\chapter{Basis Adaptation Models}\label{Chap:BasAdapt}
The idea behind the basis adaptation is similar to the one employed in the active subspaces that is to find the directions
in the input space where the variations of the QoI are negligible. One of the main differences between the basis adaptation and
the active subspaces strategy is that the basis adaptation rely on the construction of a Polynomial Chaos Expansion (PCE) that is 
subsequently rotated to decrease the dimensionality of the problem.