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Entropy 2017, 19(7), 294; doi:10.3390/e19070294

An Exploration Algorithm for Stochastic Simulators Driven by Energy Gradients

1
Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08544, USA
2
Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA
3
Department of Mathematics, University of Toronto, Room 6290, 40 St. George Street, Toronto, ON M5S 2E4, Canada
4
Energy Department, Politecnico di Torino, 10129 Torino, Italy
5
Department of Chemical and Biological Engineering and Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA
6
TUM Institute for Advanced Study, Technische Universität München, 85748 Garching, Germany
*
Author to whom correspondence should be addressed.
Academic Editors: Giovanni Ciccotti, Mauro Ferrario and Christof Schuette
Received: 28 February 2017 / Revised: 24 April 2017 / Accepted: 8 May 2017 / Published: 22 June 2017
(This article belongs to the Special Issue Understanding Molecular Dynamics via Stochastic Processes)
View Full-Text   |   Download PDF [7112 KB, uploaded 22 June 2017]   |  

Abstract

In recent work, we have illustrated the construction of an exploration geometry on free energy surfaces: the adaptive computer-assisted discovery of an approximate low-dimensional manifold on which the effective dynamics of the system evolves. Constructing such an exploration geometry involves geometry-biased sampling (through both appropriately-initialized unbiased molecular dynamics and through restraining potentials) and, machine learning techniques to organize the intrinsic geometry of the data resulting from the sampling (in particular, diffusion maps, possibly enhanced through the appropriate Mahalanobis-type metric). In this contribution, we detail a method for exploring the conformational space of a stochastic gradient system whose effective free energy surface depends on a smaller number of degrees of freedom than the dimension of the phase space. Our approach comprises two steps. First, we study the local geometry of the free energy landscape using diffusion maps on samples computed through stochastic dynamics. This allows us to automatically identify the relevant coarse variables. Next, we use the information garnered in the previous step to construct a new set of initial conditions for subsequent trajectories. These initial conditions are computed so as to explore the accessible conformational space more efficiently than by continuing the previous, unbiased simulations. We showcase this method on a representative test system. View Full-Text
Keywords: stochastic differential equations; model reduction; gradient systems; data mining; molecular dynamics stochastic differential equations; model reduction; gradient systems; data mining; molecular dynamics
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Georgiou, A.S.; Bello-Rivas, J.M.; Gear, C.W.; Wu, H.-T.; Chiavazzo, E.; Kevrekidis, I.G. An Exploration Algorithm for Stochastic Simulators Driven by Energy Gradients. Entropy 2017, 19, 294.

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