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 (AS) where the random input exhibits most of its variability. In the case where a One-dimensional (1D) AS exists, the methodology can be applicable to generalized polynomial chaos expansions (PCE), 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.
Gradient-Informed Basis Adaptation for Legendre Chaos Expansions
Manuscript received November 10, 2016; final manuscript received July 5, 2018; published online July 30, 2018. Assoc. Editor: Sez Atamturktur.
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Tsilifis, P. A. (July 30, 2018). "Gradient-Informed Basis Adaptation for Legendre Chaos Expansions." ASME. J. Verif. Valid. Uncert. March 2018; 3(1): 011005. https://doi.org/10.1115/1.4040802
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