An extended functional network model and its application for a gas sensing system

Functional networks (FNs) are a promising numerical scheme that produces accurate solutions for several problems in science and engineering with less computational effort than other conventional numerical techniques such as neural networks. By using domain knowledge in addition to data knowledge, functional networks can be regarded as a generalization of neural networks: they allow to design arbitrary functional models without neglecting possible functional constraints involved by the model. The computational efficiency of functional networks can be improved by combining this scheme with finite differences when highly oscillating systems have to be considered. The main focus of this paper is on the possible questions arising from the application of this combined scheme to an identification problem when non-smooth functions are involved and noisy data are possible. These issues are not covered by the current literature. An extended version, based on a piecewise approach, and a stability criterion are proposed and applied to the quantitative identification problem in a gas sensing system in its transient state. Numerical simulations show that our scheme allows good accuracy, avoiding the error accumulation and the sensitivity to noisy data by means of the stability criterion.