Some Comments

As you can see, until now, all the experiments done on the sinusoidal functions do not rigorously approximate the proposed functions, but this has several purposes.

1. The most important, as a teaching tool. When using somewhat demanding functions as an example, I like to show the difficulties so they can be resolved in the next section and thus introduce new strategies.

2. That the neural network is easily differentiated from the function to be approximated. And in the case where the error is shown (as $f:\mathbb{R}^2\to\mathbb{R}$), it is noted where there are difficulties, such as in the borders (especially in the corners), in the axes and/or origin.

3. If the reader is determined to run the experiments and has a modest computer, they will notice that it will take a couple of hours to complete the training sessions, and this is something that happens to me. By being generous with the domain points, neurons, layers, and epochs, it could take up to days to complete everything, and it would go from being an educational website to a torture.