(253ao) Adaptive Coarse-Graining of Molecular Dynamics through Diffusion Maps

In many molecular dynamics (MD) applications, the system variables (or their statistics) quickly become slaved to a reduced set of coarse variables, which parameterize a low-dimensional manifold in the high-dimensional space of the full system. However, exploration of the energy landscape on the manifold can be hindered by deep potential wells and high transition barriers. Methods to alleviate this time limitation, such as umbrella sampling and equation-free modeling, require advance knowledge of good coarse variables.

When this advance knowledge is not available, we couple equation-free methods to diffusion maps, a nonlinear manifold learning algorithm, to learn the coarse variables â??on the flyâ? based on relatively short bursts of the MD simulator. By establishing the low dimensionality of an attracting manifold and geometrically extrapolating outwards, the simulator can be biased towards rare events, effectively moving up potential gradients and out of potential wells. This allows the simulator to time-effectively search the potential landscape for new stable states and transition pathways. We demonstrate our approach on a toy stochastic simulator as well as MD simulations of alanine dipeptide.