Intrinsic map dynamics exploration for uncharted effective free-energy landscapes

Eliodoro Chiavazzo, Roberto Covino, Ronald R. Coifman, C. William Geard, Anastasia S. Georgiou, Gerhard Hummer, and Ioannis G. Kevrekidis. PNAS June 20, 2017
Contributed by Jesper Madsen

The desire to use enhancing sampling to save computational expense in simulations has been there from the beginning. Broadly speaking, there are two main approaches of enhancing molecular dynamics (MD) simulations in order to determine the free-energy surface (FES) of a computationally expensive Hamiltonian: 1) Trajectory-based enhanced sampling (e.g. temperature replica-exchange) and 2) collective variable (CV)-based methods (e.g. umbrella sampling). It is worth noting that the “zoo” of actual techniques to date is rather large. Either type of method, trajectory-based or CV-based, comes with its own set of advantages and disadvantages and mixing-and-matching is popular. 

Here I highlight a newcomer that is spun off from the rapidly growing field of Machine Learning – a field that most of us is keeping a keen eye on these days. 

The algorithm is called intrinsic map dynamics (iMapD) and it is conceptually simple (See Fig. 1 from the paper). 

1. Run a MD trajectory

2. Figure out, in some abstract sense, what region of configuration space you have sampled.

3. Determine the (non-linear) boundary of the sampled region in the abstract space

4. Initialize new MD trajectories in these boundary areas and explore the uncharted territories of the FES.

It is with the concretization of each step above that machine learning has contributed its ideas and tools. Specifically, the map of the configuration space is data mined and a d-dimensional manifold learning technique called diffusion maps (DMAPs) is applied to find the appropriate manifold and its dimensionality. The (d-1)-dimensional boundary manifold of the explored region is determined by a “wrapping” algorithm (here they use alpha shapes). Outward extrapolation is done by performing local principal component (LPC) analysis in ambient space. New simulations are seeded from these extended initial configurations and the algorithm loops back to the beginning. 

Fig.1: Pictorial illustration of the iMapD exploration procedure with (Left) 1D and (Right) 2D effective FESs. In Left Inset, a good collective coordinate is already available—the collective coordinates in Left and Right are not a priori known. "Copyright (2017) National Academy of Sciences

Since iMapD is a trajectory-based approach, absolutely no prior knowledge about the mechanistics of the process we study is required, which is appealing. One can think of the method as a clever hybrid MD/Monte Carlo algorithm and time will show how it stacks up against other alternative approaches in terms of practical usefulness. 

WInote that the algorithm is pedagogically presented in the paper and if you fancy Indiana Jones, well then there’s a little treat for you in the main text. Enjoy.