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

TL;DR

This paper explores advanced Bayesian inference techniques, particularly Hamiltonian Monte Carlo, to efficiently estimate high-dimensional, nonlinear poroelastic fields from pressure data, addressing challenges of uncertainty quantification in complex PDE models.

Contribution

It introduces a novel application of HMC for high-dimensional nonlinear PDE-based inverse problems in geomechanics, improving sampling efficiency and understanding the impact of distribution characteristics.

Findings

HMC outperforms traditional MCMC in high-dimensional settings.

Dimensionality and non-Gaussianity significantly affect sampling performance.

The methods effectively infer soil permeability fields from pressure measurements.

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.