Assume that I want to solve an issue with a neural network that either I can't fit to already existing topologies (perceptron, Konohen, etc) or I'm simply not aware of the existence of those or I'm unable to understand their mechanics and I rely on my own instead.

How can I automate the choice of the topology (that is, the number of layers, the type of activations, the type and direction of the connections, etc.) of a neural network for an arbitrary problem?

I'm a beginner, yet I realized that in some topologies (or, at least in perceptrons) it is very hard if not impossible to understand the inner mechanics as the neurons of the hidden layers don't express any mathematically meaningful context.