Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The model was evaluated using data from three sites located exclusively in China. Although the selected data cover various climatic conditions within that country, how would the network perform if applied to data from other regions with different climates?

Is the claim of “good robustness” supported only for the specific dataset used? Or was it tested in other ways? Can the model make predictions under different conditions without retraining or fine-tuning?

There is no internal description of the GNN showing the relationships between the variables the model learned, or indicating which factor is most influential. Could the adjacency matrix of the model also be presented?

Given the complexity of the architecture, what is its computational cost?

How much training time or computational resources does it require compared with other models? Considering this, even if its performance is better, is it worthwhile given the resource consumption?

A deeper analysis is missing on why the proposed architecture is not optimal for short-term predictions (even though this is mentioned as future work).

Were the models used optimized? Were the baseline models used for comparison also optimized?

Table 5 is poorly formatted and difficult to interpret.

On page 6, equations (11) and (12) are duplicated—if this is not an error, why are they repeated?

In Table 6, MSE and MAE are missing (as shown in Table 7). If they are intentionally omitted, a clearer explanation should be provided.

The conclusion states that the best performance is achieved when k = 4. However, Table 6 shows that for Horizon96 the MAE is better when k = 2 or 3. Why is this the case? For the other cases the results are consistent, but why not for Horizon96?

Improve the conclusions

Author Response

Reviewer 1:

1.The model was evaluated using data from three sites located exclusively in China. Although the selected data cover various climatic conditions within that country, how would the network perform if applied to data from other regions with different climates?

The proposed framework, based on graph neural networks (GNNs), is capable of capturing complex spatiotemporal dependencies among variables. The model leverages multidimensional environmental variables (e.g., irradiance, temperature, humidity) as inputs, the physical significance of which is generally applicable across different regions worldwide, enabling the model to be transferred to forecasting tasks under varying climatic conditions. As indicated by the cross-site transfer experiments in Table 1, theoretically, the model’s transferability remains effective and may even yield improved performance, when the variation patterns of environmental variables in a new region are similar to those of the existing sites. For regions with climate patterns substantially different from the three sites in China, such as extreme polar or tropical rainforest climates, the model may require fine-tuning or retraining to adapt to the new statistical characteristics.

 

 

2.Is the claim of “good robustness” supported only for the specific dataset used? Or was it tested in other ways? Can the model make predictions under different conditions without retraining or fine-tuning?

1）The robustness of the proposed model is demonstrated by its ability to maintain relatively high prediction accuracy on the Site 1 and Site 2 datasets, which contain outliers, even for long-term forecasts at 384-step and 768-step horizons.

2）The model was not evaluated through additional independent tests.

3）To further assess the model’s generalization capability, a cross-site transfer experiment was conducted. Specifically, the model was trained on the dataset from one site and directly transferred to the other two sites for prediction. The results are summarized in Table 1, where the bolded metrics represent the performance obtained from local training on the current site, and the non-bolded metrics correspond to the results of direct transfer.

Notably, when the models trained on Site 1 or Site 2 were transferred to Site 3, they achieved higher prediction accuracy for both 384-step and 768-step horizons compared to the model trained solely on Site 3. In contrast, the model trained on Site 3 showed inferior accuracy when transferred to Site 1 or Site 2. This suggests that the data characteristics of Site 1 and Site 2 are more representative and consistent, enabling the model to learn more universal temporal dependencies. Moreover, the parameters learned from Site 1 or Site 2 implicitly encode global variation patterns (e.g., diurnal and seasonal cycles), which remain valid for Site 3.

As shown in Figures 4–6 in the manuscript, the prediction curves for Site 3 exhibit greater fluctuations, particularly in 768-step forecasts, indicating that its local variability may hinder generalization. These findings further validate the robustness of the proposed model and its capacity to transfer knowledge effectively across different but related environments.

