Algorithm 1: Neural Network Training

Require: train_data: Matrix of input training data

Require: desired_output: Matrix of corresponding desired output data

Require: num_epochs: Number of training epochs

Ensure: Trained neural network weights and biases

1: Initialize the network weights and biases randomly

2: for epoch = 1 to num_epochs do

3:   for i = 1 to size(training_data,1) do

4:     input_data = training_data(i,:)

5:     output_data = desired_output(i,:)

6:     Perform the forward phase

7:     predicted_output = neural_network(input_data)

8:     Calculate the error between the predicted output and the desired output

9:     loss = loss_function(output_data, predicted_output)

10:     Perform the backward phase

11:     gradients = backward_phase (loss, neural_network)

12:     Update the weights and biases of the network

13:     neural_network=update_weights(neural_network, gradients)

14:   end for

15: end for

16: return Trained neural network weights and biases