Dynamics Identification in Evolution Models Using Radial Basis Functions

The problem of identifying an unknown function of the state of an evolution model with differential equations is considered in the framework of a minimization problem. The well-posedness of this minimization problem as well as unique solvability is proven. The analysis of the dependence of the identified function on the data is presented by means of the derivative of the "data-to-function" mapping. Moreover, the infinite dimensional function space, where the unknown function is sought, is discretized by suitable radial basis functions that are chosen such that optimal approximation results are obtained. The numerical treatment of a representative evolution model and the application to a bio-chemical model illustrate the proposed approach.