Exploration of nonlinear parallel heterogeneous reaction pathways through Bayesian variable selection

Oyanagi, Ryosuke; Kuwatani, Tatsu; Omori, Toshiaki

doi:10.1140/epjb/s10051-021-00053-7

Cited by 4 publications

(3 citation statements)

References 44 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Owing to these improvements, data-driven approaches have attracted attention as a method to extract the system structure and features from data [1][2][3]. Notably, the extraction of dynamical systems from time-series data is challenging in various fields, encompassing natural sciences, such as earth science [4,5] and neuroscience [6,7], and engineering domains, such as fluid engineering [8][9][10]. Moreover, methods for state estimation have been proposed for various systems ranging from physical systems with unknown governing equations to networked autonomous vehicles with event-triggered control, robustness against disturbances, and time-varying delays [11,12].…”

Section: Introductionmentioning

confidence: 99%

Sparse Estimation for Hamiltonian Mechanics

Note,

Watanabe,

Yoshimura

et al. 2024

Mathematics

Self Cite

View full text Add to dashboard Cite

Estimating governing equations from observed time-series data is crucial for understanding dynamical systems. From the perspective of system comprehension, the demand for accurate estimation and interpretable results has been particularly emphasized. Herein, we propose a novel data-driven method for estimating the governing equations of dynamical systems based on machine learning with high accuracy and interpretability. The proposed method enhances the estimation accuracy for dynamical systems using sparse modeling by incorporating physical constraints derived from Hamiltonian mechanics. Unlike conventional approaches used for estimating governing equations for dynamical systems, we employ a sparse representation of Hamiltonian, allowing for the estimation. Using noisy observational data, the proposed method demonstrates a capability to achieve accurate parameter estimation and extraction of essential nonlinear terms. In addition, it is shown that estimations based on energy conservation principles exhibit superior accuracy in long-term predictions. These results collectively indicate that the proposed method accurately estimates dynamical systems while maintaining interpretability.

show abstract

Section: Introductionmentioning

confidence: 99%

Sparse Estimation for Hamiltonian Mechanics

Note,

Watanabe,

Yoshimura

et al. 2024

Mathematics

Self Cite

View full text Add to dashboard Cite

show abstract

“…A Bayesian inversion analysis method with sequential Monte Carlo and expectation–maximization (EM) algorithms was proposed to simultaneously estimate the kinetic rate constants and time series of multi-dimensional hidden variables for heterogeneous reactions [ 4 ]. Moreover, a Bayesian approach, using Markov chain Monte Carlo and widely applicable information criteria, was proposed to estimate heterogeneous reaction pathways using spatial data [ 5 ]. In these previous Bayesian methods [ 4 , 5 ], the types of reaction terms are assumed to be known.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, a Bayesian approach, using Markov chain Monte Carlo and widely applicable information criteria, was proposed to estimate heterogeneous reaction pathways using spatial data [ 5 ]. In these previous Bayesian methods [ 4 , 5 ], the types of reaction terms are assumed to be known. However, it is important to establish a method for estimating reaction constants while assuming that the types of reaction terms are unknown since there exist many kinds of candidates in reaction terms in heterogeneous reactions.…”

Section: Introductionmentioning

confidence: 99%

Data-Driven Analysis of Nonlinear Heterogeneous Reactions through Sparse Modeling and Bayesian Statistical Approaches

Ito

Kuwatani

Oyanagi

et al. 2021

Entropy

Self Cite

View full text Add to dashboard Cite

Heterogeneous reactions are chemical reactions that occur at the interfaces of multiple phases, and often show a nonlinear dynamical behavior due to the effect of the time-variant surface area with complex reaction mechanisms. 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.

show abstract

New curved boundary scheme in lattice Boltzmann framework for simulation of dissolution through nonlinear heterogeneous reactions in general form

Izadi,

Mohebbi,

Feili Monfared

2024

Physics of Fluids

View full text Add to dashboard Cite

Nonlinear heterogeneous reactions are important for simulating dissolution as they involve reactant adsorption, reaction, and product desorption, leading to nonlinear behavior. This study proposes a new curved reaction boundary condition in general form in the lattice Boltzmann framework. This method calculates the unknown distribution functions and the interface concentration using extrapolated distribution functions on actual interface position. Various analytical benchmarks were used to compare this method's accuracy with two available schemes, including Kashani et al. and Huber et al. methods. According to the results, in the simulation of reactant transport on straight and curved surfaces with and without dissolution, errors obtained by the proposed method did not exceed 1.7% in different conditions, while errors of the two other methods were up to 50%. The convergence rate of different methods was determined, and based on the results, the convergence rate of the proposed method was second-order, while the corresponding values for the two other methods were only first-order. The results of different root-finding methods in the proposed method including Bisection, Newton-Raphson, and linear approximation were compared to determine the interface concentration. The results showed that Bisection errors did not exceed 1%. At the same time, using Newton-Raphson and linear approximation led to errors of 12.9% and 25.3%, respectively. The effect of reaction orders on an obstacle dissolved under reactive flows in a channel was investigated. According to the results, in each Damköhler number, increasing the reaction order decreased the dissolution rate; however, increasing the Damköhler number significantly restricted the effect of orders.

show abstract

Exploration of nonlinear parallel heterogeneous reaction pathways through Bayesian variable selection

Cited by 4 publications

References 44 publications

Sparse Estimation for Hamiltonian Mechanics

Sparse Estimation for Hamiltonian Mechanics

Data-Driven Analysis of Nonlinear Heterogeneous Reactions through Sparse Modeling and Bayesian Statistical Approaches

New curved boundary scheme in lattice Boltzmann framework for simulation of dissolution through nonlinear heterogeneous reactions in general form

Contact Info

Product

Resources

About