Ionospheric characteristic parameter prediction method based on physical information neural network

Abstract

The application belongs to the technical field of ionosphere space weather prediction, and discloses an ionosphere characteristic parameter prediction method based on a physical information neural network, which aims at the defects of incomplete data set fusion, non-systematic physical constraint selection, unreasonable input feature design, and non-optimized model structure for ionosphere data characteristics, so that the prediction accuracy and reliability are difficult to meet the actual application requirements, and proposes an ionosphere characteristic parameter prediction method which fuses multi-source observation data, systematically incorporates basic physical laws of the ionosphere as constraints, optimizes the model input features and the network structure, so as to improve the prediction accuracy and the generalization ability. The ionosphere characteristic parameter prediction method based on the physical information neural network effectively solves the problems of low prediction accuracy, poor generalization ability and insufficient response to extreme space weather of the existing method, and can realize accurate and efficient prediction of the ionosphere characteristic parameters.

Description

Technical Field

[0001] This invention belongs to the field of ionospheric space weather prediction technology, specifically relating to a method for predicting ionospheric characteristic parameters based on a physical information neural network. Background Technology

[0002] As the region with the highest degree of ionization in the Earth's atmosphere, the ionosphere's characteristic parameters (including the peak electron density of the F2 layer, the peak height of the F2 layer, the thickness of the top and bottom of the F2 layer, and the peak electron density of the E layer) directly affect the stability of shortwave communication links, navigation and positioning accuracy, and the operational safety of space probes. Accurately predicting these parameters is of great significance for space weather services.

[0003] Current methods for predicting ionospheric characteristic parameters are mainly divided into two categories: one is numerical models based on physical mechanisms. These models rely on the description of complex ionospheric physical processes. Although they can reflect the physical essence, they suffer from high computational complexity, delayed response to extreme space weather such as solar activity bursts and geomagnetic storms, and cumbersome parameterization processes. The other is prediction models based on traditional machine learning. These models rely on training with a large amount of observational data and can capture nonlinear relationships in the data. However, they lack the integration of basic physical laws of the ionosphere, resulting in a significant decrease in prediction accuracy and insufficient generalization ability in sparse data regions or under extreme conditions.

[0004] Physical Information Neural Networks (PINNs) incorporate physical laws as constraints into neural network training, balancing the flexibility of data-driven approaches with the rationality of physical mechanisms, thus providing a new technical path for solving the aforementioned problems. However, existing PINN-based methods for predicting ionospheric characteristic parameters suffer from shortcomings such as incomplete dataset fusion, unsystematic selection of physical constraints, unreasonable input feature design, and model structures not optimized for ionospheric data characteristics. These shortcomings result in prediction accuracy and reliability that fail to meet practical application requirements, especially under extreme solar flares and geomagnetic storms, making accurate prediction of ionospheric characteristic parameters difficult.

[0005] Therefore, there is an urgent need for a method to predict ionospheric characteristic parameters that integrates multi-source data, incorporates physical constraints into the system, and optimizes the model structure, so as to improve prediction accuracy and generalization ability. Summary of the Invention

[0006] The purpose of this invention is to propose a method for predicting ionospheric characteristic parameters based on a physical information neural network. This method solves the problems of low prediction accuracy, poor generalization ability, and insufficient response to extreme space weather in existing methods by fusing multi-source observation data, incorporating the basic physical laws of the ionosphere as constraints, and optimizing model input features and network structure. It can achieve accurate and efficient short-term prediction of ionospheric characteristic parameters.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: A method for predicting ionospheric characteristic parameters based on a physical information neural network includes the following steps: Step 1. Collect and preprocess data from ground-based ionospheric altimeters, COSMIC satellite data, and auxiliary data to construct a multi-source observation dataset; Step 2. Construct the Physical Information Neural Network (PINN) model, which includes an input layer, hidden layers, and an output layer; Step 3. Select the fundamental physical laws of the ionosphere as constraints, transform each constraint into a loss function term, and integrate them into the overall loss function of the model; Step 4. Train the PINN model based on the multi-source observation dataset constructed in Step 1 and the total loss function of the model obtained in Step 3 to obtain the trained PINN model; Step 5. Input the data to be predicted into the trained PINN model, and after inverse normalization and error correction of the predicted values ​​output by the model, obtain the prediction results of ionospheric characteristic parameters.

[0008] Furthermore, based on the above-mentioned method for predicting ionospheric characteristic parameters based on physical information neural networks, this invention also proposes a computer device, which includes a memory and one or more processors. The memory stores executable code, and when the processor executes the executable code, it implements the steps of the ionospheric feature parameter prediction method based on physical information neural networks mentioned above.

[0009] Furthermore, based on the aforementioned method for predicting ionospheric characteristic parameters using a physical information neural network, this invention also proposes a computer-readable storage medium storing a program thereon; when executed by a processor, this program is used to implement the steps of the aforementioned method for predicting ionospheric characteristic parameters using a physical information neural network.

[0010] The present invention has the following advantages: As described above, this invention relates to a method for predicting ionospheric characteristic parameters based on a physical information neural network. This method integrates ground-based ionospheric altimeter data and COSMIC satellite data, combined with auxiliary data such as solar activity index, geomagnetic activity index, and neutral wind field parameters, covering multiple influencing factors of ionospheric characteristic parameter changes. It solves the problems of sparse data and limited coverage of single data sources, and provides comprehensive and high-quality data support for model training.

