Ionized layer TEC prediction method and device based on parameterized multi-scale gated convolution

Abstract

The invention discloses an ionized layer TEC prediction method and device based on parameterized multi-scale gated convolution, and belongs to the technical field of ionized layer TEC prediction. The method comprises three links of data preparation, model design and strategy training. In the data preparation step, standardized input data is constructed through multi-scale feature expansion, Fourier time coding and physical consistency data enhancement; according to the model design, a parameterized context coding module is adopted to extract global space environment context information, and a space feature coding and decoding module carries out space feature extraction and reconstruction through spherical topology boundary processing and a double-reference residual structure. The parameterized modulation spatio-temporal evolution module utilizes a two-stage low-rank time adapter and a parameterized multi-scale gated convolution block to model TEC spatio-temporal evolution under the latitudinal band differentiation modulation of global parameter context information; the training strategy adopts a loss function to constrain a prediction error in an effective physical region.

Description

Technical Field

[0001] This invention belongs to the field of ionospheric TEC prediction technology, specifically referring to a parametric multi-scale gated convolution method and apparatus for predicting ionospheric TEC. Background Technology

[0002] The Global Ionospheric Total Electron Content Grid Map (TEC Grid Map) is a spatiotemporal data product obtained by integrating the electron density in the Earth's ionosphere along the vertical direction and discretizing it globally in the form of a regular latitude and longitude grid. The spatiotemporal variation of ionospheric TEC is mainly influenced by external space environmental factors such as the solar activity cycle, solar radiation, and space weather events like geomagnetic disturbances, exhibiting significant non-stationarity and regional variability. During periods of strong solar activity or geomagnetic storms, TEC may undergo drastic changes in a short period, demonstrating complex dynamic evolution characteristics. Existing research on predicting global ionospheric TEC can be mainly divided into two categories: empirical models and prediction models based on deep learning.

[0003] Empirical models are typically constructed based on long-term observational data and statistical regularities to build mathematical approximations, used to characterize the average behavior of ionospheric parameters as they vary with time, space, and solar activity. Representative models include the Klobuchar model, the International Reference Ionosphere (IRI) model, and the NeQuick model. The Klobuchar model, proposed by the US GPS control department, is primarily used for ionospheric delay correction for single-frequency Global Positioning System (GPS) users, with its model parameters broadcast via navigation messages. Due to its simple structure and high computational efficiency, this model can reduce the impact of ionospheric delay on positioning results to some extent. The IRI model, jointly recommended by the International Union of Radio Science (URSI) and the Committee on Space Research (COSPAR), is built based on extensive ground-based and space-based observational data. It provides global climatological distributions of various ionospheric parameters, including electron density, and is used to describe the statistical variations of ionospheric parameters with time, geographical location, and solar activity levels. The NeQuick model is a three-dimensional, time-varying electron density model, initially recommended by the International Telecommunication Union (ITU) and adopted by the European Galileo system as its ionospheric correction model for single-frequency users. This model improves its adaptability to ionospheric variations under different space environment conditions by incorporating the solar activity index as a driving parameter. Although these empirical models have been applied in Global Navigation Satellite Systems (GNSS), they still have significant limitations in global ionospheric TEC grid prediction missions. Due to the limited ability of empirical models to characterize the dynamic evolution of the ionosphere, accurate modeling of TEC grids is difficult. Especially during periods of strong solar activity or geomagnetic storms, the accuracy and stability of empirical models decrease significantly.

[0004] Existing deep learning-based methods for predicting global ionospheric TEC include:

[0005] (1) Spatiotemporal prediction model based on recursive structure:

[0006] Recursive-structure-based models, grounded in Recurrent Neural Networks (RNNs), characterize sequence dependencies through temporal recursion. Typical examples include Convolutional Long Short-Term Memory (ConvLSTM) networks and their improved versions. Previous research has successfully applied ConvLSTM to global TEC prediction tasks, enhancing the ability to characterize the evolution of global ionospheric TEC to some extent. For instance, an improved ConvLSTM-based model has been proposed for predicting global TEC grid maps under geomagnetic storm conditions. However, these methods generally rely on recursive computational structures, making full parallelization difficult. They incur significant computational costs in long-term series and global-scale prediction tasks and are prone to error accumulation and prediction instability during multi-step prediction processes.

[0007] (2) Hybrid spatiotemporal prediction model of convolution and recursion:

[0008] To alleviate the shortcomings of pure recursive models in terms of computational efficiency and prediction stability, some studies have further proposed hybrid modeling approaches that combine convolution and recursion. These methods typically utilize Convolutional Neural Networks (CNNs) to extract spatial features, and then use LSTMs or their variants to model the temporal dimension. For example, global TEC prediction models based on CNN-LSTM-Attention and CNN-BiLSTM have been proposed, achieving some accuracy improvements compared to single models during geomagnetic storms. However, these models often employ a spatial-temporal modeling concatenation structure, resulting in limited coupling between spatial and temporal features, high overall structural complexity, and continued reliance on recursive units for temporal modeling, leading to efficiency bottlenecks in long-sequence prediction and engineering deployment.

[0009] (3) Pure convolutional spatiotemporal prediction model:

[0010] Building upon this foundation, to further improve computational efficiency and parallelism, some studies have begun exploring spatiotemporal prediction models based on pure convolutional structures, unifying the temporal and spatial dimensions within the convolutional modeling framework. For example, existing technologies have proposed spatiotemporal convolutional network models, which have demonstrated good computational efficiency and a certain degree of predictive stability in global TEC grid map prediction. However, pure convolutional models typically rely on fixed convolutional kernels and connection structures, lacking the ability to explicitly characterize changes in external spatial environment driving factors, and their adaptability to complex perturbation processes under strongly non-stationary spatial environments remains limited.

