Locating landmarks on high-dimensional free energy surfaces

Coarse graining of complex systems possessing many degrees of freedom can often be a useful approach for analyzing and understanding key features of these systems in terms of just a few variables. The relevant energy landscape in a coarse-grained description is the free energy surface as a function of the coarse-grained variables, which, despite the dimensional reduction, can still be an object of high dimension. Consequently, navigating and exploring this high-dimensional free energy surface is a nontrivial task. In this paper, we use techniques from multiscale modeling, stochastic optimization, and machine learning to devise a strategy for locating minima and saddle points (termed landmarks) on a high-dimensional free energy surface on the fly and without requiring prior knowledge of or an explicit form for the surface. In addition, we propose a compact graph representation of the landmarks and connections between them, and we show that the graph nodes can be subsequently analyzed and clustered based on key attributes that elucidate important properties of the system. Finally, we show that knowledge of landmark locations allows for the efficient determination of their relative free energies via enhanced sampling techniques.