Local and Global Perspectives on Diffusion Maps in the Analysis of Molecular Systems

Zofia Trstanova, Benedict Leimkuhler, Tony Lelievre

Research output: Contribution to journalArticlepeer-review

Abstract

Diffusion maps approximate the generator of Langevin dynamics from simulation data. They afford a means of identifying the slowly-evolving principal modes of high-dimensional molecular systems. When combined with a biasing mechanism, diffusion maps can accelerate the sampling of the stationary Boltzmann-Gibbs distribution. In this work, wecontrast the local and global perspectives on diffusion maps, based on whether or not the data distribution has been fully explored. In the global setting, we use diffusion maps to identify metastable sets and to approximate the corresponding committor functions of transitions between them. We also discuss the use of diffusion maps within the metastable sets,formalising the locality via the concept of the quasistationary distribution and justifying the convergence of diffusion maps within a local equilibrium. This perspective allows us to propose an enhanced sampling algorithm. We demonstrate the practical relevance of these approaches both for simple models and for molecular dynamics problems (alanine dipeptide and deca-alanine).

Original languageEnglish
Article number20190036
Number of pages24
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume476
Issue number2233
Early online date15 Jan 2020
DOIs
Publication statusPublished - 31 Jan 2020

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