Spatiotemporal Ionospheric TEC Prediction with Deformable Convolution for Long-Term Spatial Dependencies

Abstract

SA-ConvLSTM is a recently proposed spatiotemporal model for total electron content (TEC) prediction, which effectively catches long-term temporal evolution and global-scale spatial correlations in TEC. However, its reliance on standard convolution limits spatial feature extraction to fixed regular regions, reducing the flexibility for irregular TEC variations. To address this limitation, we enhance SA-ConvLSTM by incorporating deformable convolution, proposing SA-DConvLSTM. This achieves adaptive spatial feature extraction through learnable offsets in convolutional kernels. Building on this improvement, we design ED-SA-DConvLSTM, a TEC spatiotemporal prediction model based on an encoder–decoder architecture with SA-DConvLSTM as its fundamental block. Firstly, the effectiveness of the model improvement was verified through an ablation experiment. Subsequently, a comprehensive quantitative comparison was conducted between ED-SA-DConvLSTM and baseline models (C1PG, ConvLSTM, and ConvGRU) in the region of 12.5° S–87.5° N and 25° E–180° E. The experimental results showed that the ED-SA-DConvLSTM exhibited superior performance compared to C1PG, ConvGRU, and ConvLSTM, with prediction accuracy improvements of 10.27%, 7.65%, and 7.16% during high solar activity and 11.46%, 4.75%, and 4.06% during low solar activity, respectively. To further evaluate model performance under extreme conditions, we tested the ED-SA-DConvLSTM during four geomagnetic storms. The results showed that the proportion of its superiority over the baseline models exceeded 58%.

1. Introduction

The ionosphere, an ionized region of Earth’s upper atmosphere, contains abundant charged particles that influence electromagnetic wave propagation through velocity and path alterations, causing ionospheric delay [1]. Ionospheric delay is the primary error source in Global Navigation Satellite System (GNSS) applications [2,3]. The ionosphere total electron content (TEC) is an important parameter for describing the ionosphere [4], which can be used to calculate ionospheric delay [5,6]. Accurate TEC prediction enables precise ionospheric delay correction, thereby enhancing the reliability and accuracy of GNSS-based positioning, navigation, and timing services [7,8].

The TEC exhibits complex spatiotemporal variations driven by multiple geophysical factors including local time, seasonal cycles, solar activity levels, and geomagnetic conditions. These complex changes pose a great challenge to accurately predicting TEC [9,10,11]. Deep learning methods have emerged as powerful tools for this task due to their superior capacity in modeling nonlinear relationships [12,13,14], demonstrating remarkable success across various prediction applications [15,16,17].

There are currently two main deep learning methods used for TEC prediction: (1) Time series models, which consider TEC prediction as time series prediction. Early implementations adopted basic recurrent architectures such as LSTM [18,19,20] and GRU [21], which were subsequently enhanced through bidirectional variants offering improved temporal modeling capabilities [22,23]. The field then progressed to hybrid architectures combining convolutional layers with recurrent networks to capture both temporal patterns and local spatial features [24,25,26]. Most recently, attention mechanisms have been successfully integrated into these frameworks to enable dynamic feature weighting [27,28]. While these temporal approaches have achieved reasonable performance, they are fundamentally limited by their inability to incorporate broader spatial correlations. (2) Spatiotemporal models. This kind of model processes the continuous TEC map sequences by convolution operation and realizes the dual feature extraction of the temporal and spatial features of TEC. Therefore, its prediction effect is often superior to those of time series models. Among them, the most famous spatiotemporal prediction model is ConvLSTM [29]. In recent years, it and its variants have been widely used in TEC prediction [30,31], including Attention ConvLSTM [32], ED-ConvLSTM [33,34,35], ConvGRU [36], BiConvGRU [37], etc.