Table 1. Experimental Results of Transfer Learning

Horizon	Site1		Site2		Site3
	MSE	MAE	MSE	MAE	MSE	MAE
768	1.444	0.782	1.228	0.662	0.935	0.690
384	1.241	0.707	1.027	0.560	0.917	0.679
192	0.999	0.620	0.908	0.466	0.867	0.653
96	0.776	0.603	0.997	0.553	0.779	0.609
768	1.501	0.734	0.979	0.483	0.922	0.665
384	1.325	0.735	0.922	0.496	0.876	0.651
192	1.467	0.774	0.870	0.459	1.049	0.704
96	1.015	0.603	0.820	0.405	0.803	0.600
768	1.891	0.898	1.317	0.619	0.950	0.684
384	1.842	0.878	1.292	0.621	1.036	0.700
192	1.572	0.913	1.162	0.649	0.814	0.632
96	1.188	0.738	0.997	0.553	0.776	0.603

 

There is no internal description of the GNN showing the relationships between the variables the model learned, or indicating which factor is most influential. Could the adjacency matrix of the model also be presented?

The adaptive graph neural network employed in this study generates an adjacency matrix that reflects whether correlations exist among variables but does not quantify the relative influence of each factor. The adjacency matrix obtained from the model for the 768-step horizon is shown in Figure 1-3, A masking operation was applied to the correlation coefficients along the diagonal of the adjacency matrix to suppress self-correlations and prevent self-connections in the graph structure.

 

Figure 1. the adjacency matrix of the model in Site 1

 

Figure 2. the adjacency matrix of the model in Site 2

 

Figure 3. the adjacency matrix of the model in Site 3

 

3.Given the complexity of the architecture, what is its computational cost?

The model complexity analysis is summarized in Table 1, while detailed measurements of computational resource consumption are reported in Table 8.

Table 1. Time Complexity Analysis

Components	Time Complexity
Graph Learning Layer
Graph Convolution Module
Temporal Convolution Module
LightTS

 

4.How much training time or computational resources does it require compared with other models? Considering this, even if its performance is better, is it worthwhile given the resource consumption?

We have added a model performance analysis in Section 4.4 of the paper, as presented below:

The computational efficiency and resource consumption of the model directly influence the real-time scheduling speed and deployment of photovoltaic (PV) systems, serving as critical factors for maintaining stable and continuous power output. In this section, a comprehensive evaluation of the model’s computational efficiency and resource utilization is conducted. The experiments employ the torchinfo.sum function to report each model’s architectural statistics, including the number of parameters (Param), computational complexity (MACs), memory consumption (Memory), and iteration time per training step (Train-time), the results are presented in table 8.

As shown in the table 8, the proposed model exhibits relatively larger parameter counts and memory consumption; however, its computational complexity (MACs) and iteration time per training step are comparatively small, ranking just after the lightweight CNN_LSTM and LightTS models. In conjunction with Table 2, it can be observed that although the proposed model sacrifices a certain amount of training time and computational resources, it achieves a substantial improvement in forecasting performance compared with the baseline models. This moderate increase in computational cost, accompanied by a significant enhancement in predictive accuracy, is therefore considered worthwhile.

Table 2. Computational efficiency comparison of different methods

Method	Params	Memory (MB)	MACs(M)	Train-time s/iter
LightTS	83930	0.320167542	0.090806	0.0226
CNN_LSTM	814144	3.105712891	14.731904	0.0211
Transformer	864135	3.296413422	269860.2787	0.4286
Informer	901191	3.437770844	256598.0943	0.1056
GWNet	1404224	5.098876953	277.673152	0.2300
Proposed	1520141	5.769996643	63.944918	0.0650
MTGNN	1521568	5.780517578	64.460928	0.0589
Crossformer	3027428	11.37586975	71.13578	0.1989
Autoformer	35879197	7.774822235	75.135751	0.5964
RANK	6	6	3	4

 

5.A deeper analysis is missing on why the proposed architecture is not optimal for short-term predictions (even though this is mentioned as future work).

