HIGH-DIMENSIONAL NONLINEAR BAYESIAN INFERENCE OF POROELASTIC FIELDS FROM PRESSURE DATA

This is a Preprint and has not been peer reviewed. The published version of this Preprint is available: https://doi.org/10.1177/10812865221140840. This is version 1 of this Preprint.

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Authors

Mina Karimi, Mehrdad Massoudi, Kaushik Dayal, Matteo Pozzi

Abstract

We investigate solution methods for large-scale inverse problems governed by partial differential equations (PDEs) via Bayesian inference. The Bayesian framework provides a statistical setting to infer uncertain parameters from noisy measurements. To quantify posterior uncertainty, we adopt Markov Chain Monte Carlo (MCMC) approaches for generating samples.
To increase the efficiency of these approaches in high-dimension, we make use of local information about gradient and Hessian of the target potential, also via Hamiltonian Monte Carlo (HMC). Our target application is inferring the field of soil permeability processing observations of pore pressure, using a nonlinear PDE poromechanics model for predicting pressure from permeability.
We compare the performance of different sampling approaches in this and other settings. We also investigate the effect of dimensionality and non-gaussianity of distributions on the performance of different sampling methods.

DOI

https://doi.org/10.31223/X5F95F

Subjects

Engineering, Physical Sciences and Mathematics

Keywords

Hamiltonian Monte Carlo, high-dimensional inference, Markov Chain Monte Carlo, poroelastic model, high-dimensional inference, Markov chain Monte Carlo, poroelastic model

Dates

Published: 2023-02-10 12:00

License

CC BY Attribution 4.0 International