While spatiotemporal models such as ConvLSTM and ConvGRU currently dominate TEC prediction, they face two critical limitations. One of the challenges faced by TEC prediction is how to effectively model the long-term spatial correlation of TEC. Although the existing spatial–temporal model based on ConvLSTM can effectively capture local spatial features, in order to capture long-term spatial features, it is necessary to stack multiple convolution layers. However, the inherent limitations of convolution operation will cause the effective receptive field to be much smaller than the theoretical receptive field, which makes the long-term correlation modeling inefficient [38]. Another issue is the shape of the convolution kernel. Most existing models use standard convolution, and the sampling points of their convolution kernels are fixed regions. However, TEC is dynamically changing, and predictions for the future may come from irregular regions. Therefore, it is very important to flexibly capture the changing characteristics in spatially irregular TEC regions.

SA-ConvLSTM [39] innovatively introduces self-attention memory into ConvLSTM, dynamically models the long-term spatial correlation of TEC through self-attention memory, and aggregates it with short-term memory. It solves the problem of ConvLSTM and ConvGRU obtaining long-term dependencies through convolution operations and effectively extracts long-term features, improving the modeling ability of the model for complex spatial dynamics of the ionosphere. Additionally, to extract irregular region features, we introduced deformable convolution [40] into SA-ConvLSTM and proposed a novel unit SA-DConvLSTM. This unit extracts features from irregular areas through learnable offsets. This is more effective for feature extraction of TEC. Building upon SA-DConvLSTM, we propose ED-SA-DConvLSTM, an encoder–decoder architecture for TEC spatiotemporal prediction. The encoder progressively transforms input TEC sequences into compressed spatiotemporal representations, while the decoder reconstructs these features into predicted TEC maps. The improvements in the paper allow for more flexible feature extraction of TEC while also better utilizing long-term spatial dependencies.

To evaluate model performance, we conducted experiments using a 6-year sequence of TEC maps (2013–2015, 2017–2019) covering the region of 12.5° S–87.5° N and 25° E–180° E. This study region encompasses all of Asia and surrounding regions, allowing us to assess the model under both high and low solar activity periods.

The dataset was divided into 4 years of training and 2 years of testing. We compared ED-SA-DConvLSTM against three benchmarks: (1) ConvGRU and ConvLSTM as state-of-the-art spatiotemporal models, and (2) C1PG, which is a 1-day TEC prediction product provided by Center Orbit Determination Europe (CODE). In the above description, SA-ConvLSTM and ED-SA-DConvLSTM are already simplified forms of their original technical designations, where “SA” is “self-attention”, “D” is “deformable convolution”, and “ED” is “encoder–decoder architecture”. The baseline models (C1PG, ConvLSTM, ConvGRU) are widely recognized in the field. C1PG is the official name of the IGS reference model. ConvLSTM and ConvGRU are canonical architectures.

2. Data and Data Processing

The experimental data consist of Global Ionospheric Maps (GIMs) provided by the International GNSS Service (IGS), stored in IONEX format files. Each IONEX file contains daily GIM data with a spatial resolution of 5° (longitude) × 2.5° (latitude) and a temporal resolution of 2 h, covering the global range from 87.5° S to 87.5° N and 180° W to 180° E.

Due to computational complexity, this study focuses on a specific subregion (25° E–180° E, 12.5° S–87.5° N) encompassing all of Asia and surrounding regions. The study region is illustrated in Figure 1. This area encompasses both equatorial and mid-latitude regions, including the Equatorial Ionization Anomaly (EIA) zone, making it both distinctive and representative. To account for the impact of solar activity on TEC predictions, the dataset includes TEC maps from three years of high solar activity (2013–2015) and three years of low solar activity (2017–2019). The data are partitioned into the training set (2013–2014, 2017–2018; 17,520 maps) and testing set (2015, 2019; 8760 maps).

To mitigate data scale biases, we normalized all TEC values using Min-Max standardization, which transforms the data into a $[0,1]$ range through linear scaling. The normalization formula is given by:

$$X^{\prime }={\displaystyle \frac{X-X_{min}}{X_{max}-X_{min}}}$$

(1)

where $X$ is the original TEC map, $X^{\prime }$ denotes the normalized values constrained to the range $[0,1]$, and $X_{min}$ and $X_{max}$ represent the minimum and maximum of $X$ in the training set, respectively.