The relatively lower short-term forecasting performance compared with Crossformer may be attributed to the Two-Stage Attention (TSA) module in Crossformer, where the multi-head attention mechanism enables finer modeling of short temporal dependencies. In contrast, the proposed model focuses more on leveraging multidimensional variable information, which is more advantageous for capturing long-term temporal dependencies and thus enhances long-horizon forecasting performance.

As claimed in the introduction section (and also in the paper title), our method is more suitable and has the superior performance in long-term PV output forecasting tasks. The long-term prediction, compared to short-term, usually is more difficult, and requires more complex neural network structure to achieve satisfactory results. Therefore, we believe that this work completes the literature of the PV prediction field.

6.Were the models used optimized? Were the baseline models used for comparison also optimized?

The proposed model was partially fine-tuned and optimized for this study, while the baseline models were implemented using the optimal configurations reported in their original papers.

 

7.Table 5 is poorly formatted and difficult to interpret.

We have revised the format of Table 5. Table 5 presents the results of model reproducibility experiments, which examine the range of prediction metrics within the 95% confidence interval to demonstrate the reliability of the forecasting results.

Table 5. Statistical analysis of model performance variability.

Horizon	96		192		384		768
Metric	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE
1	0.814±0.010	0.522±0.006	1.240±0.022	0.703±0.010	1.447±0.027	0.798±0.015	1.240±0.022	0.703±0.010
2	0.812±0.026	0.419±0.011	0.926±0.012	0.488±0.011	0.999±0.013	0.487±0.012	0.926±0.012	0.488±0.011
3	0.771±0.025	0.602±0.009	1.032±0.013	0.704±0.005	0.985±0.020	0.688±0.006	1.032±0.013	0.704±0.005

 

 

8.On page 6, equations (11) and (12) are duplicated—if this is not an error, why are they repeated?

We have removed the duplicated equations.

 

9.In Table 6, MSE and MAE are missing (as shown in Table 7). If they are intentionally omitted, a clearer explanation should be provided.

The MSE and MAE have been added to Table 6.

 

10.The conclusion states that the best performance is achieved when k = 4. However, Table 6 shows that for Horizon96 the MAE is better when k = 2 or 3. Why is this the case? For the other cases the results are consistent, but why not for Horizon96?

In the model, k is a parameter that adaptively determines the number of relevant variables to be extracted. For different prediction horizons, the model needs to strike a good balance between the information from relevant variables and the temporal patterns. As the amount of variable information decreases, the model places greater emphasis on temporal patterns. For a prediction horizon of 96 steps, when k=2 or 3, the model is able to effectively combine information from relevant variables with temporal patterns to predict the future 96-step photovoltaic sequence values. In contrast, for longer prediction horizons, such as the 384-step or 768-step horizons, the model tends to focus more on temporal features in short-term forecasting tasks.

 

11.Improve the conclusions

We have revised the conclusion section, and the improved version is as follows:

5 Conclusion

This study presents a long-term photovoltaic (PV) power forecasting model based on graph neural networks (GNNs), designed to capture complex spatiotemporal dependencies among multiple variables and to leverage environmental information for enhanced predictive accuracy. The model’s performance was evaluated using MSE and MAE across datasets from three PV power sites. The main experiments and findings are as follows:

1) Superior accuracy and robustness: Compared with baseline models, the proposed model achieves the highest accuracy and demonstrates stronger robustness in forecasting horizons of 384 and 768 steps. It improves MSE and MAE by an average of 2.19% and 1.57% at the 384-step horizon, and 2.81% and 2.47% at the 768-step horizon, respectively, relative to the best-performing baseline. Furthermore, models that capture hidden inter-variable relationships consistently outperform those focusing solely on temporal patterns or spatial relationships.

