Development of Enhanced Sampling Methods for Molecular Simulations – Wavelets and Birth-Death
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Abstract
To overcome the time scale problem of molecular simulations, methods that enhance phase space sampling are developed.
Two complementary enhanced sampling approaches are investigated: Improving the bias representation in the variationally enhanced sampling method, as well as a novel sampling algorithm using birth-death moves.
The variationally enhanced sampling method is based on a variational principle, where a bias potential is constructed in the space of a few slow degrees of freedom by minimizing a convex functional.
Typically, the bias potential is taken as a linear expansion in some set of basis functions.
In this work, properties of good basis functions for the method are identified to subsequently propose new basis functions and assess their performance.
In particular, Daubechies wavelets are investigated, which construct orthogonal and localized bases that exhibit an attractive multiresolution property.
Their theory is studied and they are implemented into the PLUMED2 software, together with other new basis functions.
The parameters of the new basis sets are tuned.
Benchmarking studies on systems of increasing complexity are performed, from the simulation of the movement of a single particle in a one-dimensional potential to the study of the association process of calcium carbonate in water.
The wavelet bases are found to exhibit excellent performance and yield much better convergence of the bias potential than the previously existing basis functions.
Also, a novel sampling algorithm that augments Langevin dynamics with birth-death moves is investigated.
This is a modification of a previously proposed algorithm that provides an approximation of a stochastic birth-death process for a particle-based implementation.
The method connects multiple parallel Langevin dynamics simulations of the same system with a birth-death scheme to facilitate global sampling according to the equilibrium distribution.
The algorithm is investigated theoretically, implemented into a custom molecular simulation code, and tested via numerical simulations.
The behavior of the algorithm under change of parameters is investigated.
In this process, the desired sampling is observed for all tested systems.
It is found that the performance of the method is independent of the intrinsic time scales and barriers of the system, which is favorable for systems with processes on long time scales.