[0011] (4) Spatiotemporal prediction model based on Transformer:

[0012] In recent years, with the development of self-attention mechanisms, Transformer-based prediction models have been introduced into global TEC prediction tasks to enhance the ability to model spatiotemporal dependencies in long-term series. Existing technologies include Transformer-based global TEC grid sequence prediction models and Transformer or ED-Transformer prediction frameworks for global TEC grid sequences. Although these models have advantages in capturing long-term dependencies, their computational complexity typically increases quadratically with the length of the time series and the spatial resolution. The computational and storage overhead is significant in high-resolution global TEC grids and long-term prediction scenarios, thus limiting their engineering applicability. Summary of the Invention

[0013] To address the above technical problems, this invention proposes a method and apparatus for predicting ionospheric TEC using parameterized multi-scale gated convolution. The specific technical solution is as follows:

[0014] A parameterized multi-scale gated convolution method for predicting ionospheric TEC includes the following steps:

[0015] Data preparation includes the acquisition and preprocessing of relevant data, specifically acquiring space environment parameter data and global ionospheric TEC grid map data, unifying the temporal and spatial resolution of data from different sources; on this basis, the data is normalized, and combined with space environment parameter feature expansion, temporal feature parameter encoding, and data augmentation operations that conform to physical consistency, standardized input data for model training and prediction is constructed.

[0016] The global ionospheric TEC prediction model is designed, including a parametric context encoding module, a spatial feature encoding and decoding module, and a parametrically modulated spatiotemporal evolution module. The parametric context encoding module encodes space environment parameters and extracts global parameter context information that characterizes the space environment state. The spatial feature encoding and decoding module extracts and reconstructs spatial features from historical TEC grid sequences. The parametrically modulated spatiotemporal evolution module predicts and models the spatiotemporal dynamic evolution of ionospheric TEC under the modulation of global parameter context information.

[0017] The training strategy includes designing a training loss function and obtaining optimal model parameters. The loss function is used as the training objective function to constrain the prediction error within the effective physical region, and the optimal model parameters for prediction performance are obtained through iterative training.

[0018] A parametric multi-scale gated convolutional ionospheric TEC prediction device includes the following modules:

[0019] The data preparation module includes the acquisition and preprocessing of relevant data. Specifically, it acquires space environment parameter data and global ionospheric TEC grid map data, and unifies the temporal and spatial resolution of data from different sources. Based on this, the data is normalized, and combined with space environment parameter feature expansion, temporal feature parameter encoding, and data augmentation operations that conform to physical consistency, standardized input data for model training and prediction is constructed.

[0020] The global ionospheric TEC prediction model design module includes a parametric context encoding module, a spatial feature encoding and decoding module, and a parametric modulation spatiotemporal evolution module. The parametric context encoding module encodes space environment parameters and extracts global parameter context information that characterizes the space environment state. The spatial feature encoding and decoding module extracts and reconstructs spatial features from historical TEC grid sequences. The parametric modulation spatiotemporal evolution module predicts and models the spatiotemporal dynamic evolution of ionospheric TEC under the modulation of global parameter context information.

[0021] The training strategy module includes designing the training loss function and obtaining the optimal model parameters. The loss function is used as the training objective function to constrain the prediction error within the effective physical region, and the optimal model parameters for prediction performance are obtained through iterative training.

[0022] An electronic device includes: one or more processors; and a memory for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method.

[0023] A computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, cause the processor to implement the method described thereon.

[0024] The present invention has the following beneficial effects:

[0025] 1. Improve prediction accuracy and enhance the stability of long-term series predictions:

[0026] To address the issues of declining accuracy and gradual error accumulation in existing global TEC grid prediction models during multi-step prediction, this invention proposes a global ionospheric TEC prediction model based on parameterized multi-scale gated convolution. Furthermore, by incorporating a dual-benchmark residual prediction structure, short-term continuity and long-term periodic trends are explicitly introduced during the prediction process, effectively suppressing error accumulation in long-term series predictions. This ensures prediction stability while improving overall prediction accuracy.

[0027] 2. Enhance adaptability during space weather events and improve the clarity of parameter action paths:

[0028] To address the issues of insufficient utilization of space environment parameters and unclear parameter action paths in existing global TEC grid prediction models, this invention uses a parameterized context encoding module to uniformly model space environment parameters and temporal feature parameters, generating global parameter context information. This information is then explicitly modulated and introduced into a multi-scale parameterized convolutional submodule, enabling space environment parameters to influence TEC prediction results in a stable and controllable way. This effectively improves the model's adaptability and prediction stability during severe space weather events.

[0029] 3. Heterogeneity characterizes the impact of the same space environment parameters on different latitudinal zones:

[0030] To address the issue that the global ionosphere exhibits significant differences in its response to the same space weather events across different latitudinal regions, this invention introduces a parameterized modulation mechanism based on latitudinal division. This mechanism enables the same space environment parameter to produce differentiated modulation effects across different latitudinal regions, thereby achieving a heterogeneous characterization of the ionospheric response features in the equatorial, mid-high latitude, and high latitude regions, and enhancing the model's ability to depict regional differences and spatial response inconsistencies.

[0031] 4. Reduce computational overhead:

[0032] To address the issue of high computational overhead in existing global TEC grid prediction models, this invention employs a two-stage low-rank time adapter and a pure convolutional spatiotemporal prediction model. This significantly reduces the model parameter size while maintaining prediction performance and possesses excellent parallel computing characteristics, thereby effectively reducing computational overhead in the training and inference phases and improving engineering applicability. Attached Figure Description

[0033] Figure 1 This is a diagram of the overall technical solution;

[0034] Figure 2 This is a diagram of the model structure.