[0011] Furthermore, the method of this invention selects the fundamental physical laws of the ionosphere as constraints, and integrates the Chapman function constraint, continuity equation constraint, electron generation rate constraint, electron loss rate constraint, and geomagnetic and electric field constraints into the training process of the PINN model. This ensures that the model output conforms to the laws of observation data and follows physical mechanisms, solving the problems of traditional machine learning models lacking physical constraints and having poor generalization ability. Especially under extreme conditions such as extreme solar flares and geomagnetic storms, the prediction method proposed in this invention can still maintain high prediction accuracy.

[0012] In addition, the method of this invention also designs a deep neural network structure suitable for the characteristics of ionospheric data. The PINN model adopts a combination of fully connected layers and batch normalization to capture the complex nonlinear relationships in ionospheric data. Through hyperparameter optimization and error correction, the prediction accuracy of the model is significantly improved. The average correlation coefficient between the predicted ionospheric characteristic parameters obtained by the method of this invention and the observed values ​​of ionospheric characteristic parameters in ground ionospheric altimeter data and COSMIC satellite data can reach more than 0.90. Attached Figure Description

[0013] Figure 1 This is a flowchart of the ionospheric feature parameter prediction method based on a physical information neural network in an embodiment of the present invention. Detailed Implementation

[0014] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments: Example 1 This embodiment describes a method for predicting ionospheric characteristic parameters based on a physical information neural network, applicable to the peak electron density NmF2 of the F2 ionosphere, the peak height hmF2 of the F2 ionosphere, and the thickness of the top of the F2 ionosphere. Thickness of the bottom of the F2 ionosphere The short-term prediction of key ionospheric characteristic parameters, such as the peak electron density NmE of the E layer, can be applied to fields such as space weather monitoring, shortwave communication, and navigation and positioning.

[0015] like Figure 1 As shown, the ionospheric feature parameter prediction method based on physical information neural networks specifically includes the following steps: Step 1. Collection and preprocessing of multi-source observation data: Collect and preprocess data from ground-based ionospheric altimeters, COSMIC satellite data, and auxiliary data to construct a multi-source observation dataset.

[0016] This step is used to obtain high-quality training and testing data, providing a foundation for subsequent model training and validation.

[0017] The following is a detailed description of step 1 in this embodiment.

[0018] First, we introduce the multi-source observation dataset. Each training sample in the multi-source observation dataset contains a set of observed values ​​of ionospheric characteristic parameters and corresponding auxiliary data.

[0019] Characteristic parameters of the ionosphere include the peak electron density of the F2 layer (NmF2), the peak height of the F2 layer (hmF2), and the thickness of the top of the F2 layer. Thickness of the bottom of the F2 ionosphere And the peak electron density NmE of the ionosphere E layer.

[0020] The observed values ​​of ionospheric characteristic parameters are derived from ground-based ionospheric altimeter data or COSMIC satellite data.

[0021] Ground-based ionospheric altimeter data includes NmF2, hmF2, and NmE data observed by the ground-based ionospheric altimeter, obtained by fitting the electron density profile using the NeQuick model. , Data, and corresponding spatiotemporal parameters.

[0022] COSMIC satellite data includes NmF2 and hmF2 observed by the COSMIC satellite. , NmE data, and the corresponding spatiotemporal parameters.

[0023] Specifically, this embodiment collects two types of core observation data. The first is ground-based observation data, namely ground-based ionospheric altimeter data. Multiple globally distributed ionospheric altimeter stations are selected to collect long-term, continuous NmF2, hmF2, and NmE observation data. The sampling frequency is set to 1 hour / time to ensure data coverage of different latitudes, longitudes, and different solar activity cycles and geomagnetic activity levels. The second is space-based observation data, namely COSMIC satellite data, acquiring NmF2, hmF2, and NmE observations from the COSMIC satellite. , The NmE data were collected at the same sampling frequency as the ground-based ionospheric altimeter data, while also collecting the corresponding spatiotemporal parameters.

[0024] Spatiotemporal parameters include time parameters and spatial parameters. The time parameters are used to calculate the sine component DOYs and cosine component DOYc of the annual day, and the sine component LTs and cosine component LTc of the local time LT. The spatial parameters include geographic latitude and geographic longitude, used to calculate geomagnetic latitude and solar zenith angle.

[0025] This embodiment also collects auxiliary data affecting changes in ionospheric characteristic parameters, including solar activity indices, geomagnetic activity indices, and neutral wind parameters. The solar activity indices include F10.7 solar flux and sunspot number; F10.7 solar flux refers to the solar radio flux density measured at a wavelength of 10.7 cm. The geomagnetic activity indices include the Dst index and the Kp index. The neutral wind parameters include meridional and zonal winds. The temporal resolution of all auxiliary data matches that of the observation data, ensuring data temporal consistency.

[0026] Next, the specific preprocessing process in this embodiment will be introduced.

[0027] The preprocessing process includes data cleaning and normalization.

