Skip to main content

Fisher information metric for the Langevin equation and least informative models of continuous stochastic dynamics

Author(s): Haas, Kevin R; Yang, Haw; Chu, Jhih-Wei

To refer to this page use:
Abstract: The evaluation of the Fisher information matrix for the probability density of trajectories generated by the over-damped Langevin dynamics at equilibrium is presented. The framework we developed is general and applicable to any arbitrary potential of mean force where the parameter set is now the full space dependent function. Leveraging an innovative Hermitian form of the corresponding Fokker-Plank equation allows for an eigenbasis decomposition of the time propagation probability density. This formulation motivates the use of the square root of the equilibrium probability density as the basis for evaluating the Fisher information of trajectories with the essential advantage that the Fisher information matrix in the specified parameter space is constant. This outcome greatly eases the calculation of information content in the parameter space via a line integral. In the continuum limit, a simple analytical form can be derived to explicitly reveal the physical origin of the information content in equilibrium trajectories. This methodology also allows deduction of least informative dynamics models from known or available observables that are either dynamical or static in nature. The minimum information optimization of dynamics is performed for a set of different constraints to illustrate the generality of the proposed methodology.
Publication Date: 2013
Citation: Haas, Kevin R, Yang, Haw, Chu, Jhih-Wei. "Fisher information metric for the Langevin equation and least informative models of continuous stochastic dynamics" The Journal of Chemical Physics, (12), 139, 121931 - 121931, doi:10.1063/1.4820491
DOI: doi:10.1063/1.4820491
ISSN: 0021-9606
Pages: 121931 - 121931
Type of Material: Journal Article
Journal/Proceeding Title: The Journal of Chemical Physics
Version: This is the author’s final manuscript. All rights reserved to author(s).

Items in OAR@Princeton are protected by copyright, with all rights reserved, unless otherwise indicated.