## 4 Simulations
### Introduction to Dataset and Experiment Parameters  
The solar power generation dataset used in this study is from the Global Energy Forecasting Competition 2014. We selected this dataset for our experiments because it is a benchmark dataset used to verify the effectiveness of solar power forecasting methods in numerous studies [86; 87]. Moreover, it is a public database available for free download online [88]. The dataset contains hourly weather and solar power generation data from three solar power plants in Australia (each station using a different model of solar power panel) from 1 April 2012, to 1 July 2014. There are a total of 19,704 items of data from each power plant. Each item of data includes seventeen factors, twelve of which are weather data, four of which are data related to power generation, and the last of which is the power output, as shown in Table 1. To verify that the NC-RBF-DNN can indeed process categorical factors, we adjusted the collection background of the dataset to meet the needs of our experiments. We regarded the three solar power plants as three areas using different solar panel types at a single power plant. Thus, the power plant number factor that was not considered in past studies was therefore considered a categorical input factor in this study to differentiate different solar panel models. Using this approach, our dataset contained a total of 19,704 \(\times\) 3 = 59,112 items of data. Aside from power output, the one categorical factor and 15 numerical factors in each item of data were seen as inputs of the target problem, and the power output was considered the output of the target problem. The dataset was divided into a training set (80%) and a test set (20%). The training dataset covered the period from 1 April 2012 to 17 January 2014, while the test dataset covered the period from 18 January 2014 to 1 July 2014. We used three types of models in this experiment, including the NC-RBF-DNN used to rank the factors by importance (the model in Phase 1 in Figure 3) and the lightweight NC-RBF-DNNs and a random forest used to realize the ensembling concept for robust prediction (the models in Phase 2 in Figure 3). We used two different types of models in the second phase because the evidence of past studies supports the effectiveness of both RBF-deep learning models for the extraction of factors in practical applications [52; 53]. In terms of parameters, the NC-RBF-DNN had 16 input neurons drawn from the 16 factors of the target dataset. In the RBF layer, we drew 15 numerical factors from past studies [52; 53; 54] and used three RBF neurons to describe each input neuron, so there were a total of forty-five RBF neurons. The only categorical factor had three categories, so with one RBF neuron for each category, there were three RBF neurons for this factor. In total, there were 48 RBF neurons for the numerical and categorical factors. As for the DNN behind the RBF layer, we set sixty-four neurons, thirty-two neurons, sixteen neurons, eight neurons, and one neuron in each layer according to the proposed design, and the final layer output was the predicted power output. As for the other training parameters of the model, we set the number of epochs as 100, the learning rate as 0.001, Adam for the accelerator, and early stopping to prevent overfitting. Next, the architecture of the lightweight NC-RBF-DNN was identical to that of the NC-RBF-DNN with the exception of fewer factors in the former, as only one factor combination was found by the factor combination search algorithm. So, for instance, if we suppose that a factor combination contains three numerical factors and one categorical factor, then the lightweight NC-RBF-DNN would then have twelve neurons in the RBF layer and sixteen neurons, eight neurons, and one neuron in each layer of the DNN. The training parameters of the lightweight NC-RBF-DNN were identical to those of the NC-RBF-DNN. The code of NC-RBF-DNN is extended based on the RBF-DRNN open-source code provided by [PERSON] et al. [53].