Efficient Discretization‐Independent Bayesian Inversion of High‐Dimensional Multi‐Gaussian Priors Using a Hybrid MCMC

Reuschen, Sebastian; Jobst, Fabian; Nowak, Wolfgang

doi:10.1029/2021wr030051

Cited by 11 publications

(6 citation statements)

References 52 publications

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“…Out of the 100,000 iterations, we thin out the samples by saving only every tenth iteration, resulting in a total of 10,000 samples. The step size h is chosen so that the acceptance rate amounts to approximately 23% (Reuschen et al, 2021). This corresponds to h = 10 −2 for MH, h = 7 × 10 −6 for MALA, and h = 4 × 10 −3 for Barker.…”

Section: Learning Using An Experimental Data Setmentioning

confidence: 99%

Learning Groundwater Contaminant Diffusion-Sorption Processes with a Finite Volume Neural Network

Praditia

Karlbauer

Otte

et al. 2022

Preprint

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Section: Learning Using An Experimental Data Setmentioning

confidence: 99%

Learning Groundwater Contaminant Diffusion-Sorption Processes with a Finite Volume Neural Network

Praditia

Karlbauer

Otte

et al. 2022

Preprint

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show abstract

“…Out of the 100,000 iterations, we thin out the samples by saving only every tenth iteration, resulting in a total of 10,000 samples. The step size h is chosen so that the acceptance rate amounts to approximately 23% (Reuschen et al., 2021). This corresponds to h = 10 −2 for MH, h = 7 × 10 −6 for MALA, and h = 4 × 10 −3 for Barker.…”

Section: Learning Experimentsmentioning

confidence: 99%

Learning Groundwater Contaminant Diffusion‐Sorption Processes With a Finite Volume Neural Network

Praditia

Karlbauer

Otte

et al. 2022

Water Resources Research

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Improved understanding of complex hydrosystem processes is key to advance water resources research. Nevertheless, the conventional way of modeling these processes suffers from a high conceptual uncertainty, due to almost ubiquitous simplifying assumptions used in model parameterizations/closures. Machine learning (ML) models are considered as a potential alternative, but their generalization abilities remain limited. For example, they normally fail to predict accurately across different boundary conditions. Moreover, as a black box, they do not add to our process understanding or to discover improved parameterizations/closures. To tackle this issue, we propose the hybrid modeling framework FINN (finite volume neural network). It merges existing numerical methods for partial differential equations (PDEs) with the learning abilities of artificial neural networks (ANNs). FINN is applied on discrete control volumes and learns components of the investigated system equations, such as numerical stencils, model parameters, and arbitrary closure/constitutive relations. Consequently, FINN yields highly interpretable results. We demonstrate FINN's potential on a diffusion‐sorption problem in clay. Results on numerically generated data show that FINN outperforms other ML models when tested under modified boundary conditions, and that it can successfully differentiate between the usual, known sorption isotherms. Moreover, we also equip FINN with uncertainty quantification methods to lay open the total uncertainty of scientific learning, and then apply it to a laboratory experiment. The results show that FINN performs better than calibrated PDE‐based models as it is able to flexibly learn and model sorption isotherms without being restricted to choose among available parametric models.

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“…The solutions in the ADE and MIM models for radial solute transport have been reported by Li et al (2020). In recent years, Markov Chain Monte Carlo (MCMC) methods have gained increasing popularity in subsurface flow and transport studies, as these methods can simulate complex multivariate distributions, and provide a comprehensive framework to estimate model parameters and associated uncertainties using their posterior distributions (Reuschen et al, 2021;Zhang et al, 2017). In this work, an ensemble sampler respecting affine invariance is applied to estimate dispersion parameters (Goodman & Weare, 2010;Hou et al, 2012).…”

Section: Application Of the Proposed Modelmentioning

confidence: 99%

On the Bimodal Radial Solute Transport in Dual‐Permeability Porous Media

Wen

et al. 2022

Water Resources Research

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Porous media usually exhibit distinct transport properties of a dual domain, which is attributed to layering, fracturing, or aggregation. In this study, a mobile‐mobile (MM) model of radial solute transport consisting of two advection‐dispersion equations (ADEs) is presented to describe the bimodal (or double‐peaked) breakthrough curves (BTCs) through two distinct pore domains consisting of interrelated fast‐flow and slow‐flow domains. Transport processes, including advection, dispersion, and first‐order mass transfer between the two domains, were considered in the model. Semi‐analytical solutions were derived using a Laplace transform, matrix diagonalization and numerical Laplace inversion method, and the solutions were verified against the existing analytical solution for the mobile‐immobile (MIM) model under the special case of zero velocity in the slow‐flow domain. In addition, Markov Chain Monte Carlo is applied to estimate the MM model parameters using the experimental data. The results indicate that a larger transfer coefficient between the fast‐flow and the slow‐flow domains resulted in a weaker bimodal phenomenon for concentration distribution curves, which was notably more apparent when there was a greater variation in pore flow velocities between the two domains. Also, the MM model can be used to investigate other types of abnormal transport features such as late arrival and early arrival. Finally, the ADE, MIM, and MM models were used to interpret the experimental data conducted by Fernàndez‐Garcia et al. (2004, http://doi.org.10.1029/2004wr003112), and it was found that the proposed MM model can explain the bimodal feature of BTCs while the ADE and MIM models fail to do so.

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Efficient Discretization‐Independent Bayesian Inversion of High‐Dimensional Multi‐Gaussian Priors Using a Hybrid MCMC

Abstract: A hybrid MCMC between the sequential Gibbs and the pCN-MCMC approach is presented.• This hybrid MCMC is more efficient than both special cases.

Cited by 11 publications

References 52 publications

Learning Groundwater Contaminant Diffusion-Sorption Processes with a Finite Volume Neural Network

Learning Groundwater Contaminant Diffusion-Sorption Processes with a Finite Volume Neural Network

Learning Groundwater Contaminant Diffusion‐Sorption Processes With a Finite Volume Neural Network

On the Bimodal Radial Solute Transport in Dual‐Permeability Porous Media

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