[0028] Data cleaning includes removing outliers using the 3σ criterion, replacing outliers with linear interpolation, filling in missing values ​​using quadratic interpolation, and filtering noise using the moving average method, resulting in cleaned data. .

[0029] Specifically, in this embodiment, the process of cleaning the collected multi-source data, removing outliers, supplementing missing values, and filtering noisy data includes: identifying outliers using the 3σ criterion and replacing them with linear interpolation; supplementing missing values ​​using quadratic interpolation based on historical data trends in the same region and time period; and filtering data noise using the moving average method with a window size of 3 hours to preserve the true trend of data changes.

[0030] The normalization process uses the min-max normalization method to map the data to the [0,1] interval.

[0031] Specifically, in this embodiment, all cleaned data, including observation data and auxiliary data, are normalized using the min-max normalization method to map the data to the [0,1] interval, in order to eliminate the influence of data of different magnitudes on model training. The normalization formula is as follows: .

[0032] in, This refers to the normalized data, i.e., the data obtained after preprocessing in step 1; For the cleaned data, The minimum value of the data. The maximum value of the data is recorded; during normalization, the minimum value of each data category is recorded. and maximum value This is used to inversely normalize the predicted values ​​output by the model.

[0033] Then, the process of splitting the dataset will be introduced.

[0034] In this embodiment, all preprocessed data are divided into training set, validation set and test set in a ratio of 7:2:1. The training set is used for training model parameters, the validation set is used to adjust model hyperparameters and avoid overfitting, and the test set is used to evaluate the predictive performance of the model.

[0035] Step 2. Construct the Physical Information Neural Network (PINN) model, which includes an input layer, hidden layers, and an output layer.

[0036] This step constructs a PINN model suitable for predicting ionospheric characteristic parameters and optimizes the network structure to capture complex nonlinear relationships in the data. Step 2 in this embodiment will be described in detail below.

[0037] The network structure of the PINN model is as follows: The number of neurons in the input layer is 14. Based on the multi-source observation data after preprocessing in step 1, the following input features are selected to ensure comprehensive coverage of key factors affecting ionospheric characteristic parameters. The input features of the input layer include the sine component DOYs and cosine component DOYc of the annual cumulative day, geographic latitude, geographic longitude, geomagnetic latitude, the sine component LTs and cosine component LTc of the local time LT, solar zenith angle, sunspot number, F10.7 solar flux, Dst index and Kp index, meridional wind and zonal wind.

[0038] The hidden layers consist of four fully connected layers with 128, 64, 32, and 16 neurons respectively. Each fully connected layer is followed by a batch normalization layer and a ReLU activation function to improve training stability and enhance non-linear expressiveness. The batch normalization layer accelerates model training and alleviates the vanishing gradient problem, while the ReLU activation function captures non-linear relationships in the data.

[0039] The output layer uses a linear activation function to ensure that the output value covers the entire range after normalization, facilitating subsequent inverse normalization to obtain the true prediction value. The output layer has 5 neurons, and its output is the model prediction value of the ionospheric feature parameters, including NmF2, hmF2, and... , The predicted values ​​of NmE.

[0040] In addition, this embodiment also includes model initialization, which initializes the weights and biases of each layer of the network using the He normal initialization method to ensure the stability of the model training process; and sets a random seed to ensure the repeatability of model training.

[0041] Step 3. Construction and integration of physical constraints into the design: Select the basic physical laws of the ionosphere as constraints, transform each constraint into a loss function term, and integrate it into the overall loss function of the model.

[0042] This step is used to construct constraints that conform to the physical mechanisms of the ionosphere, incorporate them into the neural network training, and ensure that the model output conforms to physical laws. Step 3 in this embodiment will be described in detail below.

[0043] Selecting core physical constraints: Based on the physical characteristics of the F2 layer of the ionosphere, the following five types of fundamental physical laws of the ionosphere are selected as physical constraints, including Chapman function constraints, continuity equation constraints, electron generation rate constraints, electron loss rate constraints, and geomagnetic and electric field constraints, covering key processes such as electron generation, loss, and transport in the ionosphere.

[0044] The Chapman function constraint is used to describe the distribution of ionospheric electron density with altitude, serving as a fundamental constraint for electron density prediction. Its expression is: .

[0045] in, Represents electron density, That is, the peak electron density of the F2 ionosphere, NmF2. Let h be a natural constant, and h represent height. That is, the peak height of the F2 layer of the ionosphere, hmF2. Elevation.

[0046] The continuity equation constraint is used to describe the relationship between the time-varying rate of change of ionospheric electron density and electron generation rate, electron loss rate, and electron transport flux divergence, constraining the time evolution characteristics of electron density. Its expression is: .

[0047] in, For time, The rate of change of electron density over time; For electron production rate, For electron loss rate, For electron transport flux divergence, Represents the gradient operator. This represents the overall transport and drift velocity of the plasma.

[0048] The electron production rate constraint treats the electron production rate as a function of the F10.7 solar flux, reflecting the influence of solar activity on ionospheric electron production. Its expression is: .

[0049] in, This is the proportionality coefficient. This represents the solar flux at F10.7. Indicates the zenith angle of the sun. This indicates the operation of taking the maximum value.

