Computing committors in collective variables via Mahalanobis diffusion maps

نویسندگان

چکیده

The study of rare events in molecular and atomic systems such as conformal changes cluster rearrangements has been one the most important research themes chemical physics. Key challenges are associated with long waiting times rendering simulations inefficient, high dimensionality impeding use PDE-based approaches, complexity or breadth transition processes limiting predictive power asymptotic methods. Diffusion maps promising algorithms to avoid mitigate all these issues. We adapt diffusion map Mahalanobis kernel proposed by Singer Coifman (2008) for SDE describing dynamics collective variables which matrix is position-dependent and, unlike case considered Coifman, not a diffeomorphism. offer an elementary proof showing that can approximate generator this discretized point cloud via map. it calculate committor functions two benchmark systems: alanine dipeptide, Lennard-Jones-7 2D. For validating our results, we compare finite-difference solution conducting “committor analysis” used practitioners. contrast outputs those standard isotropic show former gives significantly more accurate estimates committors than latter.

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ژورنال

عنوان ژورنال: Applied and Computational Harmonic Analysis

سال: 2023

ISSN: ['1096-603X', '1063-5203']

DOI: https://doi.org/10.1016/j.acha.2023.01.001