Regensburg 2019 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 36: Condensed-matter simulations augmented by advanced statistical methodologies (joint session DY/CPP)

DY 36.3: Talk

Wednesday, April 3, 2019, 15:45–16:00, H20

Localized Basis Functions for Variationally Enhanced Sampling — •Benjamin Pampel, Kurt Kremer, and Omar Valsson — Max Planck Institute for Polymer Research, Mainz, Germany

Variationally Enhanced Sampling (VES) is a recently developed method for molecular dynamics simulations. It enhances sampling by introducing a bias potential along certain collective variables that is constructed via minimisation of a convex functional.

This bias potential is usually represented by a linear expansion in some basis set, with delocalised functions such as plane waves or Chebyshev/Legendre polynomials as common choices. However, it is an open question if localised functions perform better. In particular, the wavelet family of Daubechies might be a good choice. These functions offer the favourable property of forming an orthonormal basis with a tunable number of vanishing moments. Furthermore, their intrinsic principle of multiresolution allows increasing the precision of the bias representation at specific points of interest.

We have implemented Daubechies wavelets into the VES code and have tested their performance in various systems. As a direct comparison of the different basis sets is difficult, we have developed a new measure of the error of free energy calculations. The Daubechies wavelets are observed to perform better than both Chebyshev/Legendre polynomials and Gaussian basis functions, resulting in faster convergence and yielding more accurate free energy surfaces without increases in computational cost.