Before revision: We consider the problem of robustly determining the m slowest dynamical modes of a reversible dynamical system, with a particular focus on the analysis of equilibrium molecular dynamics simulations. We show that the problem can be formulated as the variational optimization of a single scalar functional , a generalized matrix Rayleigh quotient (GMRQ), which measures the ability of a rank-m projection operator to capture the slow dynamics of the system.
After revision: We consider the problem of robustly determining the m slowest dynamical modes of biomolecular systems. However, the lack of a unified theoretical framework for choosing between alternative models has hampered progress, especially for non-experts applying these methods to novel biological systems. Here, we consider cross-validation with a new objective function for estimators of these slow dynamical modes , a generalized matrix Rayleigh quotient (GMRQ), which measures the ability of a rank-m projection operator to capture the slow dynamics of the system.