The Adjoint Petrov-Galerkin Method for Non-Linear Model Reduction

Understand

We formulate a new projection-based reduced-ordered modeling technique for non-linear dynamical systems.

• The proposed technique, which we refer to as the Adjoint Petrov-Galerkin (APG) method, is derived by decomposing the generalized coordinates of a dynamical system into a resolved coarse-scale set and an unresolved fine-scale set.
• A Markovian finite memory assumption within the Mori-Zwanzig formalism is then used to develop a reduced-order representation of the coarse-scales.
• This procedure leads to a closed reduced-order model that displays commonalities with the adjoint stabilization method used in finite elements.