## 2 Related Work  
Several methods for forecasting the SI have been proposed in the literature, and these can be broadly divided into two prediction modeling categories, namely physical modeling and data-driven modeling. In a physical model, numerical weather prediction (NWP) is used for forecasting tasks by using complex mathematical equations [22,23]. The NWP method gives a good performance in stable weather conditions. However, it has limitations for cloudy weather. The coarse resolution puts a limitation to acquire the information related to the clouds [12]. In a data-driven approach, historical data are used that may or may not contain external weather parameters (temperature, humidity, clearness index, etc.) with SI. The data-driven models are further categorized into two sub-types, namely nonlinear autoregressive (NAR) models and nonlinear autoregressive with exogenous (NARX) models. The first of these uses the endogenous input (i.e., the SI) as the prediction parameter, while the latter includes the exogenous parameters such as temperature, humidity, and clearness index, along with the endogenous parameter (SI). Within the NAR and NARX categories, the data-driven models are further categorized into statistical models, artificial intelligence (AI)-based models, and hybrid models. The statistical models used for SI forecasting are mainly based on autoregressive (AR) methods. These methods include the autoregressive moving average (ARMA), the ARMA model with exogenous variables (ARMAX) and the autoregressive integrated moving average (ARIMA) [24]. Further studies related to statistical models are available in [25, 26, 27, 28, 29, 30, 31, 32]. The AI-based models perform better for the SI prediction as compared to conventional statistical models. Among the AI models, machine learning models have the potential to address the nonlinear relationship between input and output for prediction tasks. Machine learning models include support vector machine (SVM), the feed-forward neural network (FFNN), and the adaptive fuzzy neural network (AFNN), and so on. SVM has been used to predict the solar insolation from three years of data [33]. In another study, the daily solar irradiance was forecast for three locations in China using seven SVM models based on sunshine duration as the input [34]. The findings indicated better results for the first SVM model that shows the lowest error in the winter season as compared to other seasons. For interested readers, a comprehensive review related to the SVM based forecasting of SI and wind is presented in [35]. In addition, the FFNN approach has been used to forecast the daily SI in France using 19 years of data. The results were compared with those of other statistical and machine learning models such as AR models, Markov chains, Bayesian inference, and the k-nearest neighbor (KNN). The results indicated that the FFNN provided the best performance [36]. In another study, the FFNN approach has also been used to forecast the daily SI, based on the NAR and NARX models along with a multi-output FFNN architecture to indicate that the NARX and multi-output model provided the best performance accuracy [37]. Additional studies related to use of FFNN for predicting solar irradiance are available [38, 39, 40, 41]. The accessibility to large quantities of data (\"big data\") and the potential for training and strong generalization has attracted recent attention towards deep learning as a promising branch of AI. This approach has been widely implemented in pattern recognition, image processing, detection, classification, and forecasting applications. A deep learning network consists of multiple hidden layers that are used to learn data patterns. For SI forecasting, deep learning technologies such as the recurrent neural network (RNN), the long short term memory (LSTM), the wavelet neural network (WNN), the deep belief network (DBN), the multilayer restricted Boltzmann machine (MRBM), the convolutional neural network (CNN), and the deep neural network (DNN) are used in the literature [42].