
| AX5   | 4.2%   | 100%   | 12.969s   |
|-------|--------|--------|-----------|
| AX6   | 3.6%   | 100%   | 9.671s    |

This is a small difference but AX6 has the smallest training error and hence the most optimum functional mapping. This therefore implies that the best RBF is AX6. When comparing AZ2 and AX6 it is apparent that AX6 provides the most optimum approximation of the target values of the validation set. This is due to the fact that it has 100% accuracy and a validation error of 3.6%. As a result, it is regarded as the Artificial Neural Genius (ANG). 

VII. DISCUSSION OF R**ESULTS** 
The object of this section is to compare the SVG and ANG in order to determine the OG. This is done by employing the third data set which is the testing set. This is done in order to determine the generalisation ability of these two geniuses. 

SVG Error 5.46519% 
SVG Accuracy 100% ANG Error 2.95995% ANG Accuracy 100%
It is apparent from this analysis that the ANG has better generalization ability than the SVG. This therefore implies that artificial neural networks are better approximation tools for this particular study. The functional mapping of the ANG is plotted in the fig 2 below. 

![0_image_0.png](0_image_0.png)

A further development would be to even further scrutinize the generalisation ability of this ANG. This can be done by determining the common trends in the water demand data. A model will be developed for each trend, and the theory of Hidden Markov Models [18] will be employed to determine whether the predicted value belongs to that particular date or season by looking at the model of that particular season. 

## Viii C**Onclusions**

Two machine learning techniques have been investigated in this study. These are the artificial neural networks (ANNs) and the support vector machines 
(SVMs). An approach adopted was to conduct two parallel experiments, one for the ANNs and one for the SVMs. The ANN experiment encapsulated two architectures, the multi-layer perceptron (MLP) and the radial basis function 
(RBF). The results from the two architectures were compared to come up with the Artificial Neural Genius (ANG). The SVM experiment was comprised of many models with different kernel functions and some of these kernel functions had additional arguments such as the degree and the scale. These models were compared against each other in order to determine the Support Vector Genius (SVG). The performance criteria used to determine the geniuses from each experiment were the validation error and the accuracy in their approximation of the target values of the validation data set. The two geniuses were then compared against each other in order to determine the overall genius (OG). The performance parameter used to determine the OG is the generalisation ability of each genius. The ANG has proved to outperform the SVG. 

## A**Cknowledgement**

The authors hereby thank Rand Water's Thomas Phetla for taking his time to make the data available. The financial support of the South African National Research Foundation is hereby acknowledged. 

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