[0050] The electron loss rate constraint considers the recombination process of electrons and ions in the ionosphere, constraining the electron loss rate using a two-body recombination model, the expression of which is: .

[0051] in, is the composite coefficient.

[0052] Geomagnetic and electric field constraints consider the influence of the geomagnetic and electric fields on electron transport, and the ionospheric electric field vector is... Geomagnetic field vector As a constraint, the overall plasma transport and drift velocity is incorporated. The calculation.

[0053] Overall plasma transport drift velocity Written as: .

[0054] in, The electromagnetic drift velocity vector, This represents the neutral atmospheric wind drift velocity vector; This represents the plasma diffusion drift velocity vector.

[0055] Electromagnetic drift velocity vector Represented as: .

[0056] in, That is, the velocity of plasma generated under the action of electromagnetic field coupling; Represents the electric field vector of the ionosphere With the geomagnetic field vector The cross product is used to determine the direction of electromagnetic drift. Represents the geomagnetic field vector The modulus.

[0057] The physical constraints are transformed into loss function terms and combined with the model's data fitting loss to form the model's total loss function, so that the model can simultaneously satisfy both data fitting and physical constraints during the training process.

[0058] Specifically, rearranging the expression for the continuity equation constraints yields the following continuity equation residual: .

[0059] Physical constraint loss Defined as the square of the L2 norm of the residuals of the continuity equation: .

[0060] in, The squared L2 norm is represented; the Chapman function constraint is used to limit the electron density. The vertical distribution pattern and electron generation rate constraint are used to determine the electron generation rate. Electron loss rate constraints are used to determine the electron loss rate. Geomagnetic and electric field constraints are used to solve for the overall transport and drift velocity of the plasma. .

[0061] Data fitting loss The mean square error between model predictions and observed values ​​of ionospheric characteristic parameters is defined as follows: .

[0062] in, , This indicates the number of training samples in the multi-source observation dataset; This represents the model prediction value of the ionospheric characteristic parameters, i.e., the first value output by the PINN model. Predicted values ​​of ionospheric feature parameters corresponding to each training sample; This represents the observed value of the ionospheric characteristic parameter, i.e., the th value in the multi-source observation dataset. The observed values ​​of ionospheric characteristic parameters corresponding to each training sample are the values ​​of ionospheric characteristic parameters in ground-based ionospheric altimeter data or COSMIC satellite data.

[0063] Physical constraint loss Loss of data fitting Weighted summation yields the total loss function of the model: .

[0064] in, This represents the total loss of the model; Indicates the weighting coefficient. The value ranges from 0.1 to 0.5, and the optimal value is determined through validation set debugging.

[0065] Step 4. Train the PINN model based on the multi-source observation dataset constructed in Step 1 and the total loss function of the model obtained in Step 3 to obtain the trained PINN model.

[0066] This step uses the preprocessed training and validation sets to train and optimize the hyperparameters of the constructed PINN model, ensuring that the model achieves optimal prediction performance. Step 4 in this embodiment will be described in detail below.

[0067] In this embodiment, the Adam optimizer is used during the training of the PINN model, with an initial learning rate of 0.001 and a learning rate decay strategy. The number of training epochs is set to 500, and the batch size is set to 32. Overfitting of the model is avoided through L2 regularization and early stopping strategies.

[0068] Specifically, the training parameter settings include: determining the key parameters for model training, including using the Adam optimizer, setting the initial learning rate to 0.001, and adopting a learning rate decay strategy, i.e., the learning rate decays to 0.9 every 100 epochs; setting the training epochs to 500, and the batch size to 32; and using L2 regularization with a regularization coefficient of 0.0001 to prevent model overfitting.

[0069] Model training includes: inputting the training set data into the PINN model, calculating the model's predicted values, combining the total loss function constructed in step 3, and updating the network weights and biases through the backpropagation algorithm; after each training epoch, calculating the model's validation loss using the validation set, and recording the changing trends of the training loss and validation loss.

[0070] Hyperparameter optimization includes: optimizing model hyperparameters based on the loss changes on the validation set; if the validation loss does not decrease for 20 consecutive epochs, an early stopping strategy is adopted to stop model training and avoid overfitting; adjusting the physical constraint weight coefficients. The training process is repeated until the verification loss reaches its minimum value, and the optimal combination of hyperparameters is determined. This includes setting the number of neurons in the hidden layer, the learning rate, and other hyperparameters.

[0071] In addition, after training the PINN model, model performance evaluation and updates are performed. In this embodiment, the PINN model is evaluated and updated according to a preset time period. This is used to periodically assess the model's predictive performance and update the model based on new observation data to ensure long-term stable operation. The specific process is as follows: Using test set data, the model's predictive performance is evaluated monthly. The performance evaluation process includes calculating the correlation coefficient R between the predicted values ​​of ionospheric characteristic parameters output by the PINN model and the observed values ​​of ionospheric characteristic parameters in the multi-source observation dataset; if the calculated correlation coefficient R is less than 0.90, the model performance is considered to have deteriorated, and the model update process is initiated.

[0072] The model update process includes collecting ground-based ionospheric altimeter data, COSMIC satellite data, and auxiliary data again. After preprocessing the collected data according to step 1, the data is added to the multi-source observation dataset, the hyperparameters and physical constraints are updated, and the PINN model is retrained to obtain the updated model.

