RobustInv: RobustInv - Robust Inversion of Expensive Black-box functions

In IRSN/RobustInv: "Robust inversion of expensive black-box functions"

Description

The robust inversion problem in computer experiments can be seen as a generalization of the inversion problem tackled in the KrigInv package. It applies to functions with inputs that can be classified in two categories: controlled parameters and nuisance parameters. The input domain D, of dimension d can thus be written as a tensor product D = Dinv x Dopt, where Dinv is the space of the d.inv controlled parameters and Dopt is the space of the d.opt nuisance parameters.

The goal is thus to build a sequential design of experiment which aims at identifying the set Gamma* = { xinv in Dinv : f(xinv,xopt) < T for all xopt in Dopt }. In short, we are interested in the configuration of controlled parameters such that the system at hand f remains 'safe' (i.e. below a target threshold T) for all possible values of the nuisance parameters.

The suffix 'inv' is often used in this package when we refer to the controlled parameters. This is due to the fact that the inversion is actually performed in the set of controlled parameters. The suffix 'opt' is often used when we refer to the nuisance parameters. This is due to the fact that the set Gamma* that we aim at identifying can be rewritten: Gamma* = { xinv in Dinv : max_xopt f(xinv,xopt) < T }; meaning that some kind of optimization is performed with respect to the nuisance parameters. When xinv is fixed the optimizer corresponds to the most penalysing (or most dangerous) value of xopt, leading to the highest response f(xinv,xopt).

This package shares many similarities with the KrigInv package and a good understanding of KrigInv is necessary to use it properly. The sampling criteria used to build the sequential design of experiments are detailed in Clement Chevalier's PhD manuscript.

Author(s)

Clement Chevalier [e-mail], Yann Richet [e-mail], Gregory Caplin [e-mail]

IRSN/RobustInv documentation built on Nov. 20, 2019, 10:46 p.m.