Conventional generators typically employ fully connected networks, which fail to effectively capture bidirectional temporal dependencies and global features, resulting in low-quality imputed data. To address this issue, this paper proposes a generator architecture based on a BiLSTM and multi-head attention mechanism.The core of our temporal modeling is a two-layer BiLSTM. This stacked design aims to learn hierarchical temporal representations: the first BiLSTM layer processes the input sequence and generates preliminary hidden states containing fundamental bidirectional patterns; the second BiLSTM layer builds upon this foundation to model more complex and abstract long-term dependencies at a higher level of feature abstraction. This hierarchical processing enables the network to capture intricate temporal dynamics that might be missed by a single-layer BiLSTM. Subsequently, the output from the second BiLSTM layer is fed into a single-layer multi-head attention mechanism. We employ a single attention layer not for deep feature transformation, but to serve as a powerful global weighting and aggregation module. Its function is to reweight the temporal features refined by the BiLSTM, identifying and emphasizing the most critical time steps across the entire sequence from multiple representation subspaces. This single-layer structure effectively captures global contextual relationships while avoiding the computational overhead and overfitting risks associated with multi-layer attention stacking. The detailed structure is illustrated in Fig. 2.

Generator G receives the power data with missing values X, the mask matrix M, and the noise-processed Z after masking as inputs. Through adjustments by the mask matrix, randomness is introduced only at the missing value positions, thereby aligning with the target distribution dimensions, i.e., the input data X~=G(X,M,(1−M)⊙Z).

BiLSTM is an extension of LSTM, consisting of two LSTMs: one processes information in the forward direction, while the other handles information in the backward direction. BiLSTM can capture bidirectional temporal information in sequences, making it suitable for tasks that require consideration of both past and future information.

Based on the temporal features extracted by BiLSTM, the multi-head attention mechanism further enhances the feature representation capability. The multi-head attention mechanism employs multiple attention heads to capture dependencies between different time steps of the input sequence from distinct subspaces. For the query (Query), key (Key), and value (Value) of the input sequence, denoted as Q, K and V, respectively, the computation for a single head of attention is as follows: (2)Attention(Q,K,V)=softmax(QK⊤dk)Vwhere 1dk is the scaling factor, dk is the dimension of the key, and the softmax function ensures the normalization of attention weights. The multi-head attention mechanism computes attention in parallel through multiple independent attention heads and concatenates the results of all heads. By leveraging this mechanism, the model can capture global dependencies in temporal data from diverse perspectives, further refining feature representation.

In the model proposed in this paper, a hint matrix (Hint Mechanism) and a CNN-based network architecture are introduced to enhance the discriminator’s capability, as illustrated in Fig. 3.

The hint matrix provides information about the validity of the original data, helping the discriminator more accurately distinguish between observed and imputed values. Particularly in cases of severe data missingness, the generator may produce multiple plausible imputation results, making it challenging for the discriminator to make effective judgments. The calculation formula for the hint matrix is: (3)H=B⊙M+0.8⊙(1−B)where B is a defined random variable and M is the mask matrix.

The input to the discriminator consists of the generated sample X^ and the hint matrix H. To better capture the features in the input data X^ and enhance the discriminator’s ability to distinguish between observed and imputed values, a CNN architecture is adopted for the discriminator. In this model, the discriminator is structured with three convolutional layers, which are systematically designed to extract hierarchical features from the input data through sequential convolutional operations. The initial convolutional layer functions as a low-level feature detector, capturing fundamental patterns and local structures within the input. As the network depth increases, the subsequent layers progressively learn more abstract and complex representations: the second layer integrates local features to identify intermediate patterns, while the third layer synthesizes global contextual information, enabling the discriminator to effectively distinguish subtle inconsistencies between observed and imputed values. This hierarchical feature extraction mechanism significantly enhances the discriminator’s capacity to evaluate data authenticity across multiple scales.

Datasets are shown in Table 1.

(1) Residential Load Dataset (RLD): The dataset comprises residential household electricity consumption data, with daily load profiles sampled at 15-min intervals, resulting in a feature dimension of 96. This dataset provides detailed documentation of typical residential electricity usage patterns and holds significant value for analyzing and predicting household electricity consumption behaviors. The time series plot is shown in Fig. 4.

(2) Smart Meter Dataset (SMD): The SMD aggregates hourly energy consumption and multi-dimensional electrical parameters—including voltage, current, and power factor—from smart meters deployed across urban and suburban regions in a regional power distribution network. Covering a full calendar year of 2020 (8760 hourly records), the dataset integrates metadata such as timestamps and device status, enabling comprehensive analysis of load profiles, anomaly detection, and missing data imputation under realistic grid operation scenarios. The time series plot is shown in Fig. 5.

1. KNN [14]: This method identifies the K nearest observations to a sample with missing data using Euclidean distance and performs a distance-weighted average to impute the missing values.

2. VAE [24]: By maximizing the likelihood in the latent space and minimizing the discrepancy between the generated data and the original data, this approach recovers missing values.

3. GAIN [23]: Built upon the Generative Adversarial Network (GAN) framework, this model recovers missing data by performing conditional modeling of the missing locations and adversarial training.

4. M-RNN [19]: This method constructs a generative module based on Recurrent Neural Networks (RNNs) to model temporal dependencies by integrating historical and contextual information. It achieves data recovery through recursive prediction.

5. MIVAE [25]: By jointly optimizing the posterior likelihood of latent variables and the reconstruction error, this approach generates multiple probabilistic imputations within a variational framework, effectively modeling the uncertainty of missing values and enabling high-accuracy data recovery.

