4:00 PM - 4:15 PM
[MGI33-07] Data-driven Analysis of Nonlinear Heterogeneous Reactions through Sparse Modeling and Bayesian Statistical Approaches
Keywords:Sparse Modeling, Bayesian Statistical Approaches, Heterogeneous Reactions
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. It is important not only in earth science, but also in engineering to understand heterogeneous reactions in order to figure out the dynamics of rock formation near surface of the earth. Since demand for the geosphere environment is increasing, such as the development of deposits and geothermal fields, the geological disposal of radioactive waste, and the underground storage of carbon dioxide. However, such dynamics is generally nonlinear and there are a lot of candidate nonlinear terms. Furthermore, observed time series data is generally partial and noisy. Therefore, it is necessary to establish a data driven approach for estimating the dynamics of heterogeneous reactions.
In this study, we propose a data-driven method for simultaneously extracting substantial reaction terms and surface models from a number of candidates based on sequential Monte Carlo algorithm and sparse modeling algorithm by using noisy partial observation data. We focus on surface area reactions between the solid phase and the liquid phase, and assume a model of the dissolution-precipitation reaction in which the reactant (solid phase) => intermediate product (liquid phase) => product (solid phase). Based on the state space model, we introduce sequential Monte Carlo method in order to estimate hidden variables of solid reactant, liquid intermediate product and solid product from a noisy observed data. Moreover, we employ sparse modeling algorithm to extract rate constants and determine a surface area reaction from many candidates. In addition to uniform sparsity, we introduce sparse modeling approach with non-uniform sparsity and make sparse modeling algorithm more robust in order to improve the estimation accuracy of rate constants. Therefore, we propose an effective method to simultaneously estimate rate constants and concentrations from nonlinear dynamics of heterogeneous reaction by using sparse modeling and sequential Monte Carlo method.
Using our proposed method, we show that the rate constants of dissolution and precipitation reactions, which are typical examples of surface heterogeneous reactions, necessary surface models and reaction terms underlying observable data were successfully estimated only from the observable temporal changes in the concentration of the dissolved intermediate product.
In this study, we propose a data-driven method for simultaneously extracting substantial reaction terms and surface models from a number of candidates based on sequential Monte Carlo algorithm and sparse modeling algorithm by using noisy partial observation data. We focus on surface area reactions between the solid phase and the liquid phase, and assume a model of the dissolution-precipitation reaction in which the reactant (solid phase) => intermediate product (liquid phase) => product (solid phase). Based on the state space model, we introduce sequential Monte Carlo method in order to estimate hidden variables of solid reactant, liquid intermediate product and solid product from a noisy observed data. Moreover, we employ sparse modeling algorithm to extract rate constants and determine a surface area reaction from many candidates. In addition to uniform sparsity, we introduce sparse modeling approach with non-uniform sparsity and make sparse modeling algorithm more robust in order to improve the estimation accuracy of rate constants. Therefore, we propose an effective method to simultaneously estimate rate constants and concentrations from nonlinear dynamics of heterogeneous reaction by using sparse modeling and sequential Monte Carlo method.
Using our proposed method, we show that the rate constants of dissolution and precipitation reactions, which are typical examples of surface heterogeneous reactions, necessary surface models and reaction terms underlying observable data were successfully estimated only from the observable temporal changes in the concentration of the dissolved intermediate product.