Title:  Property preserving model reduction in bracket-based dynamical systems

Abstract:  The dynamics of physical systems are implicitly constrained by conservation laws which are largely responsible for the behavior of their solutions.  However, standard methods of model reduction frequently used in practice violate these relationships, leading to artificial numerical instability and poor generalization performance in the resulting low-order surrogates.  This talk surveys the author’s recent work on property preserving model reduction from both “top down” and “bottom up” perspectives, where it is shown that enforcing appropriate variational structure in surrogate models for bracket-based dynamical systems leads to exact conservation properties, improved stability, and robust long-term behavior at computational costs reasonably competitive with general-purpose methods.