artificial-neural-networks | simple neural network using sigmoid function | Machine Learning library

No, this is a matter of experimentation to find what solves your problem. As your reference shows, the layer complexity is driven by the inherent complexity of your data and the classifications you're trying to do.

As a general principle, note that a hidden layer is a minimal convenience: a linear combination of linear combinations does not produce any additional learning capability: it's still a linear combination. Thus, you need only one hidden layer -- although for some problems, using two or three hidden layers will slightly reduce the quantity of neurons needed to train at the same rate.

When I need to do such design, I attack it simply: start with a hidden layer with my best guess at the quantity of neurons I'll need. Train the model; if it fails to converge, look at the loss function to see how badly it failed. Based on that, increase the neurons (double, 10x, ...) and try again.

Once it succeeds, then I gradually reduce the neuron count until I find the "sweet spot" for accuracy vs training time.

Some problems don't solve readily through a simple NN. Depending on the application, you may need something from the Deep Learning world, such as a simple CNN (Convolutional NN).

If your data set is complex enough, you may also want to apply PCA (Principal Component Analysis) to find the significant input parameters. You can then reduce the input data, greatly reducing the size of the NN and the training time required to converge.