3. Methodology

In this paper, we first replaced the standard convolution of SA-ConvLSTM with deformable convolution and proposed SA-DConvLSTM. Then, a TEC spatiotemporal prediction model ED-SA-DConvLSTM is proposed based on SA-DConvLSTM as the basic blocks. This section provides a detailed introduction to the core technologies implemented.

3.1. The Original SA-ConvLSTM

SA-ConvLSTM extends the standard ConvLSTM by incorporating a self-attention memory (SAM) module. The following subsections detail the SAM and the SA-ConvLSTM.

3.1.1. Self-Attention Memory (SAM) Module

The SAM module takes two inputs: the current time step’s feature $H_t$ and the previous memory state $M_{t-1}$, which memorizes long-term spatial dependencies [39]. It outputs an updated memory state $M_t$ and a fused feature ${\widehat{H}}_t$. The detailed structure of SAM is shown in Figure 2.

Specifically, the SAM module integrates three core operations: (1) feature aggregation, (2) memory updating, and (3) output.

• Feature aggregation:

This part first weights the current time step features and the long-term spatial memory features and then aggregates them together to form a new feature vector. The calculation process is as shown in Equations (2)–(4).

$$\left\{\begin{array}{c}{K}_h=W_{hk}{H}_t,Q_h=W_{hq}{H}_t,V_h=W_{hv}{H}_t\\ A_h=Q_h^T{K}_h\\ Z_h=A_h{V}_h\end{array}\right.$$

(2)

$$\left\{\begin{array}{c}{K}_m=W_{mk}{M}_{t-1},Q_h=W_{hq}{H}_t,V_m=W_{mv}{M}_{t-1}\\ A_m=Q_h^T{K}_m\\ Z_m=A_m{V}_m\end{array}\right.$$

(3)

$$Z=W_Z\left[Z_h;Z_m\right]$$

(4)

In the above formulation, the weight $A_h$ is first computed for the current feature $H_t$, generating the weighted feature $Z_h$. Similarly, the weight $A_m$ is derived for the long-term memory state $M_{t-1}$, obtaining the weighted memory state $Z_m$. These two components, $Z_h$ and $Z_m$, are then concatenated to form the aggregated feature vector $Z$. $W_{hq}$, $W_{hk}$, $W_{hv}$, $W_{mk}$, $W_{mv}$, $W_z$ are weight matrices, and $Q_h$, $K_h$, $K_m$, $V_h$, $V_m$ are the intermediate vectors that support the calculated attention scores.

• Memory updating:

This part is used for the adaptive updating of long-term spatial dependencies $M_t$, and the specific process is as follows:

$$\left\{\begin{array}{c}K=\left[H_t;Z\right]\\ i_t^{\prime }=\sigma \left(W_{mi}\ast K+b_{mi}\right)\\ g_t^{\prime }=\mathit{tanh}\left(W_{mg}\ast K+b_{mg}\right)\\ M_t=\left(1-i_t^{\prime }\right)\odot M_{t-1}+i_t^{\prime }\odot g_t^{\prime }\end{array}\right.$$

(5)

The gating mechanism computes the long-term memory features by combining the previous time step’s memory with the current feature $K$, effectively capturing long-term dependencies.

• Output:

This part generates the output ${\widehat{H}}_t$. The calculation process is as follows:

$$\left\{\begin{array}{c}{o}_t^{\prime }=\sigma \left(W_{mo}\ast K+b_{mo}\right)\\ {\widehat{H}}_t=o_t^{\prime }\odot M_t\end{array}\right.$$

(6)

The pseudocode for the SAM calculation process is shown in

Table 1. The pseudocode for the SAM calculation process.

