An exploratory study of discrete time state-space models using kriging

An exploratory study of the application of kriging as an approximated model of complex dynamic systems is presented in this paper. This technique, which has its roots in the geology community, is gaining popularity for its simplicity and ability to track the error of the reduced model, making it attractive for engineering applications. Our proposed methodology, called dynamic mapping kriging, requires the generation of representative function evaluations, and then uses them in a recursive state-space formulation to represent the evolution of the process. By demonstrating on a highly simplified model, our intention is to present the relevant elements of this methodology, focusing on the design of the function evaluations as a crucial factor in the accurate representation of the system. We illustrate the advantages that the error prediction has as a tool to improve our technique and as a measurement to bound the error dynamics, and give some final recommendations about the applications of this methodology to build approximated models.