[0073] This embodiment also includes a model maintenance process, which involves periodically checking the model's running status, fixing any abnormalities during data acquisition and preprocessing, and updating physical constraints based on error feedback results to continuously improve the model's physical rationality and prediction accuracy.

[0074] Step 5. Ionospheric characteristic parameter prediction and result processing: Input the data to be predicted into the trained PINN model, and after inverse normalization and error correction of the predicted values ​​output by the model, obtain the ionospheric characteristic parameter prediction results.

[0075] This step utilizes the trained PINN model to predict the ionospheric characteristic parameters for the next 1 to 24 hours, and performs post-processing on the prediction results. Step 5 in this embodiment will be described in detail below.

[0076] In this embodiment, the process of preparing the prediction data is as follows: Collect input feature data for the time to be predicted, including ground-based ionospheric altimeter data, COSMIC satellite data, and auxiliary data. Perform data cleaning and normalization according to step 1 above to obtain standardized prediction input data.

[0077] In this embodiment, the process of inverse normalization and error correction of the predicted values ​​output by the model is as follows: Predicted values ​​of the PINN model output Perform inverse normalization to obtain the inverse normalized predicted value. : .

[0078] in, That is, the model predictions of ionospheric characteristic parameters, including the normalized NmF2, hmF2, , NmE data; and These are the maximum and minimum values ​​of the data used during the normalization process in step 1, respectively.

[0079] The error correction process refers to constructing an error correction function using the error between the historical predicted values ​​output by the PINN model and the observed values ​​of ionospheric characteristic parameters in the multi-source observation dataset, and then correcting the inverse normalized predicted values. This process is specifically as follows: The error between the historical predicted values ​​output by the PINN model and the observed values ​​of ionospheric feature parameters in the multi-source observation dataset is calculated. The relationship between the error and the input features of the input layer is fitted using the random forest algorithm to obtain the error correction function.

[0080] Substitute the input features of the input layer corresponding to the time to be predicted into the error correction function to obtain the error correction amount.

[0081] Based on the error correction amount, the predicted value after innormalization Adjustments were made to further improve prediction accuracy, resulting in corrected prediction values. These corrected prediction values ​​were then used as the prediction results for ionospheric characteristic parameters.

[0082] In this embodiment, the predicted ionospheric characteristic parameters include the corrected NmF2, hmF2, , It can output the predicted values ​​of NmE, and also output prediction accuracy indicators including correlation coefficients to provide users with a reference for prediction reliability; it can also output prediction results in different formats such as tables, curves, and text according to actual application needs to meet the usage needs of different scenarios such as space weather monitoring and shortwave communication.

[0083] The prediction method proposed in this invention has clear steps and strong operability, covering the entire process of data preprocessing, model building, training optimization, prediction output, and performance evaluation. It can predict ionospheric characteristic parameters and is applicable to various practical application scenarios such as space weather monitoring, shortwave communication, and navigation and positioning, and has high engineering application value.

[0084] In addition, to verify the effectiveness of the method proposed in this invention, the following specific experiments are also provided: Ionospheric characteristic parameters (including NmF2, hmF2, ...) of a certain region (latitude 10°N to 30°N, longitude 100°E to 130°E) , Taking NmE prediction as an example, the specific implementation steps are as follows: Step 1. Collection and preprocessing of multi-source observation data.

[0085] Multi-source observation data were collected. Three ground-based ionospheric altimeter stations in the region were selected to collect NmF2, hmF2, and NmE observation data from 2018 to 2025, with a sampling frequency of 1 hour / time. The data were obtained by fitting the electron density profile using the NeQuick model. , Data; Obtain NmF2, hmF2, and other data from the COSMIC satellite during the same period. NmE observation data were collected at a sampling frequency of 1 hour; the corresponding spatiotemporal parameters were also recorded.

[0086] Auxiliary data collection was conducted, including concurrent data on F10.7 solar flux, sunspot number, Dst index, Kp index, meridional wind, and zonal wind, all with a time resolution of 1 hour per instance.

[0087] Data cleaning was performed, outliers were removed using the 3σ criterion and replaced with linear interpolation; missing values ​​were supplemented using quadratic interpolation; and noise was filtered using the 3-hour moving average method.

[0088] The data is normalized using the min-max method, mapping all data to the interval [0,1], and the minimum and maximum values ​​of each type of data are recorded. For example, the minimum and maximum values ​​of hmF2 are 200km and 470km, respectively.

[0089] The data from 2018 to 2024 were divided into three sets in a 7:2:1 ratio: the training set, the validation set from January to June 2025, and the test set from July to December 2025.

[0090] Step 2. PINN model construction.

[0091] The number of neurons in the input layer is set to 14; the input features of the input layer include the sine component DOYs and cosine component DOYc of the annual day, geographic latitude, geographic longitude, geomagnetic latitude, the sine component LTs and cosine component LTc of the local time LT, solar zenith angle, sunspot number, F10.7 solar flux, Dst index and Kp index, meridional wind and zonal wind.

[0092] The hidden layer contains four fully connected layers with 128, 64, 32, and 16 neurons respectively. Each fully connected layer is followed by a batch normalization layer and a ReLU activation function to improve training stability and enhance nonlinear expression.