[0035] Figure 3 This is a flowchart of the parameterized context encoding module.

[0036] Figure 4 The flowchart for the processing of the parameterized modulation spatiotemporal evolution module;

[0037] Figure 5 This is a flowchart of the multi-scale parameterized convolution submodule. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0039] This invention proposes a parameterized multi-scale gated convolutional method and apparatus for predicting ionospheric TEC (Temperature and Temperature) patterns. The method takes a historical 48-hour global TEC grid map, spatial environmental parameter data, and temporal characteristic parameters as input, and outputs a global TEC grid map for the next 24 hours.

[0040] Overall technical solutions, such as Figure 1 As shown, the model comprises three core components: data preparation, model design, and training strategy. Data preparation includes the acquisition and preprocessing of relevant data, specifically obtaining space environment parameter data and global ionospheric TEC grid map data. Interpolation and averaging are used to unify the temporal and spatial resolution of data from different sources. Based on this, the data is normalized, and combined with space environment parameter feature expansion, temporal feature parameter encoding, and data augmentation operations conforming to physical consistency, standardized input data for model training and prediction is constructed. Model design includes a parametric context encoding module, a spatial feature encoding / decoding module, and a parametrically modulated spatiotemporal evolution module. The parametric context encoding module encodes space environment parameters, extracting global parameter context information that characterizes the space environment state. The spatial feature encoding / decoding module extracts and reconstructs spatial features from historical TEC grid map sequences. The parametrically modulated spatiotemporal evolution module predicts and models the spatiotemporal dynamic evolution of ionospheric TEC under the modulation of global parameter context information. The training strategy includes designing a training loss function and obtaining optimal model parameters. The Charbonnier loss function, which is robust to outliers, is used as the training objective function. The prediction error is constrained within the effective physical region, and the optimal model parameters for prediction performance are obtained through iterative training.

[0041] (1) Data preparation:

[0042] The model's input data includes 12 categories: global ionospheric TEC grid map, time-related parameters, F10.7 index, sunspot number (SSN), X-ray index, Dst index, Ap index, solar wind (including minimum and maximum values), and flare level (including the number of occurrences of C, M, and X-level flares). The flare level represents the daily number of solar flares, and the time-related parameters are formatted as year, month, day, and hour.

[0043] 1) Data Description:

[0044] Global Ionospheric TEC Grid Map: This data comes from the Global Ionospheric Maps (GIM) published by the International GNSS Service (IGS), used to characterize the spatiotemporal distribution of the Vertical Total Electron Content (VTEC) in the ionosphere globally. The unit is TECU; the temporal resolution is 1 hour, and the data time series length within a day is 24; the spatial resolution is... The GIM data product used in this embodiment was provided by the Center for Orbit Determination in Europe (CODE).

[0045] Time characteristic parameter: year, month, day and hour in Coordinated Universal Time (UTC).

[0046] Space environment parameters: F10.7 index, sunspot number (SSN), X-ray index, Dst index, Ap index, solar wind (including minimum and maximum values), and level of flares (including the number of occurrences of C, M, and X-level flares). The raw spatiotemporal resolution of the space environment parameters is shown in Table 1.

[0047] Table 1 Spatiotemporal resolution of space environment parameters

[0048]

[0049] 2) Data preprocessing:

[0050] Unified spatiotemporal resolution: The spatial resolution of the original global ionospheric TEC grid map is The grid size is Given the overlapping characteristics of the ionospheric grid in the longitude direction (i.e., the leftmost and rightmost columns of data are duplicated), and to adapt to the input dimensionality requirements of the model, the original data needs to be preprocessed. First, redundant data in the rightmost column is removed. Then, the last row of data is copied and filled in the latitude direction, so that the grid size of the ionospheric grid is ultimately unified. .

[0051] Data normalization: The 11 data points—global ionospheric TEC grid map, F10.7 index, sunspot number (SSN), X-ray index, Dst index, Ap index, solar wind (including minimum and maximum values), and level of flares (including the number of occurrences of C, M, and X-level flares)—have different units and may have significant numerical discrepancies, affecting model inferences. Therefore, they need to be standardized separately to ensure that the mean of each data point is 0 and the variance is 1. The standardization formula is as follows:

[0052] (1)

[0053] in, This represents the mean. Indicates standard deviation, The standardized value. This is data to be processed.

[0054] Space environment parameter feature extension: To explore the nonlinear hysteresis and cumulative effects between space environment parameters and ionospheric response, this invention employs five feature construction methods for space environment parameters, namely first-order difference features. Multi-scale rolling statistical characteristics, multi-scale lag characteristics, and extreme event lag characteristics. and cumulative intensity characteristics The methods for constructing spatial environment parameter characteristics are shown in Table 2.

[0055] Table 2 Feature construction method configurations for different space environment parameters

[0056]

[0057] Set the time series of space environment parameters as follows ,in Indicates the current time; the sliding window set is (Unit: hours); the set of lag times is ; indicates time The parameter value.

[0058] ① First-order difference characteristics Used to reflect the rapid strengthening or weakening trend of a disturbance.

[0059] (2)

[0060] in, Indicates the parameter at time The first-order difference feature.

[0061] ② Multi-scale rolling statistical features: characterizing the background state level of spatial environmental parameters at different time scales (rolling mean feature) Extreme amplitude (local extreme value characteristics) and ) and cumulative intensity (rolling cumulative characteristics) ).

[0062] Rolling mean characteristics :

[0063] (3)

[0064] in, Indicates the sliding window size; local extremum feature and :

[0065] (4)

[0066] Scrolling cumulative features :

[0067] (5)

[0068] ③ Multi-scale lag characteristics Used to model the non-instantaneous response characteristics of the ionosphere to external drives.

