Computing Committors in Collective Variables Via Mahalanobis Diffusion Maps*

Abstract: Many interesting problems concerned with rare event quantification arise in chemical physics. A typical problem is finding reaction channels and transition rates for conformal changes in a biomolecule. To reduce the dimensionality and make the description of transition processes more comprehensible, often a set of physically motivated collective variables (dihedral angles, distances between particular pairs of key atoms, etc.) is introduced by means of mapping atomic coordinates to a low-dimensional space and averaging. The dynamics in collective variables remain time-reversible but acquire an anisotropic and position-dependent diffusion tensor. In this talk, I will discuss how one can adapt the diffusion map algorithm with the Mahalanobis kernel to approximate the generator of this diffusion process and use it to compute the committor function, the reactive current, and the transition rate. Applications to alanine-dipeptide and Lennard-Jones-7 in 2D will be presented.

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