An exploration algorithm for stochastic simulators driven by energy gradients

Anastasia S. Georgiou, Juan M. Bello-Rivas, Charles William Gear, Hau Tieng Wu, Eliodoro Chiavazzo, Ioannis G. Kevrekidis

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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.

Original languageEnglish (US)
Article number294
Issue number7
StatePublished - Jul 1 2017

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Electrical and Electronic Engineering
  • General Physics and Astronomy
  • Mathematical Physics
  • Physics and Astronomy (miscellaneous)


  • Data mining
  • Gradient systems
  • Model reduction
  • Molecular dynamics
  • Stochastic differential equations


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