(747e) Iterative Manifold Extension for Efficient Discovery of Transition Pathways

Authors: 
Sroczynski, D., Princeton University
Kevrekidis, I. G., Princeton University
Chiavazzo, E., Politecnico di Torino
Bello-Rivas, J., Princeton University
Wu, H. T., University of Toronto
Our understanding of high-dimensional dynamical systems, including many found in molecular modeling, can often be improved through effective free energy surfaces (FES). One of the main challenges is to find the right coarse variables upon which to construct our FES when exploration on the manifold that defines it is computationally restricted by high transition barriers. We present an algorithm to more efficiently cross transition barriers and discover new stable states by relying on the smoothness of the manifold in the original space. We first establish the effective low-dimensionality from a relatively short initial simulation burst, which gives us a local picture of the underlying manifold. After identifying the boundary of the explored region, we can extrapolate geometrically outwards to find new initial conditions to run new simulation bursts, relying on the time scale separation to correct for extrapolation errors that result in off-manifold initializations. This approach biases the simulator to cross transition barriers on the effective FES, iteratively expanding our knowledge about the underlying manifold. We demonstrate our approach on several illustrative systems.