# Enhancing Photovoltaic Power Predictions with Deep Physical Chain Model
## 5 Conclusions  
Through this study, we introduced an innovative hybrid methodology for photovoltaic power generation forecasting using a Transformer Bi-LSTM model; for the calibration block, it has been demonstrated to be superior in comparison with the traditional calibration, in terms of forecasting accuracy. Despite the fact that the preprocessing of the data does not significantly increase the accuracy of the model, the methodology of direct forecasting offers some equilibrium between precision and efficiency at the time of the development, although the chain model offers more details in the process of irradiance transformation into photovoltaic power. In particular, the deep chain model has proven to be superior compared to conventional prediction methods, achieving a reduction in MAE of 24% MAE and RMSE 4%, in comparison to the best results of the state of the art. This has allowed achieving MAE values as low as 0.894 [MW] and RMSE of 1.669 [MW], which represents a significant improvement over reference models in the literature.  
Although the results are promising, it is essential to test the model in real-field scenarios to evaluate its accuracy under real conditions. This evaluation would pave the way for implementing a fault detection system that triggers alerts when model predictions deviate significantly from actual measured values. This would improve the operation and maintenance of photovoltaic plants, allowing a significant reduction in operating costs.  
For future research, we propose exploring more advanced neural model architectures, optimizing specific components, and applying our methodology to larger datasets, such as the California-based dataset mentioned earlier. These improvements will not only enhance the accuracy of photovoltaic energy forecasts but also offer deeper insights into the overall field of renewable energy prediction. Moreover, given that our approach integrates physical models with deep learning, future work could focus on refining this hybrid method. Potential directions include tuning trainable physical equations within neural networks and embedding these equations into the loss function, replicating the Physics-Informed Neural Networks methodology, further advancing the interpretability and performance of predictive models in photovoltaic energy.  
Conceptualization, G.F. and J.R.; methodology, J.R.; software, J.R.; validation, G.G., E.F. and M.L.; formal analysis, J.R.; investigation, J.R. and M.L.; resources, G.F., E.F. and S.D.-C.; data curation, J.R. and M.L.; writing--original draft preparation, J.R. and G.G.; writing--review and editing, G.G. and E.F.; visualization, J.R.; supervision, G.F.; project administration, G.F.; funding acquisition, E.F., G.G and S.D.-C. All authors have read and agreed to the published version of the manuscript.  
This research was supported, in part, by the Chilean Research and Development Agency (ANID) under Project FONDECYT 1191188. The Ministry of Science and Innovation of Spain under Project PID2022-137680 OB-C32. The Agencia Estatal de Investigacion (AEI) under Project PID2022-139187 OB-I00.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
The authors declare no conflict of interest.