'Nonlinear model reduction via lifting transformations and POD'

9 November 2018
12:00 pm to 1:00 pm
'Nonlinear model reduction via lifting transformations and POD'
Boris Kramer

ABSTRACT:   Model order reduction for large-scale nonlinear systems is a key enabler for design, uncertainty quantification and control of complex systems. 

    I will discuss a beneficial detour to deriving efficient reduced-order models for nonlinear systems. First, the nonlinear model is lifted to a model with more structure via variable transformations and the introduction of auxiliary variables. The lifted model is equivalent to the original model - it uses a change of variables, but introduces no approximations. When discretized, the lifted model yields a polynomial system of either ordinary differential equations or differential algebraic equations, depending on the problem and lifting transformation. Proper orthogonal decomposition (POD) is applied to the lifted models, yielding a reduced-order model for which all reduced-order operators can be pre-computed. We show several examples in form of a FitzHugh-Nagumo PDE and a tubular reactor PDE model, and show how this approach opens new pathways for rigorous analysis and input-independent model reduction via the introduction of the lifted problem structure.