Algebraic inversion of an artificial neural network classifier

Artificial neural networks are, by their definition, non-linear functions. Typically, this means that it is impossible to find a closed-form solution for the inverse function of a neural network. This paper presents a special form of neural network classifier that allows for its algebraic inversion in order to find the boundary between classes. The control of the fuel-air ratio in a spark ignition engine is given as an example.