## 1 Introduction
In the first phase of our methodology, we designed a model based on the radial basis function deep neural network (RBF-DNN) [49; 50; 51; 52], which consists of a common deep neural network (DNN) with a radial basis function (RBF) layer added in the front. We chose this model for two reasons. First, the input factors discussed in the problem of this paper are weather factors, and the greatest difficulty in processing such datasets is that the distributions of the factor data are extreme; in addition to the normally-distributed factors (Figure 4a), there are also factors whose data are concentrated at the minimum value end of the \(x\) axis (Figure 4b) or at both the minimum and maximum value ends of the \(x\) axis (Figure 4c). Past studies [52; 53; 54] have demonstrated that adding an RBF layer in front of the model is an effective way of modeling such data. This is because RBFs have classifier characteristics, which enable the model to classify the values of each group of input data before deriving the relationships between the inputs and the outputs based on the classification results. Second, unlike the method of using the outputs of the hidden layers in deep learning models to obtain key features, the input factors of RBF deep learning models can be directly regarded as key features, which is more convenient for online applications. To use the outputs of a specific hidden layer as the key features, online applications require all the calculations of the original deep learning model from the input layer to said hidden layer, as shown in Figure 5. Directly using the model inputs as the key features of the lightweight models avoids these calculations. Figure 4: Distribution of weather data: (**a**) normal distribution; (**b**) data concentrated at minimum value end; (**c**) data concentrated at minimum and maximum value ends. Figure 3: Flow chart of proposed methodology. Although the concept of RBF-DNNs is well-suited to the topic of this study, the details of the model must be adjusted for the target problem, due to two underlying issues. First, RBF-DNNs designed in the past only considered numerical factors and are not suitable for categorical factors. However, categorical factors such as the model of the solar panel or the subarea of a power plant are common in solar power forecasting. We therefore modified existing RBF-DNN architecture so that it can process categorical factors as well as numerical factors. This modification is depicted by the gray box of Phase 1 in Figure 3. To differentiate it from conventional RBF-DNNs, we refer to the modified model as a numerical-categorical RBF-DNN (NC-RBF-DNN). Second, conventional RBF-DNNs mostly obtain key factors by setting threshold values to extract the top several key factors and then constructing the subsequent lightweight models. In other words, these methods can only identify the input factors that are the most important for modeling; the importance of the other factors is unknown. In the current paper, we propose using the ensembling concept to establish sub-models for multiple input factor combinations to obtain the importance ranking of all of the factors. In the second phase of our methodology, we designed a heap-based factor combination search algorithm to generate combinations of the inputs of the multiple sub-models based on the factor importance ranking obtained by the NC-RBF-DNN. This design was devised separately because the key factors that an RBF-DNN extracts vary with each iteration [52; 53]. For instance, the importance ranking of the key factors extracted may be A, B, and C in the first training but C, A, and D in the next training. This is due to the powerful modeling capabilities of deep learning models. For example, let us assume there are two input factors to a model. Even if the two factors are only moderately correlated to each other from a relational perspective, the model may only choose one of the factors as the primary factor for modeling and regard the other as useless.