## 2 Materials and Methods  
In this section, we detail the approach employed to enhance solar radiation prediction in Zacatecas, using historical data of GHI collected by CONAGUA from 2015 to 2018. The performance of various models was rigorously compared and evaluated using two key metrics: Root Mean Squared Error (RMSE %) and the coefficient of correlation (r).  
The goal of RMSE % is to measure the accuracy of a prediction by expressing the prediction error as a percentage of the actual observed values, providing a normalized error metric that facilitates comparisons across different datasets or models [14]. In solar radiation forecasting, the aim is to minimize RMSE %, indicating that the predictions closely match actual GHI values. A lower RMSE % signifies a more accurate and reliable model, which is crucial for optimizing solar energy management. Meanwhile, r measures the strength and direction of the linear relationship between predicted and actual values, ranging from \(-1\) to \(1\). In forecasting, achieving an r value close to \(1\) reflects a strong correlation, demonstrating the model's effectiveness in capturing data patterns and ensuring reliable solar energy forecasts [15].  
This study began with the implementation of a persistence model, which served as a baseline to compare the predictive performance of more advanced techniques. This model assumes that future values will be equal to the last observed value, providing a straightforward but valuable reference point.  
Subsequently, more sophisticated methods were applied. A Recurrent Neural Network (RNN) [16] was developed to capture the complex nonlinear relationships inherent in solar radiation data. The network architecture was specifically tuned using a grid search to optimize hyperparameters, including the number of hidden layers and neurons per layer, to best fit the GHI time series data. Additionally, Meta's Prophet model [17] was customized for the study by incorporating seasonal components specific to the Zacatecas region, which allowed it to effectively model local trends and cyclic patterns observed in the GHI data.  
For comparison, classical machine learning algorithms were also employed, with a particular focus on regression techniques. Linear regression [18] was implemented using past GHI values as input features, capturing the linear trend over time. More complex models like random forests [12; 19], XGBoost [13] and extra trees [20] were configured to handle the high-dimensional feature space generated from the time-lagged values of GHI. These ensemble methods were fine-tuned using cross-validation to select the optimal number of trees and maximum depth, ensuring the models could robustly predict future values despite the variability in solar radiation.  
Additionally, supervised learning techniques like Support Vector Machines (SVMs) [21] and k-Nearest Neighbors (KNN) [22] were adapted by constructing feature sets based on past GHI values to enhance the capture of local solar radiation variability. Boosting techniques, particularly Adaboost [23], were also explored, focusing on minimizing prediction errors by iteratively refining weaker learners.  
To address regularization and feature selection challenges, ElasticNet [24], Ridge [25], and lasso [26] regression models were utilized. These methods were particularly effective in handling multicollinearity among the time-lagged features and ensuring model generalization by balancing between feature selection and regularization.  
Finally, advanced approaches like Evolutionary Neural Architecture Search (ENAS) [27] were used to automatically design optimized neural network architectures tailored to the specific characteristics of local solar radiation data. Furthermore, Convolutional Neural Networks (CNNs) [16] were implemented to exploit temporal dependencies in the GHI time series, capturing intricate patterns through the use of convolutional layers applied to sequences of past observations.