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It is important to specify the kinetics of heterogeneous reactions in order to elucidate the microscopic elementary processes and predict the macroscopic future evolution of the system. In this study, we propose a data-driven method based on a sparse modeling algorithm and sequential Monte Carlo algorithm for simultaneously extracting substantial reaction terms and surface models from a number of candidates by using partial observation data. We introduce a sparse modeling approach with non-uniform sparsity levels in order to accurately estimate rate constants, and the sequential Monte Carlo algorithm is employed to estimate time courses of multi-dimensional hidden variables. The results estimated using the proposed method show that the rate constants of dissolution and precipitation reactions that are typical examples of surface heterogeneous reactions, necessary surface models, and reaction terms underlying observable data were successfully estimated from only observable temporal changes in the concentration of the dissolved intermediate products.<\/jats:p>","DOI":"10.3390\/e23070824","type":"journal-article","created":{"date-parts":[[2021,6,28]],"date-time":"2021-06-28T11:45:40Z","timestamp":1624880740000},"page":"824","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Data-Driven Analysis of Nonlinear Heterogeneous Reactions through Sparse Modeling and Bayesian Statistical Approaches"],"prefix":"10.3390","volume":"23","author":[{"given":"Masaki","family":"Ito","sequence":"first","affiliation":[{"name":"Graduate School of Engineering, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7161-9458","authenticated-orcid":false,"given":"Tatsu","family":"Kuwatani","sequence":"additional","affiliation":[{"name":"Research Institute for Marine Geodynamics, Japan Agency for Marine-Earth Science and Technology (JAMSTEC), 2-15 Natsushima-cho, Kanagawa, Yokosuka 237-0061, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ryosuke","family":"Oyanagi","sequence":"additional","affiliation":[{"name":"Research Institute for Marine Geodynamics, Japan Agency for Marine-Earth Science and Technology (JAMSTEC), 2-15 Natsushima-cho, Kanagawa, Yokosuka 237-0061, Japan"},{"name":"School of Science and Engineering, Kokushikan University, 4-28-1 Setagaya, Setagaya-ku, Tokyo 154-8515, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4011-0055","authenticated-orcid":false,"given":"Toshiaki","family":"Omori","sequence":"additional","affiliation":[{"name":"Graduate School of Engineering, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501, Japan"},{"name":"Center for Mathematical and Data Sciences, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Strogatz, S.H. 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