[0093] The output layer uses a linear activation function and has 5 neurons. Its output is the model prediction values ​​of ionospheric feature parameters, including NmF2, hmF2, and . , The predicted values ​​of NmE.

[0094] The model was initialized using He normal initialization, with the random seed set to 42.

[0095] Step 3. Constructing and integrating physical constraints into the design.

[0096] Chapman function constraints, continuity equation constraints, electron generation rate constraints, electron loss rate constraints, and geomagnetic and electric field constraints are selected as physical constraints, where the scaling factor is [missing value]. The composite coefficient is .

[0097] Construct the total loss function: .

[0098] Step 4. PINN model training and optimization.

[0099] The training parameters are set as follows: the Adam optimizer is used, the initial learning rate is set to 0.001, and the learning rate decays to 0.9 every 100 epochs; the number of training epochs is set to 500, the batch size is set to 32, and the L2 regularization coefficient is set to 0.0001.

[0100] Input the training set data, update the network parameters through backpropagation, and record the training loss and validation loss every epoch.

[0101] An early stopping strategy is adopted, where training is stopped when the validation loss does not decrease for 20 consecutive epochs, and the optimal hyperparameters are finally determined. The number of neurons in the four fully connected layers in the hidden layer are 128, 64, 32, and 16, respectively, and the learning rate is 0.001.

[0102] On the validation set, calculate the correlation coefficients RNmF2, hmF2, between the predicted values ​​of ionospheric characteristic parameters output by the PINN model and the observed values ​​of ionospheric characteristic parameters in the multi-source observation dataset. The correlation coefficients corresponding to NmE are 0.94, 0.92, 0.90, 0.91, and 0.93, respectively, which meet the preset requirements.

[0103] Step 5. Ionospheric characteristic parameter prediction and result processing.

[0104] Input feature data is collected at a certain moment on January 1, 2026, and then cleaned and normalized to obtain standardized input data.

[0105] Inputting the data into the PINN model yields the normalized predicted values, i.e., the model's predicted values. Inverse normalization then yields the true predicted values, i.e., the inverse normalized predicted values, including: the peak electron density of the F2 ionosphere, NmF2, is 1.2 × 10⁻⁶. 12 el.m -3 The peak height of the F2 ionosphere is hmF2, which is 350 km. The thickness of the top of the F2 ionosphere is... The thickness of the bottom of the F2 ionosphere is 38 km. The altitude is 21 km, and the peak electron density of the E layer of the ionosphere, NmE, is 6.0 × 10⁻⁶. 10 el.m -3 .

[0106] A random forest error correction model is constructed using the error between the historical predicted values ​​output by the PINN model and the observed values ​​of ionospheric characteristic parameters in a multi-source observation dataset. Specifically, the random forest algorithm is used to fit the relationship between the error and the input features of the input layer to obtain the error correction function, and then the error correction amount. Based on the error correction amount, the inversely normalized predicted values ​​are adjusted to obtain the corrected predicted values, including: the peak electron density NmF2 of the ionospheric F2 layer is 1.13 × 10⁻⁶. 12 el.m -3 The peak height of the F2 ionosphere is hmF2, which is 356.4 km. The thickness of the top of the F2 ionosphere is... The thickness of the bottom of the F2 ionosphere is 36.7 km. The altitude is 20.5 km, and the peak electron density NmE of the ionosphere E layer is 5.92 × 10⁻⁶. 10 el.m -3 .

[0107] Output the corrected predicted values ​​and prediction accuracy indicators, presented in tabular form.

[0108] This experiment also includes model performance evaluation and updates.

[0109] First, the performance of the test set is evaluated monthly. If the correlation coefficient R between the predicted values ​​of the ionospheric characteristic parameters output by the PINN model and the observed values ​​of the ionospheric characteristic parameters in the multi-source observation dataset is not less than 0.90, then the performance is stable.

[0110] Second, new source observation data are collected every quarter, added to the training set to retrain the PINN model, and hyperparameters are optimized to ensure the model's performance remains stable.

[0111] Third, based on the latest research in ionospheric physics, the recombination reaction coefficient, i.e., the recombination coefficient, should be optimized. To improve the physical plausibility of the model.

[0112] This invention addresses the shortcomings of existing methods, such as incomplete dataset fusion, unsystematic selection of physical constraints, unreasonable input feature design, and model structure not optimized for ionospheric data characteristics, which lead to insufficient prediction accuracy and reliability for practical applications. It proposes a method for predicting ionospheric feature parameters that integrates multi-source observation data, incorporates fundamental ionospheric physical laws as constraints, and optimizes model input features and network structure. This method improves prediction accuracy and generalization ability, effectively solving the problems of low prediction accuracy, poor generalization ability, and insufficient response to extreme space weather in existing methods. Furthermore, it enables accurate and efficient prediction of ionospheric feature parameters.

[0113] Experiments show that the ionospheric characteristic parameter prediction method based on physical information neural networks proposed in this invention can predict ionospheric characteristic parameters including NmF2, hmF2, and The system provides accurate predictions of NmE, with high prediction precision and strong generalization ability, which can meet the needs of practical applications.

