Blended reduced subspace algorithms for uncertainty quanti cation of quadratic systems with a stable mean state

Order-reduction schemes have been used successfully for the analysis and simplication of high-dimensional systems exhibiting low-dimensional dynamics. In this work we rst focus on presenting generic limitations of order-reduction techniques in systems with stable mean state that exhibit irreducible high-dimensional features such as non-normal dynamics, wide energy spectra, or strong energy cascades between modes. The reduced order framework that we consider to illustrate these limitations is the dynamically orthogonal (DO) eld equations. This framework is applied to a series of examples with stable mean state including a linear non-normal system, and a nonlinear triad system in various dynamical congurations. Af-ter illustrating the weaknesses and generic limitations of order-reduction, we develop a novel, two-way coupled, blended approach based on the quasilinear Gaussian (QG) closure and the DO eld equations. The new method (QG-DO) overcomes the limitations of its two ingredi-ents and achieves exceptional performance in the examples described previously as well as in other congurations with strongly transient character without using any tuned or adjustable parameters.