*2.5. Artificial Neural Network (ANN)*

MATLAB's Neural Network in MATLAB R2011b (MathWorks Inc., Natick, MA, USA) was used to train the backpropagation ANN developed in this study. The hyperbolic *tangent sigmoid* (Equation (7)) and the *purelin* (Equation (8)) transfer function was used for the input layer to the hidden layer and the hidden layer to the output layer, respectively.

$$\text{tangent sigmoid} \left( \mathbf{x} \right) = \frac{2}{\left( 1 + \varepsilon^{-2x} \right)} - 1 \tag{7}$$

$$A = \operatorname{purelin}\left(\mathbf{x}\right) = \mathbf{x} \tag{8}$$

The proposed ANN has an input layer with three neurons (coconut oil to ethanol molar ratio, reaction time and microwave power), a hidden layer and an output layer with one neuron (bio-jet fuel yield). The ANN model was trained until the mean square error (MSE) was minimized and the average correlation coefficient was close or equal to 1. The optimum number of hidden neurons was selected by heuristic procedure. The dataset containing the bio-jet fuel yield and the process input variables were divided into three subsets: training (70%), validating (15%), and testing (15%).