[0069] (6)

[0070] in, Indicates the length of the lag time.

[0071] ④ Lag characteristics of extreme events: Characterizing the relative time interval between the current moment and the occurrence of extreme disturbance events within a past time window:

[0072] (7)

[0073] in, This represents the normalized time interval feature, with a value range of [value range missing]. ; Take the index position corresponding to the maximum value (if you are interested in minimum events, such as the Dst exponent, then replace it with...). ).

[0074] ⑤ Cumulative intensity characteristics Used to characterize the continuous accumulation of disturbance energy:

[0075] (8)

[0076] in, Indicates time The cumulative intensity characteristics, This indicates the preset disturbance threshold (e.g., -30nT for the Dst exponent).

[0077] Temporal Feature Parameter Encoding: To explicitly capture the diurnal variation, seasonal variation, and periodic fluctuations related to solar activity of the ionospheric TEC, this invention does not directly use linear time values, but instead constructs a high-dimensional temporal feature encoding system based on Fourier series. This system mainly includes hourly harmonic encoding, annual cumulative harmonic encoding, and solar rotation period encoding. (Setting...) Indicates time Decimal hour (range of values) ); Indicates time Decimal year-day (inclusive of decimal days, range of values) ).

[0078] ① Hourly harmonic eigenvector The diurnal variation is represented by mapping the current hour to first- and second-order harmonic functions. The calculation formula is as follows:

[0079] (9)

[0080] in, This represents a vector concatenation operation; Indicates the harmonic order. Corresponding to the 24-hour base frequency, Corresponding to a 12-hour multiplier.

[0081] ② Annual accumulated daily harmonic characteristic vector Based on the current time of year, it represents seasonal variation. The calculation formula is as follows:

[0082] (10)

[0083] in, This represents the regression year period constant, with a value of 365.2422.

[0084] ③ 27-day solar rotation period code This reflects the short-term periodic effect of the solar rotation period on the TEC (Transient Energy Concentration). The calculation formula is as follows:

[0085] (11)

[0086] in, This indicates the modulo operation.

[0087] Physically Consistent Data Augmentation: To improve the robustness of the model in response to space weather events, this invention designs the following five types of data augmentation methods: geometric transformation, pixel noise, parameter perturbation, temporal augmentation, and spatial occlusion.

[0088] set up This represents the enhanced image. Represents the original image; This represents the enhanced parameter value. These are the original parameter values.

[0089] ① Geometric Transformation: By performing geometric transformations on the input data, the model's adaptability to different space weather events is increased. The calculation formula is as follows:

[0090] (12)

[0091] in, This indicates a random horizontal or vertical flip.

[0092] ② Pixel noise: To simulate the thermal noise of the observation equipment, Gaussian noise is introduced to simulate random noise in the image. The calculation formula is as follows:

[0093] (13)

[0094] in, This represents additive Gaussian noise. Indicates a Gaussian distribution. The standard deviation of all image pixel values ​​within the current training batch. This is the noise proportionality factor (with a value of 0.05).

[0095] ③ Parameter perturbation: Simulates observation errors in space environment monitoring data to enhance the model's adaptability to parameter changes. The calculation formula is as follows:

[0096] (14)

[0097] in, As a disturbance factor, Indicates uniform distribution. This represents the upper limit of the disturbance amplitude (with a value of 0.05).

[0098] ④ Time Augmentation: By discarding some time-step data and performing linear interpolation, data loss at different time granularities is simulated. The calculation formula is as follows:

[0099] (15)

[0100] in, This indicates a time enhancement operation that involves randomly discarding a portion of the time steps and interpolating the result.

[0101] ⑤ Spatial Occlusion: This simulates the occlusion of a local area using spatial occlusion. The calculation formula is as follows:

[0102] (16)

[0103] in, It is a randomly generated occlusion mask. This indicates element-wise multiplication. A value of 1 indicates an obscured area, while a value of 0 indicates an unobscured area.

[0104] The preprocessed global ionospheric TEC grid sequence was merged into a fourth-order tensor. .in, This represents the number of time steps in the historical observation sequence, which is 48 here; 1 represents the number of data channels. This represents the spatial length and width of the grid (i.e., the number of grid cells for latitude and longitude). The preprocessed and feature-expanded temporal feature parameter sequences and spatial environment parameter sequences are merged into a single second-order tensor. .in, This indicates the time step corresponding to the grid diagram sequence; This represents the total dimension of the expanded parametric features. Specifically, it consists of two parts: the first... The dimension is a vector obtained by encoding with time feature parameters, and then... The dimension is a high-dimensional physical feature obtained by feature expansion based on the original 10 types of spatial environment parameters. Global TEC grid tensor With space environment parameter tensor The data will be used together as input to the model to predict the global ionospheric TEC grid sequence for the next 24 hours. ,in, This represents the time step of the sequence to be predicted, which is 24 in this case.

[0105] (2) Model design:

[0106] The interrelationships between the three main modules of this model are as follows: Figure 2As shown, the model consists of three parts: a parameterized context encoding module, a spatial feature encoding / decoding module, and a parameterized modulation spatiotemporal evolution module. These are connected via residuals to ultimately output a predicted global ionospheric TEC grid map sequence. First, the sequence of space environment parameters. The input is fed into the parameterized context encoding module, where it is modeled through temporal aggregation and mapped into a compact parameterized context feature. Meanwhile, a global ionospheric TEC grid sequence The data is input into a spatial feature encoder, and after spatial feature extraction, intermediate latent features are obtained. Subsequently, latent features With parameter context features The common input is fed into the parameterized spatiotemporal evolution module. This module introduces a parameter-driven modulation mechanism into the multi-scale gated convolutional structure, enabling the model's spatiotemporal evolution process to adaptively adjust according to the current spatial environment conditions, thereby generating parameterized evolutionary features. .then, The data is fed into the spatial feature decoder to restore the original spatial resolution and obtain the prediction residual term. Finally, the predicted residuals will be... With baseline item By adding elements one by one, the predicted global ionospheric TEC grid sequence is finally obtained. .in From the original TEC grid sequence The last time step The previous day's TEC grid sequence corresponding to the predicted time step Through linear attenuation coefficient Add them together to get the result.