2) Enhanced long-term predictive capability: To more intuitively demonstrate the model's predictive performance in long-term photovoltaic (PV) power forecasting, predicted and true power curves for 76- step horizon were visualized. The proposed model shows significant advantages in capturing peak, trough, and fluctuation patterns compared to all baseline models, achieving superior fitting performance.

3) Impact of correlation coefficient : The correlation coefficient k determines the number of relevant variables used for prediction, and an optimal value of k exists. The model achieves its best performance when k = 4, particularly for longer forecasting horizons of 384 and 768 steps. An excessive number of relevant variables introduces informational noise, while too few variables lead to insufficient utilization of contextual information. Both extremes result in decreased prediction accuracy.

4) Impact of correlation coefficient : The type of graph structure also notably affects forecasting performance. Incorporating graph information improves accuracy in longer-horizon predictions. Compared to using an undirected graph, The proposed model with a directed graph achieved the best results at 384 and 768 steps, improving MSE and MAE by 0.67% and 0.99% at the 384-step horizon, 1.12% and 0.58% at the 768-step horizon, respectively.

Overall, the proposed GNN-based framework integrates environmental information to address the challenge of accuracy degradation in long-term PV power forecasting, demonstrating strong robustness, adaptability, and scalability in complex and dynamic environments.

Despite the promising performance of the proposed model, certain limitations remain. In particular, the adjacency matrix employed by the adaptive graph neural network is dynamic and may lack sufficient stability, limiting its ability to fully capture and explain the relationships between PV power generation and surrounding environmental factors. In future work, we will further explore the interpretability of graph-based models. These efforts aim to facilitate optimal PV installation planning by comprehensively incorporating environmental information, thereby maximizing power generation efficiency.

 

 

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The study entitled "Adaptive Graph Neural Network-Based Hybrid Approach for Long-Term 
Photovoltaic Power Forecasting" makes a useful contribution to the body of knowledge. 
While the quality of the research is valuable, the presentation of the work requires 
improvement. I recommend a minor revision based on the following suggestions: 
1. How does the proposed model handle inter-variable relationships compared to models 
that focus solely on temporal or spatial relationships? 
2. What visualizations were used to demonstrate the predictive performance of the 
model for the 76-step horizon? 
3. How could future work on the interpretability of graph-based models support optimal 
planning for photovoltaic installations? 
4. A more detailed analysis of the results is necessary. The authors should refer to 
relevant and recent literature to support comparisons and provide context for the 
findings. 
5. The number of references is insufficient and outdated. In revising the manuscript, the 
authors should include more recent literature from the past five years that supports 
their methodology and discussion. 
6. How does Crossformer compare to other models at the 96 and 192-step horizons?

Comments for author File: Comments.pdf

Author Response

 

Reviewer 2:

1. How does the proposed model handle inter-variable relationships compared to models that focus solely on temporal or spatial relationships?

In real-world scenarios, multivariate time series are often characterized by intricate temporal–spatial coupling. Focusing solely on either temporal or spatial dependencies is insufficient to effectively capture the complex dynamics inherent in such data. To address this challenge, the proposed model employs an adaptive graph neural network to model the complex spatiotemporal relationships within multivariate time series. The adaptive adjacency matrix is learned directly from the data to capture the latent spatial dependencies among variables. The temporal convolutional network (TCN) layers and the graph propagation layers based on the adaptive adjacency matrix are alternately stacked to jointly model temporal and spatial dependencies. Furthermore, a lightweight multilayer perceptron (MLP) model, LightTS, is integrated to capture both short-term and long-term temporal patterns for improved forecasting performance.

 

2. What visualizations were used to demonstrate the predictive performance of the model for the 76-step horizon?

The research focus of this study is long-term photovoltaic (PV) power generation forecasting. A 96-step horizon corresponds to short-term PV sequence prediction, while this paper presents the 768-step horizon forecasting results for three PV sites to demonstrate the superior performance of the proposed model in long-term PV time series prediction.

 

3. How could future work on the interpretability of graph-based models support optimal planning for photovoltaic installations?

