Numerical Analysis Seminars: On fundamental limitations of Wiener Chaos expansions for uncertainty quantification in dynamical systems
20 November 2015 14:00 in CM105
I will discuss the suitability of truncated Wiener Chaos expansions (WCE) and truncated Gram-Charlier expansions (GrChE) as methods for uncertainty quantification in nonlinear dynamical systems with positive Lyapunov exponents. Based on a class of statistically exactly solvable non-linear, non-Gaussian systems, I will show that efficacy of the methods exploiting such truncated spectral expansions is severely limited in the presence of intermittent instabilities, parametric uncertainties, or even for linear SDEs. Intermittency and non-Gaussian probability densities are hallmark features of the so-called inertial and dissipation ranges of turbulence and it turns out that in such important dynamical regimes WCE performs, at best, similarly to the vastly simpler Gaussian moment closure technique. Moreover, I will show that the non-realisability of the GrChE approximations is linked to the onset of intermittency in the dynamics and it is frequently accompanied by an erroneous blow-up of the second-order statistics at short times.
Contact David.Bourne@durham.ac.uk for more information