Feature Aggregation
1	Receive the short-term memory feature $H_t$ of the current time step and the long-term memory feature $M_{t-1}$ of the previous time step.
2	Obtain $K_h$, $Q_h$, $V_h$, $K_m$, $V_m$ through linear transformations of $H_t$ and $M_{t-1}$.
3	Calculate the similarity scores of $H_t$ and $M_{t-1}$ separately to obtain $A_h$, $A_m$.
4	Weight $V_h$ and $V_m$ separately to obtain $Z_h$ and $Z_m$, and concatenate them to obtain $Z$.
5	Concatenate $Z$ and $H_t$ to obtain a new feature $K$.
Memory updating
6	$K$ and $M_{t-1}$ are operated to obtain the long-term memory feature $M_t$ of the current time step.
Output
7	$K$ and $M_t$ are operated to obtain the updated short-term memory feature ${\widehat{H}}_t$ of the current time step.

.

3.1.2. SA-ConvLSTM

The SA-ConvLSTM integrates the SAM module with ConvLSTM, as illustrated in Figure 2. Each unit contains three standard gates and the SAM module, with the complete computational process as follows:

$$\left\{\begin{array}{c}{f}_t=\sigma \left(W_{xf}\ast X_t+W_{hf}\ast {\widehat{H}}_{t-1}+b_f\right)\\ i_t=\sigma \left(W_{xi}\ast X_t+W_{hi}\ast {\widehat{H}}_{t-1}+b_i\right)\\ {\widehat{c}}_t=\tanh \left(W_{xc}\ast X_t+W_{hc}\ast {\widehat{H}}_{t-1}+b_c\right)\\ C_t=f_t\odot C_{t-1}+i_t\odot {\widehat{c}}_t\\ o_t=\sigma \left(W_{xo}\ast X_t+W_{ho}\ast {\widehat{H}}_{t-1}+b_o\right)\\ H_t=o_t\odot \tanh \left(C_t\right)\end{array}\right.$$

(7)

where $X_t$ denotes the current input, $H_t$ is the current feature extracted by ConvLSTM, and ${\widehat{H}}_{t-1}$ represents the output from the previous time step.

3.2. SA-DConvLSTM

While the original SA-ConvLSTM employs standard convolution with fixed, regular receptive fields, this approach limits feature extraction to rigid patterns and struggles with complex deformations. To address this, deformable convolution [40] introduces learnable offsets to the sampling positions, enabling adaptive receptive field shapes. This modification allows the model to adaptively extract features from irregular regions, better adapting to TEC maps with continuous changes.

The calculation formulas for standard convolution and deformable convolution are Equations (8) and (9), respectively.

$$y\left(P_0\right)={\sum }_{P_n\in R}w\left(P_n\right)·x\left(P_0+P_n\right)$$

(8)

$$y\left(P_0\right)={\sum }_{P_n\in R}w\left(P_n\right)·x\left(P_0+P_n+∆P_n\right)$$

(9)

Among them, $P_0$ is an arbitrary position on the input feature map; $P_n$ represents the offset of each point in the convolution kernel from the central point $P_0$; $∆P_n$ denotes the learnable offsets at position $P_n$; $x\left(\right)$ is the value at a certain position on the input feature map; $w\left(P_n\right)$ is the weight at position $P_n$; $y\left(P_0\right)$ represents the result of convolution at position $P_0$; and $R$ is a set that contains all the sampling points in the convolutional kernel.

Figure 3 illustrates the difference in sampling point distributions between standard convolution and deformable convolution. As shown in the figure, the sampling points of standard convolution (left) follow a fixed rectangular grid pattern with a rigid and non-learnable geometric structure. In contrast, deformable convolution (right) introduces learnable spatial offsets, allowing each sampling point to dynamically adjust its position based on target features. This flexible mechanism enables the convolutional kernel to adaptively conform to geometric deformations or complex structures of objects, significantly enhancing the model’s ability to capture shape variations. The spatial arrangement of sampling points in the figure visually demonstrates the essential distinction between the two convolution methods in the feature extraction strategy.

