An Exploration Algorithm for Stochastic Simulators Driven by Energy Gradients

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.

On the Correspondence between Gaussian Processes and Geometric Harmonics

“…In our toy example, we use a relatively large kernel bandwidth due to the small sample size, which alleviates the issue. Several techniques already exist to completely alleviate it systematically, including Sine Diffusion Maps [37], Diffusion Maps for Embedded Manifolds with Boundary [38], as well as Ghost Point Diffusion Maps [39].…”

Assembling Biocompatible Polymers on Gold Nanoparticles: Toward a Rational Design of Particle Shape by Molecular Dynamics

“…Configurations with different concentrations of PLGA were simulated Unsupervised Learning to Explore PLGA Clusters. Taking advantage of the formidable ability of ML in terms of feature extraction 48,49 and cluster analysis, we applied an unsupervised learning scheme to investigate the time evolution of self-assembly pathways of the oligomer chains. We carried out a clustering analysis by adopting the algorithm of Adorf et al 50 used for crystallization events to our PLGA coating phenomena.…”

Staying the course: Locating equilibria of dynamical systems on Riemannian manifolds defined by point-clouds

“…The effective motion of the system is driven by the potential of mean force [55] and it is described by the time-evolution of a point in the m-dimensional space of collective variables M . Often, the relevant collective variables are not known in advance and practitioners rely on machine learning for identifying them [14,25,12,59,62].…”