The adjacency matrix in the graph neural network (GNN) can, to some extent, reflect the correlations between the target variable and other related variables—specifically, the relationships between photovoltaic (PV) power generation and environmental factors such as humidity, air pressure, and irradiance. In future work, we plan to further investigate which environmental factors most significantly influence PV power generation and quantify their impact. By incorporating these insights, we aim to guide the installation and configuration of PV systems to enhance overall power generation efficiency.

 

4. A more detailed analysis of the results is necessary. The authors should refer to relevant and recent literature to support comparisons and provide context for the findings.

We have incorporated recent related studies into the Introduction to provide a stronger background for our research findings and conducted a more detailed analysis of why the proposed model performs better in long-term forecasting, while showing relatively lower accuracy than Crossformer in short-term (96-step horizon) forecasting. We have added a model performance analysis in Section 4.1 of the paper, as presented below:

The relatively lower short-term forecasting performance compared with Crossformer may be attributed to the Two-Stage Attention module in Crossformer, where the multi-head attention mechanism enables finer modeling of short temporal dependencies. In contrast, the proposed model focuses more on leveraging multidimensional variable information, which is more advantageous for capturing long-term temporal dependencies and thus enhances long-horizon forecasting performance.

 

5. The number of references is insufficient and outdated. In revising the manuscript, the authors should include more recent literature from the past five years that supports their methodology and discussion.

In the revised manuscript, seven recent and relevant studies have been incorporated into the Introduction to provide stronger theoretical support for the proposed methodology and the subsequent discussion.

Hasnat et al. [29] proposed a graph attention network (GAT)-based solar power forecasting framework constructed according to geographical distances. The framework adapts to prediction horizons ranging from several minutes to multiple days by adjusting individual modules within the architecture. Graph neural networks (GNNs) have been widely employed in forecasting for distributed photovoltaic (PV) power stations, where graph structures are used to represent the relationships among distributed sites. Wang et al. [30] developed a domain-adversarial graph neural network-based method for ultra-short-term distributed PV power forecasting, addressing the challenge of data scarcity that arises in virtual power plants due to newly constructed sites or data-sharing limitations.Wang et al. [31] further proposed a dynamic graph network for ultra-short-term distributed PV power forecasting based on a shape–amplitude loss function. In this approach, dynamic graphical data are used to represent inter-station correlations, and a dynamic graph network is constructed as the forecasting model. Lin et al. [32] introduced a novel end-to-end deep learning model for short-term probabilistic forecasting of regional PV generation. The model employs a directed graph-based dynamic spatial convolutional graph neural network, in which multi-source inputs are used to determine the contribution of one PV station to another. Wang et al. [33] also proposed a domain-adversarial graph neural network approach that utilizes a GNN encoder to extract spatial features and capture inter-site spatial correlations, thereby improving ultra-short-term distributed PV forecasting under data-scarce conditions. GNNs have become powerful tools for learning non-Euclidean data representations [34], providing new ideas for modeling real-world time series data and capturing the relationships between different variables in multi-variable sequences. Combining GNNs with existing time series frameworks is expected to further improve model performance [25]. Han et al. [35] combined the attention mechanism with an adaptive graph neural network to achieve accurate building energy consumption forecasting and optimize energy structure design. Gao et al. [36] proposed an attention-driven spatiotemporal hybrid model that integrates multi-graph structures and attention-based feature fusion to enhance both single-site and multi-site PV power forecasting performance.

 

6. How does Crossformer compare to other models at the 96 and 192-step horizons?

As shown in Tables 2–4, Crossformer achieves higher prediction accuracy than other models for the 96-step horizon. For the 192-step horizon on Site 1, its forecasting performance also surpasses that of the baseline models. However, for the other two sites, its prediction accuracy remains lower than that of the proposed model.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript has been improved. So I consider that it´s ok for publication

Author Response

Thank you for your positive comments.