[0114] Example 2 This embodiment 2 describes a computer device that includes a memory and one or more processors.

[0115] The memory stores executable code, which, when executed by the processor, is used to implement the steps of the ionospheric feature parameter prediction method based on physical information neural network in Embodiment 1 above.

[0116] In this embodiment, the computer device can be any device or apparatus with data processing capabilities, and will not be described in detail here.

[0117] Example 3 This embodiment 3 describes a computer-readable storage medium storing a program that, when executed by a processor, implements the steps of a method for predicting ionospheric characteristic parameters based on a physical information neural network.

[0118] The computer-readable storage medium can be an internal storage unit of any device or apparatus with data processing capabilities, such as a hard disk or memory, or an external storage device of any device with data processing capabilities, such as a plug-in hard disk, smart media card (SMC), SD card, flash card, etc.

[0119] Of course, the above description is only a preferred embodiment of the present invention. The present invention is not limited to the above-described embodiments. It should be noted that any equivalent substitutions or obvious modifications made by those skilled in the art under the guidance of this specification fall within the scope of this specification and should be protected by the present invention.

Claims

1. A method for predicting ionospheric characteristic parameters based on a physical information neural network, characterized in that, Includes the following steps: Step 1. Collect and preprocess data from ground-based ionospheric altimeters, COSMIC satellite data, and auxiliary data to construct a multi-source observation dataset; Step 2. Construct the Physical Information Neural Network (PINN) model, which includes an input layer, hidden layers, and an output layer; Step 3. Select the fundamental physical laws of the ionosphere as constraints, transform each constraint into a loss function term, and integrate them into the overall loss function of the model; Step 4. Train the PINN model based on the multi-source observation dataset constructed in Step 1 and the total loss function of the model obtained in Step 3 to obtain the trained PINN model; Step 5. Input the data to be predicted into the trained PINN model, and after inverse normalization and error correction of the predicted values ​​output by the model, obtain the prediction results of ionospheric characteristic parameters.

2. The method for predicting ionospheric characteristic parameters based on a physical information neural network according to claim 1, characterized in that, In step 1, each training sample in the multi-source observation dataset contains a set of observed values ​​of ionospheric feature parameters and corresponding auxiliary data. Characteristic parameters of the ionosphere include the peak electron density of the F2 layer (NmF2), the peak height of the F2 layer (hmF2), and the thickness of the top of the F2 layer. Thickness of the bottom of the F2 ionosphere And the peak electron density of the ionosphere E layer, NmE; The observed values ​​of ionospheric characteristic parameters are derived from ground-based ionospheric altimeter data or COSMIC satellite data; Ground-based ionospheric altimeter data includes NmF2, hmF2, and NmE data observed by the ground-based ionospheric altimeter, obtained by fitting the electron density profile using the NeQuick model. , Data, and corresponding spatiotemporal parameters; COSMIC satellite data includes NmF2 and hmF2 observed by the COSMIC satellite. , NmE data, and corresponding spatiotemporal parameters; Spatiotemporal parameters include time parameters and spatial parameters; Among them, the time parameter is used to calculate the sine component DOYs and cosine component DOYc of the annual day, and the sine component LTs and cosine component LTc of the local time LT. Spatial parameters include geographic latitude and geographic longitude, used to calculate geomagnetic latitude and solar zenith angle; Supporting data include solar activity index, geomagnetic activity index, and neutral wind field parameters; Among them, the solar activity index includes F10.7 solar flux and sunspot number, the geomagnetic activity index includes Dst index and Kp index, and the neutral wind field parameters include meridional wind and zonal wind.

3. The method for predicting ionospheric characteristic parameters based on a physical information neural network according to claim 2, characterized in that, In step 1, the preprocessing process includes data cleaning and normalization. Data cleaning includes removing outliers using the 3σ criterion, replacing outliers with linear interpolation, supplementing missing values ​​using quadratic interpolation, and filtering noise using the moving average method. The normalization process uses the min-max normalization method to map the data to the [0,1] interval.

4. The method for predicting ionospheric characteristic parameters based on a physical information neural network according to claim 3, characterized in that, In step 2, the network structure of the PINN model is specifically as follows: The input layer has 14 neurons; the input features of the input layer include the sine component DOYs and cosine component DOYc of the annual day, geographic latitude, geographic longitude, geomagnetic latitude, the sine component LTs and cosine component LTc of the local time LT, solar zenith angle, sunspot number, F10.7 solar flux, Dst index and Kp index, meridional wind and zonal wind; The hidden layer contains four fully connected layers with 128, 64, 32, and 16 neurons respectively. Each fully connected layer is followed by a batch normalization layer and a ReLU activation function. The output layer uses a linear activation function and has 5 neurons. Its output is the model prediction values ​​of ionospheric feature parameters, including NmF2, hmF2, and . , The predicted values ​​of NmE.

