Gradient-informed basis adaptation for Legendre Chaos expansions

The recently introduced basis adaptation method for Homogeneous (Wiener) Chaos expansions is explored in a new context where the rotation/projection matrices are computed by discovering the active subspace where the random input exhibits most of its variability. In the case where a 1-dimensional active subspace exists, the methodology can be applicable to generalized Polynomial Chaos expansions, thus enabling the projection of a high dimensional input to a single input variable and the efficient estimation of a univariate chaos expansion. Attractive features of this approach, such as the significant computational savings and the high accuracy in computing statistics of interest are investigated.