Considering the merit of deformable convolution, this paper embedded it into SA-ConvLSTM and proposed SA-DConvLSTM. The structure comparison between SA-ConvLSTM and SA-DConvLSTM is shown in Figure 4, where our improvements are marked in the blue box.

3.3. The Proposed ED-SA-DConvLSTM

On the basis of the SA-DConvLSTM units introduced earlier, we organized these units into an encoder–decoder architecture to construct our TEC spatiotemporal prediction model, called ED-SA-DConvLSTM. As shown in Figure 5, the model architecture consists of two parts: an encoder for feature extraction and a decoder for prediction generation.

The encoder processes input TEC map sequences through three consecutive SA-DConvLSTM layers, progressively extracting hierarchical spatiotemporal features. Each SA-DConvLSTM layer is followed by LayerNorm (LN) to stabilize activations and mitigate gradient issues. In the recurrent neural network, LN has more advantages [41]. The final Conv2D layer with sigmoid activation consolidates the feature sequences into a compressed representation. The decoder reconstructs the TEC predictions through two SA-DConvLSTM+LN layers, which progressively expand the encoded features into output sequences. Due to limited computing resources, this study manually selected the architecture design of a three-layer encoder and a two-layer decoder. Furthermore, based on the non-negative nature of TEC, we employed a sigmoid activation in the final layer to strictly constrain predictions within the normalized $[0, 1]$ range, ensuring the physical consistency of the results.

The ED-SA-DConvLSTM model processes an input TEC map sequence through its encoder to extract a compressed spatiotemporal feature representation, which the decoder then expands into a variable-length output sequence.

4. Experimental Results

4.1. Evaluation Metrics

This study employs two evaluation metrics to quantitatively assess model performance: Root Mean Square Error ($RMSE$) and Mean Absolute Percentage Error ($MAPE$). These metrics are calculated as follows:

$$RMSE=\sqrt{{\displaystyle \frac{1}{n}}\sum _{i=1}^n{\left(y_i-{\widehat{y}}_i\right)}^2}$$

(10)

$$MAPE={\displaystyle \frac{1}{n}}\sum _{i=1}^n\left|{\displaystyle \frac{y_i-{\widehat{y}}_i}{y_i}}\right|\times 100\%$$

(11)

Among them, $n$ is the number of samples in the test set, and $y_i$ and ${\widehat{y}}_i$ are the true and predicted values, respectively.

4.2. Model Optimization

In deep learning, hyperparameter configuration has a significant impact on model performance [42,43]. Hyperparameters are usually divided into two categories: model structure hyperparameters and training process hyperparameters. Automatically optimizing all hyperparameters requires a significant amount of time. Therefore, we manually optimized the architectural hyperparameters: using the adaptive motion estimation (ADAM) optimizer, mean square error (MSE) loss function, and CosineAnnealingWarmRestarts learning rate scheduling, with an initial value of 0.001, and adjusting it every 50 iterations; the maximum number of iterations is 200. The parameters (number and size of convolution kernels) in the training process are automatically tuned by the Bayesian optimization method. Among the benchmark models evaluated, C1PG serves as a non-trainable reference product provided by CODE. In contrast, the proposed ED-SA-DConvLSTM and comparison models (ConvGRU and ConvLSTM) require hyperparameter optimization. The final optimized values are shown in

Table 2. The optimal hyperparameters obtained through Bayesian optimization.

Model	Hyperparameter Setting
	The Number of Convolution Kernels	The Size of Convolution Kernels
ConvGRU	30	3
ConvLSTM	64	5
ED-SA-DConvLSTM	30	3

and applied consistently in comparative experiments.

4.3. The Input and Output Length

This subsection identifies the optimal time window configuration for the model. As shown in Figure 6, a 2-day input window demonstrates superior prediction accuracy across varying solar activity levels, with $RMSEs$ of 3.5777 $TECU$ and 1.3417 $TECU$ in high and low solar activity, respectively. Consequently, all subsequent experiments employ this optimal “2-day input to 1-day output” configuration.

4.4. Ablation Experiment

This subsection validates the effectiveness of deformable convolution through an ablation experiment.