5. The method for predicting ionospheric characteristic parameters based on a physical information neural network according to claim 4, characterized in that, In step 3, the fundamental physical laws of the ionosphere are selected as physical constraints, including Chapman function constraints, continuity equation constraints, electron generation rate constraints, electron loss rate constraints, and geomagnetic and electric field constraints. The expression for the Chapman function constraint is: ； in, Indicates electron density, That is, the peak electron density of the F2 ionosphere, NmF2. Let h be a natural constant, and h represent height. That is, the peak height of the F2 layer of the ionosphere, hmF2. Elevation; The expression for the continuity equation constraint is: ； in, For time, The rate of change of electron density over time; For electron production rate, For electron loss rate, For electron transport flux divergence, Represents the gradient operator. This represents the overall transport and drift velocity of the plasma; The expression for the electron production rate constraint is: ； in, This is the proportionality coefficient. This represents the solar flux at F10.

7. Indicates the zenith angle of the sun. This indicates the operation of retrieving the maximum value; The expression for the electron loss rate constraint is: ； in, The composite coefficient; The geomagnetic and electric field confinement is the vector of the ionospheric electric field. Geomagnetic field vector As a constraint, the overall plasma transport and drift velocity is incorporated. Calculation of plasma overall transport drift velocity; Written as: ； in, The electromagnetic drift velocity vector, This represents the neutral atmospheric wind drift velocity vector; This represents the plasma diffusion drift velocity vector; Electromagnetic drift velocity vector Represented as: ； in, That is, the velocity of plasma generated under the action of electromagnetic field coupling; Represents the electric field vector of the ionosphere With the geomagnetic field vector The cross product is used to determine the direction of electromagnetic drift. Represents the geomagnetic field vector The modulus; Rearranging the expression for the continuity equation constraints, we obtain the continuity equation residual as follows: ； Physical constraint loss Defined as the square of the L2 norm of the residuals of the continuity equation: ； in, The squared L2 norm is represented; the Chapman function constraint is used to limit the electron density. The vertical distribution pattern and electron generation rate constraint are used to determine the electron generation rate. Electron loss rate constraints are used to determine the electron loss rate. Geomagnetic and electric field constraints are used to solve for the overall transport and drift velocity of the plasma. ; Data fitting loss The mean square error between model predictions and observed values ​​of ionospheric characteristic parameters is defined as follows: ； in, , This indicates the number of training samples in the multi-source observation dataset; This represents the model prediction value of the ionospheric characteristic parameters, i.e., the output of the PINN model, the first... Predicted values ​​of ionospheric feature parameters corresponding to each training sample; This represents the observed value of the ionospheric characteristic parameter, i.e., the th value in the multi-source observation dataset. The observed values ​​of ionospheric characteristic parameters corresponding to each training sample, which are the values ​​of ionospheric characteristic parameters in ground-based ionospheric altimeter data or COSMIC satellite data; Physical constraint loss Loss of data fitting Weighted summation yields the total loss function of the model: ； in, This represents the total loss of the model. This represents the weighting coefficient.

6. The method for predicting ionospheric characteristic parameters based on a physical information neural network according to claim 1, characterized in that, In step 4 The Adam optimizer was used during the training of the PINN model, with an initial learning rate of 0.001 and a learning rate decay strategy. The number of training epochs was set to 500, and the batch size was set to 32. L2 regularization and early stopping strategies were used to avoid model overfitting.

7. The method for predicting ionospheric characteristic parameters based on a physical information neural network according to claim 4, characterized in that, In step 5, the process of inverse normalization and error correction of the predicted values ​​output by the model is as follows: Predicted values ​​of the PINN model output Perform inverse normalization to obtain the inverse normalized predicted value. : ； in, That is, the model predictions of ionospheric characteristic parameters, including the normalized NmF2, hmF2, , NmE data; and These are the maximum and minimum values ​​used during the normalization process in step 1, respectively. The error between the historical predicted values ​​output by the PINN model and the observed values ​​of ionospheric feature parameters in the multi-source observation dataset is calculated. The relationship between the error and the input features of the input layer is fitted using the random forest algorithm to obtain the error correction function. Substitute the input features of the input layer corresponding to the time to be predicted into the error correction function to obtain the error correction amount; Based on the error correction amount, the predicted value after innormalization Adjustments are made to obtain the revised predicted value; The corrected predicted values ​​are used as the prediction results for ionospheric characteristic parameters.

8. The method for predicting ionospheric characteristic parameters based on a physical information neural network according to claim 2, characterized in that, In step 4, after training the PINN model is completed, the PINN model is evaluated and updated according to a preset time period. The specific process is as follows: The performance evaluation process includes calculating the correlation coefficient R between the predicted values ​​of ionospheric characteristic parameters output by the PINN model and the observed values ​​of ionospheric characteristic parameters in the multi-source observation dataset; if the calculated correlation coefficient R is less than 0.90, the model performance is determined to have degraded, and the model update process is initiated. The model update process includes collecting ground-based ionospheric altimeter data, COSMIC satellite data, and auxiliary data again. After preprocessing the collected data, it is added to the multi-source observation dataset, and the PINN model is retrained to obtain the updated model.

9. A computer device comprising a memory and one or more processors, wherein the memory stores executable code, characterized in that, When the processor executes the executable code, it implements the steps of the ionospheric feature parameter prediction method based on a physical information neural network as described in any one of claims 1 to 8.

10. A computer-readable storage medium having a program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the ionospheric characteristic parameter prediction method based on a physical information neural network as described in any one of claims 1 to 8.

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