Journal Article

FZJ-2021-00685

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Preconditioned Crank‐Nicolson Markov Chain Monte Carlo Coupled With Parallel Tempering: An Efficient Method for Bayesian Inversion of Multi‐Gaussian Log‐Hydraulic Conductivity Fields

Xu, T. (Corresponding author) ; Reuschen, S. ; Nowak, W. ; Hendricks Franssen, H.FZJ*

2020
Wiley [New York]

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Please use a persistent id in citations: doi:10.1029/2020WR027110

Abstract: Geostatistical inversion with quantified uncertainty for nonlinear problems requires techniques for providing conditional realizations of the random field of interest. Many first‐order second‐moment methods are being developed in this field, yet almost impossible to critically test them against high‐accuracy reference solutions in high‐dimensional and nonlinear problems. Our goal is to provide a high‐accuracy reference solution algorithm. Preconditioned Crank‐Nicolson Markov chain Monte Carlo (pCN‐MCMC) has been proven to be more efficient in the inversion of multi‐Gaussian random fields than traditional MCMC methods; however, it still has to take a long chain to converge to the stationary target distribution. Parallel tempering aims to sample by communicating between multiple parallel Markov chains at different temperatures. In this paper, we develop a new algorithm called pCN‐PT. It combines the parallel tempering technique with pCN‐MCMC to make the sampling more efficient, and hence converge to a stationary distribution faster. To demonstrate the high‐accuracy reference character, we test the accuracy and efficiency of pCN‐PT for estimating a multi‐Gaussian log‐hydraulic conductivity field with a relative high variance in three different problems: (1) in a high‐dimensional, linear problem; (2) in a high‐dimensional, nonlinear problem and with only few measurements; and (3) in a high‐dimensional, nonlinear problem with sufficient measurements. This allows testing against (1) analytical solutions (kriging), (2) rejection sampling, and (3) pCN‐MCMC in multiple, independent runs, respectively. The results demonstrate that pCN‐PT is an asymptotically exact conditional sampler and is more efficient than pCN‐MCMC in geostatistical inversion problems.

Note: Kein Post-print verfügbar

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Contributing Institute(s):

1. Agrosphäre (IBG-3)

Research Program(s):

1. 255 - Terrestrial Systems: From Observation to Prediction (POF3-255) (POF3-255)
2. DFG project 359880532 - Computergestützter Ansatz zur Kalibrierung und Validierung mathematischer Modelle für Strömungen im Untergrund - COMPU-FLOW (359880532)

Appears in the scientific report 2020

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Database coverage:
; Clarivate Analytics Master Journal List ; Current Contents - Agriculture, Biology and Environmental Sciences ; Current Contents - Engineering, Computing and Technology ; DEAL Wiley ; Essential Science Indicators ; IF < 5 ; JCR ; SCOPUS ; Science Citation Index Expanded ; Web of Science Core Collection

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