[0107] 1) Parameterized Context Encoding Module:

[0108] The parameterized context encoding module is used to uniformly model time-varying space environment parameters and generate global parameter context information for modulating the spatiotemporal evolution of the ionospheric TEC process. This module uses a sequence of space environment parameters. As input, the original parameter sequence is compressed into low-dimensional parameterized context features through multi-layer nonlinear mapping and temporal aggregation operations. The parameterized context vector, as a global parameter modulation signal, is output to the parameterized modulation spatiotemporal evolution module to modulate the evolution process of spatiotemporal features.

[0109] Parameterized context encoding module processing flow (see) Figure 3 )for:

[0110] ① Input spatial environment parameter sequence First, the original parameter sequence is processed by a multilayer perceptron to project it onto a low-dimensional feature space, generating a latent parameter representation. This representation can effectively characterize the overall variation features of spatial environment parameters, providing a compact representation for subsequent time-series aggregation. Its calculation process is as follows:

[0111] (17)

[0112] In the formula, This represents a multilayer perceptron.

[0113] ② Represent the generated latent parameters With learnable query vectors Cross-attention calculation is performed, and the data is further fused through a multi-layer perceptron to obtain a global parameter context vector. The calculation process is as follows:

[0114] (18)

[0115] In the formula, CrossAttention represents the calculation of cross-attention. This is the final generated global parameter context vector. Indicates its dimension.

[0116] 2) Spatial Feature Encoding / Decoding Module:

[0117] The spatial feature encoding and decoding module is used to extract and reconstruct spatial features from global ionospheric TEC grid map sequences. This module uses historical TEC grid map sequences. As input, spatial encoding is performed through a multi-layer convolutional structure to generate latent spatial feature representations for spatiotemporal evolution modeling. In the decoding stage, a symmetrical upsampling structure is used to restore spatial resolution, and combined with a dual-benchmark residual prediction mechanism, the TEC grid sequence for future time steps is output. .

[0118] In the spatial modeling process, this module introduces a boundary processing method that conforms to geographical features in the convolution operation. It adopts periodic continuous boundary expansion in the longitude direction and boundary extension processing in the latitude direction to maintain the spatial continuity of the global ionosphere under the spherical topology and alleviate the boundary discontinuity problem caused by latitude and longitude grid mapping.

[0119] The specific process of the spatial feature encoding and decoding module is as follows:

[0120] ① In the encoding stage, the spatial feature encoding and decoding module uses a multi-layer convolutional downsampling structure to process the input TEC grid map sequence. Spatial feature extraction is performed layer by layer, and the final output is: The calculation process can be expressed as follows:

[0121] (19)

[0122] In the formula, This represents the input TEC grid sequence; Indicates the first Spatial features after layer encoding; This represents a spatial convolutional downsampling unit, used to extract local spatial features and reduce spatial resolution.

[0123] ② In the decoding stage, an upsampling structure symmetrical to that used in the encoding stage is employed to recover the latent spatial features layer by layer, resulting in... The calculation process can be expressed as follows:

[0124] (20)

[0125] Subsequently, the predicted residual TEC grid sequence is obtained through output mapping convolution. The calculation process can be expressed as follows:

[0126] (twenty one)

[0127] In the formula, The output characteristics of the spatiotemporal evolution module representing parameterized modulation; Indicates the first Layer decoding input features; This indicates an upsampling convolutional unit, used to improve spatial resolution and restore spatial structure; Indicates feature fusion operation; Indicates the number of pages retained during the encoding phase. Layer space characteristics; This indicates the output mapping convolution.

[0128] ③ After completing all decoding layers, a dual-benchmark residual prediction mechanism is used to analyze the original TEC grid sequence. Extract the last time step of the sequence And the TEC grid sequence of the previous day corresponding to the predicted time step. As two benchmarks, and through the linear attenuation coefficient Constructing baseline terms :

[0129] (twenty two)

[0130] (twenty three)

[0131] and the predicted residual Add them together to get the final output. :

[0132] (twenty four)

[0133] in, Copy and extend to the prediction time dimension ; This represents the predicted global ionospheric TEC grid sequence. Each time step.

[0134] Among the above parameters , , , These represent the time step, number of channels, spatial length, and spatial width of the corresponding layer, respectively.

[0135] 3) Spatiotemporal evolution module of parameterized modulation:

[0136] The parameterized modulation spatiotemporal evolution module is used to model the non-stationary spatiotemporal evolution process of the ionospheric TEC under the modulation of space environment parameters, and is one of the core functional modules of this invention. This module takes the latent spatial features output by the spatial feature encoding / decoding module and the global parameter context vector generated by the parameterized context encoding module as input. Through low-rank modeling in the time dimension and multi-scale parameterized modulation in the spatial dimension, it achieves explicit control of the local spatiotemporal dynamics by the external space environment.

[0137] This module consists of a two-stage low-rank temporal adapter and multiple parametric multi-scale gated convolution (PMGC) blocks stacked sequentially. In the overall processing flow, the input features are first efficiently modeled in the temporal dimension by the two-stage low-rank temporal adapter, and then sequentially modeled in terms of spatial-temporal feature evolution by multiple PMGC blocks. Each PMGC block employs a slow-branch-fast-branch parallel structure for multi-scale spatial modeling. The slow branch is used to extract large-scale, relatively gently changing spatial structure features, while the fast branch introduces parametric multi-scale convolution (PMSC) to achieve differentiated modulation of spatial environment parameters in different spatial regions. Finally, the modulated spatiotemporal feature representation is output through feature fusion and residual update.

