Proper orthogonal decomposition for optimality systems

ESAIM: M2AN has started a new practice of occasionally selecting certain papers as "Highlight" papers. The papers so designated we believe will be of particular interest to our readership due to the topic or approach pursued or perhaps the reach and implications of the results. Highlight papers will be briefly introduced by an Editor, and will be available (without charge, and indefinitely) on the ESAIM: M2AN electronic repository.

The topic of "reduced order modelling" is increasingly important in the many-query and real-time contexts. In particular, in the areas of parameter estimation, design, optimization, and control, classical techniques are often not sufficiently responsive to be of practical value: new approaches such as reduced order modelling will be required. Many theoretical and computational issues remain unresolved within the reduced order modelling framework, from optimal and efficient sampling to effective primal-dual approaches to treatment of nonlinearities and discontinuities to sharp a priori and a posteriori error estimation. This Highlight Paper addresses one of the concerns crucial to ultimate adoption of reduced order modelling concepts in the optimization and control frameworks: how can reduced order models be constructed that reflect - and are accurate within - the parts of the parameter or "dynamical" space relevant to the desired objectives and constraints?

Claude Le Bris, and Anthony T. Patera

Proper orthogonal decomposition for optimality systems
Karl Kunisch and Stefan Volkwein
M2AN 42 (2008) 1-23