Recovering the past history of natural recording media by Bayesian inversion

Kuwatani, Tatsu; Nagao, Hiromichi; Ito, Shin Ichi; Okamoto, Atsushi; Yoshida, Kenta; Okudaira, Takamoto

doi:10.1103/physreve.98.043311

Cited by 9 publications

(6 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…When the number of observable data points (Nobs) decreases, the error on parameters estimated by the proposed methodology would increase, as suggested by previous studies on parameter estimation [57,58]. Although the effects of sparseness in the dataset on the estimation error were not…”

Section: Discussionmentioning

confidence: 74%

Multiple Kinetic Parameterization in a Reactive Transport Model Using the Exchange Monte Carlo Method

2018

Self Cite

View full text Add to dashboard Cite

Water-rock interaction in surface and subsurface environments occurs in complex multicomponent systems and involves several reactions, including element transfer. Such kinetic information is obtained by fitting a forward model into the temporal evolution of solution chemistry or the spatial pattern recorded in the rock samples, although geochemical and petrological data are essentially sparse and noisy. Therefore, the optimization of kinetic parameters sometimes fails to converge toward the global minimum due to being trapped in a local minimum. In this study, we simultaneously present a novel framework to estimate multiple reaction-rate constants and the diffusivity of aqueous species from the mineral distribution pattern in a rock by using the reactive transport model coupled with the exchange Monte Carlo method. Our approach can estimate both the maximum likelihood and error of each parameter. We applied the method to the synthetic data, which were produced using a model for silica metasomatism and hydration in the olivine-quartz-H 2 O system. We tested the robustness and accuracy of our method over a wide range of noise intensities. This methodology can be widely applied to kinetic analyses of various kinds of water-rock interactions.2 of 15 happen simultaneously. Even for monomineralic systems, such as feldspar-water or olivine-water systems in batch experiments, coupled reactions could occur, marked by the dissolution of the primary mineral and the formation of a secondary mineral [9,[20][21][22][23]. Accordingly, an effective methodology is required to simultaneously estimate the reaction-rate constants of several minerals and/or diffusivity of elements from complex water-rock systems.However, multiple parameterizations from a coupled transport and reaction system, pertaining to the dissolution and precipitation of many minerals and the transport of aqueous species (ions and complexes), raise a difficult geochemical inverse problem due to computational difficulties. This is especially true when multiple parameters are to be estimated; estimation sometimes fails to converge to the global minima due to convergence to the local minima through error minimization [24,25]. Moreover, the data used for parameterization may be "noisy" due to analytical uncertainties, and therefore, the fitted parameters would also contain errors. Such errors on rate constants are typically ignored to avoid the complex computations required to handle error propagation. Therefore, it would be ideal to develop a versatile method that can extract multiple kinetic parameters and associated errors from noisy laboratory datasets without becoming trapped in local minima.In this study, we present a novel method to estimate not only multiple reaction-rate constants, but also the diffusivity of aqueous species using only the dataset of spatial mineral distribution, and by combining the reactive transport model and the exchange Monte Carlo (EMC) method [26][27][28]. The latter is well-known as an improvement on Markov chain Monte Carlo (MCMC) ...

show abstract

Section: Discussionmentioning

confidence: 74%

Multiple Kinetic Parameterization in a Reactive Transport Model Using the Exchange Monte Carlo Method

2018

Self Cite

View full text Add to dashboard Cite

show abstract

“…We used the concept of Bayesian estima- tion from machine learning [12,13]. The concept has been applied to various fields including physics [15][16][17][18][19][20], brain science [21], astronomy [22], and Earth sciences [23]. Notably, the Bayesian estimation has been applied to identify reaction pathways in the fields of biology and chemical engineering [24][25][26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Exploration of nonlinear parallel heterogeneous reaction pathways through Bayesian variable selection

2021

Self Cite

View full text Add to dashboard Cite

Inversion is a key method for extracting nonlinear dynamics governed by heterogeneous reaction that occur in parallel in the natural sciences. Therefore, in this study, we propose a Bayesian statistical framework to determine the active reaction pathways using only the noisy observable spatial distribution of the solid phase. In this method, active reaction pathways were explored using a Widely Applicable Bayesian Information Criterion (WBIC), which is used to select models within the framework of Bayesian inference. Plausible reaction mechanisms were determined by maximizing the posterior distribution. This conditional probability is obtained through Markov chain Monte Carlo simulations. The efficiency of the proposed method is then determined using simulated spatial data of the solid phase. The results show that active reaction pathways can be identified from the redundant candidates of reaction pathways. After these redundant reaction pathways were excluded, the controlling factor of the reaction dynamics was estimated with high accuracy. Graphic Abstract

show abstract

“…In particular, data assimilation (DA) [16], which is a kind of BI mainly developed in the fields of the meteorology and oceanography [19][20][21], constructs the posterior PDF based on time series of data and forecasts based on the PDF [13][14][15]. Because the integration of physical models and observational or experimental data is an essential procedure in various scientific areas, DA has been expanding into application fields such as seismology [22], biology [23], petrology [24], and materials science [17,[25][26][27]. DA, which can be directly applied when an observational dataset is given as a time series, systematically estimates parameters that determine the dynamics of a given system, e.g., γ , L, and W in the PF models.…”

Section: Introductionmentioning

confidence: 99%

Bayesian inference of grain growth prediction via multi-phase-field models

Ito

Nagao

Kurokawa

et al. 2019

Phys. Rev. Materials

Self Cite

View full text Add to dashboard Cite

We propose a Bayesian inference methodology to evaluate unobservable parameters involved in multi-phasefield models to accurately predict the observed grain growth, such as in metals and alloys. This approach integrates models and a set of observational image data of grain structures. Because the image data set is not a time series, directly applying conventional inference techniques that require time series as the input data is difficult. The key idea in our methodology to overcome this difficulty is to construct a time series with an appropriate statistic that characterizes static image data of grain structures. Our methodology implements the empirical Bayes method. It can estimate not only a probability density function of the parameters but also an initial phase field, which is generally unobservable in real experiments. After validating the proposed method through numerical tests using synthetic data, we apply it to real experimental images of grain structures in a steel alloy. The proposed method properly estimates unobservable parameters along with their uncertainties and successfully selects the initial phase field that best explains the experimental data from among candidate initial phase fields.

show abstract

Recovering the past history of natural recording media by Bayesian inversion

Cited by 9 publications

References 31 publications

Multiple Kinetic Parameterization in a Reactive Transport Model Using the Exchange Monte Carlo Method

Multiple Kinetic Parameterization in a Reactive Transport Model Using the Exchange Monte Carlo Method

Exploration of nonlinear parallel heterogeneous reaction pathways through Bayesian variable selection

Bayesian inference of grain growth prediction via multi-phase-field models

Contact Info

Product

Resources

About