step 2. Data Assimilation and Preprocessing: Optimal Interpolation (OI) data assimilation technology is used to fuse data from different sources to ensure the spatiotemporal consistency and accuracy of the data; the collected data is cleaned to remove noise and outliers, and missing data is filled in to ensure the integrity and quality of the data;

[0064] Step 3. Implement the machine learning calculation method for physical loss: Implement and verify the three main control equations for storm surge calculation using Python, in preparation for the subsequent construction of a neural network model embedded with physical mechanisms (PINN);

[0065] Step 4. Constructing an artificial intelligence model constrained by both physics and data;

[0066] Step 5. Use a random search algorithm to tune hyperparameters and further optimize the model;

[0067] Step 6. Perform interpretability analysis on the forecast process and results.

[0068] In a further embodiment, such as Figure 1As shown, in step 1, the ocean satellite data includes: sea surface height, sea surface wind field, wave height and air pressure with wide coverage and high spatiotemporal resolution; the ocean buoy data includes: real-time storm surge increase and decrease data with high accuracy and timeliness; the meteorological station and global meteorological forecast system data include: wind speed, wind direction and air pressure.

[0069] In a further embodiment, such as Figure 1 As shown, the steps for finding the optimal interpolation in step 2 are as follows:

[0070] The initial estimate of the point to be merged is , These are observations from the surrounding area. Given the initial estimate for the observation point, the fusion value for that point is written as:

[0071] ;

[0072] when The variance of the analysis values ​​is minimized when the following conditions are met:

[0073] ;

[0074] Will Considered ,So As written as:

[0075] ;

[0076] Right now ;

[0077] ;

[0078] ;

[0079] in, For background error cocorrelation, For observation error cocorrelation, for The ratio of the standard deviation of the point observation error to the standard deviation of the initial estimate error. To analyze the error cocorrelation between the analysis point and the initial estimated field.

[0080] In a further embodiment, such as Figure 1 As shown, in step 3, the three governing equations are as follows:

[0081] (1);

[0082] (2);

[0083] (3);

[0084] Formulas (1), (2), and (3) are the continuity equations used in the physical method of storm surge calculation, respectively. For the directional momentum equation, Here is the equation for directional momentum; where, Indicates water depth; Coulomb coefficient, It is the acceleration due to gravity; , They are respectively and Sea surface wind stress in the direction of the wind; and They are respectively , Wave radiation stress gradient; It is the Xie Cai coefficient.

[0085] In a further embodiment, such as Figure 1 As shown, in step 4, because the machine learning framework based on Multilayer Perceptron (MLP) is more flexible than that based on Convolutional Neural Network (CNN), different layers of network architecture can be designed as needed, including fully connected layers, activation functions, regularization layers, etc., and the number of layers can be freely combined and adjusted to adapt to the needs of specific tasks. Furthermore, MLP can improve the interpretability of the model in certain situations through appropriate design and analysis methods. Therefore, MLP is chosen as the main body of the intelligent prediction model. The specific steps are as follows:

[0086] (a) Data splitting: The collected and processed data is split, with 80% used for model training, 10% as a validation set, and 10% as a test set;

[0087] (b) Normalize the inputs of different orders of magnitude. The normalization formula is as follows:

[0088] ;

[0089] in, It is the raw data. and These are the minimum and maximum values ​​in the dataset, respectively. It is normalized data;

[0090] (c) Design the network architecture: Set the number of nodes in the input layer to be equal to the number of features, select the number of hidden layers and the number of nodes in each layer, set the activation function between hidden layers, and set the number of nodes in the output layer; use the L-BFGS (Limited-memory Broyden-Fletcher-Goldfarb-Shanno) optimizer, which is suitable for handling large-scale unconstrained optimization problems.

[0091] (d) Multi-loss fusion processing: Using loss weight optimization methods to process the data loss generated during model training. Loss corresponding to the three governing equations , , The total loss from the fusion The losses are calculated using MSE, and the formula for calculating the losses is as follows:

[0092] ;

[0093] ;

[0094] ;

[0095] ;

[0096] ;

[0097] ;

[0098] in, , These represent the increase or decrease of water at time 𝑖. The actual and predicted values; Indicates the forecast duration; Indicates water depth; Coulomb coefficient, It is the acceleration due to gravity; , They are respectively and Sea surface wind stress in the direction of the wind; and They are respectively , Wave radiation stress gradient; It is the Xie Cai coefficient. , These represent the magnitude of each loss and its weight in the overall trend;

[0099] (e) Network training: Set an early stopping mechanism during model training to improve training efficiency, that is, stop training when the loss of three consecutive validation sets does not decrease.

[0100] In a further embodiment, such as Figure 1 As shown, in step 5, a random search algorithm is used to adjust hyperparameters to optimize model parameters. The search strategy is as follows:

[0101] (a) Determine the search space for network parameters;

[0102] (b) Random sampling based on the given hyperparameter interval probability;

[0103] (c) Substitute the hyperparameter sampling results obtained in (b) into the prediction model; repeat the operation n times without resampling, and record the model's effect each time;

[0104] (d) Compare the effects of each model, discard the combination with large error, and keep the combination with small error. Finally, we get the hyperparameter scheme with better model performance in the search space.

[0105] In a further embodiment, such as Figure 1 As shown, step 6 includes: visualizing storm surge elements (such as water level distribution maps, flow velocity and direction maps, etc.) to intuitively observe whether the prediction results of PINN are reasonable; comparing the prediction results of PINN with traditional physical models (such as numerical simulation results), analyzing the differences between the two, and verifying whether PINN can reasonably simulate physical processes; and quantifying the uncertainty of the model output through different training sets or model architectures to evaluate the credibility of the prediction results.

