  Polynomial chaos expansions (PCE) have proven efficiency in a number of
fields for propagating parametric uncertainties through computational models of
complex systems, namely structural and fluid mechanics, chemical reactions and
electromagnetism, etc. For problems involving oscillatory, time-dependent
output quantities of interest, it is well-known that reasonable accuracy of
PCE-based approaches is difficult to reach in the long term. In this paper, we
propose a fully non-intrusive approach based on stochastic time warping to
address this issue: each realization (trajectory) of the model response is
first rescaled to its own time scale so as to put all sampled trajectories in
phase in a common virtual time line. Principal component analysis is introduced
to compress the information contained in these transformed trajectories and
sparse PCE representations using least angle regression are finally used to
approximate the components. The approach shows remarkably small prediction
error for particular trajectories as well as for second-order statistics of the
latter. It is illustrated on different benchmark problems well known in the
literature on time-dependent PCE problems, ranging from rigid body dynamics,
chemical reactions to forced oscillations of a non linear system.
