title: Bayesian inversion analysis of nonlinear dynamics in surface heterogeneous reactions.
abstract: It is essential to extract nonlinear dynamics from time-series data as an inverse problem in natural sciences. We propose a Bayesian statistical framework for extracting nonlinear dynamics of surface heterogeneous reactions from sparse and noisy observable data. Surface heterogeneous reactions are chemical reactions with conjugation of multiple phases, and they have the intrinsic nonlinearity of their dynamics caused by the effect of surface-area between different phases. We adapt a belief propagation method and an expectation-maximization (EM) algorithm to partial observation problem, in order to simultaneously estimate the time course of hidden variables and the kinetic parameters underlying dynamics. The proposed belief propagation method is performed by using sequential Monte Carlo algorithm in order to estimate nonlinear dynamical system. Using our proposed method, we show that the rate constants of dissolution and precipitation reactions, which are typical examples of surface heterogeneous reactions, as well as the temporal changes of solid reactants and products, were successfully estimated only from the observable temporal changes in the concentration of the dissolved intermediate product.
authors.affiliation: Department of Electrical and Electronic Engineering, Graduate School of Engineering, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501, Japan.
authors.forename: Toshiaki
authors.initials: T
authors.lastname: Omori
authors.affiliation: Department of Solid Earth Geochemistry, Japan Agency for Marine-Earth Science and Technology, 2-15 Natsushima-cho, Yokosuka 237-0061, Japan.
authors.forename: Tatsu
authors.initials: T
authors.lastname: Kuwatani
authors.affiliation: Department of Environmental Studies for Advanced Society, Graduate School of Environmental Studies, Tohoku University, 6-6-20 Aramaki, Aoba-ku, Sendai 980-8579, Japan.
authors.forename: Atsushi
authors.initials: A
authors.lastname: Okamoto
authors.affiliation: Department of Basic Science, Graduate School of Arts and Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan.|Center for Materials Research by Information Integration, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba 305-0047, Japan.
authors.forename: Koji
authors.initials: K
authors.lastname: Hukushima