A Novel Model Reduction Strategy Using Upper Bound Theory

We propose an original model reduction technique for driven, dissipative infinite-dimensional dynamical systems. Unlike popular -- but empirical -- POD-based methods, our approach does not require \emph{a priori} data sets from experiments or full PDE simulations and, thus, yields truly predictive reduced models. Instead, the basis functions are computed by solving a constrained, non-local eigenvalue problem drawn from energy stability and upper bound theory. In contrast to \emph{a priori} bases used in spectral expansions, the upper bound eigenfunctions appear to be well suited for the low-order description of strongly driven, spatiotemporally chaotic dynamics, as we demonstrate by applying our methodology to porous medium convection.