Reduced-dimensionality Legendre Chaos expansions via basis adaptation on 1d active subspaces

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 of 1-dimensional active subspaces, the methodology can be applicable to generalized Polynomial Chaos expansions, thus enabling the efficient computation of the chaos coefficients in expansions with arbitrary input distribution. Besides the significant computational savings, additional attractive features such as high accuracy in computing statistics of interest are also demonstrated.