Table 3. Comparison results of ablation experiment.

Solar Activity	Model	$\mathit{R}\mathit{M}\mathit{S}\mathit{E}\left(\mathit{T}\mathit{E}\mathit{C}\mathit{U}\right)$	Improved
High solar activity (2015)	ED-SA-ConvLSTM	3.6150	--
	ED-SA-DConvLSTM	3.5777	1.03%
Low solar activity (2019)	ED-SA-ConvLSTM	1.3645	--
	ED-SA-DConvLSTM	1.3517	0.94%

shows the results of the ablation experiment, where the only difference between ED-SA-ConvLSTM and ED-SA-DConvLSTM is the use of standard convolution in ED-SA-ConvLSTM and deformable convolution in ED-SA-DConvLSTM. It can be seen that after adding deformable convolution, the $RMSEs$ decreased by 1.03% in 2015 and 0.94% in 2019. This indicates that deformable convolution can improve the performance of the model.

4.5. Comparison with Other Models

4.5.1. Overall Quantitative Comparison

As evidenced in

Table 4. Overall comparison on the test set (the best are bolded).

Solar Activity	Model	$\mathit{R}\mathit{M}\mathit{S}\mathit{E}\left(\mathit{T}\mathit{E}\mathit{C}\mathit{U}\right)$	$\mathit{M}\mathit{A}\mathit{P}\mathit{E}$
2015 (High)	C1PG	4.0295	16.12%
	ConvGRU	3.9144	14.76%
	ConvLSTM	3.8936	14.47%
	ED-SA-DConvLSTM	3.5777	13.20%
2019 (Low)	C1PG	1.5421	14.95%
	ConvGRU	1.4325	14.70%
	ConvLSTM	1.4222	14.01%
	ED-SA-DConvLSTM	1.3517	13.72%

, the proposed ED-SA-DConvLSTM demonstrates superior predictive performance compared to all benchmark models (C1PG, ConvGRU, and ConvLSTM) across both solar activities. During high solar activity (2015), the model achieves $RMSE$ reductions of 10.27%, 7.65%, and 7.16% relative to C1PG, ConvGRU, and ConvLSTM, respectively, while under low solar activity (2019), these improvements reach 11.46%, 4.75%, and 4.06%. Furthermore, ED-SA-DConvLSTM consistently delivers the lowest MAPE in both solar activities.

Figure 7 further illustrates the pairwise comparison of error distributions between ED-SA-DConvLSTM and three other comparative models. In Figure 5, the left side represents high solar activity, and the right side represents low solar activity. The horizontal axis of each subgraph represents the prediction error value $∆ (∆=predicted value - true value)$ of the model, and the vertical axis represents the proportion of ∆ in each interval. ED-SA-DConvLSTM shows higher proportions of zero-error predictions ($∆=0$) than C1PG, ConvGRU, and ConvLSTM, demonstrating its superior TEC prediction accuracy.

4.5.2. Visual Comparison of Various Models

To visually compare the prediction performance of different models, we selected one day during high solar activity (DOY 196, 2015) and low solar activity (DOY 196, 2019), presenting TEC prediction maps and corresponding absolute error maps at two representative time points (UT 0:00 and UT 12:00), as shown in Figure 8 and Figure 9, respectively. The $RMSE$ is marked in Figure 7 (with the minimum value in red). The results indicate that the proposed ED-SA-DConvLSTM achieves the lowest $RMSE$ among all models, particularly in the Equatorial Ionization Anomaly (EIA) region, demonstrating its superior ability to capture TEC variations.

4.5.3. Comparison Under Extreme Situations

To evaluate model robustness under extreme situations, we specifically selected four geomagnetic storm events in 2015, as shown in Figure 10. Geomagnetic storm can cause severe ionospheric disturbances, seriously challenging the accuracy of TEC prediction [44]. Each event is analyzed using continuous 3-day TEC maps centered on the minimum Dst index, capturing the complete disturbance cycle from initial onset through the recovery phase.

