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We investigate solution methods for large-scale inverse problems governed bypartial differential equations (PDEs) via Bayesian inference. The Bayesianframework provides a statistical setting to infer uncertain parameters fromnoisy measurements. To quantify posterior uncertainty, we adopt Markov ChainMonte Carlo (MCMC) approaches for generating samples. To increase theefficiency of these approaches in high-dimension, we make use of localinformation about gradient and Hessian of the target potential, also viaHamiltonian Monte Carlo (HMC). Our target application is inferring the field ofsoil permeability processing observations of pore pressure, using a nonlinearPDE poromechanics model for predicting pressure from permeability. We comparethe performance of different sampling approaches in this and other settings. Wealso investigate the effect of dimensionality and non-gaussianity ofdistributions on the performance of different sampling methods.

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