Publication 23-CNA-002

High-Dimensional Nonlinear Bayesian Inference of Poroelastic Fields from Pressure Data

Mina Karimi
Department of Civil and Environmental Engineering
Carnegie Mellon University
Pittsburgh, PA
minakari@andrew.cmu.edu

Mehrdad Massoudi
National Energy Technology Laboratory (NETL)
Pittsburgh, PA

Kaushik Dayal
Center for Nonlinear Analysis
Department of Civil and Environmental Engineering
Department of Materials Science and Engineering
Scott Institute for Energy Innovation
Carnegie Mellon University
Pittsburgh, PA 15213
Kaushik.Dayal@cmu.edu

Matteo Pozzi
Department of Civil and Environmental Engineering
Scott Institute for Energy Innovation
Carnegie Mellon University
Pittsburgh, PA

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.

Get the paper in its entirety as  23-CNA-002.pdf

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