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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

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dc.contributor.authorHaas, Kevin R-
dc.contributor.authorYang, Haw-
dc.contributor.authorChu, Jhih-Wei-
dc.date.accessioned2016-10-17T14:14:56Z-
dc.date.available2016-10-17T14:14:56Z-
dc.date.issued2013en_US
dc.identifier.citationHaas, 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:10.1063/1.4820491en_US
dc.identifier.issn0021-9606-
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr1mp45-
dc.description.abstractThe 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.en_US
dc.format.extent121931 - 121931en_US
dc.language.isoen_USen_US
dc.relation.ispartofThe Journal of Chemical Physicsen_US
dc.rightsThis is the author’s final manuscript. All rights reserved to author(s).en_US
dc.titleFisher information metric for the Langevin equation and least informative models of continuous stochastic dynamicsen_US
dc.typeJournal Articleen_US
dc.identifier.doidoi:10.1063/1.4820491-

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