  An adaptive projection-based reduced-order model (ROM) formulation is
presented for model-order reduction of problems featuring chaotic and
convection-dominant physics. An efficient method is formulated to adapt the
basis at every time-step of the on-line execution to account for the unresolved
dynamics. The adaptive ROM is formulated in a Least-Squares setting using a
variable transformation to promote stability and robustness. An efficient
strategy is developed to incorporate non-local information in the basis
adaptation, significantly enhancing the predictive capabilities of the
resulting ROMs. A detailed analysis of the computational complexity is
presented, and validated. The adaptive ROM formulation is shown to require
negligible offline training and naturally enables both future-state and
parametric predictions. The formulation is evaluated on representative reacting
flow benchmark problems, demonstrating that the ROMs are capable of providing
efficient and accurate predictions including those involving significant
changes in dynamics due to parametric variations, and transient phenomena. A
key contribution of this work is the development and demonstration of a
comprehensive ROM formulation that targets predictive capability in chaotic,
multi-scale, and transport-dominated problems.
