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.
Highlights
It is essential to extract dynamics from the observational time-series data in natural sciences
We focus the nonlinear dynamics of a surface heterogeneous reaction
We show that hidden variables of the surface heterogeneous reaction are successfully estimated from observable data
Summary
It is essential to extract dynamics from the observational time-series data in natural sciences. Kinetic parameters of chemical reactions, such as reactionrate coefficients and diffusion coefficients, govern the nonlinear dynamical behavior of chemical systems They are usually determined from observed time evolution of the amount of chemical species by laboratory experiments in various natural sciences [1,2]. Kinetic rate constants underlying the nonlinear dynamics of the heterogeneous reaction are shown to be estimated accurately using our proposed method with an adapted EM algorithm.
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