We first calculated the $RMSE$ of all models for each geomagnetic storm event and the improvement of ED-SA-DConvLSTM compared to C1PG, ConvGRU, and ConvLSTM, as shown in

Table 5. $RMSE$ of all models during geomagnetic storm events and relative improvements by ED-SA-DConvLSTM.

Events	Model	$\mathit{R}\mathit{M}\mathit{S}\mathit{E}\left(\mathit{T}\mathit{E}\mathit{C}\mathit{U}\right)$	Improvement (C1PG/ConvGRU/ConvLSTM)
Case 1	C1PG	8.9381	-
	ConvGRU	9.2155	-
	ConvLSTM	9.0865	-
	ED-SA-DConvLSTM	6.3869	+28.5%/+30.7%/+29.7%
Case 2	C1PG	5.0921	-
	ConvGRU	5.5086	-
	ConvLSTM	5.2444	-
	ED-SA-DConvLSTM	4.0530	+20.4%/+26.4%/+22.7%
Case 3	C1PG	4.0527	-
	ConvGRU	4.2831	-
	ConvLSTM	4.2376	-
	ED-SA-DConvLSTM	3.6020	+11.1%/+15.9%/+15.0%
Case 4	C1PG	5.7812	-
	ConvGRU	5.6792	-
	ConvLSTM	5.8194	-
	ED-SA-DConvLSTM	4.8164	+16.6%/+15.1%/+17.2%

. The results demonstrated that the ED-SA-DConvLSTM consistently achieved the lowest $RMSE$ across all four geomagnetic storm events, exhibiting superior prediction performance throughout the entire storm period. These proved that the ED-SA-DConvLSTM has more stable prediction ability during the whole geomagnetic storm.

To further evaluate the performance of the model, we conducted a fine-grained comparison by calculating the $RMSE$ of each model at each time step and visualized the results in Figure 11. The top-left corner of the figure indicates the percentage of time steps where ED-SA-DConvLSTM outperforms the other three baseline models.

Statistical results demonstrated that ED-SA-DConvLSTM achieves a lower $RMSE$ than baseline models (C1PG, ConvGRU, and ConvLSTM) in 58.3–86.3% of all time points across all cases, with all proportions exceeding 50%. While the ED-SA-DConvLSTM exhibits substantial superiority in aggregate predictive performance, its forecasting efficacy still has room for improvement owing to the complex nature of geomagnetic storms. This constraint underscores the persistent challenges in extreme situation event prediction.

5. Conclusions

This paper proposed ED-SA-DConvLSTM, an encoder–decoder architecture for TEC spatiotemporal prediction, with the SA-DConvLSTM unit as the basic block. This proposed model uses the SAM module to capture long-term spatial dependencies and integrates them with short-term spatial dependencies. Furthermore, by replacing standard convolution with deformable convolution, the model overcomes the rigid receptive field limitations of SA-ConvLSTM, enabling adaptive feature extraction from irregular regions. This facilitates the modeling of dynamic, long-term spatial dependencies and the adaptive extraction of complex features in TEC.

To evaluate the performance, the proposed ED-SA-DConvLSTM was compared with two state-of-the-art deep learning models (ConvGRU and ConvLSTM) and a TEC prediction product C1PG, including overall quantitative comparison and comparison under extreme situations. The overall quantitative comparison experiment shows that the $RMSE$ of our model is reduced by 10.27%, 7.65%, and 7.16% compared with those of C1PG, ConvGRU, and ConvLSTM, respectively, in high solar activity. In low solar activity, it decreased by 11.46%, 4.75%, and 4.06%, respectively. In the four geomagnetic storm events, the $RMSE$ of ED-SA-DConvLSTM outperformed the comparison models in most cases. Their proportions all exceeded 58%.

Currently, our research primarily focuses on improving prediction accuracy. In future work, we will conduct user evaluations and operational adaptation and further investigate the underlying physical mechanisms. Meanwhile, when sufficient computational resources become available, we will extend the prediction capability to global scales.