[0106] In summary, this invention constructs an artificial intelligence forecasting method for storm surge based on physical equation constraints. It considers the fusion of storm surge physical equations with the machine learning algorithm Multilayer Perceptron (MLP). By introducing physical equation loss, the forecasting effect satisfies the physical mechanism, which improves the accuracy of the model, the effective forecast duration, and reduces the dependence on training data.

[0107] This invention aims to address the "black box" problem in machine learning models, namely, the lack of interpretability. By incorporating physical mechanisms, analyzing the model's prediction process and results, and conducting uncertainty analysis, the reliability, accuracy, and interpretability of machine learning algorithms are improved.

Claims

1. A storm surge artificial intelligence forecasting method based on physical equation constraints, characterized in that, Includes the following steps: Step 1. Collection of multi-source data: Collect multi-source data from ocean satellites, ocean buoys, weather stations, and global weather forecasting systems; Step 2. Data Assimilation and Preprocessing: Utilize optimal interpolation data assimilation techniques to fuse data from different sources, ensuring the spatiotemporal consistency and accuracy of the data; clean the collected data, remove noise and outliers, and fill in missing data to ensure data integrity and quality; Step 3. Implement the machine learning calculation method for physical loss: Implement and verify the three governing equations for storm surge calculation using Python, in preparation for the subsequent construction of a neural network model embedded with physical mechanisms (PINN); Step 4. Constructing an artificial intelligence model constrained by both physics and data; Step 5. Use a random search algorithm to tune hyperparameters and further optimize the model; Step 6. Perform interpretability analysis on the forecast process and results; In step 2, the steps for finding the optimal interpolation are as follows: The initial estimate of the point to be merged is , These are observations from the surrounding area. Given the initial estimate for the observation point, the fusion value for that point is written as: ； when The variance of the analysis values ​​is minimized when the following conditions are met: ； Will Considered ,So As written as: ； Right now ; ； ； in, For background error cocorrelation, For observation error cocorrelation, for The ratio of the standard deviation of the point observation error to the standard deviation of the initial estimate error. To analyze the error cocorrelation between the analysis point and the initial estimated field; In step 5, a random search algorithm is used to tune hyperparameters to optimize model parameters. The search strategy is as follows: (a) Determine the search space for network parameters; (b) Random sampling based on the given hyperparameter interval probability; (c) Substitute the hyperparameter sampling results obtained in (b) into the prediction model; repeat the operation n times without resampling, and record the model's effect each time; (d) Compare the effects of each model, discard the combination with large error, and keep the combination with small error. Finally, we get the hyperparameter scheme with better model performance in the search space.

2. The storm surge artificial intelligence forecasting method based on physical equation constraints as described in claim 1, characterized in that, In step 1, the ocean satellite data includes: sea surface height, sea surface wind field, wave height and air pressure; the ocean buoy data includes: real-time storm surge increase and decrease data; the meteorological station and global meteorological forecast system data include: wind speed, wind direction and air pressure.

3. The storm surge artificial intelligence forecasting method based on physical equation constraints as described in claim 2, characterized in that, in step 3, the three governing equations are as follows: (1)； (2)； (3)； Formulas (1), (2), and (3) are the continuity equations used in the physical method of storm surge calculation, respectively. For the directional momentum equation, Here is the equation for directional momentum; where, Indicates water depth; Coulomb coefficient, It is the acceleration due to gravity; , They are respectively and Sea surface wind stress in the direction of the wind; and They are respectively , Wave radiation stress gradient; It is the Xie Cai coefficient.

4. The storm surge artificial intelligence forecasting method based on physical equation constraints as described in claim 3, characterized in that, In step 4, MLP is selected as the main body of the intelligent forecasting model. The specific steps are as follows: (a) Data splitting: The collected and processed data is split, with 80% used for model training, 10% as a validation set, and 10% as a test set; (b) Normalize the inputs of different orders of magnitude. The normalization formula is as follows: ； in, It is the raw data. and These are the minimum and maximum values ​​in the dataset, respectively. It is normalized data; (c) Design the network architecture: Set the number of nodes in the input layer to be equal to the number of features, select the number of hidden layers and the number of nodes in each layer, set the activation function between hidden layers, and set the number of nodes in the output layer; use the L-BFGS optimizer, which is suitable for handling large-scale unconstrained optimization problems. (d) Multi-loss fusion processing: Using loss weight optimization methods to process the data loss generated during model training. Loss corresponding to the three governing equations , , The total loss from the fusion The losses are calculated using MSE, and the formula for calculating the losses is as follows: ； ； ； ； ； ； in, , They represent in Increase or decrease water level at any time The actual and predicted values; Indicates the forecast duration; Indicates water depth; Coulomb coefficient, It is the acceleration due to gravity; , They are respectively and Sea surface wind stress in the direction of the wind; and They are respectively , Wave radiation stress gradient; , These represent the magnitude of each loss and its weight in the overall trend; (e) Network training: Set an early stopping mechanism during model training to improve training efficiency, that is, stop training when the loss of three consecutive validation sets does not decrease.

5. The storm surge artificial intelligence forecasting method based on physical equation constraints as described in claim 4, characterized in that, Step 6 includes: visualizing storm surge elements to intuitively observe whether the prediction results of PINN are reasonable; comparing the prediction results of PINN with traditional physical models, analyzing the differences between the two, and verifying whether PINN can reasonably simulate physical processes; and quantifying the uncertainty of the model output through different training sets or model architectures to evaluate the credibility of the prediction results.

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