## 5 Problem Solution--Results  
The data collection encompassed 52 unique initiatives in all. The network had already formed a testing procedure, and this significant data collection gave it structure. The primary objective of this testing process was to facilitate the comparison of the actual project expenses with the ANN model's cost projections. Each project in this collection of data was a single occurrence with an individual set of variables and outcomes. The testing method has a reliable and robust baseline because to the meticulous collection and assembly of these projects' actual expenditures. In order to estimate the accuracy of the ANN model, the sum of squares error and relative error were utilized in the present research. The relative error is a measure of the accuracy of a measurement compared to the size of the measurement itself. The relative error is calculated using the following expression:  
\[\text{Relative Error}=\left(\frac{\text{Absolute Error}}{\text{ Actual Value}}\right)\times 100\% \tag{3}\]where Absolute Error is the difference between the measured or predicted value and the actual value (actual and estimated cost) and Actual Value is the true value (actual final cost) [58]. A metric for measuring the difference between values predicted by a model and actual data points is the sum of squares error, or SSE. The computation involves the summation of the squares representing the discrepancies between the anticipated and observed values. It is calculated utilizing the following expression:  
\[\text{SSE}=\sum_{i=1}^{n}\left(y_{i}-\hat{y}_{1}\right)^{2} \tag{4}\]  
where \(y_{i}\) represents the actual observed values (actual final cost), \(\hat{y}_{i}\) represents the predicted values (estimated final cost) from the model, and n is the number of observations [58]. Figures 2 and 3 illustrate how the training sample's sum of squares error and relative error are maintained at a low level after RBF implementation. The testing sample's sum of squares error and relative error were kept low with a concern of overfitting after 43 neurons in the hidden layer following RBF implementation, as seen in Figures 4 and 5. Figure 4: Testing sample of sum of squares error after the implementation of the RBF approach. Figure 3: Training sample of relative error after the implementation of the RBF approach. Figure 2: Training sample of sum of squares error after the implementation of the RBF approach. Figures 6 and 7 below show how the relative error of the training sample and the sum of squares error have a periodic variation with MLP adoption. Figures 8 and 9 below illustrate how the implementation of MLP also causes a periodic fluctuation in both the sum of squares error and the relative error of the testing sample. Figure 5: Testing sample of relative error after the implementation of the RBF approach. Figure 6: Training sample of sum of squares error after the implementation of the MLP approach. Figure 7: Training sample of relative error after the implementation of the MLP approach. Various causes may contribute to the periodic variation seen in Figures 6 and 7 (training sample) and also Figures 8 and 9 (testing sample), depending on the characteristics of the figures and the context of the data. The model architecture selection may introduce periodicity since the results prior in the figures are dependent on model predictions, such as neural networks. Because of their layered nature, neural networks--including multi-layer perceptrons (MLPs)--can display complicated behavior. Among the many types of ANNs, MLPs are particularly intricate and versatile. Their nonlinearity, layered architecture, feature extraction, and backpropagation algorithm--which computes gradients with respect to the loss function and modifies weights to minimize prediction errors--all contribute to their effectiveness and increases in weight. Due to their complicated decision boundaries, MLPs are able to learn extremely nonlinear and irregular limits on decisions [60].