Root Mean Square Error (RMSE), Mean Square Error (MSE), Mean Absolute Error (MAE), and the Coefficient of Determination (R2) are commonly used evaluation metrics for assessing the accuracy of predictive models or algorithms. The formulas for each metric are as follows: (8)RMSE=1N∑Ni=1(yi−y^i)2 (9)MSE=1N∑Ni=1(yi−y^i)2 (10)MAE=1N∑Ni=1∣yi−y^i∣ (11)R2=1−∑Ni=1(yi−y^i)2∑Ni=1(yi−y¯)2where yi is the actual value at the missing position, y¯ is the mean value, y^i is the imputed value at the missing position obtained by the imputation algorithm, and N is the total number of missing values.

Sixty percent of the dataset was used as the training set, twenty percent was allocated to the validation set, and the remaining twenty percent was used for the test set. The experimental data were subjected to random missingness at missing rates ranging from 10% to 90%.

The selection of the optimal hyperparameters, specifically Hint = 0.9 and Alpha = 400, was driven by a systematic grid search on the validation set with a 50% missing rate, with the results detailed in Table 2.

Our analysis of the experimental data reveals a clear trend of consistent performance improvement as the Hint value increased from 0.5 to 0.9 across all Alpha groups. For instance, within the critical Alpha = 400 group, the MSE decreased monotonically from 0.0458 at Hint = 0.5 to 0.0215 at Hint = 0.9, indicating that providing more precise location information to the discriminator is crucial for guiding the generator to produce more accurate imputations in high-missing-rate scenarios. The optimality of Alpha = 400 emerges from its synergistic interaction with Hint = 0.9, as evidenced by the performance comparison with other combinations. While the combination of Alpha = 200 with Hint = 0.9 yields a relatively high MSE of 0.0678, and Alpha = 800 with Hint = 0.9 achieves a better but still suboptimal MSE of 0.0401, the pair of Alpha = 400 with Hint = 0.9 achieves the lowest MSE of 0.0215 across the entire parameter space tested. This demonstrates that Alpha = 400 provides the ideal weight for the reconstruction loss, ensuring the generator not only fools the discriminator but also accurately reconstructs the known values—a capability fully leveraged when the discriminator is well-informed through Hint = 0.9. Therefore, this specific combination was selected as it represents the configuration where the generator receives the most effective guidance from the discriminator while being simultaneously constrained to achieve the highest factual accuracy. The parameters of the network model are configured as shown in the Table 3.

The imputation results of the RLD dataset across a range of missing rates are shown in Tables 4–8. The time series after imputation for a missing rate of 0.5 is shown in Fig. 6.

At low missing rates (0.1–0.3), the models were evaluated using metrics such as MSE, RMSE, and MAE. The results indicate that the proposed model performed second only to GAIN. At medium to high missing rates (0.4–0.9), the proposed model achieved the best performance across these metrics, significantly outperforming other methods, demonstrating its strong robustness in handling high missing scenarios. Furthermore, the model exhibited favorable R2 values, indicating its ability to effectively capture the relationship between the imputed data and the ground truth. On the other hand, by comparing recovery times, the proposed model also showed favorable recovery times, suggesting that it not only excels in terms of accuracy but also efficiently handles the computational workload.

The imputation results of the RLD dataset across a range of missing rates are shown in Tables 9–13. The time series after imputation for a missing rate of 0.5 is shown in Fig. 7

The proposed model demonstrates outstanding performance across all missing-rate scenarios, with its superiority being particularly pronounced at medium to high missing rates (0.4–0.9). Under these conditions, the model significantly outperforms comparative methods in terms of imputation accuracy, robustness, and ability to capture complex temporal dependencies. Meanwhile, BAC-GAN also exhibits excellent recovery time efficiency, maintaining fast response capabilities even under high missing-rate conditions, highlighting its strong applicability in practical situations where high proportions of data loss commonly occur.

Based on the four evaluation metrics mentioned above, the proposed model demonstrates excellent recovery performance under most missing-rate scenarios. The key to its success lies in the fact that BAC-GAN integrates BiLSTM and a multi-head attention mechanism, which effectively captures complex dependencies in time-series data and enhances the learning of global relationships. Meanwhile, the incorporation of CNN improves the model’s ability to handle high-dimensional data and strengthens local feature extraction, thereby increasing the accuracy and robustness of data recovery.

To validate the effectiveness of individual components in our proposed BAC-GAN framework, we conducted comprehensive ablation studies under various missing rate scenarios (0.2, 0.4, 0.6, 0.8). As demonstrated in Tables 14 and 15, the complete BAC-GAN model consistently achieves superior or competitive performance across all missing rates, particularly excelling at higher missing scenarios (0.6–0.8).

The performance degradation observed in partial component models reveals the complementary nature of the designed modules in this work. The BA-GAN variant demonstrates consistently intermediate performance, indicating that the attention mechanism contributes significantly to feature extraction but requires the constraint module to achieve optimal results. The A-GAN and C-GAN models exhibit relatively weaker performance, confirming that individual components alone are insufficient to handle complex missing data patterns.

Furthermore, the progressive performance decline from BC-GAN to BAC-GAN highlights the challenging nature of high missing-rate scenarios and validates the robustness of the proposed model. The complete BAC-GAN model maintains the most stable performance trajectory, exhibiting the smallest performance degradation as the missing rate increases from 0.2 to 0.8. These findings collectively demonstrate that the synergistic integration of all components in BAC-GAN is crucial for achieving robust performance across diverse missing data scenarios, with each element playing a distinct yet interdependent role in the overall architecture.