Local and Global Perspectives on Diffusion Maps in the Analysis of Molecular Systems - Archive ouverte HAL
Article Dans Une Revue Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Année : 2020

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

Résumé

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, we introduce a global and local perspective 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 quasi-stationary distribution and justifying the convergence of diffusion maps within a local equilibrium. We demonstrate the practical relevance of these approaches both for simple models and for molecular dynamics problems (alanine dipeptide and deca-alanine).

Dates et versions

hal-02104963 , version 1 (19-04-2019)

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Citer

Zofia Trstanova, Ben Leimkuhler, Tony Lelièvre. Local and Global Perspectives on Diffusion Maps in the Analysis of Molecular Systems. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2020, 476 (2233), ⟨10.1098/rspa.2019.0036⟩. ⟨hal-02104963⟩
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