Application of Gaussian processes for black-box modelling of biosystems

Different models can be used for nonlinear dynamic system identification and the Gaussian process model is a relatively new option with several interesting features: model predictions contain the measure of confidence, the model has a small number of training parameters and facilitated structure determination, and different possibilities of including prior knowledge exist. In this paper the framework for the identification of a dynamic system model based on Gaussian processes is shown, illustrated on a simulated bioreactor example and then applied to two case studies. The first one addresses modelling of the nitrification process in a wastewater treatment plant and the second models biomass growth in the Lagoon of Venice. Special emphasis is placed on model validation, an often underemphasised part of the identification procedure, where the Gaussian model prediction variance can be utilised.