Mario Teixeira Parente

Mario Teixeira Parente, Steven Mattis, Shubhangi Gupta et al.

Methane gas hydrates have increasingly become a topic of interest because of their potential as a future energy resource. There are significant economical and environmental risks associated with extraction from hydrate reservoirs, so a variety of multiphysics models have been developed to analyze prospective risks and benefits. These models generally have a large number of empirical parameters which are not known a priori. Traditional optimization-based parameter estimation frameworks may be ill-posed or computationally prohibitive. Bayesian inference methods have increasingly been found effective for estimating parameters in complex geophysical systems. These methods often are not viable in cases of computationally expensive models and high-dimensional parameter spaces. Recently, methods have been developed to effectively reduce the dimension of Bayesian inverse problems by identifying low-dimensional structures that are most informed by data. Active subspaces is one of the most generally applicable methods of performing this dimension reduction. In this paper, Bayesian inference of the parameters of a state-of-the-art mathematical model for methane hydrates based on experimental data from a triaxial compression test with gas hydrate-bearing sand is performed in an efficient way by utilizing active subspaces. Active subspaces are used to identify low-dimensional structure in the parameter space which is exploited by generating a cheap regression-based surrogate model and implementing a modified Markov chain Monte Carlo algorithm. Posterior densities having means that match the experimental data are approximated in a computationally efficient way.

Mario Teixeira Parente

This paper develops a comprehensive probabilistic setup to compute approximating functions in active subspaces. Constantine et al. proposed the active subspace method in (Constantine et al., 2014) to reduce the dimension of computational problems. It can be seen as an attempt to approximate a high-dimensional function of interest $f$ by a low-dimensional one. To do this, a common approach is to integrate $f$ over the inactive, i.e. non-dominant, directions with a suitable conditional density function. In practice, this can be done with a finite Monte Carlo sum, making not only the resulting approximation random in the inactive variable for each fixed input from the active subspace, but also its expectation, i.e. the integral of the low-dimensional function weighted with a probability measure on the active variable. In this regard we develop a fully probabilistic framework extending results from (Constantine et al., 2014, 2016). The results are supported by a simple numerical example.