In this paper, we consider a new framework where two types of data are available:
experimental data
Y1,...,Yn
supposed to be i.i.d from Y and outputs from a simulated reduced model.
We develop a procedure for parameter estimation to characterize a feature of the
phenomenon Y. We prove a risk bound qualifying the proposed procedure in
terms of the number of experimental data n, reduced model complexity and
computing budget m. The method we present is general enough to cover a
wide range of applications. To illustrate our procedure we provide a numerical
example.