[0138] The processing flow of the parameterized modulation spatiotemporal evolution module (see...) Figure 4 )as follows:

[0139] ① In the spatiotemporal evolution module of parameterized modulation, the latent spatial features from the spatial feature encoding and decoding module are first processed. Channel-independent temporal convolution modeling is performed to reduce the temporal dimension and obtain intermediate feature representations:

[0140] (25)

[0141] Subsequently, through cross-channel feature projection and fusion operations, the time-adapted latent feature representation is obtained: :

[0142] (26)

[0143] In the formula, Time Wise Convolution represents channel-independent time convolution operation, and Channel WiseProjection represents cross-channel feature projection operation.

[0144] ② Features after time adaptation in slow branches Large-scale spatial modeling is performed. This branch employs an axial depthwise convolution structure, performing spatial aggregation along both the latitudinal and longitude directions to extract relatively gently changing global spatial structure features, resulting in the slow branch output. The calculation process is expressed as follows:

[0145] (27)

[0146] In the formula, This indicates axial depth convolution processing performed sequentially along the latitude and longitude directions.

[0147] ③ In the fast branch, the multi-scale parameterized convolutional PMSC submodule is used to process the features. Modeling is performed, and global parameter context features are introduced in the process. This is used to characterize local dynamic changes at different spatial scales, enabling differentiated modulation of spatial environment parameters to the evolution of features at different spatial locations. The fast branch output is represented as... The specific formula is as follows:

[0148] (28)

[0149] In the formula, This indicates multi-scale parameterized convolution processing.

[0150] ④ Slow branch output Fast branch output and features The fused features are obtained by integrating the data through a grouped spatial soft maximum fusion operation. The specific formula is as follows:

[0151] (29)

[0152] Subsequently, the fused features are updated through a gated feedforward network with residuals to obtain the final output features. :

[0153] (30)

[0154] (31)

[0155] In the formula, Indicates grouped spatial soft maximum fusion; , Indicates a learnable scalar; This represents a gated feedforward network.

[0156] The specific processing flow of the PMSC submodule in the spatiotemporal evolution module of parameterized modulation (see...) Figure 5 )for:

[0157] ① Input features Perform multi-scale dilated convolution processing to obtain a multi-scale feature set. The specific formula is as follows:

[0158] (32)

[0159] In the formula, This indicates multi-scale dilated convolution processing.

[0160] ② At the same time, for input features Convolution, group normalization, and activation are performed to obtain intermediate features. The specific formula is as follows:

[0161] (33)

[0162] (34)

[0163] In the formula, Indicates convolution processing; Indicates the activation function; This indicates group normalization.

[0164] ③ Based on intermediate features Convolution and pointwise convolution are performed to generate content intensity tensors. The specific formula is as follows:

[0165] (35)

[0166] In the formula, This indicates convolution processing. This indicates pointwise convolution processing.

[0167] ④ Global context features With latitudinal learnable embedding vectors The features are then fused, normalized, and generated using a multilayer perceptron to produce weft modulation features. Finally, it is mapped to each row of spatial features to obtain The calculation process is as follows:

[0168] (36)

[0169] In the formula, Representation layer normalization; This represents a multilayer sensor; m represents the number of weft zones that are artificially separated.

[0170] ⑤ Obtain the content intensity tensor Latitudinal characteristics and two projection matrices and Multiply and obtain using a soft sign activation function and The calculation process is as follows:

[0171] (37)

[0172] (38)

[0173] In the formula, This represents a soft symbolic activation function; additionally, it involves matrix operations.

[0174] ⑥ Intermediate features It still needs to be obtained through convolution. The specific formula for the base route weight is as follows:

[0175] (39)

[0176] In the formula, This indicates convolution processing.

[0177] ⑦ In order to introduce parameter modulation, the generated parameters will now be... and To modulate the base route weight Obtain parameterized modulation routing The formula is as follows:

[0178] (40)

[0179] In the formula This represents element-wise multiplicative modulation.

[0180] ⑧ Parameterized Modulation Routing The scale weights are obtained by sequentially performing dilated convolution and a flexible maximum function. The formula is as follows:

[0181] (41)

[0182] In the formula This indicates dilated convolution processing; This represents the flexible maximum value function.

[0183] ⑨ For multi-scale features Perform weighted fusion and obtain through convolutional mapping The calculation process is as follows:

[0184] (42)

[0185] In the formula, This indicates convolution processing. This represents element-wise multiplicative modulation.

[0186] In the above parameters, r represents the dimension in the low-rank space; K represents the number of dilated convolution kernels; , and This represents the channel dimension, length, and width of the corresponding feature space.

[0187] (3) Training strategy:

[0188] The key points for model training are as follows:

[0189] 1) Data selection and processing:

[0190] To enable the model to fully learn the impact of space weather events on the global ionospheric TEC grid, this invention selects historical observation data covering different time periods and space environmental conditions during the data selection stage. This ensures the diversity of training samples in terms of time scale and space environment, thereby improving the model's ability to model the TEC evolution process under different solar activity levels and space weather events.

[0191] Because the data sources and observation methods for different space environment parameters vary, their time resolution may differ from 1 hour to 1 day. Therefore, time alignment processing is performed on the space environment parameters during the data preprocessing stage. Specifically, various space environment parameters are uniformly converted to a 1-hour time resolution through interpolation or time averaging to ensure the consistency of the space environment parameter sequence with the TEC grid sequence in the time dimension.

[0192] Given the overlapping characteristics of the global ionospheric TEC grid map along the longitude direction (i.e., the leftmost and rightmost longitude grid data are duplicated), this invention performs spatial adjustment processing on the original TEC grid map during the preprocessing stage to avoid redundant information and adapt to the model input dimensionality requirements. Specifically, this includes removing the rightmost column of redundant data along the longitude direction and copying and filling the boundary rows along the latitude direction, so that the preprocessed TEC grid map has a uniform size. This facilitates subsequent spatial modeling and network training.

[0193] 2) Loss function:

[0194] To avoid interference from global ionospheric TEC data during spherical topology mapping and boundary filling in model training, this invention introduces a loss calculation strategy with effective region constraints during the model training phase. Prediction errors are calculated only within effective grid areas with real physical significance, thereby avoiding adverse effects of boundary filling areas on model parameter updates.

[0195] This invention employs a dual-benchmark residual prediction structure. The backbone network models the non-stationary perturbations of the ionospheric TEC in residual form, and combines this model with the benchmark TEC field in the output stage to obtain the final TEC prediction result. Although the model internally uses residual modeling, the loss function still applies to the difference between the final reconstructed TEC prediction result and the true TEC value during model training.

[0196] Under the aforementioned residual modeling structure, the model output corresponds to the perturbation component relative to the reference field, and its numerical distribution typically exhibits asymmetry and large local amplitude variations. Using a mean squared error loss function can easily lead to excessive penalty for a small number of samples with large perturbations, thus affecting the stability of model parameter updates. Therefore, within the effective region, this invention employs the Charbonnier loss function, which is more robust to outliers, to measure the difference between the predicted TEC grid and the true TEC grid. This loss function is formally equivalent to a smoothed L1 loss function and is more suitable for stable optimization of model structures driving residual output. During training, the effective region mask remains fixed to ensure that the model consistently adheres to physical constraints during optimization, achieving stable and physically consistent model training.

[0197] The mathematical expression for the loss function is:

[0198] (43)

[0199] in, This represents the final TEC prediction value output by the model; This represents the actual TEC value at the corresponding location; Indicates the effective grid area; Indicates the number of grid points within the effective area; This is the smoothing constant.

[0200] 3) Model training parameters:

[0201] When setting model hyperparameters, the number of layers in the spatial feature encoding / decoding module should be moderate. Too many layers will result in insufficient feature spatial resolution and blurred features, while too few layers will lead to excessively high spatial resolution and significantly increased computational resources. Similarly, the PMGC module in the parameterized modulation spatiotemporal evolution module should not be too numerous, otherwise it will lead to overfitting and increased training time. Testing showed that setting both the spatial feature encoding / decoding module and the PMGC module to 4 layers yielded good results. The model is recommended to be optimized using the AdamW algorithm, with a learning rate set to [value missing]. An exponentially decaying dynamic learning rate can be used to gradually reduce the learning rate during training. Testing showed that the model can be trained smoothly and quickly on an NVIDIA RTX 4090D graphics card (24GB VRAM), indicating low hardware requirements. Specific parameters for model training are detailed in Table 3.

[0202] Table 3. Details of Model Training Parameters

[0203]

[0204] A parametric multi-scale gated convolutional ionospheric TEC prediction device includes the following modules:

[0205] The data preparation module includes the acquisition and preprocessing of relevant data. Specifically, it acquires space environment parameter data and global ionospheric TEC grid map data, and unifies the temporal and spatial resolution of data from different sources. Based on this, the data is normalized, and combined with space environment parameter feature expansion, temporal feature parameter encoding, and data augmentation operations that conform to physical consistency, standardized input data for model training and prediction is constructed.

[0206] The global ionospheric TEC prediction model design module includes a parametric context encoding module, a spatial feature encoding and decoding module, and a parametric modulation spatiotemporal evolution module. The parametric context encoding module encodes space environment parameters and extracts global parameter context information that characterizes the space environment state. The spatial feature encoding and decoding module extracts and reconstructs spatial features from historical TEC grid sequences. The parametric modulation spatiotemporal evolution module predicts and models the spatiotemporal dynamic evolution of ionospheric TEC under the modulation of global parameter context information.

[0207] The training strategy module includes designing the training loss function and obtaining the optimal model parameters. The loss function is used as the training objective function to constrain the prediction error within the effective physical region, and the optimal model parameters for prediction performance are obtained through iterative training.

[0208] An electronic device includes: one or more processors; and a memory for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method.

[0209] A computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, cause the processor to implement the method described thereon.

[0210] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of the present invention can be implemented using various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0211] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0212] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0213] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0214] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0215] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A parametric multi-scale gated convolution method for predicting ionospheric TEC, characterized in that, Includes the following steps: Data preparation includes the acquisition and preprocessing of relevant data, specifically acquiring space environment parameter data and global ionospheric TEC grid map data, unifying the temporal and spatial resolution of data from different sources; on this basis, the data is normalized, and combined with space environment parameter feature expansion, temporal feature parameter encoding, and data augmentation operations that conform to physical consistency, standardized input data for model training and prediction is constructed. The global ionospheric TEC prediction model is designed, including a parametric context encoding module, a spatial feature encoding and decoding module, and a parametrically modulated spatiotemporal evolution module. The parametric context encoding module encodes space environment parameters and extracts global parameter context information that characterizes the space environment state. The spatial feature encoding and decoding module extracts and reconstructs spatial features from historical TEC grid sequences. The parametrically modulated spatiotemporal evolution module predicts and models the spatiotemporal dynamic evolution of ionospheric TEC under the modulation of global parameter context information. The training strategy includes designing a training loss function and obtaining optimal model parameters. The loss function is used as the training objective function to constrain the prediction error within the effective physical region, and the optimal model parameters for prediction performance are obtained through iterative training.

2. The ionospheric TEC prediction method based on parameterized multi-scale gated convolution according to claim 1, characterized in that, In the data preparation steps, the expansion of the space environment parameter features includes: constructing first-order difference features to reflect the trend of disturbance changes; constructing multi-scale rolling statistical features to characterize the background state level, extreme amplitude, and cumulative intensity; constructing multi-scale hysteresis features to model the non-instantaneous response characteristics of the ionosphere to external drives; constructing extreme event hysteresis features to characterize the time interval between the current moment and historical extreme disturbance events; and constructing cumulative intensity features to characterize the continuous accumulation characteristics of disturbance energy. The multi-scale rolling statistical features include rolling mean features, local extreme value features, and rolling cumulative features.

3. The ionospheric TEC prediction method based on parameterized multi-scale gated convolution according to claim 1, characterized in that, In the data preparation step, the time feature parameter encoding adopts a high-dimensional time feature encoding system based on Fourier series, including: mapping the number of hours at the current moment to represent the daily variation of hourly harmonic features by first-order and second-order harmonic functions, mapping the annual accumulated days at the current moment to represent the seasonal variation of annual accumulated day harmonic features, and solar rotation period encoding that reflects the short-term periodicity of TEC.

4. The ionospheric TEC prediction method based on parameterized multi-scale gated convolution according to claim 1, characterized in that, In the design of the global ionospheric TEC prediction model, the parameterized context coding module first projects the spatial environment parameters onto a low-dimensional feature space through a multilayer perceptron to generate a latent parameter representation. Then, the latent parameter representation is cross-attentioned with a learnable query vector, and finally fused through a multilayer perceptron to generate the global parameter context information, so as to establish a stable global parameter modulation signal.

5. The ionospheric TEC prediction method based on parameterized multi-scale gated convolution according to claim 1, characterized in that, In the design of the global ionospheric TEC prediction model, the spatial feature encoding and decoding module extracts spatial features from the historical TEC grid sequence through a multi-layer convolutional downsampling structure during the encoding stage, and restores spatial resolution through a symmetrical upsampling structure during the decoding stage. Specifically, a boundary processing method conforming to geographical features is introduced into the convolution operation: periodic continuous boundary expansion is used in the longitude direction, and boundary extension processing is used in the latitude direction to maintain spatial continuity under the spherical topology. Furthermore, the spatial feature encoding and decoding module adopts a dual-baseline residual prediction structure, constructing a baseline term based on the most recent historical TEC grid and the predicted TEC grid of the previous day using a linear decay coefficient, and adding it to the prediction residual to obtain the final TEC prediction result.

6. The ionospheric TEC prediction method based on parameterized multi-scale gated convolution according to claim 1, characterized in that, In the design of the global ionospheric TEC prediction model, the parameterized modulation spatiotemporal evolution module includes a two-stage low-rank time adapter and multiple parameterized multi-scale gated convolutional blocks stacked sequentially. The two-stage low-rank time adapter achieves efficient modeling of the time dimension through channel-independent temporal convolution and cross-channel feature projection. The parameterized multi-scale gated convolutional blocks employ a parallel structure of slow and fast branches. The slow branch uses axial depth convolution to extract gently changing global spatial structure features, while the fast branch extracts local dynamic change features under the zonal modulation effect of the global parameter context information through a multi-scale parameterized convolutional submodule. The multi-scale parameterized convolutional submodule performs parameterized weighted fusion of the multi-scale dilated convolutional features based on the zonal modulation features generated by fusing content intensity tensors and zonal learnable embedding vectors, thereby achieving an explicit characterization of the heterogeneity of ionospheric responses in different zonal regions by spatial environmental parameters.

7. The ionospheric TEC prediction method based on parameterized multi-scale gated convolution according to claim 1, characterized in that, In the training strategy, the Charbonnier loss function, which is robust to outliers, is used as the training objective function. The prediction error is calculated only within the effective grid area with real physical meaning, avoiding interference from boundary filling regions on model parameter updates. The loss function acts between the final TEC prediction value and the true TEC value output by the model, and the optimal model parameters with stable prediction performance under strongly non-stationary spatial conditions are obtained through iterative training.

8. A parametric multi-scale gated convolutional ionospheric TEC prediction device, characterized in that, Includes the following modules: The data preparation module includes the acquisition and preprocessing of relevant data. Specifically, it acquires space environment parameter data and global ionospheric TEC grid map data, and unifies the temporal and spatial resolution of data from different sources. Based on this, the data is normalized, and combined with space environment parameter feature expansion, temporal feature parameter encoding, and data augmentation operations that conform to physical consistency, standardized input data for model training and prediction is constructed. The global ionospheric TEC prediction model design module includes a parametric context encoding module, a spatial feature encoding and decoding module, and a parametric modulation spatiotemporal evolution module. The parametric context encoding module encodes space environment parameters and extracts global parameter context information that characterizes the space environment state. The spatial feature encoding and decoding module extracts and reconstructs spatial features from historical TEC grid sequences. The parametric modulation spatiotemporal evolution module predicts and models the spatiotemporal dynamic evolution of ionospheric TEC under the modulation of global parameter context information. The training strategy module includes designing the training loss function and obtaining the optimal model parameters. The loss function is used as the training objective function to constrain the prediction error within the effective physical region, and the optimal model parameters for prediction performance are obtained through iterative training.

9. An electronic device, characterized in that, include: One or more processors; A memory for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors implement the parameterized multi-scale gated convolution ionospheric TEC prediction method according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, It stores executable instructions that, when executed by a processor, cause the processor to implement the ionospheric TEC prediction method of parameterized multi-scale gated convolution